TRIBOLOGY a systems approach to the science and technology of friction lubrication and wear

TR IBO LOGY SERIES

Vol. 1 Tribology - a systems approach to the science and technology of friction, lubrication and wear (Czichos)

TRIBOLOGY SERIESJ

TRIBOLOGY a systems approach to the science and technology of friction, lubrication and wear

HBRST CZICHOS Bundesanstalt fur Materiaipru fung (BA Ml (Federal institute for Testing Materials) Berlin - Dahlern and Technixhe Fachhochschule Berlin

ELSEVIER SCIENTIFIC PUBLISHING COMPANY AMSTERDAM - OXFORD - NEW YORK 1978

ELSEVIER SCIENTIFIC PUBLISHING COMPANY 336 Jan van Galenstraat P.O. Box 211, Amsterdam, The Netherlands

Distributors for the United States and Canada:

ELSEVIER NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017

164 figures, 36 tables, 430 references

Lihrar, 01 Congrr*\ Cataloging in Publication Data

Czichos , Horst. Tribology.

(Tribology s e r i e s ; v. 1) Bibliographv: p. Includes indexes. 1. Tribology. 2. SyEitem analysis. T. T i t l e .

11. Series . mJ1075. C94 621.8'9 77-28510 ISBN 0-444-41676-5

ISBN 0-444-41676-6 (Vol. 1) ISBN 0-444-41677-3 (Series)

0 Eleevier Scientific Publishing Company, 1978 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechan- ical, photocopying, recording or otherwise, without the prior written permieoion of the publisher, Eleevier Scientific Publiahing Company, P.O. Box 380, Amsterdam, The Netherlands

Printed in The Netherlands

V

Preface

T h i s volume g i v e s a s y s t e m a t i c u n i f i e d approach t o t r i b o l o g y : t h e fundamen-

t a l s o f f r i c t i o n , l u b r i c a t i o n and wear and t h e i r i n f l u e n c e s on t h e s t r u c t u r e

and f u n c t i o n o f dynamic mechan ica l sys tems . S i n c e f r i c t i o n i s r e s p o n s i b l e

f u r a m a j o r l o s s o f u s e f u l mechan ica l ene rgy , and wear i s a m a j o r reason f o r

r e p l a c i n g equ ipmen t , a b e t t e r u n d e r s t a n d i n g and u t i l i z a t i o n o f t h e p r i n c i p -

l e s o f t r i b o l o g y i s p a r t i c u l a r l y i m p o r t a n t f o r t h e c o n s e r v a t i o n o f e n e r g y

and m a t e r i a l s i n e n g i n e e r i n g d e s i g n .

The p l a n t o w r i t e t h i s book grew f r o m t h e p a r t i c i p a t i o n i n co -opera -

t i v e work o f t h e " I n t e r n a t i o n a l Research Group ( I R G ) on Wear o f E n g i n e e r i n g

M a t e r i a l s " o p e r a t i n g under t h e a u s p i c e s o f t h e " O r g a n i z a t i o n f o r Economic

C o - o p e r a t i o n and Development" (OECD) i n w h i c h I have been t a k i n g p a r t s i n c e

t h e b e g i n n i n g o f t h e 1 9 7 0 ' s . T h e o r e t i c a l c o n s i d e r a t i o n s and p r a c t i c a l ex -

p e r i e n c e have shown t h a t t h e r e i s an u r g e n t need f o r a g e n e r a l , y e t p r a c t i -

c a l l y u s e f u l , f ramework i n o r d e r t o l i n k t h e many i n t e r d i s c i p l i n a r y a s p e c t s

o f t r i b o l o g y , r a n g i n g f ro i i i c o n t a c t mechanics, s u r f a c e p h y s i c s and hyd rodyna-

m i c s t o b e a r i n g t e c h n o l o g y and q u e s t i o n s o f ma in tenance and r e l i a b i l i t y o f

mechan ica l equ ipmen t . Moreover , i t became o b v i o u s i n r e c e n t y e a r s , t h a t spe-

c i f i c a n a l y t i c a l methods o f i s o l a t i n g and s t u d y i n g s i n g l e e v e n t s and t r e a t i n g

f r i c t i o n and wear i n a n a l o g y t o o t h e r ( b u l k ) mechan ica l m a t e r i a l p r o p e r t i e s

a r e o n l y p a r t l y u s e f u l t o t h e s t u d y o f complex t r i b o l o g i c a l p rob lems . Indeed ,

t h e o r i g i n a l d e f i n i t i o n o f t r i b o l o g y : " t h e s c i e n c e and t e c h n o l o g y o f i n t e r -

a c t i n g s u r f a c e s i n r e l a t i v e m o t i o n and t h e p r a c t i c e s r e l a t e d t h e r e t o " i s ob-

v i o u s l y t h a t o f a dynamic mechan ica l system. Thus, f r i c t i o n , wear and t h e

many r e l a t e d pheeomena a r e e s s e n t i a l l y due t o dynamic i n t e r a c t i o n s between

t h e mov ing components o f sys tems . ( A c o m p i l a t i o n o f mechan ica l systems i n

vi

which f r i c t i o n and wear processes occur i s g i v e n i n t h e Appendix A.) I t was

concluded t h a t t h e a p p l i c a t i o n o f systems t h i n k i n g and general systems the -

o r y a r e e s p e c i a l l y s u i t e d f o r deve lop ing a conven ien t framework o f t r i b o l o -

gy, b r i n g i n g toge the r i t s many aspects c u r r e n t l y s c a t t e r e d th roughout t h e

s c i e n t i f i c and t e c h n i c a l l i t e r a t u r e . I t f o l l o w s t h a t a t r ibo-mechan ica l sys-

tem shou ld be analyzed and descr ibed i n terms o f i t s " s t r u c t u r e " (elements

o f t h e system, p r o p e r t i e s o f elements, i n t e r r e l a t i o n s between elements) as

w e l l as i n terms o f i t s " f u n c t i o n " ( i n p u t s , ou tpu ts , t r a n s f e r f u n c t i o n s ) .

Whereas i n the a n a l y s i s o f e l e c t r i c a l systems the i n t e r e s t i s concent ra ted

ma in l y on the f u n c t i o n a l i n p u t - o u t p u t r e l a t i o n s , i n t r i b o l o g y t h e a n a l y s i s

and d e s c r i p t i o n o f t h e (dynamic) sys tem's s t r u c t u r e i s t h e c r u c i a l p o i n t .

Sec t i on 1.4. I t i s suggested t h a t t he reader who i s i n t e r e s t e d ma in l y i n the

p r a c t i c a l a p p l i c a t i o n o f systems techniques t o t r i b o l o g i c a l problems may

t u r n t o Chapter 8 on " P r a c t i c a l Systems Methodology", a f t e r read ing t h e i n -

t r o d u c t o r y Chapters 1 and 2, and may f o l l o w then t h e sequence o f Chapters

3,4 and so on. Because o f t he immense scope o f t r i b o l o g y , t h i s volume con-

cen t ra tes ma in l y on the b a s i c general p r i n c i p l e s o f t he s u b j e c t m a t t e r i n

o rde r t o f i t the huge amount o f m a t e r i a l i n t o t h e l e n g t h a v a i l a b l e . Thus,

t he book i s a iming t o p rov ide u n i f i e d i n t e r d i s c i p l i n a r y background knowledge

f o r engineers, p h y s i c i s t s , chemists and m a t e r i a l s c i e n t i s t s work ing i n t h e

va r ious s p e c i a l i z e d f i e l d s o f t r i b o l o g y . When used as a tex tbook , t h e t e x t

i s s u i t e d t o t h e l e v e l o f s e n i o r undergraduate o r f i r s t - y e a r graduate courses

i n eng inee r ing and t h e n a t u r a l sciences.

Some p a r t o f t h e m a t e r i a l o f t h i s book has been presented as l e c t u r e s

a t t h e IRG-OECD Meet ings h e l d a t (a ) I m p e r i a l Co l lege, London, J u l y 1973,

( b ) BAM, Ber l in-Dahlem, October 1974, ( c ) CNRS, Pa r i s , A p r i l 1976. A t these

Meetings h e l p f u l comments have been made by P ro fesso r R. Cour te l , CNRS,

P a r i s , and Pro fesso r H. Chri stensen, SINTEF, Trondheim. F u r t h e r acknowledge-

ments a re due t o t h e fo rmer Chairman o f IRG-OECD, Pro fessor R.L. Johnson,

Rensselaer Po ly techn ic I n s t i t u t e , Troy, New York, f o r h i s c o n t i n u i n g i n t e r e s t

i n t h e a p p l i c a t i o n o f systems techniques t o t r i b o l o g i c a l problems and t o t h e

p resen t Chairman o f IRG-OECD, D r . G. Salomon, The Hague, f o r f r u i t f u l j o i n t

work i n t h i s f i e l d . I n p a r t i c u l a r , I l i k e t o express my s i n c e r e thanks t o

P ro fesso r G.W. Rowe, U n i v e r s i t y o f Birmingham, who reviewed t h e complete

d r a f t o f t h i s book making var ious va luab le suggest ions.

The c e n t r a l t h e o r e t i c a l p a r t o f t h i s book, namely Chapter 3, "General

Theory o f T r ibo logy " has been worked o u t t oge the r w i t h P ro fesso r J . Mfilgaard,

The o r g a n i z a t i o n o f t h e book i s s t r a i g h t f o r w a r d and i s o u t l i n e d i n

vii

Memorial U n i v e r s i t y o f Newfoundland, d u r i n g h i s s t a y a t BAM f rom September

1975 t o June 1976 as Fe l l ow o f t he Alexander-von-Humboldt-Foundation o f t h e

Federal Repub l ic o f Germany. I am very g r a t e f u l t o P ro fesso r Mdlgaard f o r

t he e x c e l l e n t co -opera t i on and h i s c o n t r i b u t i o n t o t h i s book. Thanks a r e

due a l s o t o Ir. A.W.J. de Gee and A. Bege l inger , M e t a a l i n s t i t u u t TNO, Ape l -

doorn, f o r t h e i r c o n t r i b u t i o n o f p r a c t i c a l a p p l i c a t i o n examples presented

i n Sec t ions 8.5.3, 8.5.5, and 8.5.7. I n o r d e r t o make t h e r e s u l t s o f t h i s

i n t e r n a t i o n a l j o i n t work e a s i l y access ib le t o t h e i n t e r n a t i o n a l community,

t h e book has been w r i t t e n i n t h e E n g l i s h language.

The e n t i r e manuscr ip t has been g r a c i o u s l y read by my co l l eague D r . K.-H.

Habig who a l s o c o n t r i b u t e d some u s e f u l comments. I n a d d i t i o n , my co l l eague

D r . H.-U. Mittmann reviewed Chapter 6 and D r . D.H. Buckley and D r . L.D.

Wedeven, NASA Lewis Research Center, Cleveland, reviewed Sect ions 4.4 and

4.5, r e s p e c t i v e l y , making h e l p f u l remarks. The Appendix was checked by

P.M. Ku, Southwest Research I n s t i t u t e , San Antonio, who a l s o c o n t r i b u t e d

some supplements. F u r t h e r I am indebted t o many au tho rs and p u b l i s h e r s f o r

k i n d l y supp ly ing i l l u s t r a t i o n s and pe rm iss ion t o p u b l i s h them; acknowledge-

ments a re p resented i n the f i g u r e cap t ions and i n t h e l i s t o f re fe rences .

L a s t l y , I acknowledge the va luab le ass i s tance o f my co l leagues a t BAM, i n -

c l u d i n g t h e exper imenta l h e l p o f t h e eng ineers W . Evers, M. Gienau, W.

Schrag and J . Schwenzien.

I n s p i t e o f a l l t he encouraging suppor t , t h e book would never have been

f i n i s h e d w i t h o u t t h e cont inuous h e l p o f my w i f e Barbara who n o t o n l y typed

t h e p r e l i m i n a r y d r a f t s b u t a l s o produced the e x c e l l e n t camera-ready manu-

s c r i p t . I n smal l token f o r t h e i r pa t i ence d u r i n g t h e t ime o f t he p r e p a r a t i o n

o f t he manuscr ip t , t h e book i s ded ica ted t o my f a m i l y , my w i f e Barbara and

my son Carsten.

Ber l in-Dahlem

May 1977

Hors t Czi chos

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ix

Contents

1. INTRODUCTION AND BACKGROUND

1.1 Dynamics o f p h y s i c a l systems and t h e

o c c u r r e n c e o f f r i c t i o n and wear

1 .2 H i s t o r i c a l deve lopmen t o f t r i b o l o g y

1 . 2 . 1 F r i c t i o n s t u d i e s

1 .2 .2 Wear s t u d i e s

1 . 2 . 3 L u b r i c a t i o n s t u d i e s

1 .3 The meaning o f t r i b o l o g y

1 .4 The scope o f t h i s volume

2. THE SYSTEM CONCEPT

2 . 1 I n t r o d u c t i o n

2 . 2 D e s c r i p t i o n o f a sys tem

2 . 3 Energy b a l a n c e , n e t w o r k s , a n a l o g i e s

2.4 Bond g r a p h methods ’

2.5 C l a s s i f i c a t i o n o f systems

1

1

3

3

6

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20

2 1

X

3. GENERAL THEORY OF TRIBOLOGY

3 . 1

3 . 2 Func t ion o f t r ibo-mechan ica l systems

3.3 ' S t r u c t u r e o f t r ibo-mechan ica l systems

3 .4 T r i b o l o g i c a l i n t e r a c t i o n s

A p p l i c a t i o n o f systems concepts t o t r i b o l o g y

3 .4 .1 Func t i ona l p lane

3.4.2 Mechanical work p lane

3.4.3 Thermal p lane

3.4.4 M a t e r i a l p lanes

3.5 Conclusions

4. TRIBOLOGICAL PROCESSES

4 . 1 Role o f t r i bo -p rocesses i n mechanical systems

4 . 2 Contact processes

4.2.1 Contac t mechanics

4.2.2 Contac t phys ics and chemis t ry

4 . 3 . 1 Tangent ia l f o r c e s i n con tac t processes

4 .3 .2 S l i d i n g f r i c t i o n

4.3.3 R o l l i n g f r i c t i o n

4.3.4 Energy t ransmiss ion and d i s s i p a t i o n

4.4.1 General d e s c r i p t i o n

4.4.2 Sur face f a t i g u e wear mechanisms

4.4.3 Abras ive wear mechanisms

4.4.4 Adhesive wear mechanisms

4.4.5 Tr ibo-chemical wear mechanisms

4.4.6

4.3 F r i c t i o n processes

4 . 4 Wear processes

The comp lex i t y o f wear processes

4 .5 L u b r i c a t i o n modes

4 . 5 . 1 S t r i b e c k curve and l u b r i c a t i o n modes

4.5.2 Hydrodynamic 1 u b r i c a t i o n

4.5.3

4.5.4 Mixed l u b r i c a t i o n

4.5.5 Boundary l u b r i c a t i o n

4.5.6 The l i m i t s o f l u b r i c a t i o n

E l as t ohyd rodyn ami c 1 u b r i c a t i on

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5. INFLUENCE OF

TRIBOLOGICAL PROCESSES ON THE

STRUCTURE OF MECHANICAL SYSTEMS

5 . 1 Genera l c o n s i d e r a t i o n s

5 . 2 Changes i n s y s t e n i ' s e lemen ts p r o p e r t i e s

5 . 2 . 1 S u r f a c e t o p o g r a p h y changes

5 . 2 . 2 S u r f a c e c o m p o s i t i o n changes

5 . 2 . 3 S u r f a c e s t r e n g t h p r o p e r t i e s changes

5 . 3 M a t e r i a l l o s s e s

5 . 4 S o l u t i o n s f o r no-wear c o n d i t i o n s

5 . 4 . 1 F l u i d f i l m s

5 . 4 . 2 M a g n e t i c f i e l d s

5 . 4 . 3

5 . 4 . 4 F l e x u r a l means

5 . 4 . 5 Wear r e s i s t a n t c o a t i n g s

I n t e r f ac i a 1 e l as tomers

6 . INFLUENCE OF

TRIBOLOGICAL PROCESSES ON THE

FUNCTION OF MECHANICAL SYSTEMS

6 .1 Genera l c o n s i d e r a t i o n s

6.2 T r a n s m i s s i o n o f m o t i o n and s t i c k - s l i p e f f e c t s

6 . 2 . 1 Dynamics o f t r i b o - m e c h a n i c a l systems

6.2.2 S i m u l a t i o n o f s t i c k - s l i p b e h a v i o u r

6 . 3 M e c h a n i c a l e f f i c i e n c y

6 . 4 F u n c t i o n a l f a i l u r e s

6 . 4 . 1 Causes o f f a i l u r e

6 . 4 . 2 A case s t u d y : f a i l u r e modes o f g e a r s

6 . 5 Mechan ica l equ ipmen t r e l i a b i l i t y

6 . 6 Requ i remen ts f o r p r o p e r f u n c t i o n a l b e h a v i o u r

6 . 6 . 1 S t u d y o f a l t e r n a t i v e s o l u t i o n s

6 . 6 . 2

6 . 6 . 3

6 . 6 . 4

P r o p e r d e s i g n o f sys tem s t r u c t u r e

P r o p e r c h o i c e of o p e r a t i n g v a r i a b l e s

M o n i t o r i n g t h e f u n c t i o n o f t h e sys tem

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xii

7. TRIBOMETRY: TEST, SIMULATION AND CONTROL METHODS

7 . 1 I n t r o d u c t i o n

7.2 F r i c t i o n and wear t e s t methods

7.2.1 T r i b o m e t e r t e s t sys tem t y p e s

7.2.2 C o n t r o l o f o p e r a t i n g v a r i a b l e s

7.2.3 T r i b o m e t r i c c h a r a c t e r i s t i c s

7.3 S i m u l a t i v e tri b o - t e s t i n g

7.4 T e s t i n g o f t r i b o - t e c h n i c a l components

7.5 Mach ine ry c o n d i t i o n m o n i t o r i n g

7.6 S u r f a c e i n v e s t i g a t i o n t e c h n i q u e s

.

8 .1 I n t r o d u c t i o n

8.2 A t r i b o l o g i c a l systems d a t a s h e e t

8.2.1 T e c h n i c a l f u n c t i o n o f t h e sys tem

8.2.2 O p e r a t i n g v a r i a b l e s

8.2.3 S t r u c t u r e o f t h e sys tem

8.2.4 T r i b o l o g i c a l c h a r a c t e r i s t i c s

8.3 The d e s c r i p t i o n o f t r i b o - e n g i n e e r i n g systems

8 . 4 The p r e s e n t a t i o n o f f r i c t i o n and wear r e s e a r c h d a t a

8.5 A p p l i c a t i o n o f systems methodo logy t o t h e s o l u t i o n o f

t r i b o l o g i c a l p rob lems : some case s t u d i e s

8.5.1

8.5.2

8.5.3

8.5.4

8.5.5

8.5.6

8.5.7

8.5.8

I n v e s t i g a t i o n o f t h e v a l i d i t y o f

" C o u l o m b - f r i c t i o n " f o r p o l y m e r l s t e e l s1 i d i n g p a i r s

C h a r a c t e r i z a t i o n o f t h e t r i b o l o g i c a l b e h a v i o u r

o f w e a r - r e s i s t a n t d i f f u s i o n s u r f a c e c o a t i n g s

M a t e r i a l s e l e c t i o n f o r o f f - s h ' o r e b e a r i n g a p p l i c a t i o n

L u b r i c a n t s e l e c t i o n f o r i n s t r u m e n t p i v o t b e a r i n g

R e d u c t i o n o f s e v e r e wear o f cam- tappe t d e s i g n

R e d u c t i o n o f f r i c t i o n - i n d u c e d n o i s e o f

w h e e l / r a i l sys tem

F a i l u r e i n v e s t i g a t i o n o f e l e c t r i c a l c o n t a c t s

Compi 1 a t i o n o f c h a r a c t e r i s t i c s o f m e t a l w o r k i n g

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p rocesses 345

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APPENDIX 350

( A )

( 6 ) E lemen ts o f t r i b o - e n g i n e e r i n g systems

( C ) B i b l i o g r a p h i c w o r k : DOCUMENTATION TRIBOLOGY

A c o m p i l a t i o n o f b a s i c t r i b o - e n g i n e e r i n g systems

Re fe rences

L i s t o f symbols

A u t h o r i n d e x

S u b j e c t i n d e x

350

354

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382

388

393

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To

B a r b a r a and C a r s t e n

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1

1 Introduction and background

1,l DYNAMICS OF PHYSICAL SYSTEMS

AND THE OCCURRENCE OF FRICTION AND WEAR

The t e c h n i c a l f u n c t i o n o f numerous eng ineer ing systems - machines, i n s t r u -

ments, veh ic les , e t c . , - depends on processes o f mot ion. Accord ing t o i t s

bas i c p h y s i c a l d e f i n i t i o n , t h e te rm mot ion denotes t h e change o f t h e p o s i -

t i o n o f an o b j e c t w i t h t ime. I n a l a r g e r sense, t h e s tudy o f how t h i n g s

change w i t h t ime, and o f t h e fo rces t h a t cause them t o do so i s t h e ob jec -

t i ve o f dynamic i n v e s t i g a t i o n .

A g r e a t many processes i n n a t u r e and techno logy depend on t h e mot ion

and the dynamic behav iour o f s o l i d s , l i q u i d s and gases. Fo r example, p ro -

cesses o f mot ion l i k e the f l o w o f b lood i n ve ins o r t he t ransmiss ion o f

f o rces by moving machine components a r e e s s e n t i a l l y necessary f o r t h e func-

t i o n i n g o f coun t less b i o l o g i c a l systems and mechanical eng inee r ing systems.

Moreover, some obv ious l y non-mechanical d i s c i p l i n e s , l i k e e l e c t r o n i c s o r

o p t i c s , a r e a l s o based on mot ion processes, i n these cases on t h e mot ion o f

sub-microscopic p a r t i c l e s , i .e. , e l e c t r o n s , i o n s o r l i g h t quanta. I t appears

t h a t processes o f mot ion l i n k the d i f f e r e n t d i s c i p l i n e s as an u n d e r l y i n g

impor tan t p r i n c i p l e . Consequently, t he a n a l y s i s of dynamic behav iour has

become a keystone t o niuch contemporary sc ience and techno logy (Ref . 1.1).

A f e a t u r e common t o a l l processes o f mot ion i s t h e occur rence o f e f -

f e c t s o f " r e s i s t a n c e t o mot ion" , i . e . , t he occurrence o f f r i c t i o n o f some

k i n d o r another . The e f f e c t s o f f r i c t i o n a re due t o p h y s i c a l i n t e r a c t i o n s

between bod ies o r o b j e c t s moving r e l a t i v e l y t o each o t h e r . A s a consequence

o f f r i c t i o n , t h e process o f mot ion and t h e dynamic behav iour o f t h e whole

2

system are in f luenced o r d is turbed and some p a r t o f the energy o f motion i s

dissipated. Further, i f i n a dynamic system one mo.ving component consis ts o f

a s o l i d body, the e f f e c t o f f r i c t i o n i s accompanied i n general by wear: "the

progressive l oss o f substance from the operat ing surface o f a body occurr ing

as a r e s u l t o f r e l a t i v e motion a t the surface" (Ref. 1.2). I n F igure 1.1,

the bas ic types o f motion o f s o l i d bodies together w i t h re levan t engineering

systems and types o f res is tance t o motion and mechanisms o f damage are il- l u s t r a t e d schematical ly.

Surface motion Tech'nical systems Resistance t o motion Mechanism of damage - a i r bear ing

tu rb ine enaine a i r f r i c t i o n f l u i d eros ion

hyd rau l i c d r i ves viscous f r i c t i o n c a v i t a t i o n eros ion

d ry bearing wheel and r a i l s o l i d f r i c t i o n wear brakes

FSgure 1.1 Types o f surface motion and r e l a t e d subjects.

Contemporary technology has developed t o a l e v e l where the problems o f mov-

i n g surfaces requ i re carefu l cons iderat ion and an i n t e g r a t i o n o f a l l the

knowledge re levant t o the dynamics o f multicomponent systems. For example,

i n an a i r c r a f t l i t e r a l l y thousands of pa r t s are subject t o f r i c t i o n and

wear, f o r example brakes, bearings, seals, gears, actuators, pumps, f l i g h t

con t ro l systems, instruments, sp l i nes and even " s t a t i c " j o i n t s . Whereas, i n

the past, i n the design o f dynamic mechanical systems the problems o f f r i c -

t ion-induced energy losses and wear-induced mate r ia l s losses have been over-

looked t o some extent , the f u t u r e w i l l be se r ious l y concerned w i t h the con-

servat ion o f energy and ma te r ia l s i n engineering design. I n order t o embrace

a l l aspects o f moving surfaces and the transmission and d i s s i p a t i o n o f energy

and mater ia ls i n mechanical systems, the word "Tribology" was coined by a

B r i t i s h committee i n 1966 from the word " t r i b o s " , which means "rubbing" i n

c l a s s i c Greek (Ref. 1.3).

The phenomena o f t r i b o l o g y - i t s fundamental concepts, i t s bas ic physi-

ca l processes and i t s influences on the func t i on and s t ruc tu re o f mechanical

engineering systems - are the subject o f t h i s book.

3

1 I 2 H I STOR I CAL DEVELOPMENT OF TR I BOLOGY

I ' I t i s q u i t e d i f f i c u l t t o do a c c u r a t e q u a n t i t a t i v e

exper iments i n f r i c t i o n , and t h e laws o f f r i c t i o n

a r e s t i l l n o t ana lyzed v e r y w e l l , i n s p i t e o f t h e

e n o r m u s e n g i n e e r i n g v a l u e o f an a c c u r a t e a n a l y s i s " .

R ichard P . Feynrnan

- Nobel l a u r e a t e - Feynrnan l e c t u r e s , 1963

I t appears incomprehens ib le t h a t such obv ious l y o l d problems l i k e f r i c t i o n

and wear s t i l l remain unsolved problems i n many aspects. Moreover, i n many

f i e l d s o f advanced technology, these problems seem t o be more impor tan t a t

p resen t than i n fo rmer t imes. Some o f t he reasons f o r t h i s f a c t w i l l be

v i s i b l e f rom a c o n s i d e r a t i o n o f t he h i s t o r i c a l development o f s t u d i e s i n

these f i e l d s . Wi thout go ing i n t o a l l d e t a i l s , i t may t h e r e f o r e be va luab le

t o g i v e a survey o f t h e development o f ou r knowledge on t h i s s u b j e c t ma t te r .

(Fo r f u r t h e r d e t a i l s see Refs. 1.4 - 1.8.) I n ch rono log ica l o rde r , t h e r e -

v iew dea ls f i r s t w i t h f r i c t i o n and then t u r n s t o t h e sub jec ts of wear and

l u b r i c a t i o n .

1,2,1 FRICTION STUDIES

It i s l i k e l y t h a t even i n p r e h i s t o r y man was i n t e r e s t e d i n two aspects o f

f r i c t i o n . The f i r s t p r a c t i c a l a p p l i c a t i o n seems t o have been t h e use o f

f r i c t i o n a l hea t i n the l i g h t i n g o f f i r e s . The second p r a c t i c a l aspec t was

t o overcome f r i c t i o n i n t h e t r a n s p o r t a t i o n o f m a t e r i a l s . It seems probab le

t h a t man has used sledges f o r t r a n s p o r t a t i o n f o r a lmost 9,000 yea rs . Fo r

t h e enormous eng ineer ing t r a n s p o r t a t i o n problems connected w i t h t h e e rec -

t i o n o f t h e pyramids, t h e Egypt ians were a l ready u s i n g l i q u i d l u b r i c a n t s i n

o r d e r t o min imize t h e work r e q u i r e d t o t r a n s p o r t heavy ob jec ts .

I t has been s a i d t h a t one o f t h e g r e a t e s t i n v e n t i o n man eve r made was

t h a t o f t h e wheel. I n f a c t , by p roper use o f t h i s i n v e n t i o n i t i s p o s s i b l e

t o reduce t h e work needed t o overcome f r i c t i o n cons ide rab ly . From t h e r e -

s u l t s o f a rchae log ica l s t u d i e s , i t migh t be concluded t h a t t h e m e r i t s o f

r o l l i n g mot ion compared w i t h s l i d i n g had been recogn ized some 5,000 yea rs

i n Mesopotamia.

4

The s c i e n t i f i c s tudy o f t h e dynamics o f mot ion and o f f r i c t i o n phenom-

ena i s , however, much more recen t than these e a r l y a p p l i c a t i o n s migh t sug-

gest. I t s t a r t s , as i s known, w i th t h e work done 360 years ago by G a l i l e o .

G a l i l e o made a g r e a t advance i n t h e unders tand ing o f mot ion when he d i scov -

e red t h e " p r i n c i p l e o f i n e r t i a " : i f a moving o b j e c t i s unper tu rbed - i f i t

i s n o t d i s t u r b e d by f r i c t i o n fo rces - i t cont inues t o move w i t h a cons tan t

v e l o c i t y i n a s t r a i g h t l i n e . The n e x t s tep i n t h e s c i e n t i f i c development o f

dynamics was done by Newton i n f o r m u l a t i n g the ce leb ra ted b a s i c laws o f

c l a s s i c a l mechanics.

Supplementing t h e laws o f G a l i l e o and Newton on the mechanics o f i d e a l

mot ion, Amontons i n 1699 and Coulomb i n 1785 fo rmu la ted some r u l e s o f s o l i d

f r i c t i o n based on ex tens i ve exper iments (Ref. 1.9, 1.10). F o r t h e purpose

o f h i s f r i c t i o n exper iments, Coulomb developed a spec ia l measuring equip-

ment named a " t r i b o m e t e r " (see F igu re 1 . 2 ) .

d i r e c t i o n o f mot ion

_t s o l i d body I

/ / I / / / / / / / / / / / / / / / / / A / / / / /

/ / /

"8" / Fweight' FF

suppor t

c o e f f i c i e n t o f f r i c t i o n

f = FF/FN = t a n 8 A

F igu re 1.2 Tr ibometer used by Coulomb f o r f r i c t i o n measurements.

The exper imenta l r e s u l t s o f Amontons and Coulomb showed t h a t t h e f r i c t i o n

f o r c e FF i s p r o p o r t i o n a l t o the normal l oad FN. The r a t i o o f t h e f r i c t i o n

f o r c e t o t h e normal l o a d has been termed t h e " c o e f f i c i e n t o f f r i c t i o n "

f = FF/FN. The exper iments i n d i c a t e d t h a t t h e va lue o f t h e c o e f f i c i e n t o f

f r i c t i o n i s independent o f t he geomet r ic c o n t a c t area. I n e x p l a i n i n g these

r e s u l t s , i t has been hypothes ized t h a t t he su r faces were f u l l o f i r r e g u l a r -

i t i e s and t h a t t he f r i c t i o n o r i g i n a t e d i n t h e i n t e r l o c k i n g o f a s p e r i t i e s

o f t he c o n t a c t i n g sur faces . Th is theo ry became known as t h e "roughness hy-

po thes i s o f f r i c t i o n " . Coulomb a l s o cons idered t h e p o s s i b i l i t y o f adhesion

processes i n f r i c t i o n as suggested by Desagu l ie r i n 1724. Desagu l ie r

5

observed s t r o n g adhesion between l e a d spheres when they a r e pressed t o g e t h e r

and he cons idered t h a t s i m i l a r f o r c e s m i g h t be i n v o l v e d i n f r i c t i o n (Ref .

1.11). Coulomb i n h i s i n t e r p r e t a t i o n o f t he f r i c t i o n process, however, r e -

j e c t e d t h i s adhesion hypothes is . Preced ing t h e work o f Amontons and Coulomb,

Leonard0 da V i n c i had a l ready found, by t h e m idd le o f t h e f i f t e e n t h cen tu ry ,

t h a t t he f r i c t i o n f o r c e was p r o p o r t i o n a l t o t h e l oad (Ref . 1 . 1 2 ) . From t h e

r e s u l t s o f h i s exper iments, he concluded t h a t t h e f r i c t i o n f o r c e was one

q u a r t e r o f t h e l o a d and cons tan t f o r a l l m a t e r i a l s ( i . e . , f = 0.25 = con-

s t a n t ) .

n i c a l eng inee r ing , f rom a p h y s i c a l p o i n t o f view the o r i g i n o f f r i c t i o n

cannot be exp la ined i n terms o f t he c l a s s i c a l mechanics o f r i g i d bod ies .

I f t h e s u r f a c e a s p e r i t i e s a re assumed t o be r i g i d , an energy ba lance shows

t h a t t he process o f mere ly l i f t i n g one s l i d i n g s u r f a c e ove r the bumps o f t h e

coun te r face consumes no mechanical energy whereas i n r e a l i t y energy i s d i s -

s ipa ted . It f o l l o w s t h a t t h e f i n d i n g s o f Amontons and Coulomb can be regarded

o n l y as rough e m p i r i c a l r u l e s o f l i m i t e d v a l i d i t y . However, s i n c e these r u l e s

were fo rmu la ted a t a very e a r l y s tage o f t h e sc ience o f mechanics, these

f i n d i n g s have been taken as " laws" o f f r i c t i o n . Moreover, t h e f r i c t i o n be-

hav iou r of mechanical systems had been t r e a t e d i n terms o f cons tan t c o e f f i -

c i e n t s o f f r i c t i o n which a r e assumed t o be " i n t r i n s i c m a t e r i a l p r o p e r t i e s " .

As a consequence o f :

( i ) t h e development o f i d e a l i z e d t h e o r i e s o f mechanics i n which the e f f e c t s

o f f r i c t i o n a r e neg lec ted e n t i r e l y ,

( i i ) t he m i s i n t e r p r e t a t i o n o f t he c o e f f i c i e n t o f f r i c t i o n as " i n t r i n s i c ma-

t e r i a 1 cons t a n t" ,

Although these f i n d i n g s seem t o answer some b a s i c ques t i ons o f mecha-

no a c t u a l p rogress beyond t h e roughness hypo thes i s was made i n t h e f i e l d o f

f r i c t i o n th roughout the n i n e t e e n t h c e n t u r y and i n t o t h e t w e n t i e t h .

As an a l t e r n a t i v e e x p l a n a t i o n o f t h e o r i g i n o f s o l i d f r i c t i o n , t h e

"adhesion theo ry " o f f r i c t i o n was p u t f o rward by Hardy (Ref. 1 .13) and Tom-

l i n s o n (Ref . 1.14) i n t h e 1 9 2 0 ' s . I n t h i s theo ry i t i s assumed t h a t t h e

f r i c t i o n f o r c e i s needed t o overcome mo lecu la r adhesion f o r c e s a c t i n g between

the c o n t a c t i n g sur faces . Al though t h i s theo ry appears r a t h e r obvious, i t

r e q u i r e s a f r i c t i o n f o r c e p r o p o r t i o n a l t o t h e area o f c o n t a c t . Th i s , however,

i s i n disagreement w i t h the r e s u l t s o f numerous f r i c t i o n exper iments i n d i -

c a t i n g t h a t t h e f r i c t i o n f o r c e i s independent o f t h e c o n t a c t area.

A t t h i s s tage o f t he h i s t o r i c a l development o f t he a n a l y s i s o f f r i c t i o n ,

i t was recogn ized t h a t t h e p h y s i c a l o r i g i n s o f f r i c t i o n a re a ve ry comp l i ca ted

6

m a t t e r which can n o t be exp la ined by a s imp le theo ry b u t need bo th accura te

exper iments and d e t a i l e d phys i ca l analyses. Since, d u r i n g t h e 1920's and

1930's, p h y s i c i s t s were ma in l y i n t e r e s t e d i n t o p i c s l i k e a tomic phys ics and

quantum mechanics i t was n o t u n t i l about 1940 t h a t t h e d i sc repanc ies de-

s c r i b e d above were c l a r i f i e d . A t t h i s t ime, Holm (Ref. 1.15), E rns t and

Merchant (Ref. 1.16) and Bowden and Tabor (Ref. 1.17) found a g r e a t d i f f e r -

ence between t h e apparent geomet r ica l area o f con tac t and t h e " r e a l " a rea

o f con tac t formed by t h e touch ing a s p e r i t i e s o f t h e two sur faces . I n u s i n g

t h i s observa t ion , t oge the r w i t h t h e assumption t h a t adhesive molecu la r f o r c e s

a c t i n t h e a s p e r i t y j u n c t i o n s , Bowden and Tabor (Ref. 1.18) cou ld e x p l a i n t h e

e m p i r i c a l r u l e s o f Amontons and Coulomb. I t f o l l o w s t h a t f r i c t i o n has a

"dua l " na tu re i n t h a t bo th de format ion processes and adhesion processes a r e

i n v o l v e d i n f r i c t i o n . Th is dual molecular-mechanical concept has been gener-

a l l y accepted as a "genera l i zed" theo ry o f f r i c t i o n .

1,2,2 WEAR STUDIES

Some o f t h e f i r s t sys temat ic s t u d i e s on t h e wear behav iour o f m a t e r i a l s were

performed by t h e g r e a t genius Leonardo da V i n c i . I n h i s manuscr ip t , found i n

1967 i n Madrid (Codex Madrid I) (Ref. 1.12), Leonardo desc r ibed h i s s t u d i e s

on t h e wear o f s imp le s l i d i n g bear ings . He found t h a t wear inc reases w i t h

l o a d and t h a t the d i r e c t i o n o f wear i s n o t n e c e s s a r i l y i n a v e r t i c a l d i r e c -

t i o n b u t f o l l o w s t h e main vec to r o f t h e load. I n o rde r t o min imize wear he

developed a s l i d i n g bear ing , suggest ing an a l l o y o f 30 pe rcen t copper and

70 pe rcen t t i n t o be used as bear ing bush.

a s c i e n t i f i c bas i s i s f a r more recen t . An e a r l y p e r i o d o f sys temat ic wear

s tud ies - which has passed almost unnot iced by Eng l ish-speak ing research

workers - s t a r t e d i n Germany around 1930. Fuchsel exp la ined t h e d r y wear of

metals as a process o f de format ion f o l l o w e d by a process o f separa t i on

(German: " A b b l a t t e r n " ) o f t h e deformed metal p a r t s (Ref. 1 .19) . T h i s theo ry

has been extended by F ink , and Mai lander and D ies (Ref. 1.20, 1.21). They

found t h a t the deformed metal p a r t s may o x i d i z e d u r i n g t h e wear process, and

emphasized t h e impor tan t i n f l u e n c e o f t h e environmental atmosphere on t h e

wear o f metals. The s t a t e o f t h e a r t o f t h e e a r l y p e r i o d o f sys temat ic wear

research had been reviewed by S iebe l i n 1938 (Ref. 1.22). Depending on t h e

na tu re o f ex te rna l c o n d i t i o n s o f wear a t t a c k , he d i s t i n g u i s h e d between t h e

f o l l o w i n g d i f f e r e n t types o f wear:

Apar t f rom t h e work o f Leonardo, t h e beg inn ing of t h e s tudy o f wear on

7

1.

2.

3.

4.

5 . Wear d u r i n g o s c i l l a t i n g c o n t a c t

6. Wear by moving s o l i d p a r t i c l e s ( e r o s i o n )

7. Wear by moving f l u i d s ( c a v i t a t i o n )

S iebe l p o i n t e d o u t t h a t as a consequence o f t h e g r e a t v a r i e t y o f d i f f e r e n t

types o f wear i t seems t o be imposs ib le t o de termine t h e wear behav iour o f

a m a t e r i a l by one s i n g l e t e s t and t o o b t a i n unique wear va lues . I n a r a t h e r

modern way o f t h i n k i n g , he suggested c l o s e j o i n t research work t o be done

by p h y s i c i s t s , chemists, metal l u r g i s t s , t h e o r i s t s o f e l a s t i c i t y and p l a s t i -

c i t y , des igners , and p l a n t eng ineers i n o r d e r t o o b t a i n r e a l p rogress i n

t h e most complex f i e l d o f wear.

The f i r s t p e r i o d o f wear research ended i n t h e yea rs o f World War 11.

Therea f te r , i n t h e 1 9 5 0 ' s a c e r t a i n r e p e t i t i o n and ex tens ion o f t h i s work

cou ld be noted, performed m a i n l y i n USA and England. Fo r the case o f me ta l /

metal wear, Feng, Bu rwe l l and S t rang were p robab ly the f i r s t t o recogn ize

the d i f f e r e n c e between meta l t r a n s f e r f rom one s u r f a c e t o another and t h e

process o f a t t r i t i o n o f meta l (Ref . 1 .23) . Ke r r i dge showed t h a t t he t r a n s -

f e r o f meta l may be f o l l o w e d by o x i d a t i o n o f t he t r a n s f e r r e d meta l and t h a t

t h e l a s t s tage o f such a process o f " m i l d " wear i s g i ven by t h e a t t r i t i o n

of meta l ox ides (Ref. 1 .24) . I n c o n t r a s t t o m i l d wear, i n processes o f

"severe" wear t h e a t t r i t i o n takes p lace d i r e c t l y a t t h e t r a n s f e r r e d me ta l .

For c e r t a i n c o n d i t i o n s o f s l i d i n g d r y meta l su r faces i n a regime o f m i l d

wear, Archard found the e m p i r i c a l r u l e t h a t t h e wear volume i s d i r e c t l y

p r o p o r t i o n a l t o t h e l o a d and t h e s l i d i n g d i s t a n c e and i n v e r s e l y p ropor -

t i o n a l t o t h e hardness o f t h e s o f t e r o f t h e two i n t e r a c t i n g me ta l s (Ref .

1 .25) . A t about t h e same t ime a t which Archard pub l i shed t h e e m p i r i c a l r u l e

o f d r y wear, t he main p h y s i c a l mechanisms o f wear were c l a s s i f i e d by Burwe l l

(Ref. 1 .26) . Accord ing t o t h i s c l a s s i f i c a t i o n , a t l e a s t f o u r d i f f e r e n t main

p h y s i c a l mechanisms must be d i s t i n g u i s h e d , namely:

1. adhesive wear

2. ab ras i ve wear

3. c o r r o s i v e wear

4. su r face f a t i g u e wear.

Having b r i e f l y rev iewed t h e h i s t o r i c a l development o f t h e s t u d i e s o f f r i c -

t i o n and wear up t o the end o f t h e 1950's, i n r e t r o s p e c t i t appears t h a t a t

Wear d u r i n g s l i d i n g f r i c t i o n o f d r y su r faces

Wear d u r i n g s l i d i n g f r i c t i o n o f l u b r i c a t e d su r faces

Wear d u r i n g r o l l i n g f r i c t i o n o f d r y sur faces

Wear d u r i n g r o l l i n g f r i c t i o n o f l u b r i c a t e d su r faces

8

t h a t t ime these subjects were p a i d i nc reas ing l y more a t t e n t i o n by most o f

the h i g h l y i n d u s t r i a l i z e d nations, mainly f o r economic reasons. Before con-

t i n u i n g the chronological review, as a f u r t h e r aspect the science and tech-

nology o f l u b r i c a t i o n - the most important means o f reducing f r i c t i o n and

wear-induced energy and mater ia l losses - should be taken i n t o considerat ion.

1 I 2 I 3 LUBRICATION STUD1 E S

The purpose o f l u b r i c a t i o n i s t o separate t w o surfaces moving r e l a t i v e t o

each other by a f l u i d f i l m which can e a s i l y be sheared w i thou t causing any

damage t o the surfaces. As mentioned above, l u b r i c a n t s were already i n use

about 5,000 years ago by the Assyrians and Egyptians i n f a c i l i t a t i n g the

movement o f sledges ca r ry ing l a r g e statues o r bu i l d ings blocks o f stone.

i e s o f Leonard0 da Vinc i , i t was only w i t h the advent o f accurate ly made

m e t a l l i c machine p a r t s dur ing the so-cal led I n d u s t r i a l Revolut ion t h a t the

s c i e n t i f i c and engineering aspects o f l u b r i c a t i o n were consequently studied.

Before t h i s period, the s c i e n t i f i c i n t e r e s t was concentrated mainly on the

development o f "pure" theories o f f l u i d mechanics. In t h i s connection an

i n t e r e s t i n g remark o f the mathematician John v. Neumann should be quoted

(Ref. 1.27). He pointed ou t t h a t dur ing most o f the development o f hydro-

mechanics u n t i l about 1900, the main i n t e r e s t was v i r t u a l l y the so l v ing o f

b e a u t i f u l mathematical problems neglect ing terms o f i n t e r n a l f l u i d f r i c t i o n .

These approximations, however, had almost noth ing t o do with r e a l f l u i d s .

John v . Neumann characterized the t h e o r i s t making such analyses as a man who

stud ied the f low o f "dry" water.

t o j ou rna l bearings. I n 1883 P e t r o f f proposed the fo l l ow ing formula f o r the

f r i c t i o n a l force FF between two coaxia l cy l i nde rs

Apart from t h i s ancient use o f the l u b r i c a n t s and the l u b r i c a t i o n stud-

M o s t e a r l y work on the motion o f l u b r i c a t e d machine pa r t s was devoted

FF = x (wetted area)

where 7 i s the v i scos i t y , v the surface v e l o c i t y o f the s h a f t and ha, the

mean e f f e c t i v e f i l m thickness. This was the f i r s t expression der ived f o r t he

f u l l - f l u i d - t y p e o f l u b r i c a t i o n . (The work o f P e t r o f f i s discussed i n d e t a i l

i n Ref. 1.7.)

9

The mathematical foundat ions o f a l l hydrodynamic l u b r i c a t i o n theo ry were

l a i d i n 1886 by Reynolds i n d e r i v i n g t h e famous equat ions named a f t e r h im

which a re t h e b a s i s on which a l l subsequent l u b r i c a t i o n theo ry has been

based (Ref . 1 .28) . Fundamental exper imenta l work i n t h i s f i e l d was performed

around t h e t u r n o f t he 20 th cen tu ry by S t r i b e c k a t a predecessor i n s t i t u t e

o f t h e Bundesansta l t f u r M a t e r i a l p r u f u n g (BAM), Ber l in-Dahlem. S t r i b e c k

s t u d i e d i n d e t a i l t he i n f l u e n c e o f t h e d i f f e r e n t o p e r a t i n g v a r i a b l e s , l i k e

l o a d and v e l o c i t y , on t h e l u b r i c a t i o n and f r i c t i o n o f s l i d i n g and r o l l i n g

bear ings (Ref . 1 .29) . The exper imenta l r e s u l t s o f S t r i b e c k were compared by

Sommerfeld w i t h h i s own t h e o r e t i c a l f r i c t i o n r e s u l t s which he had d e r i v e d i n

i n t e g r a t i n g Reynolds equa t ion us ing an ingen ious s u b s t i t u t i o n (Ref . 1.30).

B i e l i n 1920 was t h e f i r s t t o p o i n t o u t t h a t t h e type o f f r i c t i o n curve mea-

sured by S t r i b e c k - the genera l i zed S t r i b e c k curve - i s l i k e l y t o desc r ibe

t h e general behav iour o f l u b r i c a t e d sur faces as a f u n c t i o n o f l u b r i c a n t v i s -

c o s i t y , s l i d i n g v e l o c i t y and l o a d (Re f . 1 . 3 1 ) . Based on these fundamentals

o f l u b r i c a t i o n theory , c r i t e r i a f o r t he eng ineer ing des ign o f hydrodynamical

l u b r i c a t e d bear ings have then been developed (Ref . 1.32).

One impor tan t ques t i on , however, which i s l e f t open by t h e hydrodynamic

l u b r i c a t i o n theo ry concerns t h e l i m i t s o f f u l l - f l u i d l u b r i c a t i o n . I f , f o r

i ns tance , t he s p e c i f i c l oad i s very h i g h and the r e l a t i v e v e l o c i t y i s low,

i t i s d i f f i c u l t t o b u i l d up a s u f f i c i e n t l y t h i c k f i l m even w i t h very v i s -

cous l u b r i c a n t s . I n t h i s l u b r i c a t i o n regime, some p a r t s o f t h e s l i d i n g su r -

faces may be covered by l u b r i c a n t f i l m s o n l y one o r two mo lecu la r dimensions

t h i c k . Hardy i n 1922 was the f i r s t t o s tudy i n d e t a i l t h i s regime o f "bound-

a ry " l u b r i c a t i o n , where t h e l u b r i c a n t a c t i o n i s determined by t h e chemical

c o n s t i t u t i o n o f t he l u b r i c a n t r a t h e r than by i t s v i s c o s i t y (Ref . 1 . 3 3 ) .

S ince t h e work o f Hardy, the non-hydrodynamic regimes o f l u b r i c a t i o n have

been s t u d i e d i n t e n s e l y under d i f f e r e n t aspects. Fu r the r , d i f f e r e n t chemi-

c a l l y a c t i v e l u b r i c a n t a d d i t i v e s - l i k e extreme pressure a d d i t i v e s o r a n t i -

wear a d d i t i v e s - were developed. The development o f l u b r i c a n t s w i t h chemi-

c a l l y a c t i v e a d d i t i v e s a l lowed the eng ineer ing a p p l i c a t i o n o f machine e l e -

ments under c o n d i t i o n s which had l e d t o c a t a s t r o p h i c f a i l u r e s i f l u b r i c a t e d

w i t h pure m ine ra l o i l s . (Fo r ins tance, t he t e c h n i c a l a p p l i c a t i o n o f hypo id

gears f o r r e a r - a x l e d r i v e , i n t roduced i n 1927 by t h e Packard Motor Car Com-

pany was p o s s i b l e o n l y by u s i n g l u b r i c a n t s w i t h chemical a d d i t i v e s . )

h i g h e r loads, h i g h e r v e l o c i t i e s and h i g h e r o p e r a t i n g temperatures was ob-

served i n connect ion w i t h a t tempts t o reduce t h e we igh ts o f t he moving p a r t s

i n machinery. S ince t h a t t ime the re has been a s teady i nc rease o f i n t e r e s t

A f t e r World War 11, a general t r e n d i n mechanical eng inee r ing towards

10

i n the problems of f r i c t i o n , l u b r i c a t i o n and wear. Tokens o f t h i s i n c r e a s i n g

i n t e r e s t were, among o t h e r t h i n g s , t h e appearance o f t h e f i r s t i n t e r n a t i o n a l

j o u r n a l e n t i t l e d WEAR ( s i n c e 1957) e n t i r e l y devoted t o the sc ience and tech-

no logy o f f r i c t i o n , wear and l u b r i c a t i o n . A f u r t h e r new j o u r n a l , t h e

TRANSACTIONS o f ASLE, has been pub l i shed ( s i n c e 1958) by the American

Soc ie ty o f L u b r i c a t i o n Engineers. I n t h e Federal Repub l ic o f Germany a

research programme ("Schwerpunkt-Programm") had been 1 aunched i n 1961 spon-

sored by the Deutsche Forschungsgemeinschaft (Ref . 1.34). About t h e same t ime

i n England, a Working Group was s e t up t o i n v e s t i g a t e t h e p resen t s t a t e o f

l u b r i c a t i o n and research and t o g i v e an o p i n i o n on t h e needs o f i n d u s t r y

t h e r e o f . I n 1966 t h i s Working Group pub l i shed a r e p o r t i n wh ich f o r t h e f i r s t

t ime t h e te rm " t r i b o l o g y " appeared (Ref . 1 .3 ) . The o r i g i n o f t r i b o l o g y was

descr ibed i n t h e r e p o r t "The i n t r o d u c t i o n o f a new technology" (1973) as

f o l l o w s (Ref. 1 .35) .

I n the e a r l y 1960's t h e r e was a steep inc rease i n the repo r ted f a i l u r e

o f p l a n t and machinery due t o wear and assoc ia ted causes. A t t h e same t ime,

inc reased technology and increased c a p i t a l i n t e n s i t y o f p l a n t , and t h e use

o f more cont inuous processes, made breakdowns o f such p l a n t and machinery

more c o s t l y , c o m p e t i t i v e l y more se r ious , and t h e r e f o r e even l e s s d e s i r a b l e

than be fore . Th is t r e n d was recogn ized by s p e c i a l i s t s i n v o l v e d i n t h e sub-

j e c t s o f wear, f r i c t i o n and l u b r i c a t i o n . The s i t u a t i o n seemed t o c a l l f o r

more and b e t t e r educat ion i n the sub jec ts and f o r more and b e t t e r co -o rd i -

na ted research.

Whi le t r y i n g t o e s t a b l i s h t h e reasons f o r t he wide n e g l e c t o f t he sub-

j e c t i n t h e pas t , d e s p i t e i t s t echno log ica l and economic importance, t h r e e

p r i n c i p a l reasons f o r t h i s n e g l e c t may be mentioned:

( i ) The i n t e r - d i s c i p l i n a r y n a t u r e o f t h e s u b j e c t which i n c l u d e d the

d i s c i p l i n e s o f mechanical eng ineer ing , phys ics , m e t a l l u r g y and

c h emi s t ry .

The f a c t t h a t o n l y w i t h the advances i n techno log ica l development

i n p roduc t i on methods o f r e c e n t yea rs had a t t e n t i o n been focused on

t h e importance and inter-dependence o f t h e c o n s t i t u e n t s o f t h i s i n t e r -

d i s c i p l i n a r y sub jec t .

( i i i ) The term " l u b r i c a t i o n " , used i n i t s nar rower sense, had n o t o n l y p re -

vented many peop le f rom f u l l y a p p r e c i a t i n g t h e economic s i g n i f i c a n c e

o f t he s u b j e c t ma t te r , b u t i t was a l s o a hisnomer f o r t h e d e s c r i p t i o n

o f t h e sphere o f " t rans fe rence o f f o r c e f rom one moving su r face t o

another " (whether the purpose o f t h e t r a n s f e r o f such fo rces was

( i i )

11

A f t e r

assoc ia ted w i t h h i g h f r i c t i o n , e.g., on brakes , c lu t ches , conveyors

o r a l t e r n a t i v e l y w i t h low f r i c t i o n , e.g., bear ings , s l i d e s , e t c . )

c o n s u l t a t i o n w i t h t h e E d i t o r s of t h e Supplement o f t he Oxford E n g l i s h

D i c t i o n a r y , t h e te rm "T r ibo logy " (T r ibosc ience o r T r ibo techno logy ) was

recommended f o r d e s c r i b i n g t h e s u b j e c t ma t te r . T r i b o l o g y i s d e f i n e d as:

"The sc ience and techno logy o f i n t e r a c t i n g su r faces i n

r e l a t i v e mot ion and o f r e l a t e d sub jec ts and p r a c t i c e s " .

1 , 3 THE M E A N I N G OF TRIBOLOGY

Since i t s d e f i n i t i o n i n 1966, t h e te rm t r i b o l o g y has been w i d e l y recogn ized

as a new genera l concept embracing a l l aspects o f t he t ransmiss ion and d i s -

s i p a t i o n o f energy and m a t e r i a l s i n mechanical equipment i n c l u d i n g t h e var -

i ous t o p i c s o f f r i c t i o n , wear, l u b r i c a t i o n and r e l a t e d f i e l d s o f sc ience and

technology. I n o r d e r t o c h a r a c t e r i z e t h e s i g n i f i c a n c e o f t r i b o l o g y , among

o t h e r t h i n g s , t h r e e p o i n t s have been emphasized (Ref. 1.36):

( i ) The economic aspec t o f t r i b o l o g y :

I t has been es t ima ted t h a t about 30% of t h e energy generated i n t h e

i n d u s t r i a l p a r t s o f t h e w o r l d i s consumed u l t i m a t e l y i n f r i c t i o n pro-

cesses and t h a t i n h i g h l y i n d u s t r i a l i z e d c o u n t r i e s , l i k e England,

Japan o r t h e Federal Repub l ic o f Germany, some $ 2,000 m i l l i o n p e r

annum a r e l o s t as a r e s u l t o f wear processes (Ref . 1 . 3 7 ) . Even i f

these f i g u r e s a r e taken as rough es t imates o n l y , (Ref . 1 .38) , they

c l e a r l y i n d i c a t e t h e importance o f t r i b o l o g y f o r t h e conserva t i on o f

energy and m a t e r i a l s .

The s c i e n t i f i c aspect o f t r i b o l o g y :

I t i s w e l l known t h a t a l l macroscopic processes i n n a t u r e a re i r r e -

v e r s i b l e . Science i n i t s "pure" t h e o r i e s has l a r g e l y o m i t t e d t h i s

i r r e v e r s i b i l i t y s i n c e t h e laws o f " i d e a l " processes were much e a s i e r

t o develop. T r i b o l o g y shou ld a t tempt t o i n v e s t i g a t e t h e i r r e v e r s i b l e

processes o f mechanics i n d e t a i l and t o e x p l a i n the complex e f f e c t s

o f energy and m a t e r i a l s d i s s i p a t i o n .

( i i i ) The m u l t i d i s c i p l i n a r y aspec t o f t r i b o l o g y :

S ince t r i b o l o g y i s d e f i n e d as "Science and techno logy o f i n t e r a c t i n g

sur faces i n r e l a t i v e mot ion" , i t inc ludes n o t o n l y t h e work o f p h y s i -

c i s t s , chemists and m a t e r i a l s s c i e n t i s t s i n t e r e s t e d i n t h e su r face

( i i )

12

p r o p e r t i e s o f m a t e r i a l s b u t a l s o t h e work o f eng ineers who use " i n t e r -

a c t i n g sur faces" f o r t he t ransmiss ion o f mot ion, f o rces , work, e t c . ,

i n var ious types o f machinery. There fore , t r i b o l o g y i s connected w i t h

severa l branches of sc ience and technology, l i k e phys ics , chemis t ry ,

ma te r i a1 s science, mechanical eng ineer ing , 1 u b r i c a t i o n eng ineer ing ,

e t c .

The v a r i e t y o f economic, s c i e n t i f i c and techno log ica l aspects o f t r i b o l o g y

i s a l s o ev iden t when cons ide r ing t h e l i t e r a t u r e . I n t h e e leven years t h a t

have passed s ince t h e c r e a t i o n o f the term t r i b o l o g y i n 1966, t h e huge num-

b e r o f some 55,000 papers have been pub l i shed i n t h e f i e l d o f t r i b o l o g y .

According t o the BAM T r i b o l o g y Documentation Serv ice , which annua l l y pub-

l i s h e s a c o m p i l a t i o n ( t i t l e c o l l e c t i o n ) o f t r i b o l o g y papers appear ing

th roughout the wor ld , a t p resent about 8,000 papers a re pub l i shed every

yea r i n t h i s f i e l d (Ref. 1.39). Due t o t h e m u l t i d i s c i p l i n a r y na tu re o f

t r i b o l o g y , t he papers s c a t t e r b r o a d l y i n purpose and conten t . There fore ,

a1 though some progress i n t h e d i f f e r e n t s p e c i a l i z e d sub top ics o f t r i b o l o g y

were obtained, s u i t a b l e t o o l s a r e needed i n o rde r t o l i n k these r e s u l t s and

t o p repare the way f o r coopera t i on between people o f w i d e l y d i f f e r i n g d i s -

c i p l i nes.

1,4 THE SCOPE OF THIS VOLUME

The i n t r o d u c t o r y remarks have focussed a t t e n t i o n on the problem t h a t tr i-

bo logy , l i k e any m u l t i d i s c i p l i n a r y branch of sc ience and technology, poses

se r ious d i f f i c u l t i e s of communication. The very d e f i n i t i o n o f t r i b o l o g y - " i n t e r a c t i n g sur faces i n r e l a t i v e mot ion" - i n d i c a t e s a l ready t h a t t h e be-

hav iou r o f t r i b o - t e c h n i c a l c o n s t r u c t i o n s cannot be p r e d i c t e d f rom a mere

knowledge o f s i n g l e components and t h e i r fea tures . Whenever t h e i n t e r p l a y

and interdependence between components i s s t r o n g e r and more compl ica ted

than the a c t i o n o f t he i n d i v i d u a l components, a "systems approach" i s

needed. An unders tand ing o f t h i s new ou t look i s r a p i d l y growing i n many

areas o f contemporary sc ience and technology. I n r e t r o s p e c t , i t appears

t h a t t he ove r look ing of the systems aspects o f f r i c t i o n , l u b r i c a t i o n and

wear problems has been obv ious l y one o f t he major reasons f o r t h e many

m i s i n t e r p r e t a t i o n s and t h e slowness o f p rogress i n these f i e l d s i n the

past.

13

I n t h i s volume, we a t tempt t o p resen t a sys temat i c u n i f i e d approach t o

t r i b o l o g y based on systems t h i n k i n g . The book has been w r i t t e n b e a r i n g i n

mind bo th t h e s p e c i a l i s t who seeks t o i n c o r p o r a t e h i s knowledge and p r a c t i -

c a l exper ience i n a genera l framework, and the genera l s c i e n t i s t who seeks

a sys temat ic o v e r a l l v iew o f t h e whole sub jec t . As a r e s u l t o f t h e u n i f y i n g

a t tempt , t h e s p e c i a l i s t may f i n d t h a t h i s s p e c i a l t o p i c i s t r e a t e d i n a

somewhat unusual manner. I t must be borne i n mind, however, t h a t i n a u n i -

f y i n g i n t e r d i s c i p l i n a r y t r e a t i s e a u n i f o r m nomenclature and d e s c r i p t i o n i s

necessary which i s e q u a l l y use fu l f o r t he va r ious s p e c i a l i s t s i n the f i e l d ,

i . e . , p h y s i c i s t s , chemists, m a t e r i a l s c i e n t i s t s , l u b r i c a t i o n eng ineers and

mechanical eng ineers . I n o r d e r t o ease the c l a s s i f i c a t i o n o f t h e va r ious

aspects o f t r i b o l o g y i n t o a genera l framework, some o f t h e genera l systems

d e f i n i t i o n s a r e repeated i n a lmost every chapter .

concept a re compi led. I n a p p l y i n g t h e system concept, a general t h e o r y o f

t r i b o l o g y i n the fo rm o f a conceptual framework i s o u t l i n e d i n Chapter 3.

The theo ry shows t h a t a complete d e s c r i p t i o n o f a t r i bo -mechan ica l system

requ i res the c h a r a c t e r i z a t i o n o f t he " s t r u c t u r e " o f t h e system (sys tem e l e -

ments, p r o p e r t i e s o f elements, i n t e r a c t i o n s o f e lements) as w e l l as t h e

c h a r a c t e r i z a t i o n o f t h e " f u n c t i o n " o f t h e system ( i n p u t s , ou tpu ts , t r a n s f e r

f u n c t i o n s ) . The t h e o r e t i c a l framework o f t r i b o l o g y i s supplemented i n Chap-

t e r 4 by a d e t a i I e d t r e a t i s e o f t r i b o l o g i c a l processes, i . e . , con tac t , f r i c -

t i o n and wear processes and l u b r i c a t i o n modes. The system approach i s then

used i n s t u d y i n g i n Chapters 5 and 6 t h e i n f l u e n c e o f t r i b o l o g i c a l processes

on t h e s t r u c t u r e and f u n c t i o n o f mechanical systems i n connect ion w i t h

t r i b o - i n d u c e d changes of t he p r o p e r t i e s o f t h e system elements and m a t e r i a l

losses as w e l l as s t i c k - s l i p e f f e c t s , mechanical e f f i c i e n c y , f u n c t i o n a l

f a i l u r e s and r e l i a b i l i t y . From these d i scuss ions , conc lus ions f o r s o l u t i o n s

o f no-wear c o n d i t i o n s and t h e requ i rements f o r a p roper f u n c t i o n a l behav iour

o f mechanical systems a re drawn. I n Chapter 7, t h e va r ious methods o f t r i b o -

metry, i . e . t h e t e s t , s i m u l a t i o n and c o n t r o l methods a r e descr ibed, rang ing

f rom l a b o r a t o r y f r i c t i o n and wear t e s t s and s i m u l a t i v e t r i b o - t e s t i n g t o ma-

ch ine ry c o n d i t i o n mon i to r i ng . F i n a l l y , i n Chapter 8 a t r i b o l o g i c a l systems

data sheet s u i t e d f o r a comprehensive da ta r e p r e s e n t a t i o n i s developed and

the a p p l i c a t i o n o f "systems methodology" t o p r a c t i c a l f r i c t i o n and wear prob-

lems i s o u t l i n e d . The Appendix g i ves a c o m p i l a t i o n o f b a s i c t r i b o - e n g i n e e r i n g

systems and i t s components and r e f e r s t o b i b l i o g r a p h i c work i n t h e f i e l d o f

t r i b o l o g y p rov ided by t h e DOCUMENTATION TRIBOLOGY.

As a s t a r t i n g p o i n t , i n Chapter 2, t h e b a s i c aspects o f t he system

14

2 The system concept

2 I 1 INTRODUCTION

The problem o f d e a l i n g w i t h complex m u l t i d i s c i p l i n a r y sub jec ts l i k e tr i-

bo logy appears t o be e s s e n t i a l l y one o f t h e 1 i m i t a t i o n s o f " a n a l y t i c a l

procedures" i n sc ience and technology. The t h e o r e t i c a l b i o p h y s i c i s t Ludwig

von B e r t a l a n f f y , t h e founder o f "General Systems Theory", has g i ven t h e

f o l l o w i n g d e f i n i t i o n o f meaning o f a n a l y t i c a l procedure (Ref . 2.1): An en-

t i t y ; i . e . , t h e o b j e c t o f an i n v e s t i g a t i o n , shou ld be reso lved i n t o t h e

Par t s f rom which i t i s combined; hence i t cou ld be c o n s t i t u t e d o r recon-

s t i t u t e d from the same Par t s . These procedures shou ld be understood b o t h

i n t h e i r m a t e r i a l and conceptual sense. Th is b a s i c p r i n c i p l e o f " c l a s s i c a l "

sc ience can be a p p l i e d a n a l y t i c a l l y i n a v a r i e t y o f d i r e c t i o n s , e.g., reso-

l u t i o n o f causal r e l a t i o n s i n t o separa te Par t s , search ing f o r "a tomic u n i t s "

i n sc ience o r f o r " m a t e r i a l cons tan ts" i n eng ineer ing .

on two cond i t i ons (Ref. 2.1):

( i )

A p p l i c a t i o n o f t h e a n a l y t i c a l procedure t o any o f these areas depends

The i n t e r a c t i o n s between P a r t s must be non-ex i s ten t o r , a t l e a s t , weak

enough t o be neg lec ted f o r c e r t a i n research purposes. Only under these

c o n d i t i o n s can the Par t s be f i r s t s i n g l e d o u t a c t u a l l y , l o g i c a l l y , and

mathemat ica l l y , and then reassembled.

then i s t he c o n d i t i o n o f summat iv i t y g iven , i . e . , an equa t ion d e s c r i b i n g

t h e behav iour o f t h e Whole has t h e same fo rm as t h e equat ions d e s c r i b i n g

the behav iour o f t h e Par ts ; p a r t i a l processes can then be superimposed

t o o b t a i n t h e t o t a l process, and so on.

( i i ) The r e l a t i o n s d e s c r i b i n g t h e behav iour o f P a r t s must be l i n e a r ; o n l y

15

These c o n d i t i o n s a r e n o t met i n t h e e n t i t i e s c a l l e d systems, they con-

s i s t o f "Pa r t s i n i n t e r a c t i o n " . A system o f "o rgan ized comp lex i t y " may be

c i r cumscr ibed as one i n which s t r o n g i n t e r a c t i o n s , which a r e " n o n - t r i v i a l " ,

i .e . , non - l i nea r , p r e v a i l .

To deal w i t h complex, n o n - l i n e a r systems, a d d i t i o n a l r e s t r a i n i n g p r i n -

c i p l e s have t o be in t roduced. The economist Kenneth Bou ld ing has suggested

a h i e r a r c h y o f systems based on the f o l l o w i n g t h r e e r u l e s (Ref . 2 . 2 ) :

( i ) Systems be long t o c lasses o f d i f f e r e n t l e v e l s o f comp lex i t y .

( i i ) A l l l o g i c a l and e m p i r i c a l laws, v a l i d a t a low l e v e l (system) a r e

a l s o a p p l i c a b l e t o any o f t h e h i g h e r l e v e l systems.

( i i i ) The h i g h e r t h e l e v e l , t h e l a r g e r t h e number o f unknown elements and

und iscovered laws t h a t make a p a r t i c u l a r system work.

To i l l u s t r a t e t h e system concept and t h e p r i n c i p l e o f t h e h i e r a r c h i c a l o r d e r

o f systems cons ider , f o r example, a t r a f f i c system shown schemat i ca l l y i n

F igu re 2.1.

rank

rank

rank

rank

rank

b t 4

b + 3

b t 2

b + l

b

F igu re 2 .1 Example o f a h i e r a r c h y o f systems.

Depending on t h e l o c a t i o n o f a s o - c a l l e d "systems envelope", s e p a r a t i n g

h y p o t h e t i c a l l y t he sub jec ts under c o n s i d e r a t i o n f rom t h e i r "environment",

d i f f e r e n t l e v e l s o f comp lex i t y o r d i f f e r e n t " ranks" o f t h e system under

c o n s i d e r a t i o n can be d i s t i n g u i s h e d (Ref . 2 .3 ) . The systems o f t h e l owes t

rank a r e i n general g i ven by t h e elementary s i n g l e t e c h n i c a l components.

( I f these elementary p a r t s o f t e c h n i c a l systems a re reso lved f u r t h e r , t h e

16

micro-phys ica l and chemical c o n s t i t u e n t s o f t h e t e c h n i c a l systems components

a re ob ta ined . ) Techn ica l systems o f t he n e x t rank up are ob ta ined i n p u t t i n g

t o g e t h e r systems o f a lower rank by c e r t a i n t e c h n i c a l means o r th rough i n t e r -

a c t i o n s o f lower rank ing systems.

denoted by the symbol "b" , are, f o r ins tance, t e c h n i c a l components l i k e

gears, sha f t s , e t c . Through t h e dynamic i n t e r a c t i o n s o f these co iponents , a

gear t r a i n system o f rank b t 1 i s formed. T h i s system t o g e t h e r w i t h o t h e r

systems o f t he rank b t 1 ( i . e . , t h e engine system, the c l u t c h system and

the power t ransmiss ion system) fo rm a system o f rank b t 2, t he d r i v e system.

A t t h e n e x t rank up, b t 3, c h a r a c t e r i z i n g t h e whole v e h i c l e , t h e topmost

l e v e l o f t h i s t e c h n i c a l system i s reached. A t t he f o l l o w i n g l e v e l b t 4

man-machine i n t e r a c t i o n s must be taken i n t o cons ide ra t i on . I n f a c t , t he

whole t r a f f i c system o f rank b t 4 r e s u l t s th rough dynamic i n t e r a c t i o n s o f

v e h i c l e t d r i v e r t road t atmospher ic c o n d i t i o n s .

I n t h e example shown i n F i g u r e 2.1, t h e elements o f t h e lowest rank,

2,2 DESCRIPTION OF A SYSTEM

A f t e r t he general survey o f t h e systems concept, a b r i e f s i m p l i f i e d compi-

l a t i o n o f r e l e v a n t systems d e f i n i t i o n s and c h a r a c t e r i s t i c s s u i t e d f o r t h e

purpose o f t h i s book i s g iven i n t h i s sec t i on . (Fo r f u r t h e r d e t a i l s see

Refs. 2.4 t o 2 . 7 . )

" A system i s a s e t o f elements i n te rconnec ted by s t r u c t u r e and f u n c t i o n " .

" o u t e r wor ld " occur , w h i l e such in te rchanges a r e assumed t o be n e g l i g i b l e

i n a "c losed" system. I n the f i r s t case, f o r example, t he t rans fo rma t ion o f

k i n e t i c energy i n t o hea t o r o t h e r forms o f energy th rough i r r e v e r s i b l e p ro -

cesses leads t o " d i s s i p a t i v e systems".

The main c h a r a c t e r i s t i c s o f a system are summarized i n F i g u r e 2.2, t h e

symbols used have t h e f o l l o w i n g meaning.

( I ) S t r u c t u r e

The s t r u c t u r e o f a system i s d e f i n e d by

( a ) t h e s e t o f i t s elements (A) ,

( b ) t h e r e l e v a n t p r o p e r t i e s o f t h e elements ( P ) ,

( c ) t h e coup l i ng o f elements, s p e c i f i e d as r e l a t i o n s between t h e

The general d e f i n i t i o n o f a system i s con ta ined i n the sentence:

A system i s termed open when in te rchanges o f mass and energy w i t h t h e

elements ( R ) .

17

With these definitions the structure of a system is represented by the se t :

S = { A , P , R }

(11) Inputs , Outputs Each system can be separated schematically by a hypothetical system envelope

(or control surface) from i t s "environment". The connections between the system and i t s environment, which are cut by the envelope may be classified

as:

( a ) Inputs { X } and

( b ) Outputs (Y)

(111) Function

The function o f a system - util ized for a certain (technical) purpose - i s

t o transform the inputs ( X ) i n t o the outputs \ Y ) . The transformation ( T ) of the inputs into the outputs may be described e i the r i n terms of mathematical equations or as a physical a n a l o g , o r as a verbal description, e tc .

Definition: A system i s a s e t of elements interconnected by structure and function

( I ) Structure S = ( A , P , R)

( a ) Elements

A = ( a l Y a2, . . . , an}

P I P ( a i ) l

R = I R ( a i , a j ) l

(n : number of elements)

( b ) Properties

( c ) Relations

(11) Inputs ( x ) O u t p u t s ( Y 1

outputs S = ( A , P, R )

Inputs

( X I systems envelope

(111) Function T

( X I 4 Y )

Figure 2.2 General description of a system.

18

For t h e c h a r a c t e r i z a t i o n o f t h e f u n c t i o n o f a system, ma in l y t h r e e

d i f f e r e n t methods may be d i s t i n g u i s h e d ( f o r f u r t h e r d e t a i l s , see Ref. 2 .7 ) :

( a ) Dynamic Sta te , D i f f e r e n t i a l Equat ions

I f the i n p u t s and ou tpu ts vary w i t h t ime, the system i s s a i d t o be i n

a "dynamic s t a t e " . T h i s dynamic s t a t e may be represented by a s e t of

d i f f e r e n t i a l equat ions , named "equat ions o f mot ion" .

In c e r t a i n cases a system may be i n dynamic e q u i l i b r i u m , i . e . , "s teady

s t a t e " . Fu r the r , t he ou tpu ts { Y ) can o f t e n be descr ibed as l i n e a r super-

p o s i t i o n s o f t h e i n p u t s { X I th rough an a l g e b r a i c rep resen ta t i on .

( c ) S t o c h a s t i c Processes, "Noise"

I n r e a l systems the f u n c t i o n a l i n p u t - o u t p u t - r e l a t i o n s may be i n f l u e n c e d

by s t o c h a s t i c processes, i . e . , dynamic e f f e c t s o f u n c e r t a i n t y and ran-

dom d is tu rbances , "no i se " . I n such cases, an es t ima te o f t h e l i m i t s o f

p roper f u n c t i o n behav iour by means o f t h e theo ry o f p r o b a b i l i t i e s can be

at tempted.

( b ) Steady Sta te , L i n e a r i t y

I n d e s c r i b i n g the behav iour o f a system by t h e terms " s t r u c t u r e " and " func-

t i o n " a fundamental d i f f e r e n c e shou ld be noted:

- A " s t r u c t u r a l " d e s c r i p t i o n o f a system i s e s s e n t i a l l y an " i n t e r n a l " one,

v i z . , an a t tempt t o unders tand t h e sys tem's behav iour i n terms o f i t s

e lements ( t h e P a r t s ) and t h e i r interdependence.

A " f u n c t i o n a l " d e s c r i p t i o n o f a system i s " e x t e r n a l " , c h a r a c t e r i z i n g t h e

sys tem's behav iour by i t s i n t e r a c t i o n s w i t h the environment th rough i t s

i n p u t - o u t p u t r e l a t i o n s .

-

2 , 3 ENERGY BALANCE, NETWORKS, ANALOGIES

I n c h a r a c t e r i z i n g t h e dynamical behav iour o f systems, t h e concept o f a gener-

a l i z e d energy ba lance has t o be in t roduced. T h i s means t h a t t he sys tem's n e t

power e q u a l s - z e r o i f we summarize a l l impor tan t processes o f s to rage and

t r a n s f o r m a t i o n o f energy:

AE = 0

I n t h i s connect ion i t i s impor tan t t o cons ide r ana log ies between p h y s i c a l

systems (Ref. 2.8), Tab le 2.1.

f i e d conven ien t l y as e i t h e r " th rough" o r "across" v a r i a b l e s . Through v a r i -

The phys i ca l v a r i a b l e s of a system ( i n p u t s and o u t p u t s ) may be c l a s s i -

19

D i s c i p l i ne Across v a r i a b l e

( e f f o r t )

E l e c t r o t e c h n i c s e l e c t r i c

vo l tage u

Mechanics v e l o c i t y v

(d isp lacement )

Mechanics angu la r

( r o t a t i o n ) v e l o c i t y (,J

Thermodynamics abso lu te

temperature T

F1 u i d i cs p ressure P

ables measure t h e t ransmiss ion o f something th rough an element, e i t h e r an

e l e c t r i c c u r r e n t th rough a r e s i s t o r o r a f o r c e th rough a dashpot. Across

v a r i a b l e s measure a d i f f e r e n c e i n s t a t e between t h e ends o f an element, as

the vo l tage drop across a r e s i s t o r o r t h e d i f f e r e n c e i n v e l o c i t y between

t h e ends o f a dashpot. O f s p e c i a l importance i s t h e e l e c t r i c analogy o f me-

chan ica l systems desc r ibed by t h e two genera l i zed K i r c h h o f f ' s laws:

I K i r c h h o f f ' s node law.

The sum o f a l l " t h rough v a r i a b l e s " i n t o any node o f a system must be

zero. ( I n t h e case o f mechanical systems t h i s i s represented by f o r c e

e q u i l i b r i u m r e l a t i o n s acco rd ing t o D 'A lember t ) .

The sum o f a l l "across v a r i a b l e s " around a complete l o o p o f t h e system

i s equal t o zero.

I 1 K i r c h h o f f ' s mesh law.

These e q u i l i b r i u m and c o m p a t i b i l i t y r e l a t i o n s a re v a l i d f o r th rough and

across v a r i a b l e s o f e l e c t r i c a l systems, mechanical systems, thermodynamic

systems, and f l u i d systems. I n many a p p l i c a t i o n s one s t a r t s d i r e c t l y f rom

K i r c h h o f f ' s laws i n o r d e r t o o b t a i n t h e r u l e s d e s c r i b i n g t h e f u n c t i o n a l

behav iour o f t e c h n i c a l systems.

Through v a r i a b l e

( f l o w )

e l e c t r i c

c u r r e n t i

f o r c e F

to rque M

en t ropy

f l o w s

f l o w P vo 1 ume

Table 2 . 1 Ana log ies between v a r i a b l e s o f phys i ca l systems.

20

It should be mentioned t h a t i n the bondgraph technique descr ibed below,

i n s t e a d o f the fo rce - f l ow , v e l o c i t y - e f f o r t analogy shown i n Table 2.1, a

reverse analogy, i . e . , a f o r c e - e f f o r t , v e l o c i t y - f l o w analogy i s o f t e n used.

Al though mathemat ica l ly i t i s o f no consequence which analogy i s taken, t h e

d i f f e r e n c e i n analogy i s impor tan t f o r t he comparison o f s p e c i f i c r e s u l t s .

A comparison o f bo th analogies can be found i n Ref. 2.9.

2 ,4 BOND GRAPH METHODS

The bond graph method, i n i t i a t e d by H. Paynter i s a f u r t h e r g e n e r a l i z a t i o n

o f t h e mode l l i ng o f engineer ing systems (Ref. 2.10). The o r i g i n a l concept

c e n t r a l t o the bond graph method i s t h a t o f a mul t i -energy p o r t represen-

t a t i o n associated w i t h a " r e t i c u l a t i o n " , i . e . , t he making o f a network o f

t h e system ( r e t i , L a t i n : f i s h n e t ) . Paynter cons idered t h a t phys i ca l o r eng i -

nee r ing systems cou ld be represented by a m u l t i - p o r t r e t i c u l a t i o n i n a g i ven

reg ion o f space, n o t u n l i k e t h a t used t o represent t h e bonding between atoms

i n complex chemical molecules. The graphica l symbolism o f t h e bond graph

method i s economical and e f f i c i e n t . The bond graph elements can be repre-

sented i n i t i a l l y by words and t h e bonds f o r power exchange between them as

s imple l i n e s . For example, F i g u r e 2.3 con ta ins a v a r i a b l e d r i v e , e.g. , a

Diesel engine w i t h a pump t h a t supp l i es f l u i d t o a consumer (Ref. 2.9). The

energy f l u x o r power i n a bond i s always the p roduc t o f two v a r i a b l e s - t h e

p o t e n t i a l v a r i a b l e c a l l e d e f f o r t and the f l o w o r c u r r e n t v a r i a b l e , s imp ly

r e f e r r e d t o as f l ow .

C o n t r o l l e r - D r i v e Pump Consumer V W V

F igu re 2.3 Word bond graph f o r a pump d r i v e .

I n recen t years, t h e bond graph methods have been developed f u r t h e r , t a k i n g

i n t o account the e f f e c t s o f energy convers ion and d i s s i p a t i o n and p r o v i d i n g

methods f o r t he s i m u l a t i o n and e l e c t r o n i c da ta process ing d i r e c t l y f rom a

bond graph w i t h t h e ENPORT program (Ref. 2.11). The ENPORT computer program

can p rov ide dynamic responses d i r e c t l y f rom a s u i t a b l e bond graph model and

s p e c i f i e d e x c i t a t i o n s , w i t h o u t r e q u i r i n g the e x p l i c i t p r i o r f o r m u l a t i o n o f

s t a t e equat ions. Thus bond graph methods o f f e r a u n i f i e d way t o proceed f rom

the b a s i c phys i ca l mode l l i ng o f components, devices, and t h e i r connect ions t o

21

a n a l y t i c a l and computa t iona l r e s u l t s f o r complex systems i n v o l v i n g a v a r i e t y

o f types o f energy f l ow .

2 ,5 CLASSIFICATION OF SYSTEMS

The a b s t r a c t f o rma l i sm o f t h e d e s c r i p t i o n o f a system reviewed i n b r i e f i n

the fo rego ing sec t i ons shou ld be supplemented by a c l a s s i f i c a t i o n scheme

i n d i c a t i n g t h e " t ype" o f system under s tudy . C l e a r l y , p h y s i c a l o r eng ineer -

i n g systems a r e composed o f m a t e r i a l s components whose p r o p e r t i e s , i n t e r r e -

l a t i o n s , e t c . , may change w i t h t ime. There fore , parameter t ime i s an inde-

pendent a t t r i b u t e o f any o f these systems.

s i f i c a t i o n i s complete and p e r f e c t f o r a l l purposes. The d i f f e r e n t methods

o f c l a s s i f i c a t i o n a r e d iscussed i n d e t a i l i n Ref. 2.5. Accord ing t o Norbe r t

Wiener, t he founder o f " cybe rne t i cs " , t he i n p u t s and ou tpu ts o f systems may

be b road ly c l a s s i f i e d i n t o the t h r e e ca tegor ies "ma t te r " , "energy", and

" i n f o r m a t i o n " (Ref . 2 .12) . (See a l s o Ref. 2.13, p. 99 f . ) Wi thout spec i -

f y i n g the i n t e r n a l s t r u c t u r e o f a system, t h e most genera l c h a r a c t e r i z a t i o n

o f a system i s then g i v e n by a "black-box' ' d iagram as shown i n F i g u r e 2.4.

Systems can be c l a s s i f i e d f rom many d i f f e r e n t p o i n t s o f v iew. No c l a s -

System's f u n c t i o n : ( X ) - ( Y )

f m a t t e r m a t t e r t 1

* energy

i n f o rma ti on c S = ( A , P, R } i n f o r m a t i o n

F igu re 2.4 General b lack-box diagram r e p r e s e n t a t i o n o f a system.

I n u s i n g t h e broad c l a s s i f i c a t i o n o f t h e i n p u t s and ou tpu ts o f a system,

f rom a f u n c t i o n a l p o i n t o f v iew t h e e n t i t y o f p h y s i c a l and eng ineer ing

systems can be f o r m a l l y desc r ibed by a m a t r i x r e p r e s e n t a t i o n as shown i n

Table 2 .2 . I n t h i s scheme t h e t h r e e b a s i c ca tegor ies o f i n p u t s and ou tpu ts

a r e sub-d iv ided i n t o some o f t h e i r sub -quan t i t i es . Every p o i n t o f i n t e r -

s e c t i o n o f i n p u t s and ou tpu ts rep resen ts a c e r t a i n c l a s s o f systems and,

cor respond ing ly , a c e r t a i n f i e l d o f sc ience o r techno logy . The systems and

22

outputs Inputs

top ics character ized by Table 2 . 2 range f rom the c l a s s a t the upper l e f t :

(corresponding f i e l d s of science and technology a r e t ransportat ion technol-

ogy and manufacturing)

t o the c l a s s a t the lower r igh t :

information ( d i g i t a l ) information ( d i g i t a l )

(corresponding f i e l d s of science and technology are the many branches o f

computer science)

Table 2.2 Matrix c l a s s i f i c a t i o n scheme. o f systems.

23

I n r e f i n i n g t h e m a t r i x r e p r e s e n t a t i o n as i l l u s t r a t e d i n Tab le 2.2 s t i l l

f u r t h e r , i t i s a l s o p o s s i b l e t o o b t a i n s u b - c l a s s i f i c a t i o n schemes f o r t h e

va r ious groups o f systems.

The system concept as reviewed i n t h i s Chapter i s used i n t h e n e x t

Chapter as b a s i s f o r t he development o f a u n i f i e d genera l t heo ry o f t r i b o l o g y

i n t h e fo rm o f a conceptua l framework. The reader who i s m a i n l y i n t e r e s t e d i n

t h e p r a c t i c a l a p p l i c a t i o n o f systems techn iques may f i r s t read Chapter 8 on

" P r a c t i c a l Systems Methodology" and may then t u r n back t o Chapter 3.

24

3 General theory of tribology

3,l APPLICATION OF SYSTEMS CONCEPTS TO TRIBOLOGY

The review o f the system concept given i n Chapter 2 shows t h a t a system

should be analyzed i n terms o f i t s " s t ruc tu re " (elements, p roper t i es o f

elements, i n t e r r e l a t i o n s between elements) as we l l as i n terms o f i t s

" funct ion" ( inputs , outputs, t r a n s f e r f unc t i ons ) . In developing f u r t h e r

the methods o f the app l i ca t i on of the system concept t o t r i b o l o g y (see

Refs. 3.1 t o 3.4) we w i l l attempt i n the fo l l ow ing t o o u t l i n e a s i m p l i f i e d

general theory o f t r i b o l o g y (Ref. 3.5).

The systems approach t o t r i b o l o g y i s n o t intended t o replace more t r a -

d i t i o n a l analyses o f f r i c t i o n and wear processes. Much o f the in format ion

requi red f o r the po r t raya l of t r i b o l o g i c a l phenomena from a systems stand-

p o i n t can be obtained through conventional procedures o f analys is . For i n -

stance, important var iab les such as force, v e l o c i t y , temperature, chemical

p o t e n t i a l and the r e l a t e d var iab les s t ress, s t r a i n , work, power, heat f l ow

and reac t i on rates can on ly be determined by standard methods. I n the a p p l i -

ca t i on o f systemanalyt ical methods t o a c e r t a i n complex subject, systems

analys is o f t e n takes the form o f "model bu i l d ing " , i .e., the representat ion

o f a system g raph ica l l y o r a n a l y t i c a l l y i n a manner which may permi t the

model t o be used f o r a mathematical study o f the systems performance. This

i s n o t i n ten ted here, nor genera l ly poss ib le a t the present l eve l o f our

understanding o f the t r i b o l o g y of mechanical systems. The purpose o f t h i s

chapter i s the development o f a l o g i c a l systemanalyt ical framework, whereby

cu r ren t t r i b o l o g i c a l knowledge can be b e t t e r organized, t ak ing i n t o account

the various aspects and in f luenc ing factors . In t h i s general theory, a

26

d e t a i l e d mathematical a n a l y s i s i s n o t necessary f o r a d i s c u s s i o n o f t h e

p e r t i n e n t b a s i c concepts. Thus, i n t h e f o l l o w i n g , systems t h i n k i n g i s ap-

p l i e d r a t h e r than a fo rmal systems a n a l y s i s .

I n a t tempt ing t o app ly t h e system concept t o t h e s u b j e c t o f t r i b o l o g y ,

a fundamental d i f f e r e n c e between the behav iour and t h e d e s c r i p t i o n o f e l e c -

t r i c a l systems and mechanical systems i n which f r i c t i o n and wear processes

occur must f i r s t be emphasized.

box, i l l u s t r a t e d i n F i g u r e 3.1 as b l o c k diagrams. The t e c h n i c a l des ign o f

bo th systems i s t o t rans fo rm c e r t a i n i n p u t s - vo l tage u and c u r r e n t i i n t h e

e l e c t r i c a l system and angu la r v e l o c i t y w and to rque M i n t h e mechanical sys-

tem r e s p e c t i v e l y - i n t o ou tpu ts used f o r t h e t e c h n i c a l purposes. The t e c h n i -

c a l f u n c t i o n o f b o t h systems can be desc r ibed f o r m a l l y as a t r a n s f o r m a t i o n

o f t he i n p u t s i n t o t h e ou tpu ts v i a a c e r t a i n t r a n s f e r f u n c t i o n (T ) .

The dynamic performance o f bo th systems i s accompanied by p e r t u r b a t i o n s

on t h e i r f u n c t i o n and s t r u c t u r e . I n bo th systems, energy l osses due t o

e lec t ro -magne t i c o r f r i c t i o n res i s tances , r e s p e c t i v e l y , occur . The fundamen-

t a l d i f f e r e n c e between t h e behav iour o f t h e e l e c t r i c a l and mechanical systems

i s t h a t i n the e l e c t r i c a l case t h e s t r u c t u r e o f t h e system g e n e r a l l y remains

cons tan t w i t h t ime. I n t h i s case, t h e t r a n s f e r f u n c t i o n ( T ) can be worked o u t

mathemat ica l l y . T h i s has l e d t o va r ious a p p l i c a t i o n s o f t h e power fu l systems

eng ineer ing methods o f network theo ry and r e l a t e d methods c h a r a c t e r i z i n g t h e

f u n c t i o n a l behav iour o f e l e c t r i c a l systems o r r e l a t e d models. I n t h e mechani-

c a l case, however, t h e s t r u c t u r e o f t he system g e n e r a l l y changes w i t h t ime

th rough t h e a c t i o n o f t h e t r i b o l o g i c a l processes o f f r i c t i o n and wear. There-

f o r e , f o r mechanical systems a systems d e s c r i p t i o n i n mere terms o f i n p u t -

o u t p u t r e l a t i o n s i s n o t s u f f i c i e n t : t h e f u n c t i o n a l d e s c r i p t i o n o f t h e system

must be supplemented b y a d e t a i l e d s tudy o f t he s t r u c t u r e o f t h e system and

the i n f l u e n c e s o f t r i b o - i n d u c e d s t r u c t u r a l changes on t h e f u n c t i o n a l behav-

i o u r o f t he system.

I n o r d e r t o deve lop a conven ien t framework f o r t h e d e s c r i p t i o n o f sys-

tems w i t h b o t h a dynamic f u n c t i o n a l behav iour and a dynamic s t r u c t u r e s t a t e ,

some s i m p l i f i c a t i o n s must be i n t roduced : a f i r s t s i m p l i f i c a t i o n shou ld be

made b y a p p l y i n g t h e methods o f "black-box c u t t i n g " o r "systems t e a r i n g " .

Black-box c u t t i n g has worked exceed ing ly w e l l i n phys i cs and chemis t ry : a

model i s c u t down t o s m a l l e r boxes u n t i l f i r s t p r i n c i p l e s can be app l i ed .

Systems t e a r i n g can be ach ieved by l o c a t i n g t h e h y p o t h e t i c a l systems enve-

l ope i n a conven ien t manner. I n t h e f o l l o w i n g t rea tmen t t h e systems envelope

i s l oca ted , as narrow as poss ib le , around t h e c e n t r a l p a r t s o f t h e mechanical

Consider, f o r example, an e l e c t r i c a l t rans fo rmer and a mechanical gear

26

Inputs ~

*.

vol tage ux

cu r ren t i

System's s t r u c t u r e outputs

voltage u 71 Ill c cu r ren t i w Y

Y

(111) In f luences on f u n c t i o n and s t r u c t u r e

Inputs

v e l o c i t y wx

t o q u e Mx

~~

F e r w losses due t o

System's s t r u c t u r e outputs

v e l o c i t y w Y

MY - % - > torque

I electro-magnetic res is tance I constant w i t h t ime

energy losses due t o

f r i c t i o n processes

system's s t r u c t u r e changes

due t o wear processes

F igure 3.1 Comparison o f t h e c h a r a c t e r i s t i c s o f an e l e c t r i c a l and a mechanical system.

27

system, forming the well-known " i n t e r a c t i n g surfaces i n r e l a t i v e motion".

With these reservat ions i n mind, a d e t a i l e d systems d e s c r i p t i o n must i nvo l ve

the f o l l o w i n g steps:

( I ) System's func t i on

( i ) Separate the system from i t s environment by the choice of a system's envelope,

(ii) Compile a l l inputs and outputs

( i i i ) Describe the func t i ona l input -output r e l a t i o n s

(11) System's s t r u c t u r e

( i )

( i i )

( i i i ) Speci fy the re levan t p roper t i es o f t he elements.

I d e n t i f y the "elements" o f t he system,

Characterize the i n t e r r e l a t i o n s and i n t e r a c t i o n s between

the elements,

Based on t h i s systemanalyt ical procedure, i n the f o l l o w i n g sect ions we w i l l attempt t o study and compile the bas ic i n f l u e n c i n g fac to rs and mechanisms

re levan t t o the f u n c t i o n and s t r u c t u r e o f mechanical systems i n which f r i c -

t i o n and wear processes occur. The t h e o r e t i c a l framework obtained w i l l then

be used f o r various analyses and app l i ca t i ons i n the f o l l o w i n g chapters o f

t h i s book.

3 , 2 FUNCTION OF TRIBO-MECHANICAL SYSTEMS

I n the attempt t o apply the system concept t o the phenomena o f f r i c t i o n ,

l u b r i c a t i o n and wear, the question o f the func t i ona l , t echn ica l purpose o f

the system under considerat ion has f i r s t t o be answered. A tr ibo-mechanical

system i s def ined as an e n t i t y whose func t i ona l behaviour i s connected with

i n t e r a c t i n g surfaces i n r e l a t i v e motion. (The words " t r i b o l o g i c a l system"

o r "tr ibo-system" may be used synonymously t o the word "tr ibo-mechanical

system".) The technica l aims r e a l i z e d through moving surfaces may range from

aerospace app l i ca t i ons t o biomechanical j o i n t s . However, from a phys ica l p o i n t

of view, f o u r b a s i c a l l y d i f f e r e n t groups o f techni-cal purposes can be d i s t i n -

guished as i l l u s t r a t e d by the examples shown i n F igure 3.2.

r e a l i z a t i o n o f motion through various types o f "bearings". The o the r bas ic

groups are the transmission o f mechanical work, the t ransmiss ion o f i n f o r -

mation - f o r instance the con t ro l o f machine funct ions w i t h cams - and the

forming o f ma te r ia l s . As a supplement t o the bas i c c l a s s i f i c a t i o n o f t r i b o -

The most general technica l purpose o f a tr ibo-mechanical system i s the

28

mechanical systems into four different groups, illustrated in Figure 3.2, a detailed function-oriented compilation of tribo-mechanical systems is given in the Appendix (A).

1

Guidance of mofion I Jransmission of work I

I Transmission of information i Forming of materials

Figure 3.2 Types o f tribo-mechanical systems.

In an abstract and highly simplified description, the function of the dif- ferent tribo-mechanical systems consists, basically, In converting the inputs - for instance, motion, mechanical energy and materials - into out- puts, which are used technically, The functional cause-and-effect relations between inputs and outputs are accompanied by loss-outputs o f mechanical energy and of materials, denoted sumnarily by the terns friction and wear

29

losses. From a point of view external t o the system, the system may be

treated as a black-box with inputs and outputs, as shown schematically

i n Figure 3.3.

(LOSS-OUTPUTS] Frictional losses (entropy,noise, A vibration) Wear products

l r n 1 [USE-OUTPUTSI Motion {X I Motion Work - + Work Information {y) Information Mate r i a Is Materials

~ I S T U R B A N C E s] En tropy(Heat1 Vibration Materials (including dirt)

Figure 3.3 Black-box description of tribo-mechanical systems.

The technical function can often be expressed as a relationship between an

input and a useful output. Not a l l the inputs may be considered desirable,

some may be regarded as disturbances. Not a l l the outputs may be desired:

such o u t p u t s may, from the practical point of view, be considered as losses.

In general, part of a functional input may be lo s t , appearing as a loss out-

p u t . However, the loss output need not be quite the same type of quantity as

the input or useful outputs. In relating a system to i t s function, we are concerned with operational

variables which can be controlled by a designer or an operator, i . e . , vari-

ables which we can a l t e r before or during the operation of a system without

altering the physical composition of the system in terms of the materials or

shapes of the elements. Table 3.1 l i s t s some operational parameters tha t we

may be concerned with, and which we may also refer to as operational vari-

ables in the environment. The actual variables used to describe the relation-

30

s h i p between a system and i t s environment w i l l depend t o some e x t e n t on t h e

system under cons ide ra t i on , b u t w i l l g e n e r a l l y be r e l a t e d to , o r d e r i v e d

from, the v a r i a b l e s l i s t e d .

~~ ~

I n p u t and

o u t p u t

q u a n t i t i e s

Work

(Mo t ion )

T herma 1

(Heat t r a n s f e r )

Mass

(Mass t r a n s f e r )

I n f o r m a t i o n

Pr imary v a r i a b l e s Re1 a t e d and d e r i ved v a r i a b l e s

Fo rce/To r q ue

Pos i t ion /D imens ion R o t a t i o n a l v e l o c i t y

Work r a t e (Power)

L i n e a r v e l o c i t y

Temperature Heat t r a n s f e r r a t e

S p e c i f i c hea t Ent ropy t r a n s f e r r a t e

S p e c i f i c en t ropy

Composition Rate o f mass t r a n s f e r

Free energy

P o s i t i o n

Force/Torque Phase

Rate o f f ree-energy t r a n s f e r

F req u en cy

Table 3 .1 Opera t iona l i n p u t s and ou tpu ts o f mechanical systems.

3,3 STRUCTURE OF TR IBO-MECHAN I CAL SYSTEMS

According t o systems theory , t he s t r u c t u r e o f a system i s cha rac te r i zed by

the elements o r components o f t h e system, t h e i r r e l e v a n t p r o p e r t i e s and

t h e i r i n t e r r e l a t i o n s . The s i m p l e s t s t r u c t u r e o f a t r ibo-mechan ica l system

i s g i ven by two s o l i d s (1) and ( 2 ) exchanging mechanical i n p u t s and ou tpu ts

through t h e i r c o n t a c t i n t e r f a c e . A c o m p i l a t i o n o f examples o f t he elements

o r components o f t r ibo-mechan ica l systems i s p rov ided i n t h e Appendix ( 6 ) .

A few words may be approp r ia te here on t h e f l o w o f one o r more q u a n t i -

t i e s through a system, i m p l i e d by the use o f t h e terms " i n p u t " and "ou tpu t " ,

e.g., work o r mass. A mass f l o w i s obv ious l y a f l o w o f a m a t e r i a l q u a n t i t y .

However, t h e " f l o w " o f o t h e r q u a n t i t i e s , such as work, can perhaps be re -

garded more c o r r e c t l y as an i n f l u e n c e o f one element upon another. The no-

t i o n t h a t a q u a n t i t y " f l ows" i s t h e r e f o r e mere ly a u s e f u l convent ion, which

31

i n c i d e n t a l l y helps us t o d i s t i n g u i s h between the d i f f e r e n t k inds o f process

which can occur i n a system.

q u a n t i t y i s t o t r e a t each fo rma l l y on a plane o f i t s own, l i n k e d t o the

o the r q u a n t i t i e s by transformations between the planes. This leads t o a

conceptual three-dimensional i n t e r n a l view o f a tribo-mechanical system,

shown i n F igure 3.4. The p i c t u r e can be understood as a r e s o l u t i o n o f the

systems s t r u c t u r e ( t h e cen t ra l box o f F igure 3.3) i n t o greater d e t a i l , see

a lso F igure 2.4. I t i s l i k e l y t h a t a l l the parameters, i d e n t i f i e d i n a study

o f the f u n c t i o n o f the system, w i l l be represented on planes f o r the, func-

t ion, work and thermal processes. Separate planes may be used f o r each o f

the chemical species tak ing p a r t i n t r i b o l o g i c a l processes. This inc ludes

chemical reac t i on products.

F igure 3.4 might be taken t o represent a very "simple" system o f j u s t

two s o l i d mechanical elements o f the same mate r ia l i n contact, so t h a t the

i n t e r f a c i a l space a t the reg ion o f contact i s the t h i r d element, i.e.,

The most sens ib le manner, i n which t o handle the d i f f e r e n t types o f

Element (1) F i r s t machine element

Element ( 2 ) Second machine element

Element (3 ) The i n t e r f a c i a l volume

The poss ib le t ransact ions and processes between three such elements are, i n

fac t , q u i t e complex even f o r t h i s elementary system (Ref. 3.6). We do n o t

attempt here t o represent a l l the poss ib le processes i n F igure 3.4, b u t

ra the r t o i l l u s t r a t e and c l a s s i f y the various types o f processes which may

occur.

Consider f i r s t the t r a n s f e r of the t e c h n i c a l l y used inpu ts ( X I and

outputs ( Y ) o f the system. On each conceptual plane, the t r a n s f e r o f such

a q u a n t i t y from one element t o another may occur i nd i ca ted by ho r i zon ta l

arrows. The term " t r a n s l a t i o n " i s chosen f o r these t rans fe rs . Consider now

the processes o f t rans fe rs between d i f f e r e n t planes, r e f e r r e d t o as " t rans -

formations". The v e r t i c a l s o l i d arrows i n F igure 3.4 represent a t rans fo r -

mation i n ma te r ia l o r chemical species, occurring, f o r instance, as a re -

s u l t o f wear processes w i t h i n the system. The v e r t i c a l do t ted arrows repre-

sent the t ransformat ion o f work o r mechanical energy t o heat o r entropy,

occurr ing as a r e s u l t of f r i c t i o n processes w i t h i n the system. Both t rans-

l a t i o n s o f mass, e.g., the f low o f l u b r i c a n t through the system and t rans-

formations o f mass i n w e a r processes are l i k e l y t o i nvo l ve work, accompanied

by the simultaneous t ransformat ion of the work i n t o heat o r entropy which

appears on the thermal plane.

32

FUNCTIONAL PLANE

WORK PLANE

THERMAL PLANE

MATERIAL 1 (solid)

I MATERIAL PLANES 1

MATERIAL n (fluid)

MATERIAL m (Reaction products)

I I APJ I

Figure 3.4 The Tribo-process diagram: Conceptual planes o f parameters and Processes i n a tribo-mechanical system.

33

The a b s t r a c t i o n s o f t he t r i bo -p rocess diagram, F igu re 3.4, c l e a r l y

demonstrate the s i g n i f i c a n c e o f the systems approach t o t h e a n a l y s i s and

d e s c r i p t i o n o f mechanical systems i n which f r i c t i o n and wear processes

occur:

The c h a r a c t e r i s t i c f e a t u r e o f t r i b o l o g y i s t he i n t e r a c t i o n between the

d i f f e r e n t planes o f F i g u r e 3.4, w h i l e the conceptual a n a l y s i s o f s i n g l e se-

pa ra te planes r e v e r t s t o more convent ional a n a l y t i c a l s i m p l i f i c a t i o n .

A t t h i s p o i n t i t i s r e l e v a n t t o i n d i c a t e t h e aspect o f l u b r i c a t i o n i n

r e l a t i o n t o the general framework of t r i b o l o g y . L u b r i c a t i o n represents a

d e l i b e r a t e at tempt t o avo id o r reduce t h e e f f e c t o f f r i c t i o n and wear upon

a mechanical system. A l u b r i c a n t can a l s o ac t , as i t f l ows away, as a c o o l i n g

agent removing hea t f rom the l o c a t i o n o f t he f r i c t i o n process. I f t h e s l i d i n g

o r r o l l i n g surfaces, i . e . , elements (1) and ( 2 ) i n F igu re 3.4, a re complete ly

separated by the a c t i o n o f the element ( 3 ) a t a l l t imes, t h e r e may be no wear

process. I n t h i s event, t he a n a l y s i s i s s i m p l i f i e d , s ince a m a t e r i a l s t rans -

f e r between the m a t e r i a l s planes shown i n F igu re 3.4 w i l l be o f no concern

("no-wear model") . However, i f i n a l u b r i c a t e d s t a t e the re i s some c o n t a c t

between the sur faces o f t he elements (1) and ( 2 ) , o r between boundary l u b r i -

cants on t h e surfaces, t h e processes represented on and between t h e m a t e r i a l s

planes a r e o f paramount concern. I n such cases, t he presence o f a l u b r i c a n t

may compl icate the a n a l y s i s r e l a t i v e t o the u n l u b r i c a t e d system, p a r t l y be-

cause t h e r e a c t i o n products present may be complex and d i f f i c u l t t o charac-

t e r i z e , and p a r t l y because t r a n s i e n t c o n d i t i o n s may be t h e major concern.

3 4 TRI BOLOG I CAL INTERACTIONS

The separa t i on and rep resen ta t i on o f t he processes w i th in a mechanical sys-

tem, onto conceptual p lanes shown i n F igu re 3.4, a l l ows us t o concen t ra te

on one aspect o f t h e system a t a t ime.

3 , 4 , 1 FUNCTIONAL PLANE

The emphasis on the f u n c t i o n a l p lane, "ex t rac ted " f rom F i g u r e 3.4 and shown

i n F i g u r e 3.5, must be on a rep resen ta t i on o f t he t e c h n i c a l purpose o f t h e

system and t h e e v a l u t i o n and r e p r e s e n t a t i o n o f t h e parameters which have

most imnediate re levance t o t h i s t e c h n i c a l purpose.

34

(11 First machine element

( 2 ) Second machine element

( 3 ) The interfacial volume

F igu re 3.5 The f u n c t i o n a l q laqe o f t h e Tr ibo-process diagram: Func t i ona l t r a n s a c t i o n s i n a t r ibo-mechan ica l system.

We may w ish t o c l a s s i f y mechanical systems accord ing t o t h e i r f u n c t i o n .

I n v a r i a b l y , mot ion i s a c h a r a c t e r i s t i c of a t r ibo-mechan ica l system. T h i s

mot ion may c o n s t i t u t e a t r a n s f e r o f work, m a t e r i a l s o r i n fo rma t ion . I n some

ins tances , t h e purpose o f a system may be t o change a r a t e o f mo t ion o r t o

e l i m i n a t e i t a l t o g e t h e r . I t i s a l s o o f t e n d e s i r e d t o r e s t r i c t mot ion , i .e . ,

t o reduce the number o f degrees o f freedom a machine element may possess.

I n o t h e r ins tances , m a t e r i a l s a r e n o t mere ly moved, b u t a l s o changed i n

s t a t e o r form. Mechanical dev ices which produce o r t r a n s f e r i n f o r m a t i o n a r e

s t i l l common, b u t a r e be ing s t e a d i l y rep laced by devices i n which t h e r e i s

l i t t l e o r no mechanical mot ion ( v i z . t h e replacement o f t h e mechanical c l o c k

by d i g i t a l e l e c t r o n i c c locks . ) These main aspects o f t h e f u n c t i o n o f mecha-

n i c a l systems a re l i s t e d i n Tab le 3.2.

I n o r d e r t o rep resen t the f u n c t i o n o f t h e system i n terms of ( X ) - { Y ]

i n p u t - o u t p u t r e l a t i o n s , e l e c t r i c a l network ana log ies have been a p p l i e d t o

mechanical systems (Ref . 3.7). As exp la ined i n Chapter 2, these approaches

a re based on a c l a s s i f i c a t i o n o f t he o p e r a t i n g v a r i a b l e s i n t o " th rough and

across" v a r i a b l e s o r . " f l o w and e f f o r t " v a r i a b l e s and t h e a p p l i c a t i o n o f t h e

we1 1 known K i r c h h o f f ' s node and mesh laws. Recent ly, the. bondgraph methods

have a l s o been a p p l i e d t o t r i b o l o g i c a l sub jec ts (Ref. 3.8). As i n d i c a t e d

above, these appl i c a t i o n S o f t h e o r i e s o f e l e c t r i c a l ana log ies a re r e s t r i c t e d ,

however, t o no-wear, steady s t a t e models. Therefore, f rom a t r i b o l o g i c a l

p o i n t o f view, a d d i t i o n a l aspects must be taken i n t o account.

able. These c h a r a c t e r i s t i c s may be dependent on t h e o p e r a t i n g parameters.

P a r t i c u l a r c h a r a c t e r i s t i c s i n f r i c t i o n and wear a re g e n e r a l l y be d e s i r -

I n add i t i on , and perhaps more important, t he re may be c e r t a i n l i m i t s t o be

i d e n t i f i e d f o r these cha rac te r i s t i cs , outs ide which l i m i t s the system w i l l

n o t perform i t s f u n c t i o n s a t i s f a c t o r i l y . The i d e n t i f i c a t i o n o f p roper t i es

which are c r i t i c a l t o the func t i on o f each element concerned w i l l serve as

a guide f o r the analyses c a r r i e d ou t on work, thermal and mass planes, t o

ensure t h a t such analyses are re levan t t o the func t i on o f t he system. The

r e l a t i o n s h i p between the values o f these p roper t i es and the f u n c t i o n o f t he

system and the manner i n which the operat ion o f the system a f f e c t s these

proper t ies, i s , from a p r a c t i c a l p o i n t o f view, the crux o f a t r i b o l o g i c a l

study.

Inputs and outputs

needed f o r technica l

Primary technica l Examples

func t i on o f t he

system func t i on L Main outputs

I Y )

Motion

Main i npu ts I ( X I

Guidance o f motion Bearings

Coupling o f motion Clutches

A n n i h i l a t i o n o f motion Brakes Motion

Work

In format ion

Materi a1 s

+

Work

Power transmission Gears

(mech., hydr., pneum. )

Generation o f Clocks; Cams

i n forma t i on and fo l l owers

Reproduction o f ffata transducer

in format ion (audio, video;

tape b r record)

Transpor tat ion Wheel/rai 1

P i pel i ne

Forming o f ma te r ia l s Wiredrawing

Motion

Table 3.2 Technical f unc t i ons o f mechanical systems.

A l l t h i s can be seen on the func t i ona l plane i n a systems analys is . We-may

then imagine ourselves l ook ing down i n t o the t r i b o l o g i c a l s t r u c t u r e depic ted

36

below the functional plane i n Figure 3.4, in order t o ascertain the physi-

cal and chemical relationship which determine the functional characterist ics.

3,4,2 MECHANICAL WORK PLANE

In Figure 3.6, we concentrate our attention on the prL?esses involving me- chanical work i n the system. I t may be tha t one function of the system i s , i n f ac t , t o transmit and transform work, in which case this analysis will duplicate to a large extent the analysis on the functional plane. Although this does occur quite often, i t i s nevertheless a special case.

A system or element may perform mechanical work upon another system or element. Such mechanical work may be measured as the product of a force times a distance (o r the product o f related variables). Work may also be transferred between elements by the transfer of material i n which work i s

stored. The transfer of work i n e i ther manner is referred t o as a transla- tion work. Work may also be transmitted from an element or a system as me- chanical vibration, or work m a y be transformed through the tribological interactions i n other forms of energy and e l ther storedr emitted or passed to other conceptual planes of the system.

[LOSS-OUT PUTS^

I I

Power to thermal lane + 1

(due to friction P

Figure 3.6 The work plane of the Tribo-process diagram: Work transactions i n a tribo-machanical system.

37

From a general ized energy balance- considerat ion o f F igure 3.6, i t fo l l ows

t h a t the i n p u t work must be equal t o the use-output work t t he loss-output

energy + the energy s tored i n the system t the energy transformed t o o the r

conceptual planes o f t he system.

the various po r t i ons o f power, f o r a system as a whole, a power balance

equation i s

The r a t e o f performance o f mechanical work i s power. I n summarizing

where

i! : i n p u t power

i! : use-output power

EZ : loss-output energy r a t e

A Es : stored energy

EwT : thermal energy transformed from mechanical work

Viewing on ly one element, j:

where the subsc r ip t i r e f e r s t o a l l elements w i t h which the element j has

work t ransact ions and kWM t o the absorption o f mechanical power, as discussed

below i n the sec t i on on ma te r ia l s planes.

The transmission o f power k, - i!, i n a mechanical system i s u s u a l l y

a r e l a t i v e l y simple a p p l i c a t i o n o f mechanics. The quest ion which i s l ess

w e l l understood and which o f t e n cons t i t u tes a bas ic problem i n mechanical

systems i s the manner i n which mechanical power i s n o t t ransmi t ted, i.e.,

“absorbed” by f r i c t i o n o r v i b r a t i o n . Thus, the energy o r power balance con-

s ide ra t i ons should be supplemented by a d iscuss ion o f the t r i b o l o g i c a l pro-

cesses invo lved i n the storage, transformation, emission and d i s s i p a t i o n o f

mechanical work. Clear ly , a1 1 these phenomena a re c l o s e l y connected w i t h the

contact, deformation and f r i c t i o n processes occu r r i ng a t t he i n t e r f a c e be-

tween elements (1) and ( 2 ) o f a t r ibo-mechan ica l system. I n Tab le 3.3 some

o f t h e b a s i c processes a re l i s t e d . A d e t a i l e d d i scuss ion o f t h e r e l e v a n t

t r i b o l o g i c a l processes i s g i ven i n Chapter 4.

I ( e l a s t i c h y s t e r e s i s 1

Work t r a n s a c t i o n s

Trans1 a t i o n o f work

Transformat ion o f work

p l a s t i c de fo rma t i on

Emission o f energy

Conduct ion t o o t h e r

Processes

E l a s t i c deformat ion

F r i c t i o n mechanisms:

I ( conceptual p lanes 1

Tab le 3.3 Mechanisms and processes o f work t r a n s a c t i o n s .

F i g u r e 3.7 shows t h e p r i n c i p l e s o f an a n a l y s i s on a thermal p lane o f a

t r ibo-mechan ica l system. We have a l ready r e f e r r e d t o t h e t r a n s f o r m a t i o n of

mechanical work t o ent ropy, i .e., mechanical power t o thermal power, wh ich

proceeds accord ing t o t h e equa t i on

where i . i s t h e r a t e o f gene ra t i on o f en t ropy i n element j and T . i s t h e J J

absol Ute temperature.

The thermal power gene ra t i on w i l l u s u a l l y r e s u l t i n t h e temperature of

l o c a t i o n s o f en t ropy gene ra t i on b e i n g app rec iab l y h i g h e r t han t h e i r su r -

roundings, r e s u l t i n g i n t h e t r a n s f e r o f t he thermal power, by conduct ion o r

r a d i a t i o n away f rom t h e l o c a t i o n s o f f r i c t i o n . Heat and en t ropy can be t r a n s -

f e r r e d between systems elements. The t r a n s f e r o f thermal power down a tem-

p e r a t u r e g r a d i e n t i s a unique work process i n t h a t t he work i n v o l v e d appears

as thermal power, i . e . , a f l o w o f t h e same t y p e o f q u a n t i t y as t h e one b e i n g

t r a n s f e r r e d . The n e t r e s u l t i s t h a t i n thermal conduct ion o r r a d i a t i o n , t h e

39

t o t a l thermal -power - f low r a t e remains cons tan t , i .e. ,

where ir i s t h e t o t a l f l o w r a t e o f en t ropy across a s u r f a c e a t a d i s t a n c e r

from a source o f en t ropy and a t an abso lu te tempera ture T- su r round ing a

source o f en t ropy S . a t an abso lu te temperature T

h e a t - f l ow-generat i on r a t e .

6. i s ' t h e assoc ia ted J j ' J

Thermal energy I from work plane

[LOSS- OUTPUT^

I I I Thermal energy produced by processes on the materials planes

F igu re 3.7 The thermal p lane o f t h e Tr ibo-Process diagram: Thermal t r a n s a c t i o n s i n a t r i bo -mechan ica l system.

Work may a l s o be performed when t h e p o t e n t i a l o f a system o r an element i s

changed. T h i s concept can be a p p l i e d n o t o n l y t o mechanical work, b u t a l s o

t o chemical work (change o f chemical p o t e n t i a l ) , e l e c t r i c a l work (change o f

e l e c t r i c a l p o t e n t i a l ) and thermal work (change o f tempera ture) . A1 1 these

d i f f e r e n t forms o f work w i l l g e n e r a l l y l e a d t o t h e f o r m a t i o n o f en t ropy

(Ref. 3 . 9 ) . Thermal power may be s to red , i n wh ich case t h e l o c a t i o n o f t h e

s to rage increases i n temperature. V ice versa, t he tempera ture drops when

s t o r e d thermal power i s g i ven up.

as the temperature changes i n v o l v e d a f f e c t f r i c t i o n and wear processes.

I n genera l , thermal processes a r e o f i n t e r e s t i n t r i b o l o g y i n so f a r

40

That i s , we are concerned w i t h the r e l a t i o n s h i p between temperature and the

mechanical f unc t i on o f the system. This amounts t o a concern f o r the e f f e c t

o f temperature on p roper t i es which determine the processes o f v ib ra t i on ,

f r i c t i o n and wear. These aspects are a lso discussed i n some d e t a i l i n

Chapter 4.

3 I 4 I 4 MATERIAL PLANES

A p r i n c i p l e purpose o f a representat ion on the mater ia l planes as shown i n

Figure 3.8 i s t o f a c i l i t a t e i n s i g h t i n t o the mass t r a n s f e r and mass t rans-

formation processes which are i n v a r i a b l y p a r t o f the wear o f a mechanical

system.

Reaction energy t o thermal plane

+LOSS - OUTPUTS t I Materials ‘

I

F igure 3.8 Mater ia l planes o f the Tribo-process diagram: Mater ia l t ransact ions i n a tribo-mechanical system,

41

I n some cases. the purpose o f t h e mechanical system may be t o t r a n s p o r t

some m a t e r i a l , i n which case an e v a l u a t i o n o f aspects o f t h e t r a n s p o r t o f

t he m a t e r i a l w i l l be d u p l i c a t e d on t h e f u n c t i o n a l p lane and on a m a t e r i a l

p l ane.

The b a s i c c h a r a c t e r i s t i c o f wear i s t h e removal o f m a t e r i a l f rom one

o r more machine elements. I n some ins tances , mere ly a permanent change i n

shape, th rough de format ion , o f a machine element i s cons idered t o c o n s t i -

s t u t e wear. I t may be p r e f e r a b l e t o c a l l t h e a c t u a l process o f t h e removal

o f m a t e r i a l a process o f " a t t r i t i o n " , and t o app ly t h e te rm "wear" t o cove r

a l l t h e processes i n a system which combine t o cause a t t r i t i o n .

I n wear, m a t e r i a l may be deformed w i t h i n an element. I t may a l s o be

t r a n s f e r r e d f rom one element t o another . T h i s process i s c a l l e d t r a n s l a t i o n ,

which i nc ludes n o t o n l y t r a n s f e r f rom one s o l i d element t o another , b u t

a l s o a t t r i t i o n , i n which case m a t e r i a l becomes, as d e b r i s , p a r t o f t h e i n -

t e r f a c i a l volume. Furthermore, a m a t e r i a l may, th rough chemical reac t i on ,

be t rans formed t o another m a t e r i a l .

Us ing i a . as the symbol f o r t he f l o w r a t e o f a mass spec ies a f rom

element i t o element j, l e t t i n g i a b r e f e r t o a t r a n s f o r m a t i o n o f a mass

spec ies a t o mass spec ies b w i t h i n element j, and l e t t i n g m? be t h e mass

o f spec ies a i n element j, then a mass ba lance equa t ion f o r spec ies a i n

element j would be

1J

J

J

where i r e f e r s t o a l l elements f rom which t h e m a t e r i a l i s t r a n s l a t e d t o j ,

k t o a l l e lements t o wh ich the m a t e r i a l i s t r a n s l a t e d f rom j , c a l l t h e

chemical spec ies which i n chemical r e a c t i o n become p a r t o f m a t e r i a l a, and

b rep resen ts a l l t h e chemical spec ies t o wh ich t h e m a t e r i a l i s t rans formed.

( I n o r d e r t o a l s o d i s t i n g u i s h g r a p h i c a l l y between t h e d i f f e r e n t m a t e r i a l

species, i t may be a p p r o p r i a t e i n c e r t a i n cases t o s p l i t up t h e m a t e r i a l

p lanes shown i n F i g u r e 3.8 i n t o m a t e r i a l sub-planes.)

I n a t t r i t i o n , we w i l l expec t ma t o be n e g a t i v e f o r elements which l o s e J

mass by a t t r i t i o n . However, t h e equa t ion i l l u s t r a t e s t h a t c e r t a i n elements

may r e t a i n a more o r l e s s s teady mass, i . e . , mj = 0, w h i l e s i g n i f i c a n t

t r a n s l a t i o n and t r a n s f o r m a t i o n processes occu r on t h e element. T h i s i s

o f t e n t h e case i n p r a c t i c e .

.a

42

F o r a system as a whole, we may w r i t e

where X and Y,Z r e f e r t o i n p u t s and ou tpu ts r e s p e c t i v e l y .

The processes on and between t h e m a t e r i a l p lanes a r e l i k e l y t o i n v o l v e

en t ropy changes, g e n e r a l l y t he p roduc t i on o f en t ropy which w i l l appear as

sources o f en t ropy i n t h e thermal p lane o f t h e same element. It i s p o s s i b l e

t h a t work may be performed i n c e r t a i n aspects o f mass - t rans la t i on processes,

n o t a b l y the fo rma t ion o f new f r e e sur faces as i n f r a c t u r e o r o t h e r forms o f

t he separa t i on o f m a t e r i a l . The oppos i te process, t he j o i n i n g o f two sur -

faces, e l i m i n a t i n g some f r e e su r face , i s l i k e l y t o be accompanied by the

fo rma t ion o f en t ropy . Thus, a repeated sequence o f s e p a r a t i o n - j o i n i n g -

separa t i on and so on w i l l , i n e f f e c t , conve r t mechanical power i n t o thermal

power and appear as a mechanisms o f f r i c t i o n . L i m i t i n g ou r concern t o t h e

m a t e r i a l p lanes, we can l i s t some p e r t i n e n t processes i n Tab le 3.4. The wear

mechanisms a re d iscussed i n d e t a i l i n Sec t i on 4.4.

Wear mechanism

Sur face f a t i g u e

Abras ion

Adhesion t

f r a c t u r e

T r i bochemical

r e a c t i o n s

W i t h i n element

and p lane

Cycl i c

de f o rma t i on

Deformat ion

Deformat ion

Deforma t i on

Processes

T r a n s l a t i o n

F rac tu re

F r a c t u r e

T r a n s f e r

F r a c t u r e

Adsorp t ion

F r a c t u r e

Trans format ion

-

-

- -

Chemical

r e a c t i o n s

Table 3.4 Wear mechanisms and processes.

43

3 , 5 CONCLUSIONS

The a n a l y s i s o f a t r ibo-mechan ica l system f rom t h e systems v i e w p o i n t as

i l l u s t r a t e d i n t h e t r i bo -p rocess diagram, F i g u r e 3.4, c l e a r l y shows t h a t

t he c h a r a c t e r i s t i c f e a t u r e o f t r i b o l o g y i s t h e i n t e r a c t i o n between t h e

d i f f e r e n t conceptual p lanes o f F i g u r e 3.4. Concluding t h e d i scuss ion on

t h e processes w i t h respec t t o the d i f f e r e n t p lanes o f t h e conceptual frame-

work o f F i g u r e 3.4, some remarks on the c o r r e l a t i o n s o f p r o p e r t i e s shou ld

be made.

We have a l ready no ted above t h a t each o f t h e p r o p e r t i e s o f concern on

t h e work p lane i s l i k e l y t o be a f f e c t e d by tempera ture and a l s o p o s s i b l e by

mechanical s t r e s s o r s t r a i n . The same a p p l i e s t o t h e p r o p e r t i e s o f concern

on t h e m a t e r i a l p lanes. As a general p r i n c i p l e , c e r t a i n p r o p e r t i e s o f t h e

elements may be regarded as dependent p r o p e r t i e s on c e r t a i n p lanes and

independent p r o p e r t i e s on o t h e r p lanes . For example, temperatures a r e

c l e a r l y dependent on the processes represented on t h e thermal p lane, b u t

may be regarded as independent p r o p e r t i e s i n f l u e n c i n g processes on o t h e r

planes. A complete a n a l y s i s must t h e r e f o r e i n c l u d e a c o r r e l a t i o n o f t h e

p r o p e r t i e s on the d i f f e r e n t planes f o r each l o c a t i o n o f i n t e r e s t i n t h e

system. Temperatures c o n s i s t e n t w i t h the process on t h e thermal p lane must

e n t e r i n t o ou r c o n s i d e r a t i o n o f t h e processes on t h e o t h e r p lanes . L i kew ise ,

s t resses , s t r a i n s and v e l o c i t i e s c o n s i s t e n t w i t h t h e processes on t h e me-

chan ica l work p lane must e n t e r i n t o ou r cons ide ra t i ons o f t h e processes on

the thermal and m a t e r i a l s p lanes .

Th is a n a l y s i s n o t o n l y i l l u s t r a t e s t h e comp lex i t y o f t h e t r i b o l o g y o f

mechanical systems, b u t a l s o the i n e v i t a b l e i n t e r d i s c i p l i n a r y n a t u r e o f

e f f o r t s made t o deal w i t h such systems.

Thus t h e work o f a mechanical des igner o r t h e p roduc t i on eng ineer

takes p lace , so t o speak, on the " f u n c t i o n a l p lane" o f F i g u r e 3.4. The

mechanical eng ineer w i l l a l s o be concerned w i t h t h e analyses on t h e work

and thermal p lanes . These analyses a re a l s o i n the p rov ince o f t h e phys i -

c i s t . P h y s i c i s t s , a long w i t h m a t e r i a l s s c i e n t i s t s , w i l l be q u a l i f i e d t o

i n v e s t i g a t e t h e processes on t h e m a t e r i a l p lanes, w h i l e chemists and che-

m ica l eng ineers w i l l be c l o s e l y concerned w i t h the i n t e r p l a y between t h e

m a t e r i a l p lanes, i .e., t h e chemical r e a c t i o n s caus ing t h e t r a n s f o r m a t i o n

o f m a t e r i a l .

The s p e c i a l i s t s , however, i n e v i t a b l e seeks t o i n c o r p o r a t e h i s know-

ledge and p r a c t i c a l exper ience i n some k i n d o f conceptual framework. Given

44

t he complex i ty o f t r i b o l o g i c a l processes, a theo ry o f t r i b o l o g y based on

systems t h i n k i n g i s l i k e l y t o p rov ide the b e s t type o f framework a v a i l a b l e .

The ana lys i s shows t h a t a s a t i s f a c t o r y d e s c r i p t i o n o f a t r ibo-mechani-

ca l system would be one which c l e a r l y r e l a t e s the elements o f a system, the

processes between t h e elements and t h e i r r e l e v a n t p roper t i es , t o the opera-

t i o n a l va r iab les and the i npu ts and outputs , i n p a r t i c u l a r i n r e l a t i o n t o a

p a r t i c u l a r f u n c t i o n f o r t he system. The in fo rma t ion compi led i n the var ious

F igures and Tables o f t h i s chapter w i l l be used as a convenient g u i d e - l i n e

f o r t h e d iscuss ions o f these aspects i n the f o l l o w i n g chapters.

I

45

4 Tr i bological processes

4 , l ROLE OF TRIBO-PROCESSES I N MECHANICAL SYSTEMS

The general theory o f t r i b o l o g y as o u t l i n e d i n Chapter 3 can be regarded as

a general framework l i n k i n g t h e va r ious processes and v a r i a b l e s connected

w i t h f r i c t i o n and wear o f mechanical systems. I t has been shown t h a t i n an

a b s t r a c t manner a t r ibo-mechanica l dev ice can be cha rac te r i zed as a system

i n which c e r t a i n i n t e r f a c i a l processes o f " t r a n s l a t i o n " and " t rans fo rma t ion "

o f f u n c t i o n a l q u a n t i t i e s , e.g., mot ion, work, m a t e r i a l s , occur. The i n t e r -

f a c i a l processes connected w i t h t h e i n t e r a c t i o n o f m a t e r i a l surfaces i n re -

l a t i v e mot ion a re termed " t r i b o l o g i c a l processes" o r , b r i e f l y , " t r i b o -

processes': I n t h i s connect ion t h e f o l l o w i n g quest ions a r i s e :

( a ) What a re the mechanisms by which t h e use -quan t i t i es o f a mechanical

system a r e t r a n s m i t t e d through the system, i .e . , what a re the ac tua l

phys i ca l processes by which, f o r instance, work i s t r a n s m i t t e d through

t h e system as descr ibed on the conceptual f u n c t i o n a l p lane (see F i g u r e

(b ) What a r e t h e t r i b o l o g i c a l processes which l e a d t o t h e genera t i on o f

3.5)?

loss-outputs , i .e . , what a re the ac tua l phys i ca l mechanisms o f power

d i s s i p a t i o n due t o f r i c t i o n (see F igu re 3.6) and t h e genera t i on o f wear

products (see F i g u r e 3.8)?

( c ) How can the d i s s i p a t i v e loss-mechanisms (b ) be i n f l u e n c e d o r minimized?

Since the general t heo ry o f t r i b o l o g y as developed i n Chapter 3 i s a con-

ceptual framework on ly , t h e answers o r s o l u t i o n s t o these quest ions must be

worked o u t by convent ional methods o f ana lys i s . These d e t a i l s must then be

i n t e g r a t e d i n t o the framework of t he general theory.

46

Obviously, t h e answers t o t h e above ques t i ons ( a ) , ( b ) , ( c ) depend on

the t ype o f system under cons ide ra t i on . It has been shown above t h a t t he

d i f f e r e n t t r ibo-mechan ica l systems can be c l a s s i f i e d accord ing t o t h e i r

f u n c t i o n i n t o d i f f e r e n t groups (see Tab le 3 .2 ) . Fo r any o f these d i f f e r e n t

groups, d i f f e r e n t mechanisms o f t r a n s l a t i o n and t rans fo rma t

tems q u a n t i t i e s a r e r e l e v a n t , f o r ins tance:

( I ) I f t h e t e c h n i c a l f u n c t i o n o f a mechanical system cons

t ransmiss ion o f mot ion o r mechanical power, as i n the

o f a to rque th rough a b e a r i n g s h a f t , t h e ac tua l t r a n s

on o f t he sys-

s t s i n the

t ransmiss ion

i s s i o n process

( a ) i s g i ven by a b u l k e l a s t i c de format ion o f t h e s h a f t . No p r a c t i c a l

devices e x i s t , however, which can t r a n s m i t power w i t h o u t cor respond ing

p a r a s i t i c "guidance" - o r "suppor t - losses" ( b ) . These losses can be

min imized ( c ) th rough proper l u b r i c a t i o n , as i n a h y d r o s t a t i c o r hy-

drodynamic bear ing , f o r example.

I f the t e c h n i c a l f u n c t i o n o f a mechanical system c o n s i s t s i n t h e

i n t e r f a c i a l t ransmiss ion o f mechanical power, as i n a gear t r a i n f o r

ins tance, t h e t ransmiss ion o f mechanical work ( a ) i s ob ta ined th rough

con tac t de format ion processes. The con tac t de format ion i n e v i t a b l y i n -

vo lves some f r i c t i o n processes ( b ) which can be i n f l u e n c e d ( c ) by

l u b r i c a t i o n o f an elastohydrodynamic o r boundary l u b r i c a t i o n mode.

(111) I f t h e t e c h n i c a l f u n c t i o n o f a mechanical system c o n s i s t s o f f o rm ing

m a t e r i a l s , as i n w i redrawing f o r ins tance, an e s s e n t i a l p a r t o f t he

m a t e r i a l s t ransmiss ion mechanism ( a ) c o n s i s t s o f p l a s t i c de format ion

processes. I n t h i s case, some energy- loss-processes ( b ) may r e s u l t

through d i s l o c a t i o n damping. A l so these processes may be i n f l u e n c e d

cons ide rab ly by p roper l u b r i c a t i o n ( c ) .

(11)

The i n s p e c t i o n o f t h e p o s s i b l e t r i b o l o g i c a l processes o f " t r a n s l a t i o n " and

" t rans fo rma t ion " o f q u a n t i t i e s w i t h i n a mechanical system i n d i c a t e s t h a t

t he f o l l o w i n g main e f f e c t s shou ld be s tud ied :

( i ) b u l k e l a s t i c de format ion and i n t e r f a c i a l c o n t a c t de format ion pro-

cesses,

( i i ) t h e mechanisms o f energy and m a t e r i a l d i s s i p a t i o n th rough i n t e r f a c i a l f r i c t i o n and wear processes,

( i i i ) t he processes and modes o f l u b r i c a t i o n as t he most e f f e c t i v e means o f i n f l u e n c i n g t h e d i s s i p a t i o n mechanisms.

I n o r d e r t o complete t h e general framework d e r i v e d i n Chapter 3, a survey

o f t h e main t r i b o l o g i c a l processes g e n e r a l l y recogn ized as be ing r e l e v a n t

47

t o mechanical systems i s g i ven i n t h i s chapter . The t rea tmen t does n o t

a t tempt t o e n t e r i n t o s p e c i f i c d e t a i l s o f t h e t r i b o l o g i c a l behav iour o f

m a t e r i a l s b u t t r i e s t o p resen t a u n i f i e d p i c t u r e o f t h e i m p o r t a n t b a s i c

phenomena. Since t h e t rea tmen t i n t h i s chap te r i s based on conven t iona l

analyses, t h e survey can be regarded - bes ides t h e systems aspec ts - as

a rev iew o f t he p resen t knowledge o f t h e mechanisms o f f r i c t i o n , l u b r i c a t i o n

and wear f rom a p h y s i c a l p o i n t o f view. The i n t e g r a t i o n o f t h e r e s u l t s o f

t h i s chapter t o the general systems concepts i s g i ven i n Chapter 5 and 6.

4 ,2 CONTACT PROCESSES

I n a g r e a t deal o f t r i b o l o g i c a l systems, t h e t r a n s a c t i o n s o f t h e r e l e v a n t

i n p u t s and ou tpu ts occu r th rough t h e c o n t a c t i n t e r f a c e between t r i b o -

element (1) and t r i bo -e lemen t ( 2 ) . I n these i n t e r f a c i a l c o n t a c t processes,

t h e fo rces and displacements o f t h e i n t e r a c t i n g bod ies , i . e . , t h e " c o n t a c t

mechanics", as w e l l as t h e m a t e r i a l s i n t e r a c t i o n s i . e . , t h e " c o n t a c t phys i cs

and chemis t r y " must be taken i n t o account. I n t h i s s e c t i o n t h e d i s c u s s i o n i s

r e s t r i c t e d t o t h e c o n t a c t processes between d r y sur faces ; t h e c o n t a c t p ro-

cesses between l u b r i c a t e d sur faces a re t r e a t e d separa te l y (see Sec t ion 4.5).

4 2 , 1 CONTACT MECHAN I cs

I n c o n t a c t mechanics, a g r e a t v a r i e t y o f s i t u a t i o n s can be cons idered de-

pending on:

( a ) t h e number o f bod ies t a k i n g p a r t i n t h e c o n t a c t process,

( b ) t he macro-geometry o f t h e bod ies ( two- o r th ree-d imens iona l p rob lems) ,

( c ) t h e su r face topography (smooth o r rough su r faces ) ,

( d ) t h e mechanical p r o p e r t i e s o f t h e bod ies (modules, hardness, e t c . ) ,

( e ) t h e de format ion mode ( e l a s t i c , p l a s t i c , e l a s t o - p l a s t i c ) ,

( f ) t h e c o n t a c t f o r c e s (normal f o rces FN, t a n g e n t i a l f o r c e s FT) ,

( 9 ) t h e t ype o f r e l a t i v e mot ion ( s t a t i c con tac t , r o l l i n g , s l i d i n g , sp inn ing ,

( h ) t he v e l o c i t y o f r e l a t i v e mot ion .

I t i s n o t t h e i n t e n t i o n here, n o r i s i t p o s s i b l e w i t h i n t h e scope o f t h i s

volume, t o dea l w i t h a l l these s i t u a t i o n s . ( E x c e l l e n t rev iew a r t i c l e s on

r o l l i n g w i t h s l i p , e t c . ) ,

various aspects o f contact mechanics can be found i n the proceedings o f a

symposium on "The mechanics o f the contact between deformable bodies", see

Ref. 4.1.) The purpose o f t h i s sect ion i s t o ga in a general physical p i c -

t u re o f the contact-deformation process and the mechanisms o f the t rans fe r

o f mechanical work through a contact ing i n te r face . Obviously, a work t rans-

f e r can be obtained only through e l a s t i c contact-deformation processes. I t

the re fo re seems appropr ia te t o consider f i r s t the e l a s t i c contact o f smooth

s o l i d bodies under the app l i ca t i on of a pure normal load FN ( e l a s t o s t a t i c s )

and then t o study the i n f l uence o f the e f f e c t s o f surface roughness, impul-

s i ve loading and e l a s t o - p l a s t i c condi t ions.

Consider as a s t a r t i n g p o i n t a s e m i - i n f i n i t e e l a s t i c s o l i d under an

a r b i t r a r y load d i s t r i b u t i o n p (xl, x2) , as i l l u s t r a t e d i n Figure 4.1. In- t eg ra t i ng over the contact reg ion A,, i t w i l l be recognized t h a t load FN i s given by

The c l a s s i c a l problem o f e las tos ta t i cs , shown i n F igure 4.1, which was f i r s t

solved by Boussinesq, can be t rea ted by the Four ier - t ransform method. (Fo r

d e t a i l s , see Ref. 4.2.)

Figure 4.1 Load d i s t r i b u t i o n a c t i n g on a s e m i - i n f i n i t e body.

I n t r i bo logy , i n a great many contact problems we are concerned w i t h the

contact o f curved bodies such as cy l inders, spheres, as i n ro l l ing-e lement-

type bearings, gear-teeth contacts, e tc . The c l a s s i c bas is f o r a l l o f these

49

c o n t a c t problems o f "cont ra fo rmal su r faces " i s g i ven by t h e famous Her t z

theory (Ref . 4 . 3 ) .

problem under t h e f o l l o w i n g r e s t r i c t i o n s :

( i ) p e r f e c t l y e l a s t i c m a t e r i a l s ,

( i i ) ( i i i ) t o p o g r a p h i c a l l y smooth sur faces ,

( i v )

( v )

( v i ) no t a n g e n t i a l ( t r a c t i v e ) f o r c e i s t r a n s m i t t e d .

However, t he r e s u l t s o f t h e H e r t z i a n theo ry have a l s o been w i d e l y a p p l i e d

s u c c e s s f u l l y t o many s i t u a t i o n s i n which t h e bod ies under ques t i on a re

moving. Owing t o the g r e a t importance o f t h e H e r t z equat ions i n t r i b o l o g y ,

some o f t he r e s u l t s o f t h e H e r t z theo ry w i l l be reproduced here . Fo r t h e

purpose o f t h i s t rea tmen t , i t i s conven ien t t o r e s t r i c t o u r a t t e n t i o n t o

the case o f t h e e l a s t i c c o n t a c t of two s p h e r i c a l bod ies under a pure normal

l o a d FN.

The c o n t a c t s i t u a t i o n i s i l l u s t r a t e d i n F i g u r e 4.2, where rl and r2

are t h e r a d i i o f cu rva tu re o f t h e two bod ies and E l , E2 and vl, v2 t h e i r

e l a s t i c modul i and t h e i r Po isson 's r a t i o s , r e s p e c t i v e l y . Us ing t h e abbre-

v i a t i ons :

Th is theo ry t r e a t s t h e c o n t a c t o f e l a s t i c bod ies as an e l a s t o - s t a t i c a l

b o t h bod ies have the same e l a s t i c cons tan ts ,

t he two su r faces a r e n o t c l o s e l y conforming i n t h e c o n t a c t reg ion ,

no r e l a t i v e angu la r v e l o c i t y o f " s p i n " about t h e common normal t o

t h e c o n t a c t su r face ,

L 4

r: e q u i v a l e n t r a d i u s

o f c u r v a t u r e

E: composi te e l a s t i c

modulus

t h e c o n t a c t p ressure p a t a l o c a t i o n 1 w i t h i n t h e c o n t a c t area, and t h e

rad ius o f c o n t a c t aH under the a c t i o n o f a normal l o a d F,,, i s g i ven by

For t h e c o n t a c t area AH, i t f o l l o w s t h a t

50

FN = 0

FN = 0

F i g u r e 4.2 H e r t z i

2/3 AH = n a Z H = TC [ g] F:I3

pressure

d i s t r i b u t i o n , P

n t c t betwe n two spheres.

area, A,,

Cons ider ing now t h e process o f a t r a n s f e r o f work pe rpend icu la r through the

i n t e r f a c e , i t i s necessary t o c a l c u l a t e t h e va lue o f approach z o f the two

bod ies as a consequence of t h e i r e l a s t i c de format ion . From H e r t z i a n theo ry

i t f o l l o w s t h a t

Using t h e express ion i t i s p o s s i b l e t o determine t h e p o t e n t i a l e l a s t i c

energyAU o f t he two c o n t a c t i n g bod ies . Since FN =

g i ven by

the p o t e n t i a l i s a z

51

I f t h e c o n t a c t s i t u a t i o n i s e n t i r e l y e l a s t i c , t h e p o t e n t i a l energy can

be t rans formed i n t o k i n e t i c energy i n r e l e a s i n g the con tac t . I n t h i s case,

t he system o f t he e l a s t i c bod ies per fo rms work a g a i n s t i t s environment. I n

cons ide r ing t h e whole process o f c o n t a c t f o r m a t i o n and c o n t a c t re lease , i t

t u r n s o u t t h a t t h e q u a s i - s t a t i c H e r t z i a n c o n t a c t s i t u a t i o n can be regarded

as model o f t h e i n t e r f a c i a l t r a n s f e r o f mechanical energy th rough a system

o f c o n t a c t i n g bod ies .

energy th rough an e l a s t i c c o n t a c t i n t e r f a c e can be understood on t h e b a s i s

o f H e r t z i a n theo ry , i n any c o n t a c t s i t u a t i o n o f " r e a l su r faces " the e f f e c t

o f s u r f a c e topography must be taken i n t o account (Refs . 4.4, 4 .5 ) .

i d e a l smooth s u r f a c e can be c l a s s i f i e d i n t o d i f f e r e n t groups:

( a ) d e v i a t i o n s i n shape

( b ) waviness ( l a r g e - s c a l e su r face d e v i a t i o n s )

( c ) roughness ( sma l l - sca le d e v i a t i o n s )

( d ) l a t t i c e s t r u c t u r e

I n o r d e r t o desc r ibe t h e roughness o f su r face , a coup le o f parameters have

been d e f i n e d i n r e l a t i o n t o a c ross -sec t i on o f t he su r face , see F i g u r e 4.3.

A l though t h e main f e a t u r e s o f an " i d e a l " t ransmiss ion o f mechanical

Accord ing t o t h e German s tandard D I N 4760, t h e d e v i a t i o n s f rom an

s u r f a c e topography

(3-dim.)

( a ) h e i g h t d i s t r i b u t i o n

( b ) bear ing-area cu rve

su r face p r o f i l e (2 -d im. ) ( a ) ( b ) /

sample l e n g t h 1 w 0 100 %

s o l i d

/ v o i d mean l i n e : area o f s o l i d = area of. v o i d

F i g u r e 4.3 C h a r a c t e r i s t i c s o f s u r f a c e roughness.

62

The most commonly used h e i g h t parameter i n su r face p r o f i l o m e t r y i s t h e

Ra va lue o r cen te r - l i ne -ave rage va lue (c .1 .a . ) . It i s s imp ly t h e average de-

v i a t i o n o f t he p r o f i l e f rom t h e re fe rence mean l i n e . Other h e i g h t parameters

i n c l u d e t h e maximum peak - to -va l l ey h e i g h t Rt w i t h i n t h e sample l e n g t h 1, t h e

average d e v i a t i o n o f t he f i v e h i g h e s t peaks and f i v e l owes t v a l l e y s , R,, and

many more, a l l o f which are w e l l documented i n t h e l i t e r a t u r e (Refs. 4.6,

Another approach t o desc r ibe the topography o f su r faces i s t o rega rd

4.7).

t he p r o f i l e , as de tec ted by a p r o f i l e m e t e r , as an e l e c t r i c a l s i g n a l and t o

ana lyze i t s t a t i s t i c a l l y (Ref. 4.8). I t i s then p o s s i b l e t o c l a s s i f y t h e

p r o f i l e i n terms o f t h e f o l l o w i n g f u n c t i o n s :

( I ) The p r o b a b i l i t y d i s t r i b u t i o n o f o r d i n a t e he igh ts . Fo r many eng ineer ing

surfaces f i n i s h e d by g r i n d i n g o r ab ras ion processes i t was found t h a t

t he he igh ts o f t he p r o f i l e s were d i s t r i b u t e d i n a Gaussian manner.

(11) The a u t o - c o r r e l a t i o n f u n c t i o n o f t he p r o f i l e d e f i n e d as:

+y 1

Z ( A ) = l i m T y ( x ) y ( x + A ) dx 'i* 1-00 -% 7

where y ( x ) i s t he h e i g h t o f t he p r o f i l e a t a g i ven co -o rd ina te x and

y ( x t A ) i s t h e h e i g h t a t an ad jacen t co -o rd ina te ( x + A ) . Pek len ik

has analyzed the sur faces produced by many d i f f e r e n t techniques and

has proposed a system o f c l a s s i f y i n g su r faces based upon t h e n a t u r e of

the a u t o - c o r r e l a t i o n f u n c t i o n s o f t h e i r p r o f i l e (Ref. 4.9).

/ 4 / r I

a

n . A, = a - b >> A = A: (n: number o f con tac ts ) r

i =1

F i g u r e 4.4 Nominal and r e a l a rea o f con tac t .

53

Now, r e t u r n i n g t o c o n t a c t mechanics, i n o r d e r t o avo id amb igu i t y , f o r

t he c o n t a c t o f rough sur faces two terms must be d i s t i n g u i s h e d , as i l l u s t r a t -

ed i n F igu re 4.4:

(i)

( i i ) t h e r e a l area o f c o n t a c t A,, i . e . , t h e sum o f t h e separa te m ic roscop ic

the nominal area o f c o n t a c t Ao, i .e. , t h e apparent area o f o v e r l a p o f

t h e c o n t a c t i n g s o l i d s ,

areas a t which the a s p e r i t i e s a r e i n con tac t .

S ince i t i s obvious t h a t t h e r e a l area o f con tac t , r a t h e r than t h e nominal

area, i s c r u c i a l f o r t h e i n t e r f a c i a l t ransmiss ion o f work, a g r e a t many

s t u d i e s have been devoted t o t h e e s t i m a t i o n and exper imenta l de te rm ina t ion

o f t h e r e a l area o f c o n t a c t Ar (Refs . 4.10, 4.11).

A comprehensive s tudy o f e l a s t i c de fo rma t ion u s i n g model arrangements

was made by Archard (Refs . 4.12, 4.13). A l though these models a r e over -

s i m p l i f i c a t i o n s , they i l l u s t r a t e t h a t m u l t i p l e - p o i n t c o n t a c t under e l a s t i c

de format ion can g i v e a r e a l a rea o f c o n t a c t a lmost l i n e a r l y p r o p o r t i o n a l t o

FN, i . e . ,

C

Ar = cons tan t [ :] 4/5 s C s 44/45

(depending on t h e model )

Another ex tens ion o f t h e H e r t z i a n theo ry o f e l a s t i c c o n t a c t between spheres

t o t h e case o f rough sur faces w i t h a Gaussian h e i g h t d i s t r i b u t i o n was made

by Greenwood and T r i p p (Ref . 4 .14) . T h e i r model i s d e f i n e d by t h r e e para-

meters

n

They

( i 1

( i i )

U* : mean d e v i a t i o n o f t h e a s p e r i t y ,

p : mean r a d i u s o f t h e c u r v a t u r e o f t h e a s p e r i t y - t i p s assumed t o be

cons tan t f o r a1 1 a s p e r i t i e s ,

d e n s i t y o f a s p e r i t i e s p e r u n i t area.

showed mathemat i ca l l y :

t h e t o t a l number o f m ic rocon tac ts i s a lmost p r o p o r t i o n a l t o the

l o a d FN,

t h e average s i z e o f a m ic rocon tac t i s a lmost l o a d independent,

con tac ts ,

( i i i ) t h e r e a l a rea o f c o n t a c t Ar i s p r o p o r t i o n a l t o t h e number o f

thus the r e a l area o f c o n t a c t Ar, i . e . , t h e sum o f t h e m ic ro -con tac t areas,

i s p r o p o r t i o n a l t o the l o a d FN. Whi le a t low loads t h e r e a re cons ide rab le

64

differences between the contact areas A, and Ao(Hertz), a t h igher loads i n

the rough surfaces contact s i t u a t i o n an e f f e c t i v e rad ius can be def ined

which approaches the H e r t r i a n rad ius and l i k e i t var ies as the one- th i rd

power o f the load.

I n the discussion so far , mainly r e v e r s i b l e quas i - s ta t i c e l a s t i c con-

t a c t deformations have been considered which can be regarded as models f o r

the transmission of work i n a tribo-mechanical system. However, i n contact

s i t u a t i o n s under pure normal loads some i r r e v e r s i b l e i n t e r f a c i a l processes

already e x i s t which lead t o a d i s s i p a t i o n o f mechanical energy. Unfortunate-

ly , f o r the i r r e v e r s i b l e processes i n contact deformation the re e x i s t s no

theory as there i s f o r the r e v e r s i b l e e l a s t i c case. Therefore, i n the f o l -

lowing on ly some s h o r t remarks on d i s s i p a t i v e processes i n contact mechanics

w i l l be made (a phys ica l t r e a t i s e on the o r i g i n s o f energy d i s s i p a t i o n i s

given i n Section 4.3).

contact mechanics:

The fo l l ow ing processes may con t r i bu te t o an energy d i s s i p a t i o n i n

(a) INTERFACIAL SLIP, I .E. , PARTIAL MOTION OF THE CONTACTING SURFACES

OF THE BODIES I N THE INTERFACE

I f i n a H e r t t i a n contact the two contact ing bodies have d i f f e r e n t e l a s t i c

proper t ies, an i n t e r f a c i a l shear s t ress r e s u l t s which i n t u r n in f luences the

pressure d i s t r i b u t i o n . Depending on the phys ica l nature o f the surfaces,

the i n t e r f a c i a l t angen t ia l shear may cancel ou t through l o c a l micro-sl i p

processes, thus d i s s i p a t i n g energy (see a lso Section 4.3.4). Also i f the tan-

g e n t i a l stresses are " f rozen i n " du r ing the du ra t i on o f the contact as a

consequence o f i n t e r f a c i a l adhesion forces (see Section 4.2.2), i t i s l i k e -

l y t h a t i n the release o f contact, energy i s d iss ipated.

(b )

I n any contact s i t u a t i o n a t l e a s t two t r a n s i e n t s ta tes are involved: the

formation o f the contact and the separation o f the contact. I n these t ran -

s i e n t s ta tes due t o changes i n the load o r t he pressure d i s t r i b u t i o n , t he re

may be a pronounced e f f e c t o f m i c r o - s l i p and a generation o f e l a s t i c waves.

I t has been shown exper imenta l ly t h a t under impulsive loading o f Her tz ian

contacts, gross s l i p e f fec ts occur and energy appl ied du r ing gross s l i p i s

d i ss ipa ted (Ref. 4.15).

THE GENERATION OF ELASTIC WAVES IN THE INTERFACE

55

( c ) VISCOELASTIC DAMPING

The above d i scuss ions o f con tac t -de fo rma t ion processes on t h e b a s i s o f t h e

H e r t z i a n theo ry r e f e r t o e l a s t i c so l i d s as g i ven approx imate ly by hardened

b a l l - b e a r i n g s t e e l . There are , however, o t h e r groups o f t e c h n i c a l l y impor-

t a n t m a t e r i a l s , f o r i ns tance e las tomers , which cannot be t r e a t e d i n t h i s

manner. U n l i k e a ha rd m a t e r i a l l i k e s t e e l , t h e e las tomer s t r u c t u r e i s com-

posed o f f l e x i b l e cha ins which a re i n a cons tan t s t a t e o f thermal mot ion.

The te rm " v i s c o e l a s t i c i t y " i s commonly a p p l i e d t o m a t e r i a l s which a r e n e i t h e r

i d e a l e l a s t i c s o l i d s n o r v iscous l i q u i d s (see Sec t ion 4.5.2), b u t i n f a c t

possess c h a r a c t e r i s t i c s which a re t y p i c a l o f bo th . The e l a s t i c behav iour may

be represented by an i d e a l s p r i n g and v i s c o s i t y by an i d e a l dashpot. Combin-

i n g two b a s i c mechanical models, known as t h e V o i g t and Maxwell models con-

s i s t i n g s imp ly o f s p r i n g and dashpot i n p a r a l l e l and s e r i e s r e s p e c t i v e l y , t h e

contac t -de format ion behav iour o f v i s c o e l a s t i c m a t e r i a l s may be model led. As

a genera l f ea tu re , i n t h e sequence o f c o n t a c t f o rma t ion and separa t i on o f

such m a t e r i a l s , mechanical work i s d i s s i p a t e d th rough h y s t e r e s i s damping

e f f e c t s (Ref. 4 .16) .

( d ) PLASTIC CONTACT PROCESSES

As e a r l y as 1901, S t r i b e c k p o i n t e d t o t h e l i m i t s o f t h e H e r t z i a n t h e o r y s e t

by p l a s t i c de format ion processes a t h i g h e r loads (Ref . 4 .17) . An e l a s t i c -

p l a s t i c t r a n s i t i o n c r i t e r i o n , i . e . , t he s o - c a l l e d p l a s t i c i t y i ndex + i s

g iven by Greenwood and Wi l l iamson (Ref . 4.18) as

E : composi te e l a s t i c modulus

H : hardness

6 : mean d e v i a t i o n o f su r face *

a s p e r i t y h e i g h t

p : mean a s p e r i t y r a d i u s

A s i m i l a r express ion has been d e r i v e d by Whitehouse and Archard (Ref. 4.19).

(Fo r a comparison o f bo th models see Ref. 4.20.) I f Q<0 .6 , t h e c o n t a c t

shou ld be e l a s t i c under a l l p r a c t i c a l loads . I f Q > 1 , a p a r t o f t h e c o n t a c t

w i l l i n v o l v e p l a s t i c f l o w . As most sur faces have values + i n excess o f u n i t y ,

t h e r e w i l l be some p l a s t i c c o n t a c t de format ion o f a s p e r i t i e s i n a lmost any

c o n t a c t s i t u a t i o n . Th is i s i n l i n e w i t h t h e v iew o f Bowden and Tabor (Ref.

1 .4 ) who argued t h a t , because sur faces c o n t a i n a s p e r i t i e s o f sma l l - rad ius -

o f - cu rva tu re , p l a s t i c f l o w would occu r a t t h e t r u e areas o f c o n t a c t even

66

under very smal l loads . They expressed t h e r e a l area of c o n t a c t by the

r e l a t i o n

where p

l i k e l y t h a t i n a lmost any c o n t a c t s i t u a t i o n t h e r e i s some d i s s i p a t i o n o f

mechanical energy due t o p l a s t i c asper i t y -de fo rma t ion processes. Accord ing

t o N icho las (Ref. 4.21), i n genera l , f o u r main mechanisms o f energy d i s s i -

p a t i o n i n p l a s t i c de format ion can be named:

( i ) The moving d i s l o c a t i o n s r e q u i r e a h i g h k i n e t i c energy, which i s s e t f r e e i f the d i s l o c a t i o n s a r e locked.

( i i ) The d i s l o c a t i o n s d i s s i p a t e energy con t inuous ly th rough t h e thermo- e l a s t i c damping and s c a t t e r i n g o f acous t i c waves.

(iii) D i s l o c a t i o n s a re generated and a n n i h i l a t e d d u r i n g t h e de format ion .

( i v ) P o i n t de fec ts a re generated and a n n i h i l a t e d d u r i n g t h e de format ion .

i s the y i e l d p ressure f o r t h e weaker m a t e r i a l . I t i s t h e r e f o r e Y

4 I 2,2 CONTACT PHYS I cs AND CHEMI STRY

I n t h e con tac t o f p h y s i c a l bodies, besides t h e c o n t a c t nmechanicsn, i n t e r -

f a c i a l mo lecu la r m a t e r i a l i n t e r a c t i o n s and "su r face fo rces " must be taken

i n t o account. S ince these processes depend on the phys i ca l and chemical

n a t u r e o f t h e sur faces i n con tac t , a d e s c r i p t i o n o f t h e su r face cha rac te r -

i s t i c s i s needed.

From t h e view o f s o l i d s t a t e phys ics , su r faces o f c r y s t a l l i n e bod ies

rep resen t an ab rup t t e r m i n a t i o n o f t he p e r i o d i c i t y o f t he c r y s t a l l i n e l a t -

t i c e . Compared w i t h the b u l k p r o p e r t i e s o f a c r y s t a l l i n e s o l i d , t h e i m p l i -

c a t i o n s o f such an ab rup t t e r m i n a t i o n o f l a t t i c e a re (Ref. 4.22):

( a ) s t r u c t u r a l r e o r i e n t a t i o n s ( c r y s t a l 1 i n i t y and e n e r g e t i c s )

( b ) sur face /env i ronment i n t e r a c t i o n s (phys i ca l adsorp t ion , chemisorp t ion ,

( c ) changes i n phys i ca l p r o p e r t i e s

Fo r t e c h n i c a l sur faces , due t o t h e manufac tur ing process, a d d i t i o n a l aspects must be taken i n t o account l i k e :

( d ) a work-hardened l a y e r

o x i d a t i o n o r f i l m f o rma t ion )

57

( e ) t e x t u r i n g o f t he surface

( f ) l o c a l i n t e r n a l s t r e s s f i e l d s

I n o r d e r t o desc r ibe t h e compos i t ion o f r e a l sur faces , Schmaltz as e a r l y as

1936 d i s t i n g u i s h e d between an " i n n e r su r face l aye r " , b u l k m a t e r i a l and

worked l a y e r , and an " o u t e r su r face l a y e r " , contaminants, adsorbed l a y e r s ,

ox ide l a y e r s (Ref . 4 .23 ) . The compos i t ion o f a su r face i n a c ross -sec t i ona l

v iew i s shown schemat i ca l l y i n F igu re 4 .5 . C l e a r l y , t he a c t u a l compos i t ion

o f a g i ven su r face and the s t r u c t u r e and th i ckness o f t h e d i f f e r e n t su r face

l a y e r s , as shown schemat i ca l l y i n F i g u r e 4.5, depends on t h e p r e p a r a t i o n o f

t he su r face and on the environment, a p a r t f rom the b u l k m a t e r i a l p r o p e r t i e s .

contaminant l a y e r

o u t e r adsorbed gas l a y e r su r face l a y e r s 10 nm ox ide l a y e r

i n n e r

su r face

1 ayers

> 5 pm work-hardened 1 ayer

metal s u b s t r a t e

F igu re 4.5 Schematic r e p r e s e n t a t i o n o f t h e l a y e r e d compos i t ion of a m e t a l l i c su r face .

Consider now t h e c o n t a c t process o f two s o l i d bod ies under a pure normal

l o a d FN. As desc r ibed i n t h e fo rego ing sec t i on , t h e c o n t a c t i n g su r faces

w i l l touch o n l y w i t h i n d i s c r e t e mic ro-spots whose sum forms t h e r e a l a rea

o f c o n t a c t Ar. I n t h e process o f c o n t a c t f o rma t ion , bes ides an e l a s t i c de-

fo rma t ion process the a s p e r i t i e s undergo some p l a s t i c de format ion . Due t o

t h i s de format ion processes, i n t i m a t e c o n t a c t between t h e p a r t n e r s occurs so

t h a t mo lecu la r su r face fo rces may a c t th rough t h e i n t e r f a c e , wh ich r e s u l t s

i n " i n t e r f a c i a l bonding" and t h e genera t i on o f adhesive " j u n c t i o n s " . Thus

the d i f f e r e n t types o f mo lecu la r f o rces t h a t can a c t w i t h i n t h e i n t e r f a c e

o f two c o n t a c t i n g bod ies t o produce "adhesion" and t h e energy o f i n t e r f a c i a l

adhesion bond ing must be considered.

Adhesion mechanism Bonding through: Val idi ty

I van der Waals 1

electromagnetic z > atomic

solid fluctuation dime ns ions

(*) fields '1 id

zc tunnel electrostatic distance

fields (localized

charges)

1 metallic J

F l

Fiaure 4.6

mobile

interfacial

electrons

z = atomic dimensions

(grain bound-

ary analogy)

z E atomic

(dangl i ng

bonds)

overlap o f dimensions electron

distributions

- Types of adhesion bonding mechanisms.

59

T h e o r e t i c a l l y , t h e a t t r a c t i v e i n t e r a c t i o n fo rces between two c o n t a c t i n g

s o l i d s i n c l u d e , a t l e a s t i n p r i n c i p l e , a l l those t ypes o f i n t e r a c t i o n t h a t

c o n t r i b u t e t o t h e cohesion o f s o l i d s , such as m e t a l l i c , cova len t and i o n i c ,

i . e . , p r imary chemical bonds ( sho r t - range f o r c e s ) , as w e l l as secondary van

de r Waals bonds ( long- range f o r c e s ) . Fo r example, two p ieces o f c lean g o l d

p laced i n c o n t a c t w i l l fo rm m e t a l l i c bonds o v e r t h e reg ions o f a tomic con-

t a c t and the i n t e r f a c e w i l l have t h e s t r e n g t h o f b u l k go ld . Wi th c lean d i a -

mond, the su r face fo rces w i l l resemble va lency fo rces ; w i t h rock s a l t t h e

su r face f o r c e s w i l l be p a r t l y i o n i c . A l l these a r e e s s e n t i a l l y shor t - range

fo rces . Long-range van d e r Waals fo rces a c t i n t h e adhesion between s o f t

r u b b e r - l i k e m a t e r i a l s and between po lymer i c s o l i d s . I n F i g u r e 4.6 some cha-

r a c t e r i s t i c s o f t h e adhesion bonding mechanisms a r e shown.

Due t o the g r e a t importance o f adhesion i n t r i b o l o g i c a l processes, some

fea tu res o f t h e a c t i o n o f van de r Waals fo rces and m e t a l l i c bonds - t h e main

reasons f o r an adhesion o f polymers and meta ls - w i l l be desc r ibed i n some

d e t a i l .

I f two s o l i d s a re b rough t toge the r t h e y w i l l f i r s t exper ience a t t r a c -

t i v e fo rces due t o van d e r Waals i n t e r a c t i o n s . These fo rces a r i s e f rom t h e

f l u c t u a t i n g charge d i s t r i b u t i o n s i n t h e atoms o r molecules o f t h e two bod ies ,

c r e a t i n g momentary and con t inuous ly s h i f t i n g d i p o l e s and co r respond ing ly

induced d i p o l e s i n ne ighbour ing atoms o r molecules. As a f i r s t approxima-

t i o n f o r a s o l i d body, i t may be assumed t h a t t h e van de r Waals f o r c e be-

tween any p a i r o f atoms o r molecules i s a d d i t i v e so t h a t t h e t o t a l f o r c e

may be c a l c u l a t e d by summation f o r a l l p a i r s o f atoms i n t h e two bod ies . On

the b a s i s o f t h i s assumption, Cas im i r was t h e f i r s t t o d e r i v e t h e f o l l o w i n g

formula f o r t h e f o r c e o f adhesion FA i n the i n t e r f a c e A o f two m i r r o r p lanes

(Ref. 4 .24) :

FA tl c r 2 240

A

7

h h = ( h : P lanck ' s cons tan t )

c : speed o f l i g h t

z : d i s t a n c e between the su r faces

I n t h e c a l c u l a t i o n o f t h e van der Waals fo rces , two cases must be d i s t i n -

guished:

( a ) non r e t a r d e d fo rces o c c u r r i n g between i n t e r a c t i n g d i p o l e s which a r e

i n phase,

60

(b) re tarded forces occurr ing i f the i n i t i a l d ipo le and the induced d ipo le

are no longer i n phase.

For these two cases the fo l l ow ing expressions f o r the adhesion fo rce FA

between a sphere o f radius r a t a distance o f nearest approach z from a

f l a t surface can be der ived

(a) non-retarded forces

(b ) re tarded forces J L

where kl and k2, are the Hamaker constants f o r non-retarded and retarded

forces respect ive ly . The v a l i d i t y o f these formulae has been proved i n ex-

periments w i t h c lean smooth mica surfaces. It was found t h a t a t z > 100 nm,

the formulae f o r t he retarded forces i s v a l i d whereas a t z < 20 nm the mea-

sured van der Waals a t t r a c t i v e f o r c e FA agrees w e l l w i t h the theory fo r non-

re tarded in te rac t i ons (Ref. 4.25). I f the van der Waals surface forces are

described i n terms o f surface energyy , t y p i c a l values o f about 0.02 t o

0.04 Jm" are found.

These r e s u l t s lead t o an important genera l izat ion: s ince van der

Waals i n t e r a c t i o n s occur between any type o f atoms o r molecules, i t can be

assumed t h a t the van der Waals adhesion forces a c t between a l l ma te r ia l s

t h a t are brought i n t o contact down t o distances o f a few nm.

Below 1 nm, a t atomic dimensions, sho r t range surface forces o f d i f -

f e ren t type come i n t o ac t i on which depend on the nature o f t he ma te r ia l s i n

contact. As an important example o f the ac t i on o f short-range surface forces,

the adhesion o f c lean metals w i l l be discussed.

I n order t o estimate the s t rength o f m e t a l l i c adhesion bonding, con-

s i d e r f i r s t the bu lk cohesion o f metals. Due t o the complicated e l e c t r o n i c

s t r u c t u r e o f most metals, a t present i t i s n o t y e t poss ib le t o ca l cu la te

the cohesion s t rength o f metals from f i r s t p r i nc ip les . Estimations o f the

cohesion bond st rength o f simple metals can be attempted us ing the so-ca l led

" j e l l i u m model". According t o Ziman (Ref. 4.26), i t can be seen t h a t i n the

simple p i c t u r e o f a j e l l i u m model cohesion depends, bas i ca l l y , on having an

"e lec t ron gas" o f f a i r l y h igh densi ty , n o t on the d e t a i l s o f the c r y s t a l

s t ructure. The e lec t ron gas behaves l i k e a ,ubiquitous l i q u i d g lue t h a t w i l l b i nd together more o r l ess any arrangement o f ions t h a t i s s u f f i c i e n t l y

densely packed.

61

metal 1

-.--- .I

The a p p l i c a t i o n o f t h e j e l l i u m model t o the case o f adhesion a t a

b i m e t a l l i c i n t e r f a c e i s i l l u s t r a t e d i n F i g u r e 4.7. I n t h i s model, j u s t t h e

ove r lap o f t he metal-vacuum electron-number d e n s i t i e s nl and n2 o f t h e two

c o n t a c t i n g p a r t n e r s w i t h i n the t r u e area o f con tac t i s considered.

?.? metal 2 .A *\ .---

-Lo I-

F i g u r e 4.7 J e l l i u m model o f a b i m e t a l l i c adhesion i n t e r f a c e .

A f i r s t p r e l i m i n a r y c a l c u l a t i o n o f t h e adhesive i n t e r a c t i o n o f a b i m e t a l l i c

i n t e r f a c e energy was performed by F e r r a n t e and Smith (Ref. 4.27), which has

r e c e n t l y been extended (Ref. 4.28). The theo ry proceeds f rom an exp ress ion

f o r t h e t o t a l energy o f t h e system i n terms o f e l e c t r o n number d e n s i t y , i n -

c l u d i n g exchange and c o r r e l a t i o n energ ies , and i s a p p l i e d t o t h e c lose -

packed planes o f s imp le meta ls . I n t h i s theo ry t h e s t r e n g t h o f adhesion

bonding depends, b a s i c a l l y , on t h e f r e e - e l e c t r o n d e n s i t y . As i n t e r f a c i a l

f r e e - e l e c t r o n d e n s i t y i n t u r n depends on how s t r o n g l y t h e e l e c t r o n s a r e

l o c a l i z e d i n s i d e t h e c o n t a c t i n g pa r tne rs , i n a d d i t i o n t o the f r e e - e l e c t r o n

j e l l i u m formal ism, the e l e c t r o n i c s t r u c t u r e o f meta ls and t h e c h a r a c t e r

( s , p, d) o f e l e c t r o n s f r e e f o r i n t e r f a c i a l adhesion bonding must be con-

s idered . Th is has l e d t o the hypothes is t h a t f o r l i k e me ta l s t h e s t r e n g t h

o f adhesion bonding shou ld i nc rease w i t h i n t h e p e r i o d i c t a b l e f rom l e f t t o

r i g h t i n t h e o r d e r o f t r a n s i t i o n meta ls , nob le metals, 6-subgroup meta ls

(Ref. 4.29). Fo r t h e adhesion bonding o f u n l i k e meta ls , f u r t h e r aspec ts

such as the d i f f e r e n c e s i n Fermi l e v e l s , e l e c t r o n work f u n c t i o n s and s t r u c -

t u r e and d e n s i t y o f e l e c t r o n s t a t e s o f bo th p a r t n e r s must be cons idered.

Here, t h e d e n s i t y o f s t a t e s i n t h e metal on one s i d e o f t h e i n t e r f a c e may

determine t h e t o t a l number o f e l e c t r o n s imp ing ing on t h e j u n c t i o n , and t h e

d e n s i t y o f s t a t e s i n t h e o t h e r metal may determine t h e number o f f i n a l

s t a t e s a v a i l a b l e f o r t h e passed adhesive bonding e l e c t r o n s . I t may be

hypothes ized t h a t s t r o n g adhesion bonds w i l l occur i f one p a r t n e r can a c t

62

as an "electron donor'' and the other as an "electron acceptor" (Refs. 4.29,

4.30). These considerations are, however, rather speculative because a t

present there i s no d i rec t way of studying the actual interfacial electron densities o r determining the interfacial bond strength.

bonding forces, i t should be borne i n mind tha t the net adhesion e f fec t be-

tween solids i s influenced by a t l eas t three further important factors:

( i )

Although adhesion i s essentially the resu l t of interfacial molecular

The elasto-plastic contact behaviour of the partners, determining the

size of the real area of are able to act .

( i i ) The influence of e l a s t i c

peeling junctions apart, lacking in duc t i l i ty .

contact in which the actual surface forces

stresses in contact separation, eventually

particularly i f the contacting partners a re

( i i i ) The presence of surface films and surface asperit ies which may reduce

the adhesion forces.

I 20

Figure 4.8 SEM micrograph of an adhesive junction a f t e r contact separation (copper surface).

63

Experimental ly, t he only way o f s tudy ing adhesive i n t e r a c t i o n s between

two s o l i d bodies which contact under a pure normal l oad FN i s t o destroy

the bonding and t o measure the fo rce FA necessary f o r the separation o f t he

surfaces. According t o Bowden the r a t i o

is termed the c o e f f i c i e n t o f adhesion.

The t y p i c a l appearance o f a broken m e t a l h e t a l adhesion j u n c t i o n can

be seen i n F igure 4.8 i n a scanning e l e c t r o n microscope (SEN) micrograph,

having the appearance o f d u c t i l e f rac tu re .

The e a r l y experimental work o f Bowden and Rowe (Ref. 4.31) showed

c l e a r l y t h a t very s t rong adhesion could be obtained between metal surfaces

t h a t had f i r s t been cleaned by heat ing t o a h igh temperature i n a vacuum o f

130 pPa (10-6Torr). I n these experiments, r e l a t i v e l y heavy j o i n i n g loads had

been used so t h a t the surfaces underwent p l a s t i c deformation. Likewise

under p l a s t i c contact condi t ions combined w i t h a d i s r u p t i o n o f surface con-

taminant layers, S i ko rsk i s tud ied the c o r r e l a t i o n o f the c o e f f i c i e n t o f

adhesion w i t h various bu lk p roper t i es o f metals i n apply ing the twist-com-

pression bonding method under normal atmospheric condi t ions (Ref. 4.32). I n

F igure 4.9 the r e s u l t s o f S i ko rsk i are represented showing the mean c o e f f i -

c i e n t o f various metals as a func t i on o f i t s Vickers hardness.

These r e s u l t s i n d i c a t e two bas ic features:

( i ) The adhesion c o e f f i c i e n t decreases w i t h increas ing hardness (and a l so

w i t h increas ing e l a s t i c moduli and surface energy).

( i i ) The values o f the adhesion c o e f f i c i e n t are s p l i t up f o r the d i f f e r e n t

types o f c r y s t a l s t ruc tu re ; the adhesion i s lowest f o r hexagonal

close-packed metals.

This general feature o f the adhesion o f metals has a l so been observed f o r

clean pure metals under condi t ions o f u l t r a h i g h vacuum i n extensive exper i -

ments by D. Buckley (Refs. 4.33, 4.34). It was a lso found t h a t , con t ra ry t o

a prev ious ly he ld view, s t rong adhesion could be obtained between u n l i k e

metals which had no mutual s o l u b i l i t y (Refs. 4.35, 4.36). Fur ther , on sepa-

r a t i o n of the surfaces the cohesively weaker metal has genera l ly been ob-

served t o t r a n s f e r t o the cohesively stronger.

64

0 f c c

x bcc

+ t e t r a g o n a l

tl 0

01 r U 4

+ c, E aJ

.I-

VI 4 -

P t

I 1 1

3 5

0 3 -

.r

.: 2 - Y- Lc aJ 0 u

s I - ..- Q W z

0 -

0.01 0.03 0.05 0.1 0.3 0.5 1

V icke rs hardness (GN/m2)

F igu re 4.9 C o r r e l a t i o n between t h e median c o e f f i c i e n t s o f adhesion and V ickers hardness f o r meta ls o f va r ious 1 a t t i c e s t r u c t u r e s (Ref. 4.32).

I n t r y i n g t o e x p l a i n these exper imenta l obse rva t i ons i n terms of phys i ca l

p r o p e r t i e s o f metals, two aspects have been emphasized:

( a ) The a b i l i t y o f sur faces t o deform p l a s t i c a l l y obv ious l y e x h i b i t s a

marked i n f l u e n c e on adhesion s ince i t i n f l u e n c e s t h e t r u e area o f con-

t a c t . As i l l u s t r a t e d i n F i g u r e 4.10 w i t h face-cent red-cub ic ( f c c ) me-

t a l s t h e r e a re 12 p o s s i b l e s l i p systems. Body-centred-cubic (bcc) me-

t a l s have 12 main operab le s l i p systems and 36 secondary s l i p systems

which r e q u i r e h i g h e r shear s t resses t o produce s l i p . Wi th hexagonal

meta ls (hcp) , however, a t room temperature t h e r e a r e o n l y 3 operab le

basal s l i p systems. The l i m i t e d s l i p behav iour i n t h e hexagonal meta ls ,

t he re fo re , seems t o i n d i c a t e t h a t t he hexagonal meta ls m igh t w e l l ex-

h i b i t lower adhesion behav iour than e i t h e r bcc - o r f c c - meta ls

(Refs. 4.37, 4.38).

e l e c t r o n d e n s i t y i s assumed t o determine t h e i n t e r f a c i a l bond s t r e n g t h

(Refs. 4.27 t o 4.29). Fo r example, i n c a l c u l a t i n g t h e b i n d i n g energ ies

( b ) The e l e c t r o n i c s t r u c t u r e o f t h e meta ls and t h e i n t e r f a c i a l f r e e -

66

f o r a couple o f u n l i k e fcc metals using the e lec t ron theory o f m e t a l l i c

binding, an order ing of b ind ing energies was obtained as shown i n Table

4.1. As i nd i ca ted i n Table 4 .1 the t h e o r e t i c a l f i nd ings have been ex-

pe r imen ta l l y v e r i f i e d (Ref. 4.39).

Besides the extensive experimental work on the adhesion o f metals, r e l a t i v e -

l y few stud ies have been repor ted o f adhesion between o the r types o f s o l i d

such as covalent o r i o n i c ma te r ia l s o r van der Waals bonded so l i ds . I n addi-

t i on , l i t t l e work appears t o have been c a r r i e d ou t between such s o l i d s and

clean metals. (Examples o f polymer-metal adhesion as s tud ied by o p t i c a l

microscopy and f i e l d i o n microscopy can be found i n Section 7.6.) Tabor

and co-workers described a study o f the adhesion between s o l i d s o f d i f f e r e n t

type performed i n a vacuum o f 13 nPa (lO-loTorr) (Ref. 4.40). They found

t h a t adhesion o f s o f t metals t o a hard s o l i d such as t i t a n i u m carbide can be

h igh and when the surfaces are separated fragments o f metal are found a t -

tached t o the harder surface. With o the r hard s o l i d s such as saphire o r

diamond the adhesion o f copper i s appreciably less, i n d i c a t i n g t h a t the

bonding between copper and these covalent ma te r ia l s i s i n t r i n s i c a l l y weak.

From the study o f the adhesion bonding mechanisms an impor tant general

conclusion can be drawn:

Since both par tners con t r i bu te t o the adhesion bonding, the bond

st rength i s e s s e n t i a l l y an i n t e r a c t i o n c h a r a c t e r i s t i c . Therefore, any

measure o r c h a r a c t e r i s t i c o f adhesion cannot be handled i n engineering

app l i ca t i ons l i k e a ma te r ia l s proper ty (as f o r instance the e l a s t i c modulus)

b u t r a t h e r as a q u a n t i t y r e l a t e d t o the whole system o f contact ing par tners

under consideration. I n con t ras t t o ma te r ia l p roper t i es l i k e the e l a s t i c

modulus which can be regarded as a "system-independent" parameter, the adhe-

s ion behaviour o f a mater ia l p a i r i s a s t rong ly "system-dependent" charac-

t e r i s t i c .

I n the discussion o f contact processes so f a r , the contact mechanics

as based on Her tz ian theory and the i n t e r f a c i a l adhesion sur face forces have

been t rea ted separately. An analys is o f the e l a s t i c contact between a smooth

e l a s t i c sphere and a smooth f l a t sur face tak ing i n t o account the e f f e c t o f

i n t e r f a c i a l a t t r a c t i v e adhesion forces was made by Johnson, Kendall and

Roberts (Ref. 4.41). They showed t h a t the area o f contact i s always greater

than t h a t given by c l a s s i c a l Her tz ian theory. This i s obv ious ly due t o a n e t

release o f surface energy r e s u l t i n g from the replacement o f two surfaces by

one s o l i d / s o l i d i n t e r f a c e o f lower surface energy. The change i n sur face

66

S l i p S l i p Number o f

S t ruc tu re plane d i r e c t i o n s l i p systems

FCC

Cu, A l , N i ,

y Fe, ... Pb, Au, Ag,

BCC

W, Mo, aFe,

p brass,. . .

HCP

Cd, Zn, Mg, co, ...

(1 11) 6 x 2 = 1 2

secondary s l i p sys tems :

(111) 12 x 1 12

24 x 1 = 24 (1 11)

(1120) 1 x 3 = 3

(basal s l i p )

Figure 4.10 Observed s l i p systems i n c r y s t a l s .

~

Theoretical

A1 - A1

A1 - AU A1 - CU

A1 - Ag

cu - cu

AU - AU

CU - Ag

Ag - Ag

Ordering b ind ing

energy, ergs/cm21

525

465

455

385

375

345

335

290

Experimental order ing

Table 4.1 Ordering o f adhesive b ind ing energies (Ref. 4.39).

67

I m

s! 1.0 .r -0

L

+J V rc(

K 0 V

m

+J 0.5

energy p e r u n i t area of con tac t ,Ay , may be w r i t t e n as

.

.

where y1 i s t h e sur face energy o f t h e sphere, y 2 o f t h e f l a t and y12 o f

the i n t e r f a c e . The a n a l y s i s shows t h a t t h e r e i s a f i n i t e t e n s i l e f o r c e F*N

r e q u i r e d t o p u l l t he sphere o f f t h e f l a t . The va lue o f F*N i s t h e same

whether o r n o t t h e sur faces a re i n i t i a l l y pressed t o g e t h e r w i t h an e x t e r n a l

f o rce , and i s g i ven by

3 F*,,, = IT r a y

The r e s u l t s o f t h e a n a l y s i s o f Johnson, Kenda l l and Roberts f o r t h e case o f

a rubber / rubber con tac t a r e shown i n F i g u r e 4.11. For s o f t e l a s t i c van de r

Waals s o l i d s , ( r = 22 mm,

Fo r tho rough ly c lean c r y s t a l l i n e s o l i d s where y i s a t l e a s t an o r d e r o f

niagnitude g r e a t e r one would expec t adhesive fo rces , independent o f t h e

j o i n i n g load, o f o r d e r o f 10-2N.

y = 30 mJm-2) t h e adhesion observed i s seve ra l mN.

I 1.5 E v

He r t z t h e o ry , w i t h adhesion

- "aH Her t z theory ,

w i t h o u t adhesion / / /

-1 0 1 2 3 4 Load FN (10-2N)

F igu re 4 .11 H e r t z i a n e l a s t i c c o n t a c t w i t h o u t and w i t h i n t e r f a c i a l adhesion (Re f . 4.41).

68

The ana lys i s i l l u s t r a t e d i n F igu re 4.11 i s v a l i d f o r o p t i c a l l y smooth

r u b b e r - l i k e m a t e r i a l s where o v e r a l l de format ions a r e l a r g e and l o c a l m ic ro-

a s p e r i t i e s a re e a s i l y accommodated. As a c r i t e r i o n f o r t h e i n f l u e n c e o f

su r face roughness on t h e adhesion o f e l a s t i c s o l i d s , F u l l e r and Tabor (Ref.

4.42) have d e f i n e d an "adhesion parameter" g i ven by

where p i s t h e average rad ius o f cu rva tu re o f i n d i v i d u a l a s p e r i t i e s , z t h e

d e v i a t i o n f rom t h e mean he igh t , E t h e reduced e l a s t i c modulus and b y t h e

surface-energy change d e f i n e d above. P h y s i c a l l y , t h e q u a n t i t y i s a

measure o f t h e adhesive fo rce , t h e q u a n t i t y E z3/' pl/' a measure o f t h e

f o r c e exe r ted by t h e a s p e r i t i e s i n pushing t h e sur faces a p a r t . I f 0 i s

smal l , t h i s i m p l i e s t h a t t h e adhesion i s ' d o m i n a n t , i f 0 i s l a r g e t h e asper-

i t i e s dominate and t h e adhesion i s sma l l . I t i s assumed t h a t t h e t r a n s i t i o n

f rom s t r o n g t o weak adhesion accurs i f 0 > l o . Th is corresponds t o su r face

i r r e g u l a r i t i e s o f dimensions z = 1 pm f o r van de r Waals s o l i d s , l i k e rubber,

and z E 5nm f o r ha rd m a t e r i a l s such as diamond. Th is a n a l y s i s shows t h a t

w i th hard e l a s t i c s o l i d s , ve ry smal l su r face i r r e g u l a r i t i e s a re s u f f i c i e n t

t o reduce adhesion t o a ve ry l ow value. I f , on t h e o t h e r hand, the j u n c t i o n s

can deform p l a s t i c a l l y , then adhesion dominat ing over roughness i s more

1 i k e l y t o occur.

I n summary, i n any c o n t a c t s i t u a t i o y t h e combined i n f l u e n c e s of c o n t a c t

mechanics and c o n t a c t phys ics and chemis t ry must be taken i n t o account. The

analyses, performed f o r t h e case o f two s o l i d bodies c o n t a c t i n g under t h e

a c t i o n o f a pure normal l o a d FN, show t h a t t h e f o l l o w i n g main c h a r a c t e r i s t i c s

and processes must be considered:

( I ) Sur face c h a r a c t e r i s t i c s

( a ) Sur face topography

- su r face roughness parameters

- p r o f i l e d i s t r i b u t i o n curve

- p r o f i l e a u t o - c o r r e l a t i o n f u n c t i o n

- s t a t i s t i c a l su r face parameters

( b ) Sur face compos i t ion

- contaminants

- phys i sorbed 1 ayers

- chemi sorbed 1 ayers

69

- oxide layers

- worked layers

(11) Contact formation

( a ) Contact mechanics

- Hertz theory

- apparent and real area of contact

- deformation mode ( p l a s t i c i t y index)

- e las t ic -asper i ty-contact deformation

- plast ic-asperi ty-contact deformation

- van der Waals forces

- meta l l ic bonding

- e f f e c t of o ther short-range forces

- e f f e c t of surface films

- i n t e r f a c i a l s l i p

- generation of e l a s t i c waves

- e l a s t i c recovery

- t r a n s f e r of adherent material

- f r a c t u r e

( b ) Contact physics and chemistry

(111) Contact separat ion

4,3 FRICTION PROCESSES

4,3,1 TANGENTIAL FORCES I N CONTACT PROCESSES

In t h i s sec t ion , the or ig ins and mechanisms of dry f r i c t i o n wi l l be con-

s idered i n order t o explain the d iss ipa t ion processes t h a t occur on the conceptual work plane i n a t r ibo logica l system a s i l l u s t r a t e d in Figure

3.6. Consider as a s t a r t i n g point the s t a t i c contact o f two bodies under

a pure normal force FN on which a tangent ia l force FT is superimposed without causing a macroscopic r e l a t i v e motion between the two bodies. In t h i s case,

the addi t ion o f FT t o FN modifies the i n t e r f a c i a l e l a s t i c - and p l a s t i c - contact-deformation s i t u a t i o n as described in the foregoing sec t ion . There a r e four main aspects t h a t must now be considered:

( a ) ELASTIC STRESSES AND DISPLACEMENTS

Mindlin made a detailed study of the idealized case of e l a s t i c Hertzian

contact under the additional action of a small tangential force (Ref. 4.43).

In the case of a tangential force across a c i rcu lar Hertzian contact area,

i . e . , the case of two spherical bodies in contact, the tangential traction i s everywhere parallel to the direction of the applied force. The contours of constant tangential traction are concentric circles. The magnitude o f the traction rises from one-half the average a t the centre to inf in i ty a t the edge. Obviously, the high traction stresses in some way cause micro-

s l i p between the two contacting materials depending on the shear strength

o f adhesion bonding between the materials in contact. If the resistance against motion i s expressed formally'by the coefficient of f r ic t ion f,

presumably the tangential component of traction cannot exceed the product of the coefficient of f r ic t ion and the normal component of traction. If aH

denotes the radius of the Hertzian contact c i r c l e , i t follows that no s l i p

occurs within a c i rc le of radius

I/ 3 a ' = aH [I-:]

whereas i n t h a t p a r t o'f the Hertzian contact zone i n which the radius i s between a ' and a,, s l i p occurs. The situation i s i l lus t ra ted in Figure 4 .12 .

Figure 4.12 S l ip and no-slip regions o f a Hertzian contact under combined normal and tangential forces.

71

( b ) JUNCTION GROWTH

Consider now t h e p o s s i b i l i t y o f p l a s t i c de format ion o f a s t a t i c c o n t a c t

under t h e a c t i o n o f a normal f o r c e FN and a superimposed smal l t a n g e n t i a l

f o r c e FT. Accord ing t o t h e p l a s t i c i t y t heo ry o f b u l k m a t e r i a l s , i n t h e two-

dimensional case t h e von Mises y i e l d c r i t e r i o n i s g i ven by

p2 t 3 T 2 = py 2 p : normal p ressure

‘I: : shear s t r e s s

py : y i e l d p ressure

I t has been shown i n Sec t i on 4.2 t h a t i n t h e c o n t a c t o f c lean rough m e t a l l i c

sur faces under a pure normal load, p l a s t i c de fo rma t ion o f t h e touch ing as-

p e r i t i e s occurs and adhesive j u n c t i o n s a r e formed. F o r an i d e a l two-dimen-

s i o n a l model o f an i n t e r m e t a l l i c j u n c t i o n , by analogy the y i e l d c r i t e r i o n

may be expected t o have t h e fo rm (Ref . 4 . 4 4 ) :

2 2 p t C T 2 = Po

where C i s a cons tan t w i t h a va lue o f about 10, and po i s t h e s t a t i c c o n t a c t

pressure.

Since

i t f o l l o w s t h a t

which leads t o

Ar = [$ t C .T’ 2 1 1’2 P O

o r

A p l o t of t h i s express ion i s shown i n F i g u r e 4.13.

12

R a t i o

0.1 0.2 0.3

Rat io FT/FN

F igu re 4.13 J u n c t i o n growth under combined normal and t a n g e n t i a l f o rces .

I t can be seen t h a t t h e r e may be a cons ide rab le i nc rease i n the c o n t a c t

area due t o the combined a c t i o n o f FN and FT. The v a l i d i t y o f t h i s r e s u l t s

has been proved exper imen ta l l y f o r c lean meta ls , i . e . , h i g h i n t e r f a c i a l

adhesion bonding. I t i s p o s s i b l e t h a t i n t h i s case t h e r e a l area o f c o n t a c t

Ar inc reases u n t i l i t i s equal t o the nominal geometr ic a rea o f con tac t A,.

I f t h e i n t e r f a c i a l adhesion bonding i s lowered, f o r i ns tance th rough l u b r i -

c a t i o n o f t he sur faces , s i m i l a r j u n c t i o n growth i s observed u n t i l gross

t a n g e n t i a l s l i d i n g occurs as i n d i c a t e d i n F igu re 4.13.

( c ) DISPERSAL OF CONTAMINANTS

Most sur faces under normal atmospher ic c o n d i t i o n s possess a su r face compo-

s i t i o n as shown i n F igu re 4.5. The topmost, i .e. , t h e " o u t e r " su r face l a y e r s

a re formed by contaminants, l i k e ox ides and mois tu re . Through these contami-

nants, t h e shor t - range su r face fo rces e x i s t i n g a t a s o l i d su r face a r e sa-

t u r a t e d under atmospher ic cond i t i ons . I f two sur faces a r e b rough t i n t o con-

t a c t i n the d i r e c t i o n normal t o t h e i r i n t e r f a c e , i n general o n l y (week)

long-range fo rces o f t h e van de r Waals type can a c t adhes ive ly , s ince t h e

( s t r o n g ) shor t - range fo rces a re a l ready s a t u r a t e d and the th i ckness o f t h e

contaminant l a y e r s o f bo th sur faces i s i n genera l l a r g e r than t h e range o f

the shor t - range su r face fo rces . I f , however, a t a n g e n t i a l f o r c e i s super-

imposed the re may be a d i spe rsa l o f t he contaminant f i l m s th rough the com-

b ined a c t i o n o f j u n c t i o n growth and mic roscop ic shear ing o f contaminants.

Consequently, shor t - range fo rces come i n t o a c t i o n and l e a d t o s t r o n g l o c a l

73

adhesive bonds. Fo r meta ls i t has been proved e x p e r i m e n t a l l y t h a t th rough

the super impos i t i on o f t a n g e n t i a l f o r c e s and a r e l a t i v e mo t ion a t t h e i n t e r -

face, adhesion may inc rease more than t e n f o l d .

( d ) MICRODISPLACEMENTS BEFORE SLIDING

It has been observed t h a t when a t a n g e n t i a l f o r c e FT i s a p p l i e d t o a s t a t i c

con tac t , a smal l r e l a t i v e displacement o f about 0 .1 t o 1 pm between t h e com-

ponents i n c o n t a c t i n t h e d i r e c t i o n o f FT occurs almost i ns tan taneous ly

(Ref. 4.45). These mic rod isp lacements b e f o r e gross s l i d i n g a r e i n some cases

r e v e r s i b l e and i n o the rs i r r e v e r s i b l e . T h i s i n d i c a t e s t h a t e l a s t i c o r p l a s t i c

processes on a smal l s c a l e take p lace b e f o r e gross s l i d i n g occurs.

4 , 3 , 2 SLIDING FRICTION

I f , i n a d r y s t a t i c c o n t a c t s i t u a t i o n , t h e l o a d a p p l i e d t a n g e n t i a l t o t h e

c o n t a c t sur face exceeds a c e r t a i n value, gross s l i d i n g between t h e compo-

nents i n c o n t a c t occurs, F i g u r e 4.14. I n t h i s s i t u a t i o n , t h e f o l l o w i n g

macroscopic r u l e s have i n genera l been observed exper imen ta l l y :

( i ) When t a n g e n t i a l mo t ion between two c o n t a c t i n g bod ies occurs, t h e

f r i c t i o n f o r c e FF always a c t s i n a d i r e c t i o n oppos i te t o t h a t o f

t h e re1 a t i ve v e l o c i t y o f t h e sur faces .

( i i ) The f r i c t i o n fo rce FF i s p r o p o r t i o n a

FF = f

Through t h i s r e l a t i o n s h i p i t i s poss

f r i c t i o n

t o t h e normal f o r c e FN

' FN

3 l e t o d e f i n e a c o e f f i c i e n t o f

( i i i ) The f r i c t i o n f o r c e i s independent o f t h e apparent geomet r ic a rea of

con tac t .

These r u l e s , known as t h e "Amontons-Coulomb laws" o f d r y s l i d i n g f r i c t i o n

have been used so f a r as g u i d i n g r u l e s i n eng inee r ing a p p l i c a t i o n s .

74

d i r e c t i o n o f mot ion _cc

/ / / / I / / / / / /

a s p e r i t y

i n t e r a c t i o n s

(see F i g . 4.15)

F igu re 4.14 A s o l i d body i n s l i d i n g mot ion.

In Sec t ion 1.2.1 t h e danger o f m i s i n t e r p r e t a t i o n s of these " laws" was

emphasized. There fore , a phys i ca l p i c t u r e o f t h e mechanisms o f s o l i d f r i c -

t i o n i s needed, f rom which t h e i n f l u e n c i n g f a c t o r s and t h e r e l e v a n t p roper -

t i e s o f t h e s l i d i n g components can be compi led. As exp la ined above, a ge-

ne ra l t rea tment must i n c l u d e b o t h an exp lana t ion o f t h e f o r c e s necessary t o

overcome f r i c t i o n and a phys i ca l p i c t u r e o f t h e processes o f energy d i s s i -

pa t i on , i . e . , t he mechanisms o f t h e t r a n s f o r m a t i o n o f mechanical work t o

o t h e r forms o f energy as descr ibed schemat i ca l l y i n F i g u r e 3.6.

cess wh ich may a l s o be r e l e v a n t t o d r y s l i d i n g f r i c t i o n .

i n any s t a t i c c o n t a c t s i t u a t i o n :

( a ) Two s o l i d su r faces i n c o n t a c t over a nominal geometr ic area A, a r e

a c t u a l l y t ouch ing o n l y i n d i s c r e t e spots, c a l l e d mic ro-contac ts .

( b ) The sum o f t h e mic ro-contac ts forms t h e r e a l a rea o f c o n t a c t Ar which c a r r i e s t h e normal l oad FN.

( c ) Depending on t h e de format ion mode, the f o l l o w i n g r e l a t i o n s between t h e r e a l area o f c o n t a c t A, and t h e normal l o a d F,,, e x i s t :

- e l a s t i c de format ion ( p l a s t i c i t y index JIe 0.6)

To beg in w i t h , l e t us summarize the b a s i c r e s u l t s o f t h e con tac t p ro -

The r e s u l t s o f Sec t i on 4.2 show t h a t t h e f o l l o w i n g p o i n t s a r e r e l e v a n t

FN E : composi te e l a s t i c modulus

- p l a s t i c de format ion ( p l a s t i c i t y index $ 4 1 )

FN

PY A, oc - py : y i e l d p ressure

75

( d ) I n t h e mic ro-contac ts , adhesive j u n c t i o n s a re formed th rough t h e

a c t i o n o f su r face fo rces :

- long-range fo rces , a c t i n g between any combina t ion o f m a t e r i a l s

- sho r t - range fo rces o f m e t a l l i c , i o n i c o r cova len t type , depending

down t o separa t i on o f about Inrn,

on t h e n a t u r e o f t h e m a t e r i a l s i n con tac t , a c t i n g a t separa t i ons

.c lnm.

For the case o f a s l i d i n g con tac t , based on the e x i s t i n g knowledge o f t h e

topography and compos i t ion o f s o l i d sur faces , we may p o s t u l a t e t h e f o l l o w -

i n g m ic roscop ic view o f s l i d i n g f r i c t i o n : f r i c t i o n occurs th rough a s p e r i t y

i n t e r a c t i o n s , i .e., th rough d i s s i p a t i v e processes i n v o l v e d i n t h e j o i n i n g

and separa t i on o f m ic rocon tac ts .

s tage I : e l a s t i c de fo rma t ion

p l a s t i c de fo rma t ion

p lough ing

s tage 11:

adhesion bond ing

s tage 111:

shear ing o f j u n c t i o n s

e l a s t i c recove ry

F i g u r e 4.15 Schematic r e p r e s e n t a t i o n o f a u n i t event i n t h e f r i c t i o n process.

I n t h i s model , the macroscopic f r i c t i o n f o r c e can be expressed as t h e

sum o f mic roscop ic f r i c t i o n fo rces a t t he i n d i v i d u a l mic ro-contac ts , and

the energy d i s s i p a t e d may be expressed as t h e sum o f cor respond ing elemen-

t a r y d i s s i p a t i o n processes. The elementary processes t h a t occur d u r i n g t h e

j o i n i n g and separa t i on o f a m ic ro -con tac t formed between two a s p e r i t i e s

i n t e r p e n e t r a t i n g t o a c e r t a i n depth a re i l l u s t r a t e d schemat i ca l l y i n F i -

gure 4.15.

a mic ro-contac t , t h e f o l l o w i n g main processes a re i nvo l ved :

( i ) e l a s t i c a s p e r i t y de format ion ,

( i i ) p l a s t i c a s p e r i t y de format ion ,

( i i i ) p loughing,

( i v ) shear ing o f adhesive j u n c t i o n s .

Each o f t he p a r t i a l processes i n v o l v e s a t a n g e n t i a l f o r c e necessary t o

ma in ta in the r e l a t i v e mot ion as w e l l as a p a r t i a l process o f energy d i s s i -

pa t i on . K rage lsk i (Ref. 1 .6 ) i n a d e t a i l e d a n a l y s i s s t u d i e d t h e d i f f e r e n t

causes o f f r i c t i o n t a k i n g p lace i n the m ic ro -con tac ts and expressed t h e

t o t a l macroscopic f r i c t i o n f o r c e FF as

Obviously, i n t h e d i f f e r e n t stages o f t h e fo rma t ion and separa t i on o f

where

F1 : r e s i s t a n c e caused by e l a s t i c displacement o f t he m a t e r i a l

F2 : r e s i s t a n c e caused by p l a s t i c displacement

Fg : res i s tance due t o shear ing (p lough ing) o f t he m a t e r i a l

F4 : res i s tance due t o shear ing o f t h e (adhes ive) f i l m

With t h i s model, f rom a phys i ca l p o i n t o f v iew t h e causes o f t he f r i c t i o n

force can be understood q u a l i t a t i v e l y (Ref. 4.46). A q u a n t i t a t i v e ca lcu-

l a t i o n o f f r i c t i o n fo rces or f r i c t i o n c o e f f i c i e n t s i s , however, o n l y poss i -

b l e t o very rough approximat ions under spec ia l s i m p l i f i e d cond i t i ons . Th is

i s due ma in l y t o o u r incomple te knowledge o f t h e su r face p r o p e r t i e s o f

s o l i d s . I n o rde r t o compare t h e i m p l i c a t i o n s o f t h e mic roscop ic model o f

f r i c t i o n w i t h macroscopic exper imenta l besul t s , some es t ima t ions o f t he

magnitude o f the f r i c t i o n c o e f f i c i e n t f o r meta ls i n s l i d i n g con tac t w i l l be

made i n the f o l l o w i n g based on t h e theo ry o f Bowden and Tabor (Ref. 1.4).

It shou ld be emphasized t h a t these can be regarded o n l y as rough approx i -

mat ions.

According t o t h e m ic roscop ic model o f f r i c t i o n , t h e d i f f e r e n t c o n t r i -

b u t i o n s t o f r i c t i o n may be c l a s s i f i e d b r o a d l y i n t o two groups: (a ) deforma-

t i o n processes and ( b ) adhesion processes. I n genera l , t h e processes be-

l o n g i n g t o these two groups a r e n o t independent o f each o t h e r (Ref. 4 .47) .

Under c e r t a i n s p e c i a l cond i t i ons , however, one process may dominate so t h a t

t h e o t h e r c o n t r i b u t i o n s a r e comparat ive smal l and may be neg lec ted t o a

f i r s t approx imat ion . Consider, f o r example, two spec ia l cases o f t h e f r i c -

t i o n o f me ta l s :

( a ) PLOUGHING COMPONENT OF FRICTION

Th is case may be approx imate ly g i ven i f a ve ry hard rough su r face s l i d e s

ove r a s o f t one. The f r i c t i o n a l r e s i s t a n c e i s then m a i n l y caused by t h e

a s p e r i t i e s o f t h e harder su r face p lough ing th rough t h e s o f t e r , and t h e

c o e f f i c i e n t o f f r i c t i o n may be es t ima ted f rom t h e fo rces r e q u i r e d f o r p l a s -

t i c f l o w o f t h e s o f t e r meta l . The normal l o a d FN i s balanced by t h e y i e l d

p ressure p o f t h e metal a c t i n g v i a t h e r e a l a rea o f c o n t a c t Ar: YN

The r e s i s t a n c e FT t o t a n g e n t i a l mot ion i s balanced by t h e y i e l d p ressu re

o f t he meta l a c t i n g o v e r t h e c ross -sec t i ona l a rea o f t h e groove A * pYg g '

Assuming t h a t t he p l a s t i c - y i e l d i n g metal i s i s o t r o p i c , i . e . , pyN = pyT,

t h e " f r i c t i o n c o e f f i c i e n t " i s g i ven by

I n t h i s model t h e va lue o f f i s determined by t h e r a t i o o f t h e areas A / A

depending on t h e a s p e r i t y shape model. Fo r t h e case o f a c o n i c a l i nden te r ,

as i l l u s t r a t e d schemat i ca l l y i n F igu re 4.16, i t f o l l o w s f rom s imp le geomet-

r i c c o n s i d e r a t i o n t h a t

g r s

2 f = - c o t 9 TI;

9 : semiapex ang le o f t h e c o n i c a l i d e n t e r

__t

Ag, \

F i g u r e 4.16 P lough ing component f o r a ha rd c o n i c a l i d e n t e r s l i d i n g ove r a s o f t meta l .

lo - t \

Normal su r face a s p e r i t i e s seldom have an e f f e c t i v e s lope exceeding 5' o r 6'

( i . e . , q) = 85' o r 84'). I t f o l l o w s t h a t

f = 0.05

Th is va lue may be regarded, however, o n l y as a l ower f r i c t i o n - c o e f f i c i e n t

l i m i t f o r t he de format ion component o f f r i c t i o n due t o t h e neg lec t i ons

descr ibed above and t h e exper imen ta l l y observed f a c t t h a t a p i l e - u p of

m a t e r i a l ahead o f t h e groov ing p a t h ( " b o u r r e l e t f r o n t a l " ) occurs i n most

cases o f p l a s t i c de format ions d u r i n g s l i d i n g (Ref . 4.48).

(b ) ADHESION COMPONENT OF FRICTION

Th is case may be approx imate ly g i ven f o r a s l i d i n g con tac t o f two r e l a t i -

v e l y s o f t c lean metals. Depending on t h e degree o f i n t e r p e n e t r a t i o n o f

a s p e r i t i e s and on t h e su r face composi t ion, adhesion bonding i n t h e mic ro-

con tac ts occurs. I f s l i d i n g i s t o take p lace , t h e f r i c t i o n f o r c e i s needed

t o shear the weakest t a n g e n t i a l p lanes a t t he areas o f a c t u a l con tac t . I f

t h e mean shear s t r e n g t h o f t h e weakest planes a t t he con tac t areas i s de-

no ted by z s (assumed t o be o f equal va lue i n a l l m ic ro -con tac ts ) and t h e i r

t o t a l a rea i s assumed t o be approx imate ly equal t o t h e r e a l area o f con tac t ,

I9

n e g l e c t i n g the e f f e c t o f j u n c t i o n growth, we may w r i t e

(Fo r an ex tens ion o f t h i s approx imat ion see Ref. 4 .49 . ) S ince f o r t h e p l a s -

t i c c o n t a c t c o n d i t i o n ( p l a s t i c i t y index (0 > 1) t h e r e a l area o f c o n t a c t i s

g i ven by

py : y i e l d p ressure

i t f o l l o w s t h a t t h e c o e f f i c i e n t o f f r i c t i o n i s g i ven by

FF - t s f = - _ -

FN py

For meta ls which a re n o t work-hardened, t h e shear s t r e n g t h t S o f t h e i n t e r -

face i s approx imate ly equal t o the c r i t i c a l shear s t r e s s o f t h e meta l t . The y i e l d p ressure p

t h a t

has been shown t o be approx imate ly 5 t . I t f o l l o w s Y

f z 0.2

Fu r the r , t h i s va lue can o n l y be regarded as a lower f r i c t i o n - c o e f f i c i e n t

l i m i t f o r t h e adhesion component o f f r i c t i o n o f ( t e c h n i c a l l y ) c lean meta ls ,

s ince f o r r e a l l y c lean meta ls w i t h t h e h e l p o f j u n c t i o n growth, f r i c t i o n

c o e f f i c i e n t s as h i g h as f z 40 t o 100 have been measured. On t h e o t h e r

hand, i t i s p o s s i b l e t o l ower t h e f r i c t i o n c o e f f i c i e n t down t o va lues o f

f = 0.02 w i t h boundary l u b r i c a n t s .

From t h e m ic roscop ic model o f f r i c t i o n and t h e s imp le e s t i m a t i o n s

based on t h i s model, i t i s p o s s i b l e t o v e r i f y t h e fo rm o f t h e e m p i r i c a l

Amontons-Coulomb law o f s l i d i n g f r i c t i o n . I t has been desc r ibed t h a t t h e

f r i c t i o n processes occur w i t h i n t h e r e a l a rea o f c o n t a c t Ar, and t h a t f o r

bo th the de fo rma t ion component and the adhesion component

FF oc Ar.

The r e s u l t s o f t h e c o n t a c t mechanics o f rough su r faces f o r bo th e l a s t i c -

80

and p las t i c - con tac t condi t ions show t h a t

I f i t i s assumed t h a t these r e s u l t s a lso hold f o r s l i d i n g contact condit ions,

i t fo l lows t h a t

Thus, the f r i c t i o n fo rce i s propor t ional t o the load and independent o f t he

geometric contact area, i n agreement w i t h the empir ica l Amontons-Coulomb law

o f s l i d i n g f r i c t i o n .

However, t he microscopic model o f f r i c t i o n as i l l u s t r a t e d i n F igure

4.15 i nd i ca tes t h a t f r i c t i o n i s n o t on l y a composite process b u t i s a lso

sens i t i ve t o changes i n the deformation and adhesion c h a r a c t e r i s t i c s o f

the contact ing surfaces. Depending on the operat ing condi t ions and the a t -

mospheric environment, i.e., t he " t h i r d body", i n t e r a c t i n g w i t h the two

s l i d i n g partners , i n general, changes i n the surface topography as we l l as

i n the surface composition and the surface s t rength p roper t i es w i l l take

place, see Section 5.2. These changes may in f l uence the f r i c t i o n c o e f f i c i e n t

markedly, see Section 8.5.2.

Thus, as discussed already i n Section 4.2 f o r the s t a t i c contact s i t u -

at ion, there are many proper t ies o f ma te r ia l s which i n f l uence the nature o f

the i n t e r f a c e i n s l i d i n g f r i c t i o n . For example, f o r metals these inc lude

surface o r ien ta t i on , l a t t i c e spacing, g ra in boundaries, c r y s t a l s t ruc tu re ,

nature o f adhesion bond character and a l l o y i n g elements. The e f f e c t o f

a l l o y i n g elements can a1 t e r i n t e r f a c i a l behaviour by segregation t o the

surface o f metals o r by a l t e r i n g bu lk p roper t i es through c r y s t a l t r a n s f o r -

mation k i n e t i c s (Ref. 4.50). Since i t i s n o t poss ib le t o deal w i t h the

f r i c t i o n behaviour o f the various ma te r ia l s w i t h i n the scope o f t h i s volume,

t h i s sect ion may be closed bes t i n quot ing t h e summarizing remarks from the

recent exce l l en t review o f D. Tabor on the general mechanisms o f s l i d i n g

f r i c t i o n (Ref. 4.51):

"The f r i c t i o n between unlubr icated s o l i d s i s due t o two main factors.

The f i r s t i s the adhesion occurr ing a t the regions o f r e a l contact. The

second a r i ses i f the a s p e r i t i e s on a hard surface produce grooving o r cu t -

t i n g i n the other. With metals the ploughing ac t i on invo lves p l a s t i c d i s -

81

placement, w i t h b r i t t l e s o l i d s some c r a c k i n g o r f ragmenta t ion , w i t h rubbers

and polymers h y s t e r e s i s losses . Other f a c t o r s may a l s o p l a y a p a r t i n t h e

f r i c t i o n a l process, b u t except i n spec ia l c i rcumstances these a r e g e n e r a l l y

o f o n l y t e r t i a r y s i g n i f i c a n c e .

h i g h c o e f f i c i e n t s o f f r i c t i o n , On the o t h e r hand, b r i t t l e s o l i d s w i l l g i v e

r e s t r i c t e d j u n c t i o n growth and lower c o e f f i c i e n t s o f f r i c t i o n . Again, s o l i d s

wi th w e l l - d e f i n e d a n i s o t r o p y may show a n i s o t r o p i c f r i c t i o n a l p r o p e r t i e s .

Th is i s most marked w i t h l a m e l l a r s o l i d s t h a t a r e o f t e n low f r i c t i o n ma-

t e r i a l s , though t h i s i s by no means always t h e case. W i th v i s c o e l a s t i c

s o l i d s the de fo rma t ion p r o p e r t i e s a r e r a t e - and temperature-dependent, and

the re i s a cor respond ing v a r i a t i o n o f f r i c t i o n w i t h s l i d i n g speed and tem-

pera t u r e .

l a r g e s t o v e r a l l i n f l u e n c e on f r i c t i o n i s t h e c l e a n l i n e s s o f t h e sur faces .

A smal l t r a c e o f oxygen o r some o t h e r contaminant can r a d i c a l l y reduce t h e

adhesion and f r i c t i o n . I t i s p robab le t h a t i n p r a c t i c a l a f f a i r s i n v o l v i n g

the s l i d i n g o f u n l u b r i c a t e d metals, atmospher ic contaminat ion i s t h e main

f a c t o r respons ib le f o r reduc ing f r i c t i o n and wear and f o r p r e v e n t i n g t o t a l

se izure . W i th polymers and b r i t t l e m a t e r i a l s t h e s i t u a t i o n i s n o t as c l e a r l y

de f ined, b u t , i n genera l , su r face con tamina t ion has l e s s e f f e c t than w i t h

meta ls " .

S o l i d s t h a t deform e a s i l y and i s o t r o p i c a l l y w i l l tend t o g i v e very

A l though de fo rma t ion p r o p e r t i e s a re impor tan t , t he f a c t o r t h a t has t h e

I n a d d i t i o n t o t h e d i scuss ion o f t h e f r i c t i o n f o r c e , i . e . , t h e r e -

s i s tance t o s l i d i n g mot ion as d iscussed i n t h i s s e c t i o n , t h e ques t i on on

the f r i c t i o n a l energy d i s s i p a t i o n must be s tud ied . Be fo re d i scuss ing t h e

f r i c t i o n - i n d u c e d energy d i s s i p a t i o n processes (see Sec t ion 4 .3 .4 ) , t h e me-

chanisms o f r o l l i n g f r i c t i o n f o r c e , i . e . t h e causes o f t h e r e s i s t a n c e t o

r o l l i n g mo t ion a r e reviewed i n t h e n e x t sec t i on .

4 , 3 , 3 ROLLING FRICTION

R o l l i n g f r i c t i o n , a l t hough i n general much s m a l l e r than s l i d i n g f r i c t i o n ,

i s a l s o a ve ry complex phenomenon because o f i t s dependence upon so many

fac to rs (Ref. 4.52). C l e a r l y , t h e c o n t a c t processes, i . e . , t h e c o n t a c t me-

chanics and c o n t a c t phys i cs and chemis t ry , as d iscussed i n Sec t i on 4.2, a re

adequately v a l i d i n r o l l i n g - c o n t a c t s i t u a t i o n s . The c o n t a c t de fo rma t ion i n

steady r o l l i n g i s conven ien t l y approached f rom t h e E u l e r i a n p o i n t o f view.

82

The nominal p o i n t o f con tac t i s taken as t h e o r i g i n o f coord ina tes ; m a t e r i a l

o f b o t h s o l i d s " f l o w s " s t e a d i l y through a t i m e - i n v a r i a n t s t r a i n f i e l d i n

t h e c o n t a c t reg ion .

f r i c t i o n , i t i s obvious t h a t t h e main reasons f o r s l i d i n g f r i c t i o n - l i k e

p lough ing and shear ing o f adhesive j u n c t i o n s - a re n o t met i n a r o l l i n g

s i t u a t i o n . There fore , t h e mic roscop ic model o f s l i d i n g f r i c t i o n cannot be

a p p l i e d i n o rde r t o e x p l a i n t h e occurrence o f r e s i s t a n c e t o r o l l i n g , so

t h a t o t h e r exp lana t ions a re needed. As i n t h e case o f s l i d i n g , any model of

r o l l i n g f r i c t i o n must e x p l a i n bo th t h e r o l l i n g f r i c t i o n f o r c e and the

r o l l i n g - f r i c t i o n energy d i s s i p a t i o n .

f o rces a re t ransmi t ted , e.g., t h e d r i v i n g wheels o f a locomot ive , o r i n

another type where smal l t a n g e n t i a l f o rces a r e t ransmi t ted , o f ten c a l l e d

" f r e e r o l l i n g " . Consider, as a s t a r t i n g p o i n t a H e r t z i a n con tac t . I f a

to rque i s i n t roduced which causes a r o l l i f l g mot ion, then i n a d d i t i o n t o t h e

H e r t z i a n normal s t resses , t a n g e n t i a l s t resses occur, see M i n d l i n ' s t heo ry ,

Sec t i on 4.3.1. T h i s r e s u l t s i n t h e d i v i s i o n o f t h e con tac t area i n t o a

reg ion o f m i c r o - s l i d i n g , and reg ions o f adhesion w i t h i n which the surfaces

r o l l w i t h o u t r e l a t i v e ( s l i d i n g ) mot ion.

be l i s t e d :

(a ) m i c r o - s l i p ( i - e . , m i c r o - s l i d i n g )

( b ) e l a s t i c h y s t e r e s i s

( c ) p l a s t i c de format ion

( d ) adhesion e f f e c t s

I n t h e fo l l ow ing , these d i f f e r e n t components o f f r e e - r o l l i n g f r i c t i o n w i l l be discussed i n b r i e f .

Comparing t h e i n t e r f a c i a l k inemat ics and s t r e s s c o n d i t i o n s o f s l i d i n g

R o l l i n g f r i c t i o n may be c l a s s i f i e d i n t o a type, where l a r g e t a n g e n t i a l

As main c o n t r i b u t i o n s t o r o l l i n g res j s tance , t he f o l l o w i n g e f f e c t s can

( a ) MICRO-SLIP EFFECTS

I n t h e t h e o r i e s o f m i c r o - s l i p , d i f f e r e n t cases a re d i s t i n g u i s h e d i n t h e

l i t e r a t u r e , t he most impor tan t o f which are :

( i ) Reynolds s l i p (Ref. 4 .53)

Consider a H e r t z i a n c o n t a c t o f two bod ies hav ing d i f f e r e n t e l a s t i c

cons tan ts . I f t h e two bodies r o l l f r e e l y toge the r t h e pressure which

a c t s on each g i ves r i s e , i n genera l , t o unequal t a n g e n t i a l d i sp lace -

ments o f t h e sur faces l e a d i n g t o i n t e r f a c i a l s l i p processes.

83

( i i ) Heathcote s l i p (Ref . 4.54)

Consider a r o l l i n g c o n t a c t where t h e r o l l i n g element i s a b a l l which

r o l l s i n s i d e a grooved t r a c k . I n t h i s case the p r o f i l e s may conform

c l o s e l y i n t h e t ransve rse d i r e c t i o n t o t h e t r a c k on which they r o l l .

Due t o su r face p o i n t s l y i n g a t app rec iab l y d i f f e r e n t d i s tances f rom

t h e a x i s o f r o t a t i o n , t a n g e n t i a l t r a c t i o n s a r e i n t roduced and mic ro-

s l i p e f f e c t s occur .

( i i i ) Ca r te r -Por i t sky -Fopp l s l i p (Refs. 4.55. 4.56, 4.57)

Fo r t h e two-dimensional case (e.g. , two c y l i n d e r s r o l l i n g on each

o t h e r ) w i t h a t a n g e n t i a l f o r c e i n the d i r e c t i o n o f r o l l i n g , t h e

m i c r o - s l i p a rea c o u l d be c a l c u l a t e d . T h i s work l e d t o t h e impor tan t

conc lus ion t h a t , i n r o l l i n g ,

l e a d i n g edge o f t he c o n t a c t area; i n c o n t r a s t t o t h e s t a t i c problem

where t h e adhesion zone i s c e n t r a l l y p laced, see F i g u r e 4.17.

t he adhesion zone i s ad jacen t t o the

- d r i v i n g

to rque

sl . s l i p

F igu re 4.17 S l i p and n o - s l i p reg ions i n a r o l l i n g con tac t .

Tabor s t u d i e d e x p e r i m e n t a l l y t he s l i p e f f e c t s o f t h e Reynolds and Heathcote

type u s i n g s t e e l b a l l s r o l l i n g i n grooved rubber t r a c k s (Re f . 4.58). He

showed t h a t un less t h e r e i s a h i g h degree o f geomet r ica l con fo rm i t y , bo th

m i c r o - s l i p e f f e c t s c o n t r i b u t e o n l y ve ry l i t t l e t o t h e observed r o l l i n g -

f r i c t i o n fo rce . Recent ly i t was shown e x p e r i m e n t a l l y t h a t above a c r i t i c a l

va lue o f t h e r a t i o b a l l r a d i u s rg t o groove r a d i u s rG ( r g / r G > 0.8 say) ,

r o l l i n g f r i c t i o n i s p r i m a r i l y due t o a s l i d i n g mechanism (Ref . 4 .59) . I n

genera?, however, accord ing t o Bowden and Tabor, r o l l i n g f r i c t i o n cannot be

t r a c e d back t o s l i d i n g f r i c t i o n v i a t h e e f f e c t o f m i c r o - s l i p s ince t h e

r o l l i n g - f r i c t i o n c o e f f i c i e n t i s n o t reduced by l u b r i c a t i o n as i s t h e case

84

f o r t h e s l i d i n g f r i c t i o n c o e f f i c i e n t . These exper iments i n d i c a t e t h a t

m i c r o - s l i p may c o n t r i b u t e o n l y ve ry l i t t l e t o the r o l l i n g - f r i c t i o n coef -

f i c i e n t . On t h e o t h e r hand, i t i s g e n e r a l l y recogn ized t h a t t h e ex i s tence

o f f r i c t i o n fo rces a t t h e i n t e r f a c e between r o l l i n g e l a s t i c bod ies r e s u l t s

i n t h e d i v i s i o n o f t h e con tac t area i n t o reg ions o f m i c r o - s l i p , and reg ions

w i t h i n t h e sur faces r o l l w i t h o u t r e l a t i v e mot ion . Obviously, these e f f e c t s

have impor tan t eng inee r ing i m p l i c a t i o n s f o r t h e t ransmiss ion o f mechanical

work through a r o l l i n g con tac t , as i n a f r i c t i o n d r i v e f o r example.

( b ) ELASTIC HYSTERESIS

The e l a s t i c h y s t e r e s i s theory o f r o l l i n g f r i c t i o n , proposed i n 1952 by

Tabor (Ref. 4.60), assumes t h a t t h e r o l l i n g r e s i s t a n c e i s due t o the e l a s -

t i c h y s t e r e s i s losses i n the m a t e r i a l o f t h e t r a c k . I n Sec t i on 4.2.1 i t has

been shown t h a t i n t h e case o f an i d e a l H e r t z i a n contac t , a c e r t a i n amount

o f energy i s needed t o b u i l d up the con tac t zone. For t h e fo rma t ion o f an

e l a s t i c a l l y deformed r o l l i n g t r a c k a c e r t a i n mechanical power i s needed. I n

the de format ion process t h e sur faces undergo compl ica ted combined compres-

s ions and t o r s i o n s . The e l a s t i c de format ion energy i s recovered ma in l y i n

the con tac t re lease. As a consequence o f r e l a x a t i o n e f f e c t s , however, t h e

re leased fo rces may be sma l le r than t h e p rev ious ones; t h e d i f f e r e n c e may

be i n t e r p r e t e d as r o l l i n g - f r i c t i o n loss. The e l a s t i c h y s t e r e s i s l osses o f m a t e r i a l s , be ing r e l a t e d t o t h e

damping and r e l a x a t i o n p r o p e r t i e s o f t he m a t e r i a l s , a r e obv ious l y more

pronounced f o r v i s c o e l a s t i c m a t e r i a l s than f o r meta ls .

c o e f f i c i e n t can be r e l a t e d t o t h e r e l a x a t i o n t i m e ( o r t he r e l a x a t i o n spec-

t rum) o f t h e m a t e r i a l . Represent ing a v i s c o e l a s t i c m a t e r i a l by a s e r i e s o f

para1 l e l l i n e a r Maxwell elements which undergo compression and recovery

d u r i n g r o l l i n g , i t f o l l o w s t h a t i n a s imp le model a t a c e r t a i n r o l l i n g ve-

l o c i t y , which corresponds t o t h e r e t a r d a t i o n t ime, t h e r o l l i n g - f r i c t i o n

c o e f f i c i e n t e x h i b i t s a maximum (Ref . 4.61).

t he t r a i l i n g s i d e o f t he con tac t s u f f i c i e n t l y q u i c k l y t o m a i n t a i n a f a i r l y

symmetr ical p ressure d i s t r i b u t i o n , so t h a t t h e r o l l i n g r e s i s t a n c e w i l l be

smal l . A t h i g h r o l l i n g v e l o c i t i e s t h e m a t e r i a l w i l l n o t recover s u f f i c i e n t -

l y q u i c k l y t o even make con tac t on t h e t r a i l i n g s i d e . The inc rease o f p res-

sure asymmetries w i t h i n c r e a s i n g r o l l i n g v e l o c i t i e s have been checked ex-

p e r i m e n t a l l y w i t h o p t o - e l a s t i c techniques (Ref . 4.62).

I t has been found f o r v i s c o e l a s t i c m a t e r i a l s t h a t t h e r o l l i n g - f r i c t i o n

A t low r o l l i n g v e l o c i t i e s t h e v i s c o e l a s t i c m a t e r i a l w i l l recover a t

85

( c ) PLASTIC DEFORMATION

I t i s w e l l known t h a t i f i n a r o l l i n g c o n t a c t o f m e t a l l i c bod ies t h e con-

t a c t p ressure exceeds a c e r t a i n value, gross y i e l d i n g w i l l occur . Fo r f r e e l y

r o l l i n g c y l i n d e r s y i e l d occurs f i r s t a t a p o i n t beneath t h e su r face when

where pH i s t h e maximum H e r t z p ressure and p

m a t e r i a l i n s imp le shear. I n t h i s case energy i s needed t o fo rm p l a s t i c de-

formed r o l l i n g t r a c k .

An exac t a n a l y s i s o f t h e p l a s t i c de fo rma t ion processes i n t h e r o l l i n g

o f a b a l l over a p lane i s very compl icated. An approximate s o l u t i o n i s due

t o Eldredge and Tabor (Ref, 4.63). They observed t h a t i n t h e f i r s t t r a v e r s a l

a p l a s t i c deformed r o l l i n g t r a c k i s formed, and found f o r t h e r o l l i n g - f r i c -

t i o n f o r c e an e m p i r i c a l express ion o f t h e fo rm

i s t h e y i e l d s t r e s s o f t h e Y

2/ 3 FN : normal l o a d

FFoc 7 r : b a l l r a d i u s FN

They exp la ined t h i s r e l a t i o n by assuming t h a t r o l l i n g r e s i s t a n c e i s m a i n l y

due t o t h e p l a s t i c de format ion i n f r o n t o f t h e r o l l i n g b a l l . Under w e l l -

de f i ned m e t a l l o g r a p h i c c o n d i t i o n s , i . e . , i n t h e case o f r o l l i n g de fo rma t ion

o f metal s i n g l e c r y s t a l s , t h e p l a s t i c de format ions can be exp la ined on t h e

b a s i s o f c r y s t a l l o g r a p h i c data, such as c r y s t a l l o g r a p h i c o r i e n t a t i o n and

s l i p systems (Ref . 4 .64) .

does n o t h o l d (Ref. 4.65). Dur ing the f i r s t c o n t a c t c y c l e t h e su r face ma-

t e r i a l i s p l a s t i c a l l y compressed and r e s i d u a l compressive s t resses a c t i n g

p a r a l l e l t o t h e su r face a re in t roduced. Dur ing subsequent r o l l i n g c y c l e s

t h e m a t e r i a l i s s u b j e c t t o t h e combined a c t i o n o f r e s i d u a l and c o n t a c t

s t resses , F u r t h e r y i e l d i n g i s l e s s l i k e l y and a s teady -s ta te may be reached

i n which the m a t e r i a l i s no l o n g e r s t ressed beyond i t s e l a s t i c l i m i t . T h i s

process i s known as "shakedown" and t h e maximum l o a d f o r which i t occurs

w i l l be c a l l e d t h e shakedown l i m i t , g i ven i n pure r o l l i n g by

I n repeated r o l l i n g - c o n t a c t cyc les , however, t h e above y i e l d c r i t e r i o n

P = 4Py

86

I f r o l l i n g cy l i nde rs are subjected t o loads i n excess o f the shakedown

l i m i t a new type o f p l a s t i c deformation occurs. This mode o f p l a s t i c defor-

mation i n r o l l i n g contact was f i r s t observed by Crook (Ref. 4.66) and stud-

i e d experimental ly by Hamilton (Ref. 4.61) and t h e o r e t i c a l l y by Merwin and

Johnson (Ref. 4.68). I t consis ts o f forward shearing o f the surface o f each

c y l i n d e r r e l a t i v e t o i t s core. The deformation i s cumulative i n the sense

t h a t an equal increment o f p l a s t i c s t r a i n i s acquired w i t h each revo lu t i on ,

It fo l l ows that , a t loads above the shakedown l i m i t , continuous and cumula-

t i v e p l a s t i c deformation i s observed, whereas a t loads below it, even though

some y i e l d i n g i s caused i n i t j a l l y , a f t e r a few t r ave rsa l s the system shakes

down t o an e l a s t i c cyc le o f s t ress. Accordingly, the f r i c t i o n mechanism i s changed.

(d) ADHESION EFFECTS

According t o Section 4.2.2, i n r o l l i n g - c o n t a c t condi t ions surface forces

may a c t i n the i n t e r f a c e between the r o l l i n g bodies. Comparing the j o i n i n g

and separation o f surface elements i n r o l l i n g contacts and s l i d i n g contacts

some important d i f f e rences should be noted. Due t o the d i f f e rences i n k ine-

matics, i n r o l l i n g contact the surface elements approach and separate i n a

d i r e c t i o n "normal" t o the i n t e r f a c e r a t h e r than i n a tangent ia l d i r e c t i o n .

Therefore, as described i n Section 4.3.1, j u n c t i o n growth and d ispersa l o f

surface contaminants i s u n l i k e l y i n the main p a r t o f the contact area. Con-

sequently, a t the regions w i t h i n the r o l l i n g - c o n t a c t i n t e r f a c e where no r e - l a t i v e motion i n a tangent ia l d i r e c t i o n occurs, adhesion forces may be main-

l y o f the (weak) van der Waals type. Short-range forces such as s t rong me-

t a l l i c bonds may a c t on l y i n micro-contacts w i t h i n the m ic ro -s l i p area. I f

adhesion bonds are formed they are separated a t the t r a i l i n g end o f the

r o l l i n g contact i n tens ion r a t h e r than i n shear as i n a s l i d i n g contact.

Therefore, i n general the adhesion component o f r o l l i n g f r i c t i o n may be

only a small p o r t i o n o f the f r i c t i o n resis;tance. For the r o l l i n g o f metals

under s p e c i f i c experimental s i t ua t i ons , however (e.g., d i f f e r e n t t h i n me-

t a l l i c layers on hard b a l l s ) an adhesion component can nevertheless be the

dominant f a c t o r i n determining the order o f r o l l i n g - f r i c t i o n c o e f f i c i e n t s

f o r d i f f e r e n t metal p a i r s (Ref. 4.69).

f l a t has been successfu l ly t rea ted as an adhesive j o i n t through which two

cracks propagate a t the same speed, one crack continuously opening t o break

the i n t e r f a c i a l j o i n t and the o the r c los ing t o reform i t (4.70). see F igure

Also the r o l l i n g contact between a glass c y l i n d e r and a smooth rubber

87

4.18. R o l l i n g f r i c t i o n on t h i s b a s i s i s t h e consequence o f adhesive h y s t e r -

e s i s - t h e energy l o s s assoc ia ted w i t h fo rm ing and b reak ing an adhesive

bond.

adhesive j o i n t

F i g u r e 4.18 The c o n t a c t between a r i g i d c y l i n d e r and an e l a s t i c p lane cons idered as an adhesive j o i n t c o n t a i n i n g two c racks .

Another t ype o f adhesion theo ry f o r r o l l i n g f r i c t i o n was proposed by Der ja -

g u i n and Smilga (Ref. 4.71). Accord ing t o t h i s theory , c o n t a c t p a r t n e r s o f

d i f f e r e n t e l e c t r o n i c a f f i n i t y undergo an e l e c t r o - s t a t i c charg ing . Dur ing

r o l l i n g t h e r e i s a f l o w a charge l e a d i n g t o energy d i s s i p a t i o n .

The d i scuss ion o f t he cause o f t h e r o l l i n g f r i c t i o n r e s i s t a n c e shows

t h a t r o l l i n g f r i c t i o n i s a l s o a complex composi te process de termined by a

coup le o f p r o p e r t i e s o f t h e r o l l i n g - c o n t a c t p a r t n e r s and o p e r a t i n g v a r i a b l e s .

I n s p e c i a l cases, i .e . , under s p e c i f i c exper imenta l s i t u a t i o n s , i t i s pos-

s i b l e f o r one mechanism t o predominate. I t may then be p e r m i t t e d t o r e l a t e

t h e r o l l i n g - f r i c t i o n d a t a w i th s p e c i f i c p r o p e r t i e s o f t h e r o l l i n g pa r tne rs .

I n t h e genera l case, however, t h e d i f f e r e n t mechanisms a re superimposed.

Therefore, a l l i n f l u e n c i n g parameters must be taken i n t o account sys temat i -

c a l l y on c o n s i d e r i n g t h e whole process o f energy t ransmiss ions and energy

d i s s i p a t i o n s .

4 , 3 , 4 ENERGY TRANSMISSION AND ENERGY DISSIPATION

Having d iscussed t h e main f r i c t i o n processes, i t i s now p o s s i b l e t o complete

t h e genera l framework o f t h e processes on t h e conceptual "work p lane" o f a

t r ibo-mechan ica l system (see Sec t ion 3 .4 .2 ) . Accord ing t o F i g u r e 3.6, t h e

88

i n p u t work o f a tribo-mechanical system can on ly be p a r t l y used as use-

output; some p a r t o f the work i s e i t h e r s tored w i t h i n the system o r emi t ted

as l o s s i n t o the environment o r t rans fe r red t o the thermal plane.

It was explained above (see Section 4.1) t h a t a transmission o f work

througH a mechanical system can be obtained on ly through processes o f e l a s t i c

deformation e i t h e r o f a bu lk machine element, l i k e the s h a f t o f a s l i d i n g

bearing, o r through the i n t e r f a c e o f two contact ing machine elements, as i n

the case o f contact ing gear-teeth. These e l a s t i c deformation processes a re

reve rs ib le . I n i dea l i zed cases, the transmission o f work through a mechanical

system can be ca l cu la ted o r est imated using conventional techniques o f the

mechanics o f s o l i d bodies.

mechanical system are, o f course, e s s e n t i a l l y i r r e v e r s i b l e . Since they are

the u l t i m a t e o r i g i n o f f r i c t i o n , these processes w i l l be discussed i n the

f o l l o w i n g i n order t o gain a phys ica l p i c t u r e o f the e f f e c t s t h a t take p a r t

i n the d i s s i p a t i o n o f mechanical energy i n a tribo-mechanical system. Owing

t o the great complexity o f these i r r e v e r s i b l e processes i t i s on ly poss ib le

so f a r t o o u t l i n e a q u a l i t a t i v e p i c t u r e o f t he main features o f these pro-

cesses.

mechanical system can be fo rma l l y d iv ided i n t o three phases:

I . I n t roduc t i on o f work i n t o the contact zone

-formation o f r e a l area o f contact

11. Transformation o f work w i t h i n the contact zone

--c e l as t i c de f o rma t i on

- p l a s t i c deformation

-adhesion

111. D iss ipa t i on o f energy

The processes by which mechanical work i s n o t t ransmi t ted through a

The whole course o f the " l oss " process o f mechanical energy i n a t r i b o -

(a) Storage

-generation o f p o i n t defects and d i s loca t i ons

- s t ra in energy storage

-phonons (acoust ic waves, sound)

--c photons (tri bo-1 umi nescence)

-electrons (exo-electrons, Kramer e f f e c t )

-generation o f heat and entropy

(b) Emission

(c) Transformation t o thermal plane

89

Phases ( I ) and (11 ) have been descr ibed i n some d e t a i l i n t h e f o r e -

go ing s e c t i o n i n connect ion w i t h the d i scuss ion o f f r i c t i o n fo rces . I n t h e

f o l l o w i n g , t h e main processes o f t he d i s s i p a t i o n phase (111) w i l l be con-

s idered .

( a ) STORAGE OF ENERGY

I n t h e m idd le o f t h e 1950 's i t became p o s s i b l e t o s tudy t h e mo lecu la r a r r a y

o f c r y s t a l l i n e bod ies and the d i s l o c a t i o n s and i m p e r f e c t i o n s i n t h i s a r r a y

by u s i n g o f t h e Moi re techn ique i n c o n j u n c t i o n w i t h an e l e c t r o n microscope.

Since on one hand, the p l a s t i c de format ion and shear ing o f s o l i d s i s governed

by imper fec t i ons and d i s l o c a t i o n s and, on t h e o t h e r hand, most f r i c t i o n p ro -

cesses i n v o l v e p l a s t i c de format ion processes, i t appeared obvious t o r e l a t e

t h e f r i c t i o n process d i r e c t l y t o t h e d i s l o c a t i o n e f f e c t s (4 .72) . I n 1965

Kos te tsk i and Nazarenko t r i e d t o e x p l a i n t h e Coulomb-Amontons law o f s l i d i n g

f r i c t i o n th rough a r e l a t i o n between normal f o rces , f r i c t i o n f o r c e s and the

d i s l o c a t i o n s t r u c t u r e o f t h e s o l i d s (Ref. 4.73). They ob ta ined e x p e r i m e n t a l l y

f o r t h e s l i d i n g o f armco i r o n p a r a l l e l curves f o r t h e i nc rease o f f r i c t i o n

f o r c e and the l o g a r i t h m o f d i s l o c a t i o n d e n s i t y w i t h i n c r e a s i n g normal l o a d

as shown i n F i g u r e 4.19. I t has now been w e l l e s t a b l i s h e d th rough d i r e c t ob-

s e r v a t i o n s w i t h the t ransmiss ion e l e c t r o n microscope t h a t i n s l i d i n g c o n t a c t

o f meta ls d i s l o c a t i o n s a re generated (Ref . 4.74).

' \ N = f ( FN )

200

100 60 20

8

4

h

N

I I I I I I 2 4 6 8 1 0

Load FN (kN)

F igu re 4.19 F r i c t i o n f o r c e and d i s l o c a t i o n d e n s i t y (Ref . 4.73).

From t h e theo ry o f d i s l o c a t i o n s i t f o l l o w s t h a t t h e work p e r u n i t l e n g t h t o

c rea te a d i s l o c a t i o n i n an i s o t r o p i c und is tu rbed medium i s g i ven by (Ref. 4.75)

90

rl

r O I n - Gb2

A E S = =

(edge d i s l o c a t i o n )

(screw d i s l o c a t i o n )

where G : shear modulus

b : Burgers v e c t o r

rl : core r a d i u s

ro : rad ius o f i n f l u e n c e

v : Poisson number

As an example, w i th the da ta o f copper

(G = 4 * 10 N/m , V = 0.34; b = 2.5 - 10-lom; r = lO-’m; rl = lO-‘m) 10 2. 0

i t f o l l o w s t h a t

A Ee = 4.8 . lo - ’ Jm-I

I f t h i s va lue i s compared w i t h t h e f r i c t i o n a l energy measured under e x p e r i -

mental cond i t i ons which a re comparable w i t h t h e c o n d i t i o n s o f t h e est ima-

t i o n o f AEe, i t was found t h a t t h e s t o r e d e l a s t i c energy i n a c o n d i t i o n

o f i n c i p i e n t p l a s t i c i t y can o n l y account f o r l e s s than 1% o f t h e energy

expended i n f r i c t i o n (Ref. 4.76). A s i m i l a r r e s u l t was a l s o found i n cond i -

t i o n s o f more severe p l a s t i c - d e f o r m a t i o n c o n d i t i o n s o f s l i d i n g (Ref. 4.77).

This may be due t o the f a c t t h a t i n t h e p l a s t i c - d e f o r m a t i o n mode t h e d i s l o -

c a t i o n s generated would n o t have remained i n t h e su r face a f t e r t h e passage

o f t h e s l i d i n g counter face and t h e energy would appear as hea t ( i . e . ,

t rans formed t o t h e thermal p lane o f t h e t r i b o l o g i c a l system). These r e s u l t s

i n d i c a t e t h a t some p a r t o f t h e f r i c t i o n a l energy i s indeed s t o r e d w i t h i n

the s l i d i n g p a r t n e r v i a a d i s l o c a t i o n mechanism. Since t h i s s to red energy

i s obv ious l y o n l y a smal l p a r t o f t he whole f r i c t i o n a l energy, i n general

o t h e r d i s s i p a t i o n mechanisms must a l s o be considered.

91

(b) EMISSION OF ENERGY (OTHER THAN THERMAL)

I n the microscopic model of f r i c t i o n i t has been explained t h a t dur ing

s l i d i n g o r r o l l i n g , micro-contacts are formed and destroyed. These processes

are s t a t i s t i c a l l y d i s t r i b u t e d i n t ime and l o c a t i o n w i t h i n the geometric

area o f contact . I t i s l i k e l y t h a t i n the process o f j u n c t i o n format ion

some o f the a s p e r i t i e s o r some p a r t o f them are deformed e l a s t i c a l l y . I f

then the j unc t i ons are destroyed and the adhesion bonds are broken, the

e l a s t i c deformed p a r t s of the a s p e r i t i e s snap apar t thus generat ing v ib ra -

t i ons and o the r l a t t i c e s t imu la t i ons which lead t o the emission o f energy

i n d i f f e r e n t forms. I n s o l i d s t a t e physics, d i f f e r e n t processes o f the

t ransformat ion o f energy i n t o apparently o the r forms are known (e.g., the

pho toe lec t r i c e f f e c t o r thermoionic emission). I n analogy, the main " t r i b o -

induced" energy emission e f f e c t s which have been observed exper imenta l ly

are sketched i n b r i e f ( t h e ef fect o f heat generation i s t r e a t e d separate ly

be1 ow).

( i ) Emission o f phonons (acoust ic waves, sound)

The generation of f r i c t i on - induced acoust ic waves ( cons is t i ng o f phonons)

and the emission of sound i s a common fea tu re o f most t r i b o l o g i c a l proces-

ses. Since noise i s considered as an "acoust ic p o l l u t a n t " the reduct ion o f

no ise emission i s an important task i n today 's i ndus t r y (Ref. 4.78).

Physica l ly , the generation of sound i n tribo-mechanical systems i s connected

w i th processes o f e l a s t i c deformation and release o f asper i t i es . A theory

o f na tu ra l normal micro-v ibrat ions i n s l i d i n g con tac t was p u t forward by

T o l s t o i (Ref. 4.79). He showed t h a t the s e l f - e x c i t e d micro-v ibrat ions du r ing

s l i d i n g are i n v a r i a b l y accompanied by simultaneous upward jumps o f asper i -

t i e s . The frequency o f the na tu ra l micro-v ibrat ions i s determined by the

contact s t i f f n e s s and the mass o f the s l i d i n g surface. These micro-v ibrat ions

vanish on ly when the normal v ib ra t i ons are damped by external means o r when

the v e l o c i t y i s lower than a c e r t a i n l i m i t . The value o f the c r i t i c a l velo-

c i t y , vcr, may be roughly estimated i n terms o f the creep v i s c o s i t y , q , o f

the rubbing s o l i d s , t h e i r y i e l d strength, d the f r i c t i o n c o e f f i c i e n t , f,

and both the height , y, and spacing 1, o f the surface asper i t i es : Y '

For the s l i d i n g of conventional s tee l surfaces i t fo l l ows t h a t

vcr = 5 * 'cm/s. This very low value i nd i ca tes t h a t i n almost any

92

s l i d i n g s i t u a t i o n a c e r t a i n amount o f t he mechanical energy i s d i s s i p a t e d

through t h e genera t ion o f v i b r a t i o n and t h e f o l l o w i n g emiss ion o f a c o u s t i c

waves. The abso lu te amount o f energy e m i t t e d i s , however, u s u a l l y o n l y a

very smal l p a r t o f t he whole f r i c t i o n a l energy.

( i i ) Emission o f photons ( t r ibo- luminescence)

The e f f e c t o f t r ibolurninescence i s w e l l known i n phys ics . I t occurs i f ce r -

t a i n s o l i d bodies, such as u r a n - n i t r a t e o r ZnSMn, a re rubbed a g a i n s t each

o the r . I n t h i s case, t h e mechanical work which separates adhesion bonds

a c t i v a t e s photons which a re e m i t t e d as v i s i b l e l i g h t . Th i s e f f e c t i s n o t

ra re : so f a r i t has been observed i n more than a thousand m a t e r i a l s (Ref.

4.80). A complete t h e o r e t i c a l exp lana t ion o f t h i s e f f e c t i s s t i l l needed.

Some observa t ions suppor t t h e assumption t h a t i n t h e su r face c racks o f t h e

c r y s t a l s , e l e c t r o s t a t i c doub le- layers e x i s t wh ich cause a k i n d o f spark

d i scha rg ing i f the su r face c racks a re c leaved d u r i n g t h e f r i c t i o n process.

Obv ious ly some p a r t o f t he f r i c t i o n a l mechanical energy a c t s as a c t i v a t i o n

energy and i s - v i a a mechano-e lec t ro -op t ica l t r a n s f o r m a t i o n mechani sin - e m i t t e d as o p t i c a l r a d i a t i o n . C l e a r l y , i f i t occurs, t h i s e f f e c t a l s o

consumes o n l y a smal l p a r t o f t h e whole f r i c t i o n a l energy.

( i i i ) Emission o f e l e c t r o n s (exo -e lec t ron emission, EEE, Kramer e f f e c t )

A t t h e end o f t h e 1 9 4 0 ' ~ ~ Kramer a t t h e Phys ika l i sch-Techn ische Bundesan-

s t a l t (PTB) observed t h a t e l e c t r o n s a re e m i t t e d f rom f r e s h l y abraded me-

t a l l i c sur faces . Kramer i n i t i a l l y thought t h a t these e l e c t r o n s were due t o

exo thermic processes o c c u r r i n g a t t he sur face . I t i s assumed t h a t t he f r i c -

t i o n process ac ts as an a c t i v a t i o n process f o r t h e emission o f exo-e lec t rons

and t h a t some ana log ies between EEE and o t h e r emission e f f e c t s l i k e l um i -

nescence, f i e l d emission and photoemission e x i s t . However, owing t o the

complex i ty o f t h e sequence o f events i nvo l ved i n t h e whole process, a com-

p l e t e theory o f t he EEE e f f e c t i s n o t y e t a v a i l a b l e . Recent exper imenta l

work on the EEE o f a c lean, annealed magnesium s i n g l e c r y s t a l sur face , per -

formed i n UHV, v e r i f i e s t h a t e l e c t r o n emiss ion occurs a l ready f rom a s t r a i n

f r e e surface s imp ly upon adso rp t i on o f oxygen (Ref. 4.81). On t h e o t h e r

hand, measurements o f EEE r a t e s d u r i n g f r i c t i o n exper iments on aluminium

sur faces show t h a t t he re a re c l o s e connect ions between t h e emiss ion r a t e o f

exo-e lec t rons , t he compos i t ion o f t h e topmost su r face l a y e r s and t h e f r i c -

t i o n c o e f f i c i e n t (Ref . 4.82)..An example o f t h e c o r r e l a t i o n between t h e EEE

r a t e and t h e f r i c t i o n c o e f f i c i e n t f o r t h e s l i d i n g o f a luminium a g a i n s t

a luminium i s shown i n F i g u r e 4.20. Al though i n the whole energy ba lance of

a t r ibo-mechan ica l system the energy " l o s s " due t o the emiss ion o f exo-

93

elect rons i s on l y a very small par t , i t i s obvious t h a t i f exo-electrons

are generated they may p lay an important r o l e f o r the tr ibo-chemical pro-

cesses occu r r i ng i n the system.

Revolut ion o f d i s c I CI

c s

I I I I

40 80 120 160

S l i d i n g d is tance 1 (mn)

Figure 4.20 F r i c t i o n c o e f f i c i e n t and exo-electron emission r a t e (Ref. 4.82).

I n summary, discussion of the e f f e c t s (i), ( i f ) , (iii) shows t h a t there

are some t r ibo- induced emission processes t h a t must be inc luded i n the

whole p i c t u r e o f the d i s s i p a t i o n o f energy i n a t r i b o l o g i c a l system.

Although these t r ibo- induced processes are p h y s i c a l l y very i n t e r e s t i n g

and may i n c e r t a i n cases be very important f o r the t r ibo-chemical processes

occurr ing i n the system,in general, they account f o r on l y a very small p a r t

o f the whole energy d iss ipated.

94

( c ) TRANSFORMATION TO THERMAL PLANE

The discussion o f energy d i ss ipa t i on mechanisms h i t h e r t o has shown t h a t

there are some processes o f storage and emission o f energy (o the r than

thermal) t h a t con t r i bu te t o the consumption o f energy i n f r i c t i o n . Since

these con t r i bu t i ons , i n general, are very small , t h i s r a t h e r d e t a i l e d con-

s i d e r a t i o n o f the various processes a lso leads t o the conclusion t h a t near-

l y a l l the energy d iss ipated by f r i c t i o n appears as heat. Indeed, t h i s has

been known from ancient times and i s the bas is o f the mechanical equiva lent

o f heat. From the microscopic model o f f r i c t i o n i t i s obvious t h a t a l l t he

processes invo lved i n the formation and separation o f asper i t y micro-con-

t a c t s lead t o l a t t i c e d i s to rs ions and v ib ra t i ons which mani fest as heat.

I n the general theory o f t r i b o l o g y the generation o f heat i n f r i c t i o n i s

expressed as a t ransformat ion o f work t o the conceptual thermal plane o f

the system (see Section 3.4.3). Clear ly , the hea t generated i n f r i c t i o n may

e i t h e r remain w i t h i n the system ( a c t i n g perhaps as a c t i v a t i o n energy f o r

mater ia l changes or chemical react ions) or leave the system through convec-

t ion, conduction o r rad ia t i on .

An important f ea tu re o f the generation o f heat i s the increase o f tem-

perature o f the ma te r ia l elements o f a t r i b o l o g i c a l system. Since the i n -

creased temperature and the temperature gradients i n t u r n i n f l uence the ma-

t e r i a l proper t ies o f the f r i c t i o n par tners and a c t i v a t e t r i b o l o g i c a l pro-

cesses, the knowledge o f t r ibo- induced temperatures i s o f paramount i m - portance i n t r i bo logy . I n the t r ibo- induced temperature r i s e s we must

d is t inguished between :

( i ) a bu lk temperature r i s e

(i i ) temperature gradients

(ii i ) l o c a l temperature r i s e s o r " f l a s h temperatures"

Theoret ica l treatments o f the f l a s h temperature problem were performed by

Carslaw and Jaeger (Ref. 4.83), Holm (Ref. 4.84) and Blok (Ref. 4.85).

These theor ies were combined and s i m p l i f i e d by Archard (Ref. 4.86). Owing

t o the great importance of t h i s theory t o many t r i b o l o g i c a l s i t ua t i ons , the

main r e s u l t s o f t h i s theory w i l l be sketched i n b r i e f .

The model used i n Archard's treatment i s shown i n F igure 4.21. A surface asper i t y o f body (1) forms a c i r c u l a r area o f contact A = n a2, which

moves w i t h a v e l o c i t y v over the f l a t surface o f body ( 2 ) . The temperatures

are ca l cu la ted on the assumption t h a t t he heat i s generated a t the t r u e area

o f contact and t h a t t h i s heat i s conducted away i n t o the bu lk o f the rubbing

members.

95

A’

F igu re 4.21 Model o f a s l i d i n g a s p e r i t y

The theo ry f i r s t l y r e q u i r e s t h e s o l u t i o n o f t h e equat ions f o r t h e f l o w o f

hea t i n t o each body. The de r i ved su r face temperatures a re expressed i n terms

o f t h e r a t e o f supp ly o f heat , t h e s i z e and speed o f t h e hea t source, and

the thermal p r o p e r t i e s o f t h e m a t e r i a l . Secondly, t he p r o p o r t i o n o f t h e t o t a l

heat f l o w i n g i n t o each body i s then determined by t h e c r i t e r i o n t h a t t h e

equa t ion o f hea t f l o w f o r bo th bodies s h a l l g i v e t h e same average tempera ture

ove r t h e c o n t a c t area. Depending on t h e o p e r a t i n g c o n d i t i o n s o f l o a d FN and

speed v, t h e na tu re o f m a t e r i a l s and t h e de format ion mode, d i f f e r e n t fo rmulae

have been de r i ved . For t h e case o f p l a s t i c a s p e r i t y de format ion o f bod ies o f

t he same m a t e r i a l u s i n g t h e abbrevat ions

T w 3 P p y

J P C N =

f :

9 :

PY : J :

P : c :

X :

k :

f r i c t i on coe f f i c i e n t

a c c e l e r a t i o n due t o g r a v i t y

f l o w o r y i e l d p ressure

mechanical e q u i v a l e n t o f h e a t

d e n s i t y

s p e c i f i c hea t

thermal d i f f u s i v i t y (x= -) thermal c o n d u c t i v i t y

k P C

i t f o l l o w s t h a t t he maximum f r i c t i o n - i n d u c e d temperature r i s e A T i s g i ven by

t h e f o l l o w i n g express ions :

A Tmax = 0.25 NL f o r L -= 0 .1

A Tmax = 0.25 CINL f o r 0 . 1 ~ L < 5

( C 1 = 0.95 a t L = 0.1

C1 = 0.5 a t L = 5 )

96

A Tmax = 0.435 C2NL 1/2

= 0.435 NL A Tmax

The a p p l i c a t i o n s o f these r e I1 S 0

carbon s t e e l w i t h a hardness o f V.P.N

f o r 5 c L c 100

(C2 = 1/ [l + 0.87 L-”‘])

f o r L > 100

he example o f a s l i d i n g p a i r o f p i i n

150, 250 and 850 i s shown i n F i g u r e

4.22.

l o 4

T/ f

F igu re 4.22 Maximum a t t a i n a b l e f l a s h temperatures f o r s l i d i n g contacts o f s t e e l , ( a ) : V.P.N., 150. ( b ) : V.P.N., 250. ( c ) : V.P.N., 850. (Ref. 4.86)

I n a d d i t i o n t o t h e temperature r i s e w i t h i n a f r i c t i o n a l i n t e r f a c e , the

d i s t r i b u t i o n o f hea t t o the two i n t e r a c t i n g bodies i s impor tant . C lea r l y ,

t he d i s t r i b u t i o n depends n o t o n l y on the opera t i ng parameters and the

m a t e r i a l s p r o p e r t i e s b u t a l s o on the geometry o f both bodies (Ref. 4.87).

For a system c o n s i s t i n g of two bodies o f equal k inemat ics and geometry i t

has been proposed t h a t the f r i c t i o n a l heat i s d i s t r i b u t e d between the two

bodies according t o the f a c t o r ( thermal c o n d u c t i v i t y x s p e c i f i c heat x

dens i t y ) ’ I 2 of bo th bodies (Ref. 4.88).

97

The d i scuss ion o f t h e whole c y c l e o f introduction-transformation-

d i s s i p a t i o n o f work i n a t r ibo-mechan ica l system shows t h e m a n i f o l d o f

processes and e f f e c t s i n v o l v e d i n f r i c t i o n . A l though w i t h t h e contemporary

techniques o f exper imen ta t i on i t i s p o s s i b l e t o s tudy a s i n g l e i s o l a t e d e f -

f e c t , i n genera l t h e r e i s an ove r lap and an i n t e r a c t i o n o f t h e d i f f e r e n t

processes. The d e t a i l e d d i scuss ion as performed i n t h e l a s t sec t i ons has

p rov ided a b a s i s f o r t he c o m p i l a t i o n o f t he p r o p e r t i e s o f m a t e r i a l s r e l e -

van t t o t h e d i f f e r e n t s teps o f t he t ransmiss ion and d i s s i p a t i o n o f energy.

These p r o p e r t i e s be long t o d i f f e r e n t c lasses acco rd ing t o t h e i r re levance

t o t h e d i f f e r e n t i n t e r a c t i o n s o c c u r r i n g a t t h e i n t e r f a c e i n a t r i b o l o g i c a l

sys tem:

( a ) P r o p e r t i e s "pe r se"

- volume p r o p e r t i e s : geometry, dimensions, chemical compos i t ion

- su r face p r o p e r t i e s : su r face topography, su r face compos i t ion

( b ) P r o p e r t i e s r e l e v a n t t o t r ibo-mechan ica l i n t e r a c t i o n s

- e l a s t i c i t y , p l a s t i c i t y , e l a s t o v i s c o s i ty

( c ) P r o p e r t i e s r e l e v a n t t o t r i bo -chemica l i n t e r a c t i o n s

- r e a c t i v i t y w i t h t h e environment

( d ) P r o p e r t i e s r e l e v a n t t o t r i b o - p h y s i c a l i n t e r a c t i o n s

- adhesion, t r a n s p o r t p r o p e r t i e s

A da ta sheet t o a s s i s t i n t h e c o m p i l a t i o n o f t h e r e l e v a n t p r o p e r t i e s o f

f r i c t i o n p a i r s i s g i ven i n Chapter 8.

4,4 WEAR PROCESSES

4 ,4 I 1 GENERAL DESCRIPTION

I n the fo rego ing s e c t i o n d e a l i n g w i t h f r i c t i o n processes, t h e t r a n s a c t i o n s

on the work p lane and t h e thermal p lane o f a t r i b o - m e c h a n i a l system have

been d iscussed accord ing t o t h e t r i bo -p rocess diagram, F i g u r e 3.4. I n o r d e r

t o complete t h e conceptual framework o f t h e t r i b o l o g y o f mechanical systems

as o u t l i n e d i n F i g u r e 3.4 f u r t h e r , the t r a n s a c t i o n s on t h e m a t e r i a l s p lanes

must be s t u d i e d i n connect ion w i t h t h e r e l e v a n t wear processes. Comparing

f r i c t i o n w i t h wear, depending on t h e t e c h n i c a l f u n c t i o n o f t h e t r ibo-mecha-

n i c a l system under cons ide ra t i on , b a s i c d i f f e r e n c e s between f r i c t i o n and

wear processes must be n o t i c e d . According t o Table 3.2, t h e va r ious t r i b o -

mechanical systems can be c l a s s i f i e d b road ly i n t o two d i f f e r e n t groups:

98

(a ) A f i r s t group i n which the main i n p u t s and ou tpu ts o f t h e system a r e

g i ven by phys i ca l ( i . e . , non -mate r ia l ) q u a n t i t i e s , headed by the terms

mot ion, work and in fo rma t ion .

A second group i n which t h e main i n p u t s and ou tpu ts a r e g iven by a

f l o w o f m a t e r i a l s through t h e system, as i n the case o f a w i redrawing

system.

( b )

According t o the d e f i n i t i o n o f wear as " t h e p rog ress i ve l o s s o f substance

from t h e opera t i ng su r face o f a body o c c u r r i n g as a r e s u l t o f r e l a t i v e

mot ion a t t he sur face" i t f o l l o w s t h a t i n case (b ) wear may be seen as

a process which leads t o a l o s s o f a m a t e r i a l i n p u t q u a n t i t y o f t h e system.

I n these cases, m a t e r i a l losses due t o wear may be t r e a t e d f o r m a l l y i n

analogy t o energy losses due t o f r i c t i o n . On t h e con t ra ry , f o r systems o f

group (a ) , which w i l l be cons idered ma in l y i n t h i s sec t ion , t h e t e c h n i c a l l y

r e l e v a n t i n p u t and use-output q u a n t i t i e s a re e s s e n t i a l l y non-mater ia l .

Therefore, i n t h i s case wear leads t o p r o p e r t y changes and losses from

the elements o f t h e system. To repea t t h i s e v i d e n t b u t impor tan t p o i n t :

f rom a systems p o i n t o f view, f r i c t i o n i s a process which l eads t o l osses

from the i n p u t q u a n t i t i e s o f t h e system whereas wear i s a process which

leads t o losses f rom the elements o f t h e system. Therefore, f r i c t i o n i n -

f l uences p r i m a r i l y t h e i n p u t - o u t p u t r e l a t i o n s ( i .e., t h e f u n c t i o n o f t h e

system) whereas wear p r i m a r i l y i n f l u e n c e s o r changes t h e p r o p e r t i e s o f t h e

elements o f t h e system ( i . e . , t h e s t r u c t u r e o f t h e system). I n t h e f o l l o w -

i ng , t h e main wear processes r e l e v a n t t o t r ibo-mechan ica l systems o f group

( a ) w i 11 be discussed.

s imp le t r ibo-mechan ica l system c o n s i s t i n g o f t h e pa r tne rs

(1) One machine element

(2 ) A second machine element

( 3 ) The i n t e r f a c i a l volume (gaseous atmosphere)

Fo r example, such a system may be g iven by t h e c o n f i g u r a t i o n shown schema-

t i c a l l y i n F igu re 4.23 i n which the sur faces o f (1) and ( 2 ) s l i d e a g a i n s t

each o t h e r i n a i r ( 3 ) under a normal l oad FN w i t h a s l i d i n g v e l o c i t y v.

pa r tne rs , say on element (1). Accord ing t o F igu re 3.8 t h e m a t e r i a l losses

due t o t h e wear processes may be descr ibed as:

( i ) m a t e r i a l t r a n s f e r f rom (1) t o ( 2 )

( i i ) m a t e r i a l loss f rom (1) t o (3 )

( i i i ) f o rma t ion o f r e a c t i o n produc ts

Consider, as a s t a r t i n g p o i n t , t h e d r y wear o f metals o c c u r r i n g i n a

Consider now t h e wear processes t h a t t ake p lace on one o f t h e two

99

(There may be back-and- fo r th r e a c t i o n s between t h e elements (l), (2 ) , (3 ) ;

these w i l l be cons idered below i n Sec t i on 4 .4 .6 ) .

systems envelope

wear processes (see F i g . 4.24)

F igu re 4.23 A s imp le t r ibo-mechan ica l system.

Depending on t h e amount o f m a t e r i a l which i s l o s t f rom element ( l ) , t h e

wear may be b road ly c l a s s i f i e d as " m i l d wear" o r "severe wear". Obv ious ly

t h i s c l a s s i f i c a t i o n can be r e l a t e d t o t h e compos i t ion o f t h e sur face ,

( F i g u r e 4.5). I n m i l d wear, t h e wear processes occur a t t h e " o u t e r " su r face

l aye rs . The su r faces remain r e l a t i v e l y smooth and a re u s u a l l y p r o t e c t e d by

su r face ox ide l a y e r s generated i n rubb ing . The worn d e b r i s c o n s i s t s o f smal l

p a r t i c l e s down t o some nm. I n severe wear, t h e c o n t a c t i s m e t a l l i c , t h e su r -

faces a r e deeply t o r n , and t h e worn d e b r i s c o n s i s t s o f m e t a l l i c p a r t i c l e s up

t o some 100 pm. C l e a r l y , t h e c l a s s i f i c a t i o n o f wear i n t o "m i ld " and "severe"

i s p r i m a r i l y a d i s t i n c t i o n i n t h e s c a l e o f s i z e .

o f t he wear o f meta ls under d r y s l i d i n g c o n d i t i o n s which have been e x p e r i -

m e n t a l l y observed i n s teady -s ta te s i t u a t i o n s , p rov ided t h e "na tu re " o f su r -

faces does n o t change:

I . The wear r a t e w, i . e . t h e volume V o f m a t e r i a l removed p e r u n i t s l i d i n g

A s i n the case o f s l i d i n g f r i c t i o n , t h e r e a re some "macroscopic r u l e s "

1 i s p r o p o r t i o n a l t o t h e normal l o a d FN

11. The wear r a t e w i s independent o f t he apparent area o f con tac t .

100

I n o rde r t o e x p l a i n these macroscopic r u l e s , a mic roscop ic model o f

t he wear ing process s i m i l a r t o t h a t used i n t h e d i scuss ion o f t h e f r i c t i o n

process ( F i g u r e 4.15) may be considered. C l e a r l y , t h e processes o c c u r r i n g

between i n t e r a c t i n g a s p e r i t i e s - l i k e e l a s t i c and p l a s t i c de format ion , and

so on - as d iscussed i n the fo rego ing sec t i ons , n u s t s i m i l a r l y be taken

i n t o account i n any mic roscop ic model o f t h e wear krocess, I n F igu re 4.24

a schematic rep resen ta t i on o f a u n i t event o f t he wea; process i s shown.

F igu re 4.24 Schematic r e p r e s e n t a t i o n o f a u n i t event i n t h e wear process,

There have been seve ra l a t tempts (see Sec t ion 1.2.2) t o d e r i v e formulae

express ing t h e macroscopic obseryed wear r u l e s mentioned above. The essen-

t i a l concept - as summarized by Archard (Ref. 4.89) - i s t h a t t h e worn

volume V , produced i n s l i d i n g a d i s tance 1, can be r e l a t e d t o t h e t r u e

area o f con tac t , Ar. It i s u s u a l l y assumed t h a t t he u n i t event which must

be cons idered i s t h e con tac t o f two a s p e r i t i e s on the opposing sur faces .

101

As i d e a l i z e d i n F i g u r e 4.24, t h e u n i t event i s concerned w i t h t h e es tab -

l i shmen t o f an area o f con tac t cons idered t o be a c i r c l e o f rad ius , a, and

area A A = TC a . I f i t i s assumed t h a t i n s l i d i n g a d i s t a n c e A 1 = 2a a

hemispher ica l p a r t i c l e o f r a d i u s a and volume A V = 2 / 3 n a 3 i s generated

i t f o l l o w s t h a t

2

Archard has suggested t h a t n o t every u n i t event r e s u l t s i n t h e fo rma t ion

o f a wear p a r t i c l e . I n t r o d u c i n g a f a c t o r K which represents the p r o b a b i l i t y

t h a t any g i ven event w i l l produce a worn p a r t i c l e and summing f o r a l l m ic ro-

con tac ts , t h e t o t a l wear r a t e i s

!! = ? K A r 1 1

I t has been shown above t h a t , depending on t h e de format ion mode, t h e f o l l o w -

i n g r e l a t i o n s between the r e a l area o f con tac t , Ar, and t h e normal l oad FN

e x i s t :

- e l a s t i c de format ion ( p l a s t i c i t y index $ < 0.6)

E : composi te e l a s t i c modulus FN Ar a - E

- p l a s t i c de format ion ( p l a s t i c i t y index $ >1)

t N

PY Ar DC - py : y i e l d p ressure

From these r e l a t i o n s i t f o l l o w s t h a t t h e p r o p o r t i o n a l i t y

e x i s t s , as observed exper imen ta l l y i n many s i t u a t i o n s o f t he d r y wear o f

meta ls 'under s teady -s ta te cond i t i ons .

I n t r y i n g t o desc r ibe s y s t e m a t i c a l l y t he va r ious wear processes t h a t

may occur i n a t r ibo-mechan ica l system a coup le o f severe d i f f i c u l t i e s a r i s e

These a r e n o t o n l y due t o the g r e a t comp lex i t y o f wear processes b u t a l s o

t o t h e imprec i se and ambiguous use o f t h e te rm wear. Fo r example, t h e type

102

of wear o f an u n l u b r i c a t e d metal p a i r s l i d i n g i n a dus ty atmosphere may be

termed

d ry wear

o r m e t a l l i c wear

o r s l i d i n g wear

o r sc ra tch ing wear

o r ab ras i ve wear

depending on t h e emphasis intended. Since most o f t he imprec ise wear terms

i n common use a re connected w i t h p r a c t i c a l wear problems, a wear c l a s s i f i -

c a t i o n scheme i s needed which ma in ta ins t h e known terms b u t avo ids ambi-

g u i t y . I n t h e rev iew o f t he h i s t o r i c a l development o f wear s tud ies , Sec t i on

1.2.2, two wear c l a s s i f i c a t i o n schemes have been a l ready mentioned:

( a )

( b )

C l a s s i f i c a t i o n i n r e l a t i o n t o the type o f r e l a t i v e mot ion, suggested

i n 1938 by S iebe l (Ref. 1 .22) .

C l a s s i f i c a t i o n i n r e l a t i o n t o the type o f wear mechanism, suggested

i n 1957 by Burwe l l (Ref . 1.26).

Comparing these wear te rm ino log ies w i t h the te rm ino logy used i n t h e f i e l d

o f t h e b u l k s t r e n g t h o f m a t e r i a l s , t he c l a s s i f i c a t i o n ( a ) can be seen i n

analogy t o the type o f "ex te rna l s t r e s s " (e.g. , compression, t ens ion , bend-

ing, e t c . ) and the c l a s s i f i c a t i o n ( b ) can be seen i n analogy t o t h e t ype o f

t h e mechanism o f " i n t e r n a l damage" (e.g. , d u c t i l e f r a c t u r e , b r i t t l e f r a c -

t u re , e t c . ) .

mechanical system should be r e l a t e d t o t h e i n p u t s o f t he system (e.g., t ype

o f mot ion, work) as w e l l as t o t h e s t r u c t u r e o f the system (sys tem's e l e -

ments, p r o p e r t i e s o f t h e elements, i n t e r r e l a t i o n s between t h e elements).

Combining these requirements w i t h t h e e x i s t i n g c l a s s i f i c a t i o n s ( a ) and ( b ) ,

f o r an unequivocal c h a r a c t e r i z a t i o n o f wear, t h e f o l l o w i n g c h a r a c t e r i s t i c s

should be s p e c i f i e d :

( i ) t h e type o f r e l a t i v e mot ion,

( i i ) t h e i n t e r a c t i n g elements,

( i i i ) t h e dominant wear mechanism.

Obviously, t he combina t ion o f these t h r e e c h a r a c t e r i s t i c s s p e c i f i e s t h e

" t ype" of wear. Fo r a more q u a n t i t a t i v e c h a r a c t e r i z a t i o n , i n a d d i t i o n t h e

f o l l o w i n g c h a r a c t e r i s t i c s shou ld be s p e c i f i e d :

( i v ) t h e i n p u t work: normal l oad , f r i c t i o n c o e f f i c i e n t , d i s tance o f

From a system's p o i n t o f view, the wear l oss -ou tpu t o f a g iven t r i b o -

mot ion ( a t s t a t e d v e l o c i t y ) ,

103

main l y

s t r e s s

i n t e r -

a c t i o n s mechanisms

S a J w 0 v 3 ‘7

v- .7 m LC, L

m4- lu

re1 a t i ve

mot ion l u m v)

z+lu n

I n t e r a c t i ng

elements

s t r e s s + m a t e r i a l

i n t e r -

a c t i o n s

c 7

0 lu .? I v

-c .-aJ

lu C,v

G 82 -a L T

s o l i d / s o l i d

(metals,

polymers,

minera ls ,

e t c . )

w i t h o u t

o r w i t h

l u b r i c a n t s

s l i d i n g

r o l l i n g

A- p1

2% impact 7

0 o s c i 11 a t i o n

-L f l o w

0 f low

s o l i d / l i q u i d

s l i d i n g wear

I I I

r o l l i n g wear

I I I

I I impact wear

f r e t t i n g wear

I

c a v i t a t i o n wear

I I\ / I

f l u i d e r o s i o n s o l i d/ f 1 u i d

+ p a r t i c l e s

Abras ion

Adhesion

T r i bochemical

sc ra tches , grooves, s t r i a t i o n s

cones, f l akes , p i t s

r e a c t i o n produc ts ( f i l m s , p a r t i c l e s )

Table 4.2 C h a r a c t e r i z a t i o n o f wear.

Appearance o f t h e worn su r faces I I Wear mechanisms I I Sur face f a t i g u e I cracks, p i t s I

Table 4.3 Appearances o f worn sur faces .

104

( v ) t h e m a t e r i a l p r o p e r t i e s r e l e v a n t t o wear,

( v i ) t h e wear r a t e

( v i i ) t h e appearance o f t h e worn sur faces .

I n Table 4.2 a c l a s s i f i c a t i o n scheme which t r i e s t o combine t h e above

c h a r a c t e r i s t i c s ( i ) , ( i i ) , ( i i i ) i s shown. I n t h i s t a b l e , t h e types of

wear a r e termed accord ing t o the type o f r e l a t i v e mot ion i n analogy t o t h e

c l a s s i f i c a t i o n o f f r i c t i o n modes. (Th is i s t h e most e v i d e n t way o f d i s t i n -

g u i s h i n g between d i f f e r e n t types o f wear s i n c e i n p r a c t i c a l eng inee r ing

s i t u a t i o n s t h e ac tua l i n t e r f a c i a l wear processes a re seldom easy t o d e t e c t . )

I n mechanical eng ineer ing , t h e wear o f t h e components o f t r ibo-mechan ica l

systems i s connected w i t h f o u r b a s i c types o f r e l a t i v e mot ion: s l i d i n g ,

r o l l i n g , impact, o s c i l l a t i o n . I t has been found t h a t t h e i n t e r f a c i a l wear

mechanisms a c t i n g d u r i n g these mot ions can be c l a s s i f i e d i n t o f o u r groups

under t h e headings: su r face f a t i g u e , abrasion, adhesion, t r i bo -chemica l . As i n d i c a t e d i n Table 4.2 i n any o f t he d i f f e r e n t types o f r e l a t i v e mot ion

one o r more o f t he f o u r b a s i c wear mechanisms may a c t . I n p r a c t i c e i t i s

o f t e n d i f f i c u l t t o determine what type o f i n t e r f a c i a l wear mechanism ( o r

what combinat ion) a c t s i n a g i ven s i t u a t i o n . F o r example, i n pure s l i d i n g

o f a metal /metal p a i r t he abras ion o r t he adhesion wear mechanism may domi-

na te , whereas d u r i n g o s c i l l a t i o n o f a meta l /meta l coup le f r e t t i n g occurs

e s s e n t i a l l y through the combina t ion o f a l l f o u r b a s i c wear mechanisms (see

Sec t ion 4.4.6).

A customary ( i n d i r e c t ) way o f d e t e c t i n g t h e type o f wear mechanism

a c t i n g i n a g iven wear s i t u a t i o n i s t o s tudy t h e appearance o f t h e worn

sur faces . I n Table 4.3 some t y p i c a l c h a r a c t e r i s t i c s o f su r face damage due

t o t h e f o u r bas i c wear mechanisms a re l i s t e d . With t h e combinat ion o f t h e

c h a r a c t e r i s t i c s shown i n Tables 4.2 and 4.3 t h e bas i s f o r an unambiguous

d i s t i n c t i o n between wear o f d i f f e r e n t types may be given.

A f t e r t he general d e s c r i p t i o n o f wear and i t s ex t remely complex na ture ,

i n t h e f o l l o w i n g t h e main aspects o f t h e f o u r b a s i c types o f wear mechanisms

i n r e l a t i o n t o s l i d i n g , r o l l i n g , and o s c i l l a t i n g w i l l be s t u d i e d from a

phys i ca l p o i n t o f v iew (Ref . 4.90). The d i scuss ion i s r e s t r i c t e d t o the

wear mechanisms between s o l i d bod ies . The e f f e c t s o f c a v i t a t i o n and e r o s i o n

cannot be t r e a t e d w i t h i n t h e scope o f t h i s volume. (For a d i scuss ion o f t h e

mechanisms of impact wear the reader i s r e f e r r e d t o a recen t book by Enge l )

(Ref . 4.91.) I t shou ld be emphasized aga in t h a t t he occurrence o f one s i n g l e

wear mechanism i s met o n l y under s p e c i f i c c o n d i t i o n s and t h a t , i n genera l ,

a combina t ion o f wear mechanisms occurs. Th is i s discussed below i n Sec t i on

4.4.6.

105

4,4 I 2 SURFACE FATIGUE WEAR MECHAN I SMS

A t a f i r s t glance, surface fa t i gue seems t o be a r e l a t i v e l y simple wear

mechanism s ince i t appears t o be based on ly on the ac t i on o f stresses on

the surfaces w i thou t needing a d i r e c t phys ica l s o l i d contact o f the sur-

faces under consideration. This fo l l ows from the observation t h a t surface

fa t i gue e f f e c t s are observed t o occur i n j ou rna l bearings where the i n t e r -

a c t i n g surfaces are f u l l y separated by a t h i c k l u b r i c a n t f i l m (Ref. 4.92).

The e f f e c t o f f a t i g u e wear processes i s normally associated w i t h repeated

s t ress c y c l i n g i n r o l l i n g o r s l i d i n g contact. I n fa t i gue , f a i l u r e i n the

mater ia l ar ises because o f stress-reverse e f f e c t s , i .e . , f r a c t u r e can

develop under a l t e r n a t i n g stresses w i t h a peak l e v e l which could be safe

i f imposed i n only tens ion o r compression. Scanning e lec t ron micrographs

shown i n F igure 4.25 e x h i b i t the t y p i c a l appearance o f the sur face fa t igue

damage a f t e r repeated u n i d i r e c t i o n a l s l i d i n g o f a p i n over a d i sc .

-20 pm t-------l 4 pm

Figure 4.25 Appearance o f surface f a t i g u e damage.

Since surface f a t i g u e i s the c l a s s i c f a i l u r e mode o f r o l l i n g contact, as i n

b a l l and r o l l e r bearings, the mechanisms o f sur face f a t i g u e i n r o l l i n g con-

t a c t w i l l be considered f i r s t .

Comparing the surface f a t i g u e o f r o l l i n g contacts w i t h the o rd ina ry

f a t i g u e o f b u l k ma te r ia l , there are two d i f f e rences t o be noted. F i r s t , the

f l u c t u a t i o n s i n the t ime t o f a i l u r e , the " l i f e t i m e " , are much more severe

i n r o l l i n g contact. Second, there i s the important phenomena o f f a t i g u e

106

l i m i t s t r e s s which i s observed i n o r d i n a r y b u l k t e s t i n g , i . e . , t h e r e

e x i s t s a c e r t a i n s t r e s s l i m i t f o r a g iven m a t e r i a l below wh ich the m a t e r i a l

enjoys an i n f i n i t e f a t i g u e l i f e . Such l i m i t has n o t been de tec ted i n t h e

su r face f a t i g u e case (Ref. 4.93). E m p i r i c a l l y , i t has been found i n a s e r i e s

o f exper iments t h a t t h e f o l l o w i n g r e l a t i o n f o r t h e t ime t o f a i l u r e e x i s t s :

cons t

0 m9 t = -

where dm i s the maximum e l a s t i c s t ress .

To understand how and where s u r f a c e - f a t i g u e cracks form, i t i s neces-

sary t o cons ider t h e na tu re o f t h e s t r e s s f i e l d s which e x i s t beneath t h e

sur face . The H e r t z i a n theo ry o f s t a t i c e l a s t i c con tac t shows t h a t t h e

maximum compressive s t r e s s occurs a t t he su r face and the maximum u n i d i r e c -

t i o n a l shear s t r e s s i s some d is tance, y, below i t (e.g. , i n t h e case o f two

c o n t a c t i n g c y l i n d e r s w i t h a c o n t a c t w i d t h o f 2aH a t y = 0.78aH). Under r o l -

l i n g c o n t a c t cond i t i ons the impor tan t s t r e s s parameter i s t h e maximum re-

versed shear s t r e s s and t h i s can be shown t o l i e c l o s e r t o t h e su r face than

t h e maximum u n i d i r e c t i o n a l shear s t ress . I f t h e con tac t i s sub jec ted t o

cons iderab le su r face t r a c t i o n forces then t h e p o s i t i o n s o f these shear

s t r e s s maxima change and move towards t h e su r face reg ion . The two s i t u a t i o n s

a re i l l u s t r a t e d i n F igures 4.26 and 4.27 which rep resen t combined s t r e s s

d i s t r i b u t i o n s c a l c u l a t e d f o r t h e case o f a c y l i n d e r l f l a t c o n t a c t by f i n i t e

element methods (Ref. 4.94).

r o l l i n g s t r e s s d i s t r i b u t i o n s , a coup le o f a d d i t i o n a l i n f l u e n c i n g f a c t o r s

must be considered. L i t tmann (Ref. 4.95) has compi led t h e f o l l o w i n g l i s t

o f those f a c t o r s which mod i fy the nominal c o n t a c t s t r e s s d i s t r i b u t i o n f rom

t h a t computed f o r homogeneous, i s o t r o p i c , e l a s t i c , smooth-surface m a t e r i a l s

i n d ry r o l l i n g con tac t :

A l though the re has been cons ide rab le p rogress i n t h e c a l c u l a t i o n s o f

Subsurface s t r e s s r a i s e r s

Oxides and o t h e r hard, b r i t t l e i nc lus ions ,

S u l f i d e s , carb ides , and o t h e r second phase p a r t i c l e s ,

Gra in boundar ies, sub-boundaries, tw ins , and o t h e r d i s l o c a t i o n ar rays .

Sur face cha rac te r

Sur face topography and t e x t u r e , Residual s t resses ,

Sur face energy l e v e l , Mic ros t ruc tu re ,

Contaminants.

107

6 -2 F igu re 4.26 Map o f maximum shear s t resses ( x 10 Nm

c o n t a c t due t o normal l o a d a lone ( G H Z = 10 Nm

(Ref . 4.94).

) f o r c y l i n d e r / p l a n e 9 -2

)

6 -2 F igu re 4.27 Map o f maximum shear s t resses ( x 10 Nm ) f o r c y l i n d e r / p l a n e

c o n t a c t due t o combined normal and t a n g e n t i a l loads

(FT/FN = 0.3; G H z = 10 Nm 9 -2 )

(Ref. 4 .94) .

Sur face f l aws

I n c l u s i o n s and second phase p a r t i c l e s ,

N icks and dents i n c l u d i n g t r u e and f a l s e b r i n e l l i n g ,

Grooves and scra tches ,

Cor ros ion p i t s , r u s t , wa te r e tch ,

F r e t t i n g damage,

Sk idd ing damage.

D i s c o n t i n u i t i e s i n con tac t geometry

End o f "1 i n e " c o n t a c t geometry,

Debr is p a r t i c l e s i n the c o n t a c t area.

Load d i s t r i b u t i o n w i t h i n t h e bear ing

E l as t i c de f 1 e c t i ons , Misal ignment o f bea r ing p a r t s ,

I n t e r n a l c learance - bear ing adjustment.

E l astohydrodynamics

Tangent i a1 fo rces

Wi thout gross s l i d i n g ,

R o l l i n g p l u s s l i d i n g .

Th is comp i la t i on o f i n f l u e n c i n g f a c t o r s i n d i c a t e s the complex i ty o f su r -

face f a t i g u e e f f e c t s i n r o l l i n g con tac t . An eng ineer ing model of f a t i g u e

f a i l u r e i n r o l l i n g con tac t which takes i n t o account the i n f l u e n c e o f many

f a c t o r s has been proposed by T a l l i a n and co-workers (Ref. 4.96).

under c y c l i c v a r i a t i o n (26 kHz) o f t he normal l oad a p p l i e d t o the c o n t a c t

between a b a l l and a f l a t specimen (52,100 s t e e l ) was made by Ty le r , Bu r ton

and Ku (Ref. 4.97). I n t h i s case t h e a p p l i e d c o n t a c t s t r e s s was beyond t h e

e l a s t i c range. As i l l u s t r a t e d i n F igu re 4.28, t h e r e a re two d i s t i n c t con-

t a c t c i r c l e s formed on bo th specimens cor respond ing t o t h e minimum and

maximum loads. As a consequence o f t h e o s c i l l a t o r y l o a d i n g t h r e e d i s t i n -

gu ishab le types o f su r face damage were observed:

(a )

A fundamental exper imenta l s tudy o f t h e c o n t a c t - f a t i g u e processes

In t h e t o r o i d a l r e g i o n between t h e i n n e r and t h e o u t e r con tac t c i r c l e s

" f r e t t i n g " occur red as a consequence o f shear t r a c t i o n s induced d u r i n g

the l o a d i n g and un load ing cyc les and i n f l u e n c e d by t h e d i f f e r e n c e of

t he e l a s t i c modul i o f t he specimens. (The f r e t t i n g mode o f wear p ro-

cesses i s d iscussed i n Sec t i on 4.4.6.)

The c e n t r a l p a r t o f t h e c o n t a c t area underwent a depress ion due t o

p l a s t i c de format ion which was found t o accumulate w i t h repeated

l oad ing .

( b )

109

( c ) The u l t i m a t e f a i l u r e o f the contact progressed as the f o l l o w i n g succession o f events generated i n the t o r o i d a l area: crack formation,

crack growth and interweaving and f l a k i n g ou t o f the crack-surrounded

areas. The f a t i g u e cracks d i d n o t i n i t i a t e i n the most hardened ma-

t e r i a l b u t i n the mater ia l adjacent t o it. I t was found t h a t a r a p i d

temperature r i s e occurred i n the i n i t i a l stage o f crack formation.

The propagation o f micro-cracks tended t o f o l l o w the boundary o f the

hardened reg ion along carbide s t r i n g e r s and in f luenced by the p r i o r

austeni t i c g r a i n boundaries.

s t a t i c

1 oad

I I t ime '

F igure 4.28 Var ia t i on o f load and contact area on f a t i g u e specimens (Ref. 4.97).

The experimental observations o f surface f a t i g u e i n d i c a t e t h a t - from a

phys ica l p o i n t o f view - the study o f contact f a t i g u e i s b a s i c a l l y a study

o f s t ress concentrat ion e f f e c t s t h a t govern f a t i g u e crack i n i t i a t i o n coupled

w i t h crack propagation behaviour. I n t he fo l l ow ing , the phys ica l mechanisms

o f ( i ) crack i n i t i a t i o n and (ii) crack propagation w i l l be discussed. The

models described may be of s ign i f i cance n o t on l y f o r t he ( c l a s s i c ) surface

fa t i gue mode o f wear b u t a l so - i n a broader sense - f o r the d iscuss ion o f

recen t l y developed wear models r e l a t k d t o the generation and propagation o f

surface cracks.

nisms f o r crack i n i t i a t i o n . These mechanisms were o r i g i n a l l y proposed i n On the basis o f d i s l o c a t i o n theory, there are several poss ib le mecha-

110

reference t o bulk-material behaviour b u t they can be applied equally well

to near-surface phenomena (Ref. 4.36). The main forms of crack in i t ia t ion

are (Ref. 4.98):

(a ) Pile-up o f dislocations in s l i p band against grain boundary ( C 1 . Zener).

(b) Coalescence of two s l i p dislocations t o form a crack along a cleavage plane ( A . H . Cot t re l l ) .

(c ) Crack formed a t t i l t boundary (A.N. Stroh).

These mechanisms are presented schematically in Figure 4.29.

:/" 1

Figure 4.29 Mechanisms o f crack in i t ia t ion .

Another mechanism tha t can i n i t i a t e subsurface cracks i s based on the ef-

fec t of inclusions. The mechanism o f crack in i t ia t ion can be started by

such obstacles as oxide inclusions which are very prevalent i n the near-

surface layers of relatively so f t metals such as copper. Further, w i t h

bearing and gear s t ee l s , carbide inclusions are always present. The pre-

sence of such obstacles can give rise to dislocation coalescence and the

in i t ia t ion o f subsurface crack nuclei. Although the described mechanisms o f crack in i t ia t ion a re mostly used

as s ta r t ing points for a discussion of metal fatigue, there are some other

de ta i l s of dislocation behaviour t h a t should be considered which are beyond

the scope of th i s volume (Ref. 4.99).

111

Once an atomic crack has been formed by one o f the mechanisms d i s -

cussed above, the processes t h a t govern the crack propagation must be con-

sidered. For b r i t t l e ma te r ia l s the we l l known c l a s s i c continuum theory o f

G r i f f i t h may be appl icable. Consider an e l l i p t i c a l crack o f l eng th 2a under 2

a t e n s i l e s t ress G. The sur face energy o f the crack i s equal t o 2 y C r E a . The d i s to rs ions i n f r o n t o f the crack t i p are o f the order o f G / E and ex-

tend over dimensions o f the order o f a. Thus an opening o f the crack i n the

d i s to red ma te r ia l leads t o an energy change

A U = 2 y c r n a 2 -

When the energy p u t i n t o the ma te r ia l by the app l i ed s t ress exceeds the sur-

face energy o f t he ma te r ia l , t he crack sur face area w i l l increase. A t t h a t

p o i n t

and

2 For example, f o r s tee l ( G = 700 N/mm , ycr = 1200 erg/cm2) i t fo l l ows t h a t

a zz 1 pm. The above equation shows the importance o f the parameter

Kc = dcr a 1/ 2

for the a b i l i t y o f crack propagation. Recently, there have been attempts t o

r e l a t e the wear behaviour o f metals w i t h t h i s parameter (Ref. 4.100).

I f the ma te r ia l i s ab le t o deform p l a s t i c a l l y , some o f the energy i n p u t

i n t o the ma te r ia l w i l l be absorbed i n p l a s t i c f l ow i n the regions o f the

crack t i p .

o f s l i d i n g asper i t y contacts and the poss ib le d i s l o c a t i o n i n te rac t i on , a

"delamination theory o f wear" has been p u t forward by Suh (Ref. 4.101) i n

which the generation o f shee t - l i ke p a r t i c l e s i s explained on the basis o f

the f o l l o w i n g chain o f events:

These considerations apply t o crack propagation i n b r i t t l e ma te r ia l s .

I n s tudy ing the p l a s t i c - e l a s t i c s t ress f i e l d s i n the subsurface regions

112

( i ) genera t ion o f subsurface d i s l o c a t i o n s ,

( i i ) d i s l o c a t i o n p i l e -up ,

( i i i ) f o rma t ion o f voids,

( i v )

( v )

coalescence o f vo ids l e a d i n g t o cracks p a r a l l e l t o t h e sur face ,

p roduc t i on o f s h e e t - l i k e p a r t i c l e s when t h e c rack reaches a c e r t a i n

c r i t i c a l l eng th .

I n r e f i n i n g t h i s theo ry , some i m p l i c a t i o n s o f c r y s t a l p l a s t i c i t y e f f e c t s

have been d iscussed i n c l u d i n g a s p e c i f i c d i s l o c a t i o n model f o r hexagonal

close-packed (h.c.p.) meta ls under wear c o n d i t i o n s and a c o r r e l a t i o n w i t h

s t a c k i n g f a u l t energy f o r face-cent red cub ic and h.c.p. meta ls (Ref . 4.102).

t o e x p l a i n t h e occurrence o f s h e e t - l i k e wear p a r t i c l e s , observed as e a r l y

as 1929 by Fuchsel (Ref. 1.19) and i n t e r p r e t e d through a process o f m a t e r i a l

separa t ion .

It appears t h a t , by t h e use o f d i s l o c a t i o n models, i t i s now p o s s i b l e

4,4,3 ABRASIVE WEAR MECHANISMS

As i n su r face f a t i g u e processes, t he a t t r i t i o n o f m a t e r i a l s p a r t i c l e s i n

the ab ras i ve wear mechanism i s a l s o caused m a i n l y by c o n t a c t de format ion

processes.

The e f f e c t o f abras ion occurs i n con tac t s i t u a t i o n s i n which d i r e c t

phys i ca l con tac t between two su r faces i s g i ven where one o f t h e sur faces

i s cons ide rab ly ha rde r than t h e o the r . The ha rde r su r face a s p e r i t i e s press

i n t o the s o f t e r su r face w i t h p l a s t i c f l o w o f t h e s o f t e r su r face o c c u r r i n g

around the a s p e r i t i e s f rom t h e ha rde r sur face . When a t a n g e n t i a l mot ion i s

imposed the harder su r face w i l l move, p lough ing and removing t h e s o f t e r

m a t e r i a l . The e f f e c t o f abras ion i s comparable w i t h a " m i c r o - c u t t i n g pro-

cess", as can be seen i n t h e scanning e l e c t r o n micrograph, F i g u r e 4.30,

showing an A1 sur face .

I n i n d u s t r i a l s i t u a t i o n s , ab ras i ve wear processes a r e very widespread;

i n fac t , i t has been es t imated t h a t about 50% o f wear encountered i n i n -

d u s t r y i s due t o abras ion mechanisms (Ref. 4.103). As a consequence o f t h e

g r e a t v a r i e t i e s o f ab ras i ve wear s i t u a t i o n s , d i f f e r e n t types o f ab ras i ve

wear a r e d i s t i n g u i s h e d i n p r a c t i c e .

As i l l u s t r a t e d schemat i ca l l y i n F i g u r e 4.31, f i r s t l y we d i s t i n g u i s h

between "two-body abras ion" and " three-body abras ion" . For example, t h e

two-body s i t u a t i o n i s most f r e q u e n t l y encountered i n t h e t r a n s p o r t o f l oose

113

Figure 4.30 Appearance o f surface damage due t o abrasion.

Two-body abrasion Three-body abrasion

Figure 4.31 Two-body and three-body abrasion.

114

minera l s and the three-body i n m ine ra l t rea tment and on t h e i ng ress o f

f o r e i g n p a r t i c l e s i n t o bear ings. Secondly we d i s t i n g u i s h between:

( a ) Gouging abras ion

( b ) Gr ind ing ab ras ion

( c ) Eros ion abras ion

Examples: Shovel d i p p e r t e e t h , Hammers i n impact p u l v e r i z e r s , e t c .

Examples: Gr ind ing b a l l s , e t c .

Examples: A g i t a t o r i m p e l l e r s , Sandblast nozz les , e t c .

Research i n t o t h e mechanism o f abras ion i n t h e l a b o r a t o r y takes t h e fo rm

o f examining t h e wear of s o l i d s s l i d i n g on ab ras i ve paper. Ex tens ive s t u d i e s

i n t h i s f i e l d have been performed by W e l l i n g e r and Uetz (Ref. 4.104, 4.105),

Khruschov (Ref. 4.106, 4.107) and Richardson (Ref. 4.108). The r e s u l t s o f

these s t u d i e s may be summarized as fo l l ows :

i n most cases l i n e a r l y w i t h l o a d FN and s l i d i n g d i s tance 1

I n a g i ven wear regime, t h e abraded wear volume V o f meta ls inc reases

I f d e v i a t i o n s occur , they are u s u a l l y due t o a r e d u c t i o n i n p a r t i c l e s i z e

o f t h e ab ras i ve o r c logg ing o f t h e su r face (Ref. 4.103). I n o rde r t o com-

pare t h e abras ion behav iour o f d i f f e r e n t m a t e r i a l s , t h e f o l l o w i n g measures

have been de f i ned :

( a ) t h e wear volume V,

( b ) t h e wear r e s i s t a n c e

E 1 - - wear volume

( c ) t h e r e l a t i v e wear r e s i s t a n c e

E (specimen 'W - E (s tandard ;

I t has been found t h a t t h e ab ras i ve wear depends on t h e c o r r e l a t i o n between

t h e hardness o f t h e abras ive , Ha, and t h e hardness o f t h e meta l , H,, l e a d i n g

t o t h r e e d i s t i n c t wear regimes, as shown i n F i g u r e 4.32:

115

a low-wear regime, i f

Ha -= Hm

a t r a n s i t i o n regime, i f

Ha z Hm

a high-wear regime, i f

Ha ’ Hm

I 7

Ri c, W E + 0

W

5 c

0 >

L Cu a, 3

Hardness o f ab ras i ve

F igu re 4.32 I n f l u e n c e o f t h e hardness o f t h e ab ras i ve on t h e wear o f meta ls (schematic) .

Th is leads t o t h e impor tan t conc lus ion t h a t i n o r d e r t o reduce an ab ras i ve

wear component, t h e hardness o f t h e m a t e r i a l , Hm, shou ld be h i g h e r than t h e

hardness o f t he ab ras i ve by a f a c t o r o f about 1.3, i . e . ,

may be used as a c r i t e r i o n f o r a low-wear ab ras ion r a t e . ( I t i s n o t neces-

sa ry t o i nc rease t h e hardness o f t h e m a t e r i a l beyond 1.3 t imes t h a t o f t h e

ab ras i ve because no f u r t h e r s i g n i f i c a n t improvement i s ob ta ined , Ref. 4.103.)

ab ras i ve wear behav iour i n t h e high-wear regime (111) o f F i g u r e 4.32, a g r e a t

I n o r d e r t o determine t h e r e l e v a n t m a t e r i a l p r o p e r t i e s t h a t govern t h e

116

v a r i e t y o f m a t e r i a l s has been tes ted . I n F igu re 4.33 t h e wear r e s i s t a n c e

c W o f var ious groups o f m a t e r i a l s as a f u n c t i o n o f t h e hardness o f t he ma-

t e r i a l s , Hm, measured under c o n d i t i o n s o f regime (111) o f F igu re 4.32, i s

shown schemat i ca l l y (Ref. 4.107).

40 3

W

aJ u c 9 30

2

: 20

v)

v) .r

L

3

7

aJ IX

10

c o r u n d y 0’

\

I I I I

0 5 10 15 20

Hardness H, ( G N / m 2 )

F igu re 4.33 Khrushov diagram: wear r e s i s t a n c e as a f u n c t i o n o f t h e hardness o f m a t e r i a l s .

The da ta were ob ta ined u s i n g an e l e c t r o c a l l y produced corundum abras i ve

( H = 22,900 N/m ) and a Babb i t - t ype l e a d - t i n a l l o y ( c o n t a i n i n g ant imony)

as t h e standard. The hardness o f t h e t e s t m a t e r i a l s was determined b e f o r e

t h e t e s t by diamond i n d e n t a t i o n . The bas i c conc lus ions t h a t can be drawn

f rom t h e Khrushov diagram, F i g u r e 4.33, may be summarized as f o l l o w s :

( a )

2

T e c h n i c a l l y pure meta ls i n an annealed s t a t e and annealed s t e e l s show

a d i r e c t p r o p o r t i o n a l i t y between t h e r e l a t i v e wear res i s tance ,

and t h e pyramid hardness, Hm: c W ,

‘w = ‘metal ‘ Hm

where ‘metal = 13.8 N-’ mm2

117

( b ) For non -meta l l i c hard m a t e r i a l s and m ine ra l s , a l i n e a r r e l a t i o n s h i p

between wear r e s i s t a n c e and hardness i s s i m i l a r l y found:

E - W - ‘mineral s d Hm

2 = 1 . 3 . N - ~ mm where ‘minerals

( c ) For m e t a l l i c m a t e r i a l s c o l d work-hardened by p l a s t i c de format ion , t h e

r e l a t i v e wear - res is tance does n o t depend on t h e hardness r e s u l t i n g f rom

c o l d work hardening.

A hea t - t rea tmen t o f s t r u c t u r a l s t e e l s (normal harden ing and tempering)

improves t h e ab ras i ve wear. res i s tance . ( d )

These r e s u l t s i n d i c a t e t h e g r e a t importance o f t h e hardness o f m a t e r i a l s and

o f o t h e r m e t a l l u r g i c a l f a c t o r s on t h e ab ras i ve wear r e s i s t a n c e o f m a t e r i a l s

(Ref. 4.109).

The l i n e a r r e l a t i o n s h i p between ab ras i ve wear r e s i s t a n c e and t h e ma-

t e r i a l hardness can be v e r i f i e d u s i n g t h e s imp le model o f p lough ing shown

i n F i g u r e 4 .16 . I n t h i s model an ab ras i ve a s p e r i t y i s approximated by a cone

t h a t ploughs o u t and removes m a t e r i a l f rom t h e counter face .

h a l f o f t h e con tac t , h FN i s balanced by t h e y i e l d pressure, py, o f t h e

coun te r face a c t i n g v i a t h e con tac t a rea A :

I f t h e load, 5 F N , on t h e i n d e n t e r i s o n l y suppor ted o v e r t h e l e a d i n g

A FN = A py

The volume o f m a t e r i a l A V removed i n s l i d i n g a d i s t a n c e A 1 i s g i v e n by

t h e c ross -sec t i ona l a rea o f t h e i n d e n t e r t imes A 1

d2 4

A V = - A l . c o t t p

Thus, s u b s t i t u t i n g f o r d f rom above

118

and assuming t h a t o n l y a p r o p o r t i o n , K , o f a l l t h e con tac ts produce worn

p a r t i c l e s , i t f o l l o w s t h a t

Th is express ion shows

t h e s l i d i n g d is tance,

t h a t t h e wear volume i s p r o p o r t i o n a l t o t h e l o a d and

and t h a t t h e o n l y m a t e r i a l p r o p e r t y i n v o l v e d i s t h e

y i e l d pressure. I f t h e y i e l d p ressure i s assumed t o be equal t o t h e inden-

t a t i o n hardness, H, f o r g iven values o f FN and 1, t h e l a s t equa t ion can be

simp1 i f i e d t o

1 V = cons t -A

I n t r o d u c i n g t h e wear r e s i s t a n c e de f i ned above as t h e r e c i p r o c a l wear volume

i t f o l l o w s t h a t

Abrasive wear r e s i s t a n c e = cons t . x hardness

Th is s imp le d e r i v a t i o n and the exper imenta l r e s u l t s shown i n F i g u r e 4.33

i n d i c a t e t h a t t he ab ras i ve wear r e s i s t a n c e i s o n l y dependent on t h e m a t e r i a l

hardness. There fore , t he ab ras i ve wear r e s i s t a n c e may be i n t e r p r e t e d v i a the

m a t e r i a l hardness, as a k i n d o f ' t r i b o l o g i c a l m a t e r i a l p r o p e r t y " , i . e . as an

apparent ly system-independent p roper t y . I t shou ld be borne i n mind, however,

t h a t t he ab ras i ve wear res i s tance , E ~ , i s d e f i n e d as a r e l a t i v e measure and

t h a t t he l i n e a r E - H r e l a t i o n s h i p i s v a l i d o n l y f o r c o n d i t i o n s o f regime

(111) o f F igu re 4.32, i .e . , f o r t he cases i n which t h e ab ras ion process a c t s

ma in l y i n the b u l k o f t h e m a t e r i a l under s tudy . If, on the o t h e r hand, an

abras i ve wear process a c t s i n t h e "ou te r " su r face l aye rs , then the i n f l u e n c e

of su r face contaminants and t h e a c t i o n o f t he environmental atmosphere must

a d d i t i o n a l l y be taken i n t o account (Ref. 4.110).

119

4 I 4,4 ADHESIVE WEAR MECHAN I SMS

Whereas the wear mechanisms o f su r face f a t i g u e and ab ras ion can be ex-

p l a i n e d ma in l y i n terms o f f o rces , s t resses and de fo rma t ion processes, i n

the adhesive wear mechanism, m a t e r i a l i n t e r a c t i o n s p l a y an impor tan t r o l e .

It was descr ibed i n Sec t i on 4.2.2 t h a t i f two s o l i d bod ies a re b rough t i n t o

c o n t a c t they w i l l f i r s t exper ience long- range van de r Waals fo rces . A t d i s -

tances o f about lnm s t r o n g shor t - range su r faces fo rces come i n t o a c t i o n a t

t h e r e a l areas o f con tac t , t h e t y p e o f which depends on t h e n a t u r e o f t h e

sur faces i n con tac t . Thus, s t r o n g adhesive j u n c t i o n s may be formed w i t h t h e

ass i s tance o f t h e d i s p e r s a l o f su r face contaminants and j u n c t i o n growth

(see Sec t ion 4.3.1). I n o r d e r t h a t adhesive wear shou ld t a k e p lace , f r a c t u r e

must occur i n the subsur face o f one o r bo th m a t e r i a l s . The s i t u a t i o n i s il-

l u s t r a t e d schemat i ca l l y i n F i g u r e 4.34.

mot ion ____L

adhe

/ f r a c t u r e

F i g u r e 4.34 Adhesive wear s i t u a t i o n .

I n c o n t r a s t t o t h e o t h e r wear mechanisms which g e n e r a l l y t a k e some t ime

t o develop o r t o reach a c r i t i c a l d e s t r u c t i v e magnitude, adhesive wear

e f f e c t s occur q u i t e p r e c i p i t o u s l y l e a d i n g i n t h e i r severe forms t o danger-

ous f a i l u r e i n t h e fo rm o f " s c u f f i n g " o r " s e i z u r e " o f moving p a r t s i n me-

chan ica l eng inee r ing systems. I n F i g u r e 4.35 t h e t y p i c a l appearance o f t h e

sur faces o f a s l i d i n g s t e e l / s t e e l p a i r a f t e r f a i l u r e due t o adhesive wear

processes i s shown. I t can be seen t h a t l a r g e m a t e r i a l lumps were t r a n s -

f e r r e d f rom t h e coun te rpa r tne r and adhere s t r o n g l y on one su r face i n " co ld -

we1 ded" j u n c t i o n s .

120

F igu re 4.35 Appearance o f su r face damage due t o adhesive wear processes.

Concerning the phys i ca l mechanisms o f adhebive wear, obv ious l y t h e proces-

ses and parameters o f adhesion ( S e c t i o n 4.2.2) as w e l l as those o f f r a c t u r e

(Sec t i on 4.4.2) must be taken i n t o account. S ince bo th adhesion and f r a c t u r e

a re i n f l u e n c e d by su r face contaminants and the e f f e c t o f t h e environment, i t

i s q u i t e d i f f i c u l t t o r e l a t e adhesion wear r a t e s w i t h elementary b u l k p ro -

p e r t i e s o f m a t e r i a l s . I n vacuum where these i n f l u e n c e s a re e l im ina ted , t h e

f o l l o w i n g exper imenta l r e s u l t s have been observed t o be g e n e r a l l y v a l i d f o r

t h e adhesive wear processes o f meta l /meta l p a i r s (Ref. 4.111):

( i ) I n t e r f a c i a l m e t a l l i c adhesion bonding occurs between any p a i r o f

metals; t h e r e i s no d i r e c t r e l a t i o n between the (volume) s o l u b i l i t y

o f metal p a i r s and t h e i r ( s u r f a c e ) adhesion bonding.

( i i ) C rys ta l s t r u c t u r e e x e r t s an i n f l u e n c e on adhesive wear. Hexagonal

meta ls i n general e x h i b i t l ower adhesive wear c h a r a c t e r i s t i c s than

e i t h e r body-centred cub ic o r face-cent red cub ic meta ls . T h i s d i f -

fe rence i s assumed t o be r e l a t e d t o d i f f e r e n t p l a s t i c a s p e r i t y con-

t a c t de format ion modes and the number o f operab le s l i p systems i n

t h e c r y s t a l systems.

121

( i i i ) Crysta l o r i e n t a t i o n in f luences the adhesive wear behaviour. I n general

h igh atomic densi ty , low surface energy g ra in o r i e n t a t i o n s e x h i b i t

lower adhesion and less adhesive wear than do o the r o r i en ta t i ons .

When d i s s i m i l a r metals are i n contact the adhesive wear process w i l l

genera l ly r e s u l t i n the t r a n s f e r o f p a r t i c l e s o f the cohesively weaker

o f the two ma te r ia l s t o the cohesively stronger.

Small amounts o f a l l o y i n g elements ( a few p a r t s per m i l l i o n ) such as

carbon and s u l f u r are s u f f i c i e n t t o i n h i b i t appreciably the adhesion

o f m e t a l l i c a l l o y s thereby min imiz ing t h e i r adhesive wear. ( S u l f u r and

carbon w i l l , ac t i va ted by f r i c t i o n a l heating, d i f f u s e t o a surface and

occupy a concentrat ion a t the surface f a r i n excess o f t h e i r concen-

t r a t i o n i n the bulk ma te r ia l . )

( i v )

( v )

These r e s u l t s c l e a r l y show the in f luences o f the various c h a r a c t e r i s t i c s o f

contact adhesion and contact deformation processes, as dicussed above, on

adhesive wear. The combined e f f e c t s o f adhesion and f r a c t u r e a l so a c t i n the

formation o f loose adhesive wear p a r t i c l e s .

4.112) and A n t l e r (Ref. 4.113) considered the process o f "prow" formation by

which contact i s maintained f o r a longer per iod wh i l e the j u n c t i o n i s growing

and the j u n c t i o n base i s moving along one o r both o f the running surfaces.

I n r e f i n i n g t h i s model, Landheer and Zaat (Ref. 4.114) emphasized the f o l -

lowing phenomena i n the severe adhesive wear process:

(a ) i n the i n te r face , a f i e l d o f i s o - s t r a i n l i n e s ( p l a s t i c s t r a i n ) moves through

the metal o f the wearing surface i n a d i r e c t i o n opposite t o the s l i d i n g d i -

rect ion, so t h a t metal accumulates i n the j unc t i ons and the d is tance between

the running surfaces i s enlarged,

( b ) detaches f o r t rans fe r .

An i n s t r u c t i v e experimental example o f the generation o f an adhesive wear

p a r t i c l e has been given by Buckley (Ref. 4.115). He performed s l i d i n g f r i c -

t i o n experiments w i t h a p o l y c r y s t a l l i n e copper r i d e r s l i d i n g across the sur-

face o f a b i c r y s t a l o f copper. One g r a i n o f the b i c r y s t a l was o f the (111)

o r i e n t a t i o n w h i l e the second was a (210) plane. With a s i n g l e pass o f the

r i d e r across the surface, cracks developed i n the sur face o f both gra ins o f

t he b i c r y s t a l . These surface cracks are shown i n the scanning e l e c t r o n

micrograph o f Figure 4.36. The f r a c t u r e cracks developed a t room tempera-

I n s tudy ing the d e t a i l s o f the adhesive wear mechanism, Cocks (Ref.

a j u n c t i o n development, where under the i n f l uence o f shear res is tance

crack ing o f the metal a t the backside o f the j unc t i on , by which ma te r ia l

122

F i g u r e 4.36 Areas o f wear on (210) copper g r a i n (Ref. 4.115).

Sl ip-Band FL- v=l ,4mm/mi n (J - Format i on F r a c t u r e

S1 i p Bands

Subsequent Passes

Sur face Genera t ing Wear

P r o j e c t i o n P a r t i c l e

F i g u r e 4.37 O r i g i n o f su r face f r a c t u r e and fo rma t ion o f wear p a r t i c l e (Ref . 4.115).

123

t u r e w i t h i n t h e copper. Close examinat ion o f these c racks i n d i c a t e s t h a t

t h e w a l l o f t h e c rack i s ve ry smooth. F u r t h e r , t h e m a t e r i a l a t t h e l e a d i n g

edge o f t h e c rack has been c u r l e d up above t h e p lane o f t h e b i c r y s t a l su r -

face. The measured ang le between t h e c rack and the o r i e n t a t i o n o f t h e su r -

face p lane i n d i c a t e s t h a t t he f r a c t u r e c rack occurs a long s l i p bands.

The mechanism respons ib le f o r t h e c racks shown i n F i g u r e 4.36 i s p re-

sented i n F igu re 4.37. Adhesion o f t h e r i d e r t o t h e b i c r y s t a l occurs . Wi th

t a n g e n t i a l mot ion f r a c t u r e occurs a long s l i p bands as t h e t a n g e n t i a l f o r c e

p a r t s a tomic planes. A t some a p p l i e d t a n g e n t i a l f o r c e , t h e a p p l i e d f o r c e

exceeds t h e adhesive bond ing f o r c e and t h e r i d e r breaks away f rom the b i -

c r y s t a l su r face l e a v i n g a c u r l o f metal p r o j e c t i n g above t h e surface. A

second pass shears o f f t h e c u r l and an adhesive wear p a r t i c l e has been ge-

nera ted .

4 ,4 I 5 TRIBO-CHEMI CAL W E A R MECHANISMS

Whereas t h e mechanism o f su r face f a t i g u e wear, ab ras i ve wear, and adhesive

wear can be understood i n terms o f de fo rma t ion and adhesion i n t e r a c t i o n s

between two c o n t a c t i n g sur faces , (1) and ( Z ) , i n t r i bo -chemica l wear as

t h i r d p a r t n e r t h e environment ( 3 ) and t h e dynamic i n t e r a c t i o n s between ( l ) ,

( 2 ) and ( 3 ) de termine t h e wear process (Ref . 4.116). I f t h e two su r faces

r e a c t a c t i v e l y w i t h t h e environment, t h e rubb ing o f su r faces t o g e t h e r i n

such an environment r e s u l t s i n t h e cont inuous fo rma t ion and removal o f re -

a c t i o n produc ts . S ince t h e m a t e r i a l o f t h e c o n t a c t i n g su r faces a r e con ta ined

i n t h e r e a c t i o n produc ts , m a t e r i a l i s be ing removed f rom t h e sur faces . The

t y p i c a l appearance o f t r i b o - c h e m i c a l l y formed wear p a r t i c l e s i s shown i n

F i g u r e 4.38 i n scanning e l e c t r o n micrographs.

adhesion on one hand and t r i bo -chemica l wear e f f e c t s on t h e o t h e r can be

seen i n t h e conceptual d iagram o f t h e wear processes w i t h i n a t r i b o l o g i c a l

system, F i g u r e 3 .8 and F i g u r e 3.4. The f i r s t t h r e e mechanisms can e s s e n t i -

a l l y be desc r ibed - i n t h e s imp les t case - as i n t e r a c t i o n s between o n l y two

p a r t n e r s , namely the two s o l i d sur faces (1) and (2), l e a d i n g d i r e c t l y t o t h e

genera t i on o f d e b r i s { Z ) f rom (1) and ( 2 ) . I n t h e case o f t r i bo -chemica l

wear, t he whole mechanism c l e a r l y c o n s i s t s o f t h e i n t e r a c t i o n s o f t h r e e

pa r tne rs , namely the s o l i d su r faces (1) and ( 2 ) and t h e environment ( 3 ) .

These i n t e r a c t i o n s may be expressed as a c y c l i c s tepwise process:

The d i f f e r e n c e s i n the mechanisms o f su r face f a t i g u e , ab ras ion and

M

124

( i ) A t t he f i r s t stage, t he sur faces ( I ) and ( 2 ) r e a c t w i t h the env i ron -

ment ( 3 ) . I n t h i s process, r e a c t i o n produc ts (1)-(3) and (2)-(3)

a re formed on the sur faces o f (1) and ( 2 ) , shown i n F igu re 3.8 below.

The second s tep cons is t s o f t h e a t t r i t i o n o f t he r e a c t i o n produc ts as

a r e s u l t o f c rack fo rma t ion and abras ion i n t h e c o n t a c t process i n t e r -

ac t i ons o f (1) and ( 2 ) . When t h i s occurs " f resh" , i .e. , r e a c t i v e su r -

face p a r t s , o f (1) and ( 2 ) are formed and stage ( i ) con t inues .

( i i )

C lea r l y , i n a t tempts t o s tudy t h e mechanisms o f t r i bo -chemica l wear, besides

the e f f e c t s o f de format ion and adhesion, t h e chemis t ry o f t h e r e a c t i o n p ro -

duc t f o rma t ion must be cons idered a d d i t i o n a l l y , t a k i n g i n t o account the con-

t r i b u t i o n o f f r i c t i o n a l energy i n these processes.

H 50 pm H 5

F igu re 4.38 Appearance o f t r i bo -chemica l wear p a r t i c l e s .

As a consequence o f thermal and mechanical a c t i v a t i o n , t h e a s p e r i t i e s under-

go t h e f o l l o w i n g changes:

( a )

( b )

t h e r e a c t i v i t y i s inc reased due t o t h e inc reased a s p e r i t y temperature;

t h e r e f o r e t h e fo rma t ion o f su r face l a y e r s i s acce le ra ted ,

t h e mechanical p r o p e r t i e s o f t h e su r face a s p e r i t y l a y e r s a re changed:

i n general they have a tendency t o b r i t t l e f r a c t u r e .

S t a r t i n g w i t h t h e assumption t h a t t r i bo -chemica l l y formed su r face a s p e r i t y

l a y e r s a r e detached a t a c e r t a i n c r i t i c a l t h i ckness , Qu inn proposed an

125

ox ida t i on hypothesis o f the wear o f s tee l s (Ref. 4.117). Since t h i s theory

i nd i ca tes the main i n f l uenc ing fac to rs of the tr ibo-chemical wear process,

i t w i l l be reproduced here. I t was assumed that , a t a given a s p e r i t y contact ,

on average, 1 / K encounters are necessary (K: s t a t i s t i c a l wear c o e f f i c i e n t ,

see Section 4:4.1) f o r a c r i t i c a l oxide f i l m thickness t o b u i l d up before

i t becomes detached t o form a wear p a r t i c l e . I f tc i s the du ra t i on o f a

s i n g l e wearing contact, then the t o t a l t ime t t o produce a wear p a r t i c l e o f

thickness 5 i s given by

But tc = d/v, where d i s the d is tance along which a wearing contact i s made

and v i s the speed o f s l i d i n g .

Hence

t = d/vK

Now the mass per u n i t area o f oxide growth A m depends on the t ime o f o x i -

dat ion t through the pa rabo l i c r e l a t i o n

A m2 = kp. t

where k P

assume A m = s p , where p i s the dens i t y o f the oxide, so t h a t we ge t

i s the pa rabo l i c ox ida t i on r a t e constant. It i s reasonable t o

2 g 2 = k . t/p P

El im ina t i ng t we ob ta in an expression f o r K, namely

I t i s now genera l ly accepted t h a t k

temperature o f ox ida t i on To namely

is exponen t ia l l y dependent on the P

kp = Ac exp

where Ac i s the Arrhenius constant, Q i s the

the gas constant. Combining equations and w r

t u re ) f o r To, we ge t

-Q/ RcTo)

a c t i v a t i o n energy, and R, i s t i n g Tc ( t h e contact tempera-

126

From t h e r e s u l t s o f Sec t i on 4.4.1 i t f o l l o w s t h a t under t h e assumption o f a

p l a s t i c a s p e r i t y de format ion mode ( p l a s t i c i t y index

py =: hardness H) t h e wear c o e f f i c i e n t K can be r e l a t e d w i th t h e wear vo lu -

me V v i a t h e express ion

> 1, y i e l d p ressure

K V = - F * 1 3H N

Combining t h i s r e l a t i o n w i t h t h e express ion f o r K, c a l c u l a t e d on t h e b a s i s

o f Q u i n n ' s theory , i t f o l l o w s

d A; exp (-Q/RcTc) v = FN * 1

3*g2*p2- v . H

This express ion i n d i c a t e s t h e dependence o f t h e wear volume V on t h e f o l l o w -

i n g groups o f parameters o f t he t r i b o l o g i c a l system:

( a ) o p e r a t i n g v a r i a b l e s (FN, v, 1, Tc)

( b ) genera l cons tan ts and m a t e r i a l parameters (Ac, Q, Rc ,P, H)

( c ) i n t e r a c t i o n c h a r a c t e r i s t i c s (d, Tc, 5 )

Al though i t i s q u i t e d i f f i c u l t t o per fo rm r e l i a b l e c a l c u l a t i o n s o f t h e wear

r a t e s due t o t h e u n c e r t a i n t i e s o f some o f these q u a n t i t i e s , t h e above equa-

t i o n s may serve as a b a s i s f o r a p h y s i c a l p i c t u r e o f t h e t r i bo -chemica l

wear mechanism.

4 ,4 ,6 THE COMPLEXITY OF WEAR PROCESSES

I n general , t he d i f f e r e n t wear mechanisms as d iscussed separa te l y i n t h e

fo rego ing sec t ions , a re superimposed. The processes o f t r i bo -chemica l reac-

t i o n s and adhesion l e a d t o changes i n t h e p r o p e r t i e s o f t h e sur faces . Thereby

r e a c t i o n produc ts a r e formed o r m a t e r i a l i s t r a n s f e r r e d t o t h e o t h e r pa r tne r .

The processes a r e a c t i v a t e d by t h e mechanical and thermal energy t r a n s f e r r e d

and d i s s i p a t e d i n t h e sur face a s p e r i t i e s and i n t h e b u l k m a t e r i a l . A l l these

processes promote t h e fo rma t ion o f loose wear p a r t i c l e s which, i n any case,

a re generated th rough t h e mechanisms o f su r face f a t i g u e and abrasion.

127

A w e l l known wear mode which r e s u l t s th rough t h e s u p e r p o s i t i o n o f a l l

f o u r bas i c wear mechanisms desc r ibed above i s f r e t t i n g wear (Ref. 4.118,

4.119). F r e t t i n g wear occurs i f two c o n t a c t i n g s o l i d bod ies move r e l a t i v e l y

t o each o t h e r i n an o s c i l l a t o r y mot ion w i t h an ampl i tude o f movement o f l e s s

than 100 pm. I n i n d u s t r y , f r e t t i n g occurs, f o r example, i n t h e f o l l o w i n g

mechanical systems and components: l a p j o i n t s , s p l i n e s , p u s h - f i t t e d s h a f t -

wheels, metal s t a t i c sea ls , eng ine mounts, c lu t ches , e t c . The su r face damage

due t o f r e t t i n g i s c h a r a c t e r i z e d by t h e i n i t i a t i o n o f f a t i g u e c racks and t h e

fo rma t ion o f f r e t t i n g d e b r i s . As a consequence o f f r e t t i n g , f a t i g u e - s t r e n g t h

r e d u c t i o n f a c t o r s o f 3 t o 6 a r e q u i t e normal (Ref . 4.120). The cha in o f

events t h a t leads t o f r e t t i n g i s compi led schemat i ca l l y i n Table 4 .4 (Ref.

4.121).

I Initiation and propagation

of surface cracks Formation and rupture

II

Ill

Table 4.4 Schematic r e p r e s e n t a t i o n o f t h e d i f f e r e n t stages o f f r e t t i n g .

The f i r s t s tage ( I ) i s i n i t i a t e d by the o s c i l l a t o r y c o n t a c t de fo rma t ion

l e a d i n g t o t h e genera t i on and p ropaga t ion o f su r face c racks as w e l l as t o

the d i s p e r s a l o f su r face contaminants and the fo rma t ion and r u p t u r e o f ad-

hes i ve bonds. The second s tage (11 ) i s t h e fo rma t ion o f wear p a r t i c l e s e i -

t h e r by t h e su r face f a t i g u e mechanism o r t h e adhes ion /de format ion process.

Th is i s f o l l o w e d by t h e o x i d a t i o n o f wear p a r t i c l e s i n t r i bo -chemica l r e -

ac t i ons . The t h i r d s tage (111) c o n s i s t s o f t h e ab ras i ve a c t i o n o f formed

wear p a r t i c l e s . Th is i n t u r n a s s i s t s t h e processes o f stage ( I ) , and so on.

very pronounced example o f t h e s u p e r p o s i t i o n o f t he d i f f e r e n t wear mechanisms

The f r e t t i n g mode o f wear which occurs under o s c i l l a t o r y mo t ion i s a

128

descr ibed separa te l y above. From var ious wear s tud ies i t i s obvious t h a t

under s l i d i n g and r o l l i n g c o n d i t i o n s i n most cases a superpos i t i on o f wear

mechanisms a l s o occurs. Consider, f o r example a s imp le t r ibo-mechan ica l

system c o n s i s t i n g o f two s o l i d bod ies ( l ) , ( 2 ) s l i d i n g i n a r e a c t i v e gaseous

atmosphere ( 3 ) as i l l u s t r a t e d schemat i ca l l y i n F igu re 4.39 above. As i n d i -

ca ted by the schematic diagram i n t h e c e n t r e o f F igu re 4.39, t he f o l l o w i n g

processes occur i n general s imu l taneous ly a t t h e i n t e r f a c e :

( i ) f o rma t ion o f su r face l a y e r s by adso rp t i on o r t r i bo -chemica l r e a c t i o n s

o f t h e s l i d i n g sur faces ( 1 ) and ( 2 ) w i t h the gaseous environment (3 ) ,

( i i ) adhesive t r a n s f e r o f m a t e r i a l and r e a c t i o n produc ts f rom (1)-( 2 )

and (2)--(1),

( i i i ) genera t ion o f wear p a r t i c l e s f rom t h e b u l k m a t e r i a l , t h e r e a c t i o n

produc ts or t h e adhesive t r a n s f e r r e d m a t e r i a l o f b o t h (1) and (2 )

through t h e e f f e c t s o f su r face f a t i g u e and abrasion.

The changes o f t he m a t e r i a l components o f a t r ibo-mechan ica l system due t o

t h e combined a c t i o n o f t he wear mechanisms have been s t u d i e d s y s t e m a t i c a l l y

by Mdlgaard (Ref. 4.122) and a r e shown schemat i ca l l y i n F i g u r e 4.39. The

p o s s i b l e m a t e r i a l components of a wear ing system, c o n s i s t i n g i n i t i a l l y o f

t he t h r e e pa r tne rs ( l ) , ( 2 ) , ( 3 ) , a re :

t he g i ven m a t e r i a l s M1

the gaseous atmosphere

deformed m a t e r i a l p a r t s

t r a n s f e r r e d deformed m a t e r i a l

back - t rans fe r red m a t e r i a l

r e a c t i o n produc ts

t r a n s f e r r e d r e a c t i o n produc ts

d e b r i s o f g iven m a t e r i a l

d e b r i s o f r e a c t i o n produc ts

adsorbed gas

R1

G

ZM

ZR

M2

D2

129

-1 I I n i t i a l s t a t e I

1 ope

abrasion,

surface f a t i g u e

I Final s t a t e I

G -I debr is I

Figure 4.39 Superposit ion o f wear mechanisms i n a tribo-mechanical system and the changes o f the system's elements due t o wear processes.

130

I n summary, we see f rom F i g u r e 4.39 t h a t t h e s tudy o f wear i n a t r i b o -

mechanical system i s one i n v o l v i n g a complex interdependence o f many pro-

cesses and phys i ca l parameters. I t i s most d i f f i c u l t t o i s o l a t e any one pro-

cess o r parameter f o r i n v e s t i g a t i o n , and hence we a re f o r c e d i n t o an e m p i r i -

c a l approach t o t h e sub jec t . I n o r d e r t o g i v e t h i s e m p i r i c a l approach a de-

f i n i t e d i r e c t i o n l i k e l y t o prove success fu l , one must cons ider , sys temat i -

c a l l y , a l l t he processes and parameters r e l e v a n t t o a g iven wear s i t u a t i o n .

For t h e p r a c t i c a l a p p l i c a t i o n o f t h e systems approach t o t h i s s u b j e c t t h e

data-sheet descr ibed i n Chapter 8 may be used.

4,5 LUBRICATION MODES

4 , 5 , 1 STRIBECK CURVE AND LUBRICATION MODES

The t r i b o l o g i c a l processes, i . e . , t h e contac t , f r i c t i o n and wear processes

d iscussed h i t h e r t o a re , i n genera l , r e l a t e d t o d i r e c t phys i ca l i n t e r a c t i o n s

between r e l a t i v e l y moving surfaces. A l l these processes can be i n f l u e n c e d

o r m o d i f i e d by t h e process o f l u b r i c a t i o n . The purpose o f l u b r i c a t i o n i s t o

separa te the sur faces moving r e l a t i v e t o each o t h e r w i t h a f i l m o f a m a t e r i a l

which can be sheared w i t h low r e s i s t a n c e w i t h o u t causing any damage t o t h e

sur faces . Depending on t h e th i ckness o f t h e l u b r i c a n t f i l m (which may range

from some t e n t h o f a m i l l i m e t e r down t o t h e nm range), t he i n t e r f a c i a l h e i g h t

d i s t r i b u t i o n o f t h e l u b r i c a n t f i l m and t h e degree o f geometr ic con fo rm i t y ,

d i f f e r e n t l u b r i c a t i o n modes can be d i s t i n g u i s h e d . The l u b r i c a t i o n modes can

be conven ien t l y d iscussed i n cons ide r ing the S t r i b e c k curve.

S t r i b e c k i n 1900 t o 1902 performed comprehensive exper iments on t h e

f r i c t i o n o f s l i d i n g and r o l l i n g bear ings , measuring the f r i c t i o n c o e f f i c i e n t

as a f u n c t i o n o f t h e o p e r a t i n g v a r i a b l e s l oad FN, v e l o c i t y v and temperature

T (Ref. 4.123). I n o rde r t o e l i m i n a t e the i n f l u e n c e o f t he temperature depen-

dence o f v i s c o s i t y on h i s r e s u l t s , S t r i b e c k r e c a l c u l a t e d t h e measured f r i c -

t i o n c o e f f i c i e n t as a f u n c t i o n o f l o a d and v e l o c i t y f o r a cons tan t b u l k - o i l

temperature o f 25OC. The accura te exper imenta l measurements o f S t r i b e c k

served as a bas i s f o r t h e t h e o r e t i c a l work o f Sommerfeld, Giimbel and succes-

sors i n e s t a b l i s h i n g the theo ry o f hydrodynamic l u b r i c a t e d bear ings , see

Sec t ion 1.2.3.

I t i s now g e n e r a l l y accepted t h a t t he S t r i b e c k curve represents t h e

general c h a r a c t e r i s t i c o f l u b r i c a t e d moving su r faces as a f u n c t i o n o f t h e

131

l u b r i c a n t v i s c o s i t y -q , the v e l o c i t y v and t h e normal l o a d FN ( o r p ressure

p ) . I n F i g u r e 4.40 the shape o f t h e S t r i b e c k curve i s p l o t t e d i n a s i m p l i -

f i e d manner as a f u n c t i o n o f t h e parameter 1. v . FN- l . ( T h i s parameter i s

r e l a t e d t o the r e c i p r o c a l o f t he Sommerfeld number So, see Sec t ion 4.5.2.)

t i 1

111: h-0

B 11: h - R

I

FN s o l i d 1

l u b r i c a n t

s o l i d 2

I su r face roughness R

I I I : h s R

v i s c o s i t y n x v e l o c i t y v - ,

l o a d FN

F igu re 4.40 S t r i b e c k cu rve and l u b r i c a t i o n regimes (schemat i c ) .

As i l l u s t r a t e d i n F i g u r e 4.40, depending on t h e geometry, t h e m a t e r i a l s ,

t he o p e r a t i n g c o n d i t i o n s and the separa t i on h o f t h e sur faces , t h r e e main

l u b r i c a t i o n regimes may be d i s t i n g u i s h e d :

I : Hydrodynamic l u b r i c a t i o n (and Elastohydrodynamic, EHO, l u b r i c a t i o n ) ,

I 1 : P a r t i a l EHD l u b r i c a t i o n o r Mixed l u b r i c a t i o n ,

111 : Boundary l u b r i c a t i o n .

I n regime I , t h e r i g i d su r faces a re separa ted by a cont inuous l u b r i c a n t

f i l m , whose th i ckness i s much l a r g e r than t h e combined su r face roughness

measure R o f t he sur faces . The f r i c t i o n r e s i s t a n c e i s due t o the i n t e r n a l

f r i c t i o n o f t h e l u b r i c a n t . I n t h i s regime, t h e t r i b o l o g i c a l behav iour o f

t he system i s determined by the rheo logy o f t h e l u b r i c a n t and can be c a l -

132

c u l a t e d o r es t imated by t h e methods o f f l u i d mechanics. I f t h e l u b r i c a t e d

system under cons ide ra t i on c o n s i s t s o f nonconformal concent ra ted contac ts ,

t h e e l a s t i c ( H e r t z i a n ) de format ion o f t h e su r faces and t h e pressure depen-

dence o f t he l u b r i c a n t s v i s c o s i t y must a l s o taken i n t o account. Th i s leads

t o t h e regime o f e lastohydrodynamic l u b r i c a t i o n . Since i n regime I no d i r e c t

phys i ca l con tac t i n t e r a c t i o n s between t h e su r faces qccur, wear processes

cannot take p lace (except su r face f a t i g u e wear, c a v i t L t i o n wear o r f l u i d

e ros ion ) .

I f under cond i t i ons o f hydrodynamic o r EHD l u b r i c a t i o t i , t h e l u b r i c a n t

v i s c o s i t y o r t he v e l o c i t y decreases o r t h e l o a d inc reases , t he l u b r i c a n t

f i l m ge ts " t h i n n e r " and t h e separa t i on o f t h e sur faces decreases. I f then

t h e f i r s t a s p e r i t y con tac t i n t e r a c t i o n s occur, reg ion I 1 o f p a r t i a l EHD

l u b r i c a t i o n o r mixed l u b r i c a t i o n i s reached. I n t h i s regime t h e l o a d i s

c a r r i e d p a r t l y by t h e f l u i d f i l m and p a r t l y by t h e c o n t a c t i n g su r face as-

p e r i t i e s . Consequently, i n t h i s regime t h e f r i c t i o n r e s i s t a n c e i s due p a r t l y

t o t h e shear ing o f t h e l u b r i c a n t f i l m and p a r t l y t o t h e a s p e r i t y i n t e r a c -

t i o n s . I n regime 11, i n p r i n c i p l e , a l l wear mechanisms may take p lace as

discussed i n Sec t i on 4.4. The processes exp la ined above are , o f course,

i n f l u e n c e d and m o d i f i e d by the a c t i o n o f t h e l u b r i c a t i n g f i l m .

o p e r a t i n g cond i t i ons change f u r t h e r t o t h e l e f t o f t h e S t r i b e c k curve, t h e

amount o f a s p e r i t y i n t e r a c t i o n s w i t h i n t h e c o n t a c t area inc reases , and t h e

f i l m th ickness decreases down t o some monolayers o r below. I n regime I 1 1 o f

boundary l u b r i c a t i o n , b u l k r h e o l o g i c a l p r o p e r t i e s o f t he l u b r i c a n t a re o f

l e s s importance and t h e l o a d i s c a r r i e d a lmos t e n t i r e l y th rough t h e de fo r -

mat ion of t h e a s p e r i t i e s . C l e a r l y , i n regime I11 t h e physico-chemical i n t e r -

ac t i ons a t t he s o l i d / l u b r i c a n t / s o l i d i n t e r f a c e determine t h e f r i c t i o n and

wear behav iour o f t he system.

A f t e r t h i s s i m p l i f i e d survey o f t h e d i f f e r e n t l u b r i c a t i o n modes w i th

the use of t h e genera l i zed S t r i b e c k diagram, t h e d i f f e r e n t l u b r i c a t i o n modes

w i l l be discussed i n some d e t a i l i n t h e f o l l o w i n g .

I f i n a l u b r i c a t e d system which runs i n regime I 1 o f F igu re 4.40 t h e

4,5,2 HYDRODYNAMIC LUBRICATION

I n t h e process o f hydrodynamic l u b r i c a t i o n o f a t r i b o l o g i c a l system, a

cont inuous f l u i d f i l m i s b rough t between t h e sur faces i n r e l a t i v e mo t ion i n

o r d e r t o min imize f r i c t i o n and t o e l im ina te wear. The t r i b o l o g i c a l behav iour

of a hydrodynamica l l y l u b r i c a t e d system i s then ma in l y determined by t h e two

f o l l o w i n g fea tu res :

133

( i )

( i i )

The r e s i s t a n c e t o mot ion i s g i ven by the " i n t e r n a l f r i c t i o n " o f t h e

f l u i d , i . e . , t h e shear r e s i s t a n c e o r " v i s c o s i t y " o f t h e f l u i d f i l m .

The e f f e c t s of wear a r e e l i m i n a t e d i f t h e geometry o f t h e su r faces i s

such t h a t a l o a d - c a r r y i n g pressure i s s e t up i n t h e l u b r i c a n t f i l m

d u r i n g ,the mot ion o f t he surfaces l e a d i n g t o a complete separa t i on

o f t h e sur faces .

I n ( i ) , t h e r e s i s t a n c e t o mot ion o f a hydrodynamica l l y l u b r i c a t e d system i s

determined by the shear fo rces which e x i s t i n a moving f l u i d . To g e t a mea-

sure o f t h e shear r e s i s t a n c e o r v i s c o s i t y o f t h e f l u i d , cons ide r a system

o f two s o l i d p lane su r faces , as sketched i n F i g u r e 4.41.

a rea A "' v = o

F i g u r e 4 .41 Viscous drag between two p a r a l l e l p l a t e s

I n F i g u r e 4 .41 t h e lower su r face i s kep t s t a t i o n a r y w h i l e t h e upper moves

p a r a l l e l t o i t a t a v e l o c i t y vo. S ince t h e molecules o f t h e f l u i d adhere t o

the sur faces , a t v e l o c i t i e s which a r e n o t t o o h igh , a l am ina r f l o w p r o f i l e

r e s u l t s w i t h i n t h e f l u i d w i t h v = vo a t t h e upper su r face and v = o a t t h e

lower su r face . The f o r c e , F, r e q u i r e d t o keep t h e upper su r face moving i s

then p r o p o r t i o n a l t o the area o f t he surfaces, A, and t o vo/z, where z i s

t he d i s t a n c e between t h e p l a t e s . Thus t h e shear s t r e s s F/A i s p r o p o r t i o n a l

t o t h e change o f shear s t r a i n vo/z:

o r more g e n e r a l l y :

154

The constant o f p r o p o r t i o n a l i t y 7 i s c a l l e d c o e f f i c i e n t o f v i scos i t y ,

and f l u i d s which obey p r o p o r t i o n a l i t y between the viscous shear s t ress

and the r a t e o f change o f the shear s t r a i n %are termed Newtonian f l u i d s .

As regards p o i n t ( i i ) , f o r the generation o f a load-carry ing pressure

the formation o f a converging, wedge-shaped f i l m i s necessary, as shown by

Reynolds i n 1886 (Ref. 4.124). A physical p i c t u r e o f the processes leading

t o a generation o f a pressure i n a converging o i l f i l m can be gained by

considering a simple t i l t i n g pad bearing, shown schematical ly i n Figure 4.42.

d i s t r i b u t i o n

t i l t i n g pad

F igure 4.42 A t i l t i n g pad bearing.

The t i l t i n g pad i s s ta t i ona ry w i t h an i n l e t gap z1 l a r g e r than the o u t l e t

gap z2, The whole gap i s f looded w i t h a viscous incompressible l u b r i c a n t .

Assume t h a t i n i t i a l l y the i n l e t v e l o c i t y d i s t r i b u t i o n may be l i n e a r (as i n

Figure 4.41). Since zl> z2 there would be an excess o f i n l e t f low over the

o u t l e t f l ow i n con t ras t t o the cond i t i on o f c o n t i n u i t y o f f low. This automa-

t i c a l l y leads t o the generation o f a pressure d i s t r i b u t i o n against which the

i n l e t f l ow has t o work. This i n t u r n modif ies the v e l o c i t y p r o f i l e s : a t t he

i n l e t the v e l o c i t y p r o f i l e i s concave and a t the o u t l e t i t i s convex as i n -

d i ca ted schematical ly i n F igure 4.42. The area under each v e l o c i t y - p r o f i l e

curve along the pad i s the same, thus the cond i t i on o f c o n t i n u i t y o f f l o w

i s f u l f i l l e d . I f the surfaces are f u l l y separated, r e l a t i v e motion occurs

e n t i r e l y w i t h i n the 1 u b r i cant f i I m .

135

For the t r i b o l o g i c a l behav iour o f a hydrodynamica l l y l u b r i c a t e d me-

chan ica l system, i . e . , t h e t ransmiss ion and d i s s i p a t i o n o f mechanical energy,

t he f o l l o w i n g aspects a r e impor tan t :

t h e i n f l u e n c e s o f t he o p e r a t i n g v a r i a b l e s l i k e load, v e l o c i t y , tempera-

t u r e on t h e pressure and f i l m t h i ckness generated i n t h e l u b r i c a n t f i l m ,

t he r e l a t i o n s between ( a ) and t h e system geometry and the m a t e r i a l s and

l u b r i c a n t parameters,

t h e amount o f mechanical energy d i s s i p a t e d and the va lue o f f r i c t i o n

c o e f f i c i e n t , depending on ( a ) and ( b ) ,

t h e l i m i t s o f hydrodynamic l u b r i c a t i o n i n r e l a t i o n t o ( a ) , ( b ) and ( c ) .

The main fea tu res o f these p o i n t s w i l l be d iscussed i n t h e f o l l o w i n g , s t a r t -

i n g f rom a c o n s i d e r a t i o n o f t h e general

f l u i d , t he Navier-Stokes equa t ion . The main p h y s i c a l ideas i n v o l v e d i n t h e

d e r i v a t i o n o f t h i s equa t ion a re the f o l l o w i n g (Ref. 4 .125) :

Consider an element o f volume A V w i t h i n a f l u i d o f v i s c o s i t y 7 and

d e n s i t y p which moves under t h e a c t i o n o f a s p e c i f i c p ressure p and an ex-

t e r n a l conse rva t i ve f o r c e f i e l d o f t h e p o t e n t i a l 0 w i t h a mean v e l o c i t y v,

as i n F igu re 4.43.

equa t ion o f mot ion f o r a v iscous

y1*

- t

f l u i d o f - v i s c o s i t y 1 --c

c -

and

d e n s i t y p __

Figure 4.43 A volume element w i t h i n a v iscous f l u i d .

Accord ing t o Newton's law o f mot ion , t h e t o t a l f o r c e p e r u n i t volume i s

equal t o t h e t ime r a t e o f change o f l i n e a r momentum

f o r c e = - (mass x v e l o c i t y ) d t

F = p x ( a c c e l e r a t i o n )

138

The fo rce per u n i t volume F i s given as sum o f three terms:

( i ) F1: the pressure force per u n i t volume

The pressure on the face a t x gives the fo rce p b y b z , and the pres-

sure on the face a t x t A x gives the fo rce - [ p t (#A x]A y A z, so t h a t the r e s u l t a n t f o rce i s - (#) A x A y A z. I f we take the

remaining p a i r s of the faces o f the cubes we see t h a t the pressure

fo rce per u n i t volume i s

or w i t h the use o f the Nabla operator

a a a a v = (- a x s TIT* X I

( i i ) F2: the g r a v i t y forces per u n i t volume

I t i s we l l known t h a t forces due t o g r a v i t y are conservative forces.

With a p o t e n t i a l per u n i t mass, (0 the fo rce densi ty r e s u l t s as

( i i i ) F3: the viscous forces per u n i t volume

A t the bottom face o f the volume element, the s t ress 7% acts ac-

cord ing t o the d e f i n i t i o n o f the v i s c o s i t y given above. A t y t A y

the s t ress i s

so t h a t the r e s u l t a n t s t ress i s

137

Summing, i t f o l l o w s t h a t

w i t h 2

v = - 2 a' a 2 +a (Lap1 ace o p e r a t o r ) a x 2 ' 3 a z 2

Th is express ion i s v a l i d f o r incompress ib le f l u i d s . I n t h e genera l

case o f compress ib le f l u i d s t h e r e i s another te rm i n s t r e s s which

depends on o t h e r d e r i v a t i v e s o f t h e v e l o c i t y . The genera l express ion

f o r t he v iscous fo rces i s g i ven by

where 4' i s t he s o - c a l l e d second c o e f f i c i e n t o f v i s c o s i t y (Ref . 1 .7) .

Th i s q u a n t i t y i s u s u a l l y s a i d t o be r e l a t e d t o the normal o r shear

c o e f f i c i e n t o f v i s c o s i t y 1 by t h e express ion

A f t e r t h e de te rm ina t ion o f t he fo rces a c t i n g on a volume element o f a v i s -

cous f l u i d , we need an express ion f o r t h e a c c e l e r a t i o n o f a f l u i d p a r t i c l e .

I n t r y i n g t o g e t an express ion f o r t he a c c e l e r a t i o n o f a f l u i d p a r t i c l e , i t

must be taken i n t o account t h a t i f v (x , y, z, t ) i s t h e v e l o c i t y o f a f l u i d

p a r t i c l e which i s a t t he l o c a t i o n ( x , y, z ) a t t ime t, then the v e l o c i t y o f

t he same p a r t i c l e a t t ime t t A t i s g i ven by

v ( x t v x A t , y t v A t , z t v z A t , t + A t ) . Y

The a c c e l e r a t i o n i s then A t

a v a v a v a v vx ax v y a y v z T t73T

o r s y m b o l i c a l l y

( v v ) v t- a v a t

138

Now, i n s e r t i n g i n Newton's equa t ion

F = p x ( a c c e l e r a t i o n )

the expressions ob ta ined f o r t h e f o r c e F = F1 t F2 t F3 and t h e acce le ra-

t i o n A v/A t and combining eve ry th ing , t he genera l Navier-Stokes equa t ion

f o r t h e mot ion o f a v iscous f l u i d i s

a v P{m + ( v 7 ) v } = - a p -pfj@t?lV2v t ( 7 t 7 ' ) a ( a v )

Th is equa t ion i s t h e b a s i s f o r a l l o f hydrodynamics ( s i m i l a r t o t h e Maxwell

equat ions which a r e t h e bas i s f o r a l l o f e lec t rodynamics) . The equa t ion and

i t s d i v e r s e a p p l i c a t i o n i n t r i b o l o g y have been s t u d i e d a t l e n g t h by d i f f e r -

e n t au thors . For a d i scuss ion o f t h i s aspect, see (Ref. 4.126).

S t a r t i n g f rom t h e Navier-Stokes equa t ion o f f l u i d mechanics, Reynolds

i n h i s fundamental paper o f 1886 l a i d t h e b a s i s o f hydrodynamic l u b r i c a t i o n

theo ry and p r a c t i c e . The d e r i v a t i o n o f t he Reynolds equa t ion ob ta ined e i t h e r

f rom the Navier-Stokes equat ion o r o therw ise , can be found i n any s tandard

tex tbook o f hydrodynamics, see f o r i ns tance t h e books by Cameron (Ref. 1.7)

o r Hersey (Ref. 4.126). The Reynolds equat ion i s a d i f f e r e n t i a l equa t ion

f o r t h e pressure d i s t r i b u t i o n , t a k i n g i n t o account t h e v e l o c i t i e s o f t h e

s o l i d surfaces and the p r o f i l e o r con tour o f t h e l u b r i c a n t f i l m . Since, f rom

a c o n s i d e r a t i o n o f Reynolds equat ion , a phys i ca l p i c t u r e o f t h e hydrodynamic

l u b r i c a t i o n process as w e l l as b a s i c t r i b o l o g i c a l r e l a t i o n s f o r t he load-

c a r r y i n g c a p a c i t y and f r i c t i o n r e s i s t a n c e can be ob ta ined, a b r i e f d i scus -

s i o n o f Reynolds equa t ion and i t s consequences i s g i ven i n t h e f o l l o w i n g .

f

gene r a t e d

pressure

d i s t r i b u t i on

F igu re 4-44 Two-dimensional fl u i d - f i 1 m geometry I

139

Consider aga in a s imp le t i l t i n g pad bear ing , shown s c h e m a t i c a l l y i n F i g u r e

4.44, w i t h the f o l l o w i n g assumptions:

( a ) The f l u i d i s Newtonian

( b )

( c )

( d )

( e )

( f )

The f l u i d f l o w i s l am ina r

The f l u i d adheres t o the bear ing sur faces

The f l u i d i n e r t i a can be neg lec ted

The f l u i d we igh t can be neg lec ted

The f l u i d p ressure i s cons tan t across t h e th i ckness o f t h e f l u i d f i l m

( 9 ) The f l u i d i s incompress ib le .

Fo r t h i s case, t he Reynolds d i f f e r e n

a h 23T

i a l equa t ion can be w r i t t e n as:

- "wedge" te rm

- " s t r e t c h " te rm

- "squeeze" te rm

The r i gh t -hand s i d e o f t h i s equa t ion

s i c a l s i g n i f i c a n c e .

( i ) "Wedge" te rm

con ta ins t h r e e terms o f d i f f e r e n t phy-

a h Th is c o n t r i b u t i o n i s caused by t h e shape o f t h e f l u i d f i l m , - , and t h e

r e l a t i v e v e l o c i t y (vo - vl) o f t h e sur faces .

( i i ) " S t r e t c h " te rm

Th is te rm r e q u i r e s t h a t t h e sum o f t he v e l o c i t i e s i n t h e x - d i r e c t i o n change

as a f u n c t i o n o f x - l o c a t i o n . Th is te rm never e x i s t s i n r i g i d p l a n e - s l i d e r

bear ings b u t i s a p p l i c a b l e t o s p e c i a l cases o f dynamica l l y loaded j o u r n a l

bear ings . ( i i i ) "Squeeze" te rm

Th is c o n t r i b u t i o n i s caused by r e l a t i v e mot ion normal t o the bear ing f l u i d .

S o l u t i o n o f t h e Reynolds equat ions leads t o the pressure d i s t r i b u t i o n

which, when i n t e g r a t e d i n t h e x- and z - d i r e c t i o n s , y i e l d s the l o a d - c a r r y i n g

c a pa c i ty :

140

FN = 7 y 1 p (x , Z) dxdz

0 0

The f l o w o f f l u i d p e r u n i t w i d t h i n t h e d i r e c t i o n o f v e l o c i t y v = (vo - vl)

i s

vh h3 a p qx =-- - ' - 2 1 2 7 a x

and t h e z - d i r e c t i o n i s

The f r i c t i o n f o r c e t o be overcome i n a f l u i d - f i l m - l u b r i c a t e d system i s t h a t

caused by v e l o c i t y - induced and pressure- induced f l u i d shear s t resses ,

namely

21 x1 *1 *1 FF = 5 / 1 3 dxdz - / / h g dxdz

0 0 0 0

where the p lus s i g n i s used f o r t h e f o r c e a c t i n g on the s lower moving su r -

face. C l e a r l y , i n i n t e g r a t i o n s o f t he Reynolds equat ion the f i l m th i ckness

h = h ( x ) must be known. A f u r t h e r comp l i ca t i on i s t he v a r i a t i o n o f t h e v i s -

c o s i t y as a f u n c t i o n o f bo th temperature and pressure .

temperature and increases w i t h i n c r e a s i n g pressure . The i n f l u e n c e o f these

e f f e c t s on the behav iour o f l u b r i c a t e d systems w i l l be d iscussed i n Sec t i on

4.5.3 and 4.5.6.

S o l u t i o n s o f Reynolds equat ion , as o u t l i n e d above, have been performed

I n genera l , t h e v i s c o s i t y o f l u b r i c a n t f l u i d s decreases w i t h i n c r e a s i n g

f o r va r ious types o f bear ings , such as t h r u s t bear ings and j o u r n a l bear ings ,

and t h e t h e o r e t i c a l suppos i t ions and p r a c t i c a l consequences o f these so lu -

t i o n s have been d iscussed i n d e t a i l (see f o r i ns tance Ref. 4.127). These

r e s u l t s w i l l n o t be reproduced here . I n t h e f o l l o w i n g , t h e s o l u t i o n o f t h e

Reynolds equat ion f o r t h e s imp le case o f l u b r i c a t i o n o f a c y l i n d e r nea r a

p lane w i l l be cons idered i n b r i e f , i n o rde r t o g e t an impress ion o f t h e i m -

p l i c a t i o n s o f t he Reynolds equa t ion and t o o b t a i n a s t a r t i n g p o i n t f o r t h e

d i scuss ion o f t he elastohydrodynamic l u b r i c a t i o n mode. Consider t h e geometry

o f a r i g i d c y l i n d e r nea r a plane, as i n F i g u r e 4.45.

141

F igu re 4.45 A l u b r i c a t e d c y l i n d e r - p l a n e system.

Reynolds equa t ion i n one dimension f o r a s t e a d i l y runn ing b e a r i n g i s

v : su r face v e l o c i t y

-q : v i s c o s i t y

h : f i l m t h i ckness

h : f i l m th i ckness when -

dp/dx = 0

I n t h e sur round ing o f t h e minimum o f t h e gap t h e c i r c l e o f r a d i u s r can be

approximated by t h e p a r a b o l i c equa t ion

Using t h i s f i l m - t h i c k n e s s equa t ion and a boundary c o n d i t i o n f o r p ( x ) , t h e

Reynolds equat ions can be i n t e g r a t e d . I n t h e l i t e r a t u r e , d i f f e r e n t boundary

c o n d i t i o n s f o r p ( x ) a re known:

( a ) Sommerfeld c o n d i t i o n , p = 0 a t x = + w

( b ) H a l f Sommerfeld c o n d i t i o n , p = 0 a t x 2 0

( c ) Reynolds c o n d i t i o n , p = 0 when dp/dx = 0 a t x =- 0

The i n t e g r a t i o n o f t h e Reynolds equa t ion i n u s i n g t h e Sommerfeld c o n d i t i o n

leads t o t h e p ressu re d i s t r i b u t i o n

X p = - 2 - q v - h2

142

Now u s i n g the H a l f Sommerfeld c o n d i t i o n , i t i s p o s s i b l e t o c a l c u l a t e e a s i l y

t he t o t a l l o a d c a r r i e d pe r u n i t l e n g t h o f t h e c y l i n d e r FN/L:

0

FN/L = Zy 0

Use o f t h e Reynolds c o n d i t i o n leads t o

FN/L = 2 . 4 5 y 0

I n r e w r i t i n g these equat ions f o r t h e minimum f i l m th ickness as a f u n c t i o n

o f t h e o p e r a t i n g parameters l o a d FN and v e l o c i t y v, and t h e v i s c o s i t y 7 and t h e c y l i n d e r r a d i u s r and l e n g t h L, i t f o l l o w s t h a t

( H a l f Sommerfeld)

(Reynolds)

These r e s u l t s show t h a t f o r t he c y l i nde r /p lane system t h e separa t i ng t h i c k -

ness o f t h e l u b r i c a n t f i l m decreases w i t h decreas ing v i s c o s i t y 7 , decreas ing

v e l o c i t y v, o r i n c r e a s i n g normal l oad Fp,.

A f t e r t h e s tudy o f t h e r e l a t i o n between t h e l u b r i c a n t f i l m t h i ckness

and t h e r e l e v a n t system parameters, t h e ques t i on o f f r i c t i o n must be con-

s idered . As descr ibed above, t h e f r i c t i o n f o r c e can be found by i n t e g r a t i n g

the v iscous shear fo rces on the c y l i n d e r su r face and adding t o them any

hydrodynamic f o r c e a c t i n g i n t h e d i r e c t i o n of movement. The r e s u l t s o f t h i s

c a l c u l a t i o n , a p p l y i n g the Reynolds c o n d i t i o n leads t o t h e f r i c t i o n c o e f f i -

c i e n t (Ref. 1 . 7 ) :

143

I t i s interesting t o compare the results for the cylinderlplane system

with tha t fo r a journal bearing - practically, the most important hydrody-

namically lubricated mechanical system (Ref. 4.128). I n Figure 4 .46 the geo-

metry of an operating journal bearing i s shown schematically, the clearance

being grossly exaggerated.

I

cr = I *2 -

FN : load v : velocity

e : eccentricity

radius rl : shaft

r2 : bearing radius

rl : radial

clearance

Figure 4.46 Schematic representation of the geometry of a journal beari ng .

Since i n any journal bearing a natural lubricant wedge ex is t s as a conse-

quence o f the clearance, a t sufficiently high velocit ies the pressure gene-

rated in the wedge o f lubricant supports the shaft and separates i t com-

pletely from the bearing bushing. The f r ic t iona l behaviour can be described

conveniently as a function of operating variables and the journal bearing

data in terms o f the "Sommerfeld number" (sometimes also called "GUmbel number"). The Sommerfeld number is defined as

where p = - 2rL

'r 9, = 7

rl

: load/bearing projected area

: radial clearance/shaft radius

: viscosity

: angular velocity

144

According t o Vogelpohl (Ref. 4.129), the f r i c t ion coefficient can be ex-

pressed approximately as

J1r f = - so

for

i t follows tha t

for

for

s o < 1

s o > 1

so c 1

so > 1

In this connection i t should be remembered t h a t the parameter-qv FN-’ was used as abscissa o f the Stribeck curve Figure 4.40, the general character-

i s t i c of a lubricated system.

transmission of wn*k - I-EZ-l In th i s connection i t should be remembered that the parameter-qv FN-’ was used as abscissa of the Stribeck curve Figure 4.40, the general character-

i s t i c of a lubricated system.

145

Supplementing the s tudy o f t h e f r i c t i o n r e s i s t a n c e i n hydrodynamic

l u b r i c a t i o n , t he aspec t o f energy d i s s i p a t i o n shou ld be s tud ied . As ex-

p l a i n e d e a r l i e r , i n a j o u r n a l bea r ing t h e t ransmiss ion of t h e mechanical

i n p u t work i n t o t h e t e c h n i c a l l y used o u t p u t work i s performed v i a the t o r -

s i o n a l e l a s t i c de format ion o f t he bear ing s h a f t . The f r i c t i o n a l energy los-

ses a re due t o " p a r a s i t i c " guidance losses o f t h e s h a f t . I n a f u l l - f l u i d

j o u r n a l b e a r i n g t h e f r i c t i o n r e s i s t a n c e a g a i n s t mot ion i s g i ven by t h e v i s -

cous shear r e s i s t a n c e l e a d i n g t o the genera t i on o f hea t w i t h i n t h e l u b r i -

can t which i s e i t h e r removed

the elements o f the bear ing .

3.7, i n a s i m p l i f i e d manner,

and d i s s i p a t i o n a r e dep ic ted

I f t h e whole f r i c t i o n a l

s teady -s ta te the d i s s i p a t i o n

by the c i r c u l a t i n g l u b r i c a n t o r t r a n s f e r r e d t o

R e f e r r i n g t o the conceptual F igu res 3.6 and

the processes o f mechanical energy t ransmiss ion

schemat i ca l l y i n F i g u r e 4.47.

power can be expressed as f FN v , then i n

process i s descr ibed by

f FN v = p c1 q AT, t Ch A A T2

where f :

FN :

P :

v :

c1 :

9 : AT, :

Ch :

A = 2 n r L :

A T2 :

I f A T , =

i t f o l l o w s t h a t

f r i c t i o n c o e f f i c i e n t

normal l o a d

v e l o c i t y

d e n s i t y o f l u b r i c a n t

s p e c i f i c heat o f 1 u b r i c a n t

volume f l o w r a t e o f l u b r i c a n t

mean temperature r i s e o f t h e l u b r i c a n t i n

pass ing th rough t h e bear ing

convec t i ve h e a t - t r a n s f e r c o e f f i c i e n t a t t he o i l

b e a r i n g i n t e r f a c e

area o f t h e o i l b e a r i n g i n t e r f a c e

mean temperature d i f f e r e n c e between t h e o i l

i n t h e bear ing and t h e b e a r i n g su r face

A T 2 = A T

f FN v = A T ( p c1 q + 2 ~ c ChrL)

f FN v A T = p c1 q + 2 n C h r L

146

where, as shown above, the f r i c t i o n c o e f f i c i e n t can be w r i t t e n as

f = - JIr so

+r

so I/ 2 f = -

f o r

f o r

so -z 1

so > I

From these equat ions i t f o l l o w s t h a t the de te rm ina t ion o f t h e f r i c t i o n a l

temperature r i s e i n a f u l l - f l u i d j o u r n a l bea r ing i s ext remely compl icated.

I t f o l l o w s f u r t h e r t h a t i n a p r a c t i c a l j o u r n a l bea r ing des ign problem an

i t e r a t i v e procedure must be adopted (Ref. 4.130). Th is i s due t o t h e i n t e r -

dependence o f t he opera t i ng parameter, load, v e l o c i t y , t he Sommerfeld number

which inc ludes the v i s c o s i t y and the temperature A T w i t h i n the bear ing. The

consequences o f these e f f e c t s on the p r a c t i c a l design o f bear ings are des-

c r i b e d i n books on p r a c t i c a l l u b r i c a t i o n (see f o r i ns tance the Standard

Handbook o f L u b r i c a t i o n Engineer ing, Ref. 4.131).

4 , 5 , 3 ELASTOHYDRODYNAMIC LUBRICATION

The d i scuss ion o f t h e hydrodynamic l u b r i c a t i o n mode has been performed

main ly f o r systems o f h igh "geometr ica l conformi ty" , l i k e t i l t e d pad bear-

ings. I n these cases the sur faces are assumed t o remain complete ly r i g i d

under the operat ion. I n the cases o f poor geometr ica l conformi ty , as i n t h e

cases o f Her t z ian concentrated con tac t s i t u a t i o n s , t he e f f e c t o f t he e l a s t i c

deformat ion o f t he surfaces must be taken i n t o account. Owing t o t h e h i g h

pressures t o be found i n l u b r i c a t e d Her t z ian contacts , t h e e f f e c t o f pres-

sure on the l u b r i c a n t ' s v i s c o s i t y must a l s o be considered. A l l these leads

t o the concept o f e lastohydrodynamic (EHD) l u b r i c a t i o n (Ref. 4.132).

l u b r i c a t i o n mode a re t o be discussed i n two s teps: F i r s t l y , t he isothermal

smooth sur face EHD theory i s s t u d i e d and secondly, the e f f e c t s o f tempera-

t u r e and sur face roughness a re inc luded. A lso i n t h i s s e c t i o n the emphasis

i s on the t r i b o l o g i c a l fundamentals and on the systems aspects o f t h e sub-

j e c t mat ter .

As a s t a r t i n g p o i n t , cons ider a l u b r i c a t e d cy l i nde r /p lane system de-

formed e l a s t i c a l l y under the a c t i o n o f t he load, as i l l u s t r a t e d i n F igu re

4.48.

I n t h e fo l l ow ing , t h e main fea tu res o f t h e elastohydrodynamic (EHD)

147

F igu re 4.48 An EHD c o n t a c t o f a c y l i n d e r nea r a p lane.

The s i t u a t i o n i s de termined by the f o l l o w i n g equat ions :

( i ) Hydrodynamic equa t ion

As shown above, t he one-dimensional Reynolds equa t ion i n i t s

i n t e g r a t e d fo rm i s

The s o l u t i o n o f t h i s equa t ion f o r t he hydrodynamic case has been

g i ven above. Th is s o l u t i o n i s n o t a p p l i c a b l e , however, t o EHD s i -

t u a t i o n s owing t o t h e dependence o f t h e f i l m p r o f i l e h and t h e v i s -

c o s i t y 7 on t h e pressure p, i . e . , h = h ( p ) and q = y ( p ) .

( i i ) E l a s t i c i t y equa t ion

The f i l m p r o f i l e h ( x ) i s g i ven by

2 X h = h + - + h o 2,. e l a s t

I n a p p l y i n g Bouss inesq 's equa t ion o f e l a s t o s t a t i c s (see Sec t ion

4.2.1) f o r helast i t f o l l o w s t h a t

148

( i i i ) V i scos i t y -p ressu re r e l a t i o n

Assuming t h a t t h e f l u i d i s incompress ib le and t h a t an iso thermal

s i t u a t i o n i s given, t h e v i s c o s i t y - p r e s s u r e r e l a t i o n i s u s u a l l y

expressed by an exponen t ia l equat ion

lo : v i s c o s i t y a t atmospher ic

p ressure and To

a : pressu re -v i scos i t y

c o e f f i c i e n t

The v a l i d i t y o f an exponen t ia l law i n d i c a t e s an enormous increase o f

v i s c o s i t y w i t h pressure. F o r ins tance, a t a H e r t z i a n pressure o f about

1 GN/m t h e v i s c o s i t y o f a minera l o i l may increase by a f a c t o r o f 6 10 compared w i t h i t s va lue under atmospher ic pressure.

2

The s o l u t i o n o f t h e EHD problem i n v o l v e s an i t e r a t i v e procedure t o e s t a b l i s h

a c o m p a t i b i l i t y between equat ions ( i ) , ( i i ) and ( i i i ) . I n a s i m p l i f i e d des-

c r i p t i o n t h e i t e r a t i v e procedure runs as f o l l o w s . Assuming an i n i t i a l f i l m -

t h i ckness d i s t r i b u t i o n which i s i n s e r t e d i n t h e Reynolds equat ion , a p res-

sure d i s t r i b u t i o n i s ob ta ined. T h i s i n t u r n i s i n s e r t e d i n t h e e l a s t i c equa-

t i o n g i v i n g an e s t i m a t i o n o f t h e e l a s t i c displacements which i s compared

w i t h t h e i n i t i a l f i l m - t h i c k n e s s d i s t r i b u t i o n . The i t e r a t i o n cont inues u n t i l

a s u f f i c i e n t degree o f con fo rm i t y i s ob ta ined.

Before cons ide r ing the main s o l u t i o n s o f t he EHD problem, a phys i ca l

p i c t u r e o f t he EHD pressure and f i l m p r o f i l e w i l l be ga ined i n cons ide r ing

the drawings shown schemat i ca l l y i n F igu re 4.49 f o r t h e c o n t a c t o f two cy-

l i n d e r s (Ref. 4.133).

b u t i o n o f d r y sur faces s t u d i e d i n Sec t i on 4.2.1. Var ious s t u d i e s have a l s o

i n d i c a t e d t h a t under l u b r i c a t e d cond i t i ons t h e c e n t r a l p a r t o f t h e gap i s

approx imate ly p a r a l l e l . T h i s r e q u i r e s t h a t a t t h e i n l e t r e g i o n the hydrody-

namic p ressure i s lower than t h e H e r t z i a n pressure d i s t r i b u t i o n as sketched

i n F igu re 4.49 ( b ) . I n t h e p a r a l l e l r e g i o n o f t h e gap, t he f l o w volume p e r

u n i t gap w i d t h i s approx imate ly cons tan t . Now, a t t he o u t l e t t h e H e r t z i a n

pressure r a p i d l y decreases and t h e v i s c o s i t y f a l l s severa l o rders o f magni-

F igu re 4.49 ( a ) shows t h e w e l l known Hertzian-contact-pressure d i s t r i -

149

( a ) dry Hertzian contact

( b ) pressure p r o f i l e a t the i n l e t

( c ) f i lm p r o f i l e belonging t o the pressure p r o f i l e

( d ) pressure p r o f i l e and f i lm p r o f i l e o f isothermal smooth-surface E H D contact

Figure 4.49 Schematic representat ion of an E H D contact .

160

tude t o i t s va lue under atmospher ic pressure. Under these cond i t i ons , t h e

requirement o f t h e c o n t i n u i t y o f f l o w leads t o a c o n s t r i c t i o n i n t h e f i l m

p r o f i l e as i n d i c a t e d i n F igu re 4.49 ( c ) . Th i s i s connected, i n accordance

w i t h t h e e l a s t i c i t y equat ion, w i t h a p ressure s p i k e a t t h e o u t l e t . A l l these

cons ide ra t i ons l e a d t o a f i l m p r o f i l e and a p r e s s u r e - d i s t r i b u t i o n shape as

sketched i n F igu re 4.49 (d ) . Recent ly , these d i s t r i b u t i o n s have been de te r -

mined exper imen ta l l y u s i n g spec ia l p ressure t ransducers (Ref. 4.134). A ty-

p i c a l r e s u l t i s shown i n F igu re 4.50 (Ref. 4.94). The f e a t u r e s o f EHD l u b r i -

c a t i o n as descr ibed i n F igures 4.49 and 4.50 a r e now g e n e r a l l y accepted.

F igu re 4.50 Measured pressure d i s t r i b u t i o n i n an EHD c y l i n d e r / c y l i n d e r c o n t a c t (Ref. 4.94)

4 -1 (dHz = 10 bar, n = 20s , rl = r2 = 5cm).

Now, t u r n i n g o u r a t t e n t i o n f rom the phys i ca l p i c t u r e o f EHD t o t h e i n f l u e n -

ces o f t h e va r ious o p e r a t i n g v a r i a b l e s and systems parameters, a r e l a t i o n

d e s c r i b i n g t h e f i l m th ickness was f i r s t ob ta ined by Grubin (Ref. 4.135) i n

the f o l l o w i n g fo rm

Later , Dowson and H igg inson (Ref. 4.136) were a b l e t o show t h a t t he va r ious

s o l u t i o n s o f t h e EHD problem cou ld be summarized t o the fo rmula :

161

where

hmin r

h m i n r

‘ lo

E

a

1 2 v = - (vl t v * )

FN/ L

: minimum f i l m thickness

: radius o f r e l a t i v e curvature

: v i s c o s i t y a t atmospheric pressure and a t the temperature o f the surfaces as they en te r the conjunct ion

pressure v i s c o s i t y c o e f f i c i e n t , def ined by

: composite e l a s t i c modulus

:

T = T o e x p a p

: v e l o c i t y

: load per u n i t w id th o f contact

The r e s u l t s were der ived f o r pure r o l l i n g bu t they are a l so appl icable t o

moderate degrees o f s l i d i n g . The Dowson-Higginson formula has been extended

i n various d i r e c t i o n s (Ref. 4.137, 4.138). Further, ref inements o f t h i s f o r -

mula have been obtained by the experimental methods o f o p t i c a l elastohydro-

dynamic f l u i d t e s t i n g (Ref. 4.139, 4.140). I n add i t i on , a hypo the t i ca l con-

s t i t u t i v e r e l a t i o n f o r EHD o i l f i l m s has been proposed which combines a

l i n e a r e l a s t i c response w i t h a non- l inear shear th inn ing viscous response

(Ref. 4.141).

var iab les encountered i n isothermal smooth-surface EHD problems can be re -

presented by the f o l l o w i n g dimensionless groups:

h Fi lm-thickness parameter : H = - r

The analyses o f e l astohydrodynamic l u b r i c a t i o n show t h a t the major

Load parameter FN/L

: w = - E r

TOV Ve loc i t y parameter : u = - E r

Mater ia ls parameter : G = a E

The s e t o f the f o u r dimensionless groups can be reduced t o th ree w i thou t

any l oss o f g e n e r a l i t y (Ref. 4.133, 4.142, 4.143). Two o f the poss ib le sets,

f o r instance are:

152

HG2, WG2, UG4

The r e s u l t s o f i so thermal , smooth-surface EHD theo ry have been conf i rmed

exper imen ta l l y and a r e now g e n e r a l l y accepted as an i d e a l i z e d b a s i s of t h i s

f i e l d . I n more r e a l i s t i c s i t u a t i o n s , however, two f u r t h e r aspects must be

considered (Ref. 4.144):

( i ) t he d i s s i p a t i o n o f energy w i t h i n the l u b r i c a n t f i l m , i . e . , t he v iscous

h e a t i n g and t h e genera t ion o f i n t e r f a c i a l temperatures and i t s i n f l u -

ence on the l u b r i c a n t v i s c o s i t y and the f i l m th ickness ,

e f f e c t o f a s p e r i t y i n t e r a c t i o n s .

( i i ) t h e sur face roughness. and i t s i n f l u e n c e on t h e f i l m shape and t h e

Another ope ra t i ng c o n d i t i o n which may f r e q u e n t l y be impor tan t b u t r a r e l y

cons idered i s t he supp ly and d i s t r i b u t i o n o f l u b r i c a n t i n t h e neighbourhood

o f t he con junc t i on reg ion . I t has been shown t h a t l u b r i c a n t " s t a r v a t i o n " a l -

t e r s the EHD behav iour o f t he system i n severa l impor tan t ways (Ref. 4.145).

Moreover, t he i n f l u e n c e o f s t a r v a t i o n can be an o v e r r i d i n g f a c t o r on t h e

performance o f machine elements (Ref. 4.146).

e x i t h ( W )

1 u b r i can t

T ( O C ) l 8 ' 1 & 160

temperature

b a l l su r face

temperature

0.2 0.1 0 0 .1 0.2

D is tance f rom c e n t e r (mm)

F igu re 4.51 Temperatures i n s l i d i n g EHD c o n t a c t a long c o n t a c t c e n t e r l i n e (Ref. 4.147)

( b a l l - p l a n e contac t , r = 15.9mm, CiHz = 1GN/m2, v = 1.4111s , Ty = 4OoC),

-1

153

In applying the I R temperature-detecting technique, Winer and co-

workers were able t o measure b o t h lubricant temperatures and surface tempe-

ratures in sl iding E H D point-contact si tuations (Ref. 4.147). Some represen-

tative results are reproduced in Figure 4 .51 .

conditions clearly indicate the importance of the e f fec t of the operating

variables sl iding velocity and contact pressure, on b o t h ball-surface and

f luid temperatures. They also show significant i n l e t zone heating which in

turn will reduce the lubricant viscosity and pressure viscosity coefficient,

the dominant mechanical properties affecting the E H D film thickness.

The friction-induced temperature d a t a measured under var ious operating

The influence of friction-induced temperatures on lubricant viscosity

lowers the film thickness. Therefore the e f fec t o f surface roughness and the

possibil i ty of asperity contacts cannot be neglected in E H D lubrication. The

inclusion o f these effects has led t o the concept of partial E H D lubrication.

A characterist ic factor of partial EHD i s the ra t io , h , of the theore-

t i ca l (isothermal) smooth-surface EHD film thickness h o to the combined

roughness, R , o f the surfaces: -

112 - ho where k = [ R a i t R a E ] IT'

The value of i s calculated e i ther on the basis of readily measured r.m.s.

or c.1.a. (R, ) values, o r in more sophisticated way, by using the standard

deviation of the peak-height distribution of the surface asper i t ies as des-

cribed in Section 4.2.1. The h - r a t i o n o t only i s important i n the l imits of

lubrication and film fa i lure i n roll ing and sl iding situations (see Section

4.5.61, b u t i t can a l so be used in describing the change-over from fu l l EHD t o partial EHD lubrication or "mixed" lubrication and to boundary lubrica-

tion. I f h > 3 t o 5 we expect a fu l l - f lu id EHD film t o separate the sur- faces. A t h = 3 the f i r s t asperity "contacts" occur. A t t h i s point, the fu l l EHD regime of the Stribeck's curve is l e f t and the region of partial

EHD ( a t the minimum o f Stribeck's curve) i s reached.

164

4,5,4 M I X E D LUBRICATION

A s imp le and e legan t exp lana t ion o f t h e regime o f mixed l u b r i c a t i o n i s t o

assume t h a t t he t o t a l a p p l i e d l o a d i s c a r r i e d p a r t l y by t h e hydrodynamic

a c t i o n o f t h e l u b r i c a n t f i l m and p a r t l y by a s p e r i t y con tac ts . Consequently,

t he t o t a l f r i c t i o n f o r c e i s supposed t o be due p a r t l y t o v iscous f r i c t i o n

and p a r t l y t o the a s p e r i t y con tac t . Based on t h i s assumption a coup le o f

models o f mixed l u b r i c a t i o n have been proposed which can be b road ly c l a s s i -

f i e d i n two groups:

Models o f mixed l u b r i c a t i o n , i n which t h e ( c l a s s i c a l ) hydrodynamic

l u b r i c a t i o n theo ry i s used as a s t a r t i n g p o i n t . Theor ies on t h i s b a s i s

a r e due t o Gumbel (Ref. 4.148) , Vogelpohl (Ref. 4.149) , Chr is tensen

(Ref. 4.150) .and Ber the and Godet (Ref . 4.151) .

Models o f mixed l u b r i c a t i o n , which s t a r t f rom t h e EHD l u b r i c a t i o n

theo ry t a k i n g i n t o account t h e a s p e r i t y c o n t a c t component, suggested

by Johnson , Greenwood and Poon (Ref. 4.152) and by T a l l i a n (Ref.

4.153) .

Vogelpohl i n 1954 (Ref. 4.149) extended the express ion f o r t h e f r i c t i o n

c o e f f i c i e n t o f a hydrodynamica l l y l u b r i c a t e d j o u r n a l bear ing , descr ibed i n

s e c t i o n 4.5.2

(So > 1)

t o t h e f o l l o w i n g fo rmula o f mixed l u b r i c a t i o n

where fo i s the s t a t i c c o e f f i c i e n t o f f r i c t i o n and cr and hmin a re t h e r a -

d i a l c learance and t h e f i l m th i ckness a t t he minimum o f t h e S t r i b e c k curve,

r e s p e c t i v e l y .

Chr is tensen i n h i s theory o f mixed l u b r i c a t i o n (Ref. 4.150) used a

m o d i f i c a t i o n o f Reynold’s equa t ion f o r su r faces w i t h roughnesses i n t h e

fo rm o f cont inuous l o n g i t u d i n a l r i dges and w i t h no l a rge -sca le s i d e

leakage. I n i t s i n t e g r a t e d form, t h i s equa t ion becomes

155

E " ( h ' ) - E* (boo) 6 W l + v2) dP - - _

dx E * ( h ' ) 3

where p i s t h e hydrodynamic pressure,

x i s a Car tes ian co -o rd ina te i n t h e d i r e c t i o n o f mot ion ,

1 i s t h e l o c a l dynamic v i s c o s i t y o f t h e l u b r i c a n t ,

h ' i s t he l o c a l f i l m th ickness,

v1 and v2

and E* i s t h e expec ta t i on opera tor , d e f i n e d by

a re t h e v e l o c i t i e s o f t h e sur faces r e l a t i v e t o t h e i r con junc t i on ,

00

E * ( x n ) = 1 xn f ( x ) dx

0

A m o d i f i c a t i o n o f t h e c l a s s i c a l Reynolds equa t ion f o r a p p l i c a t i o n t o t h e

c o n t a c t o f rough su r faces has a l s o been proposed by Ber the and Godet (Ref .

4.151). T h e i r approach a l s o emphasized t h e pronounced i n f l u e n c e o f s l i d i n g

v e l o c i t i e s i n t h e regime o f mixed l u b r i c a t i o n .

Johnson, Greenwood and Poon (Ref . 4.152) combined t h e smooth-surface

EHD theo ry o f Dowson and H igg inson w i t h t h e theo ry o f t h e c o n t a c t o f d r y

rough su r faces developed by Greenwood and W i 11 iamson (see Sec t ion 4.2.1)

i n o r d e r t o app ly t o c o n d i t i o n s o f mixed o r p a r t i a l con tac t .

F igu re 4.52 An EHD c o n t a c t w i t h rough su r faces : ( a ) p ressure d i s t r i b u - t i o n s , ( b ) d iagrammatic r e p r e s e n t a t i o n o f t h e f l e x i b l e elements i n an EHD con tac t .

The s i t u a t i o n i s i l l u s t r a t e d i n F igu re 4.52 ( a ) which rep resen t e i t h e r a

l i n e o r a p o i n t con tac t . The t o t a l p ressure p i s made up o f t h e f l u i d p res-

su re pf and the a s p e r i t y c o n t a c t p ressure pa. As shown d iag rammat i ca l l y i n

156

F igu re 4.52 (b ) , t h e b u l k (Her t z an) de format ion o f t he two s o l i d s under

the a p p l i e d loa t l FN, which g i ves r i s e t o the nominal c o n t a c t area A,, i s

mode l led by the s p r i n g Sh. The o 1 f i l m and t h e a s p e r i t i e s a r e represented

by t h e p a r a l l e l sp r ings S f and Sa, r e s p e c t i v e l y . A l l sp r i ngs a r e non- l i nea r ;

t h e s t i f f n e s s of each increases w i t h compression. From t h i s model i t f o l l o w s

t h a t t he a s p e r i t y p ressure i s determined p r i m a r i l y by the f i l m - t h i c k n e s s - t o -

roughness r a t i o h , de f ined above.

Likewise, i n T a l l i a n ' s theo ry o f p a r t i a l e lastohydrodynamic con tac ts

(Ref. 4.153), t h e 1 - r a t i o i s cons idered as an impor tan t parameter. From the

t h e o r i e s o f p a r t i a l EHD, as o u t l i n e d by T a l l i a n and by Johnson, Greenwood

and Poon, i t may be concluded t h a t i f h i s l ower than a c e r t a i n l i m i t , l e s s

than h = 0.4 say, t he l u b r i c a t i o n mode changes t o boundary l u b r i c a t i o n .

4 5 ,5 BOUNDARY LUBRICATION

The l u b r i c a t i o n regime o f t he u tmost l e f t p a r t o f t he S t r i b e c k curve i s

termed boundary l u b r i c a t i o n . T h i s l u b r i c a t i o n mode i s cha rac te r i zed by t h e

f o l l o w i n g fea tu res :

( a ) t he s o l i d sur faces a r e so c lose toge the r t h a t app rec iab le c o n t a c t

takes p lace between the a s p e r i t i e s ,

( b ) hydrodynamic e f f e c t s and in f l uences o f t h e b u l k rheo l og i ca l p roper -

t i e s o f t he l u b r i c a n t s a re o f l i t t l e o r no importance,

( c ) t h e t r i b o l o g i c a l behav iour i s determined by sur face i n t e r a c t i o n s

between t h i n l a y e r s o f boundary l u b r i c a n t s and the s o l i d sur faces .

Due t o these fea tu res , t h e processes which determine t h e t r i b o l o g i c a l be-

hav iou r o f s o l i d sur faces (see Sect ions 4.2, 4.3, 4.4) a re v a l i d l i k e w i s e

under boundary l u b r i c a t i o n cond i t i ons , namely:

( i )

( i i ) ( i i i ) t h e f r i c t i o n processes, e s p e c i a l l y t he shear ing o f adhesive j u n c t i o n s

( i v )

t he con tac t mechanics and the e l a s t i c and p l a s t i c a s p e r i t y deforma-

t i o n processes,

t he con tac t phys ics and chemis t ry and t h e a c t i o n o f su r face fo rces ,

and the de format ion o f a s p e r i t i e s ,

t h e wear processes which a r e g iven i n t h e genera l case by t h e super-

p o s i t i o n o f e f f e c t s o f su r face f a t i g u e , abrasion, adhesion and t r i b o -

chemical reac t i ons .

157

A l l these s o l i d / s o l i d i n t e r a c t i o n s a r e m o d i f i e d th rough the a c t i o n o f

t he boundary l u b r i c a n t , so t h a t t he t r i b o l o g i c a l behav iour o f a boundary

l u b r i c a t e d system i s determined by t h e processes a t t h e s o l i d / l u b r i c a n t /

s o l i d i n t e r f a c e i n f l u e n c e d by the env i ronmenta l atmosphere. Compared w i t h

the o t h e r l u b r i c a t i o n regimes o f t he S t r i b e c k curve and the d r y s t a t e , t he

t r i b o l o g y o f a boundary l u b r i c a t e d system i s most complex due t o t h e v a r i -

e t y o f i n t e r a c t i o n s and parameters i nvo l ved .

purpose i s t o i n t e r p o s e between the moving su r faces a f i l m t h a t i s a b l e t o

reduce the amount o f d i r e c t s o l i d / s o l i d i n t e r a c t i o n and t h a t i s i t s e l f

e a s i l y sheared. Th is i s p rov ided b e s t by an i n t e r f a c i a l f i l m c o n s i s t i n g o f

l o n g cha in molecules possessing the f o l l o w i n g p r o p e r t i e s :

( a )

( b )

( c )

Concerning t h e l u b r i c a t i n g a c t i o n o f a boundary l u b r i c a n t , i t s main

s t r o n g a t t r a c t i o n between t h e cha ins t o r e s i s t p e n e t r a t i o n by su r face

a s p e r i t i e s ( t h u s m i t i g a t i n g wear processes),

low shear s t r e n g t h t o g i v e a low f r i c t i o n ,

h i g h m e l t i n g p o i n t so t h a t i t p rov ides s o l i d - f i l m p r o t e c t i o n up t o

a h i g h temperature.

Since t h e mechanisms o f boundary l u b r i c a t i o n a re determined ma in l y by t h e

phys i cs and chemis t r y o f t h e s o l i d / l u b r i c a n t / s o l i d i n t e r f a c e , a b r i e f r e -

view o f the chemical compos i t ion o f l u b r i c a n t s i s f i r s t g i ven f o l l o w e d by

a d i scuss ion o f t h e processes o f boundary f i l m f o rma t ion and i t s t r i b o l o -

g i c a l behav iour .

The va r ious k inds o f l u b r i c a n t s may be c l a s s i f i e d i n t o t h r e e genera l

groups:

( I ) "Nonreac t ive" o r " i n d i f f e r e n t " 1 u b r i can ts

Hydrocarbons and most o t h e r base o i l s f a l l i n t h i s c lass . U s u a l l y the most

impor tan t p r o p e r t y o f these m a t e r i a l s i s v i s c o s i t y , which depends on che-

m ica l s t r u c t u r e i n a f a i r l y r e g u l a r f ash ion . The hydrocarbons o r base o i l s

f rom pet ro leum may be c l a s s i f i e d accord ing t o t h e i r s t r u c t u r e i n t o sa tu-

r a t e d ( p a r a f f i n s and naphthenes) and unsa tu ra ted ones ( o l e f i n s and aroma-

t i c s ) . The f o u r c lasses can be t y p i f i e d by t h e f o l l o w i n g s t r u c t u r e s :

( a ) P a r a f f i n

CH3 - CH2 - CH - CH2 - CH3

I CH3

168

( b ) Naphthene

'CH2 \ CH CH2

I I 7H2

CH

( c ) O l e f i n

CH2 = CH - CH - CH3

I CH 3

( d ) Aromat ic

CH CH\ CH

I I1

A l l m ine ra l o i l s c o n s i s t o f molecules which g e n e r a l l y c o n t a i n more than one

type o f hydrocarbon moie ty . C l a s s i f i c a t i o n o f o i l s as p a r a f f i n i c , naphthe-

n i c ( i . e . , c y c l o p a r a f f i n ) o r a romat ic i n d i c a t e s t h e r e l a t i v e concen t ra t i ons

o f t h e mo ie t i es .

( I I )

L u b r i c a n t a d d i t i v e s c o n t a i n i n g a p o l a r group a t tached t o l o n g cha ins o f

methylene groups ( i .e., (-CH2-)n where n > 10) a r e o f t e n r e f e r r e d t o as

" o i l i n e s s " o r " l u b r i c i t y " a d d i t i v e s ; oxygen i s t h e most usua l hetero-atom

i n t h e commonly used m a t e r i a l . Typ ica l examples are :

" O i 1 i ness " agents

159

S t e a r i c acid:

Oleic acid:

0 //

CH3 (-CH2-)15 C-OH

0 //

CH3 ( -CH2-)7 CH = CH ( -CH2-)7 C-OH

Each of these addi t ives possesses an unbranched hydrocarbon chain with a

polar group a t i t s extremity. Besides the long-chain f a t t y acids c e r t a i n

alcohols and e s t e r s of s imi la r s t r u c t u r e a r e a l so used. These mater ia ls can

be dissolved in small quant i t ies (about 1 per cent ) in a base o i l a n d wil l

then a t tach themselves t o the metal surfaces .

(111) " Extreme pressure" ( E P ) and "anti-wear'' (AW) addi t ives

These 1 ubri cant addi t ives usually contain the heteroatoms phosphorus, sul-

f u r o r chlor ine and may addi t iona l ly o r even pr inc ipa l ly contain oxygen,

lead, zinc, boron, selenium, e tc .

Examples are:

Dibenzyldisulfide:

0- CH2

Zinc d ioc ty l -d i t h io -phospha te :

Zn ij L

These addi t ives function under boundary lubr ica t ion conditions by react ing

with the contacting metal a s p e r i t i e s t o form f i lms which a id in the reduc-

tion of in te rmeta l l ic contact and wear and t o prevent ca tas t rophic surface

f a i l u r e s (Ref. 4.154, 4 .155 ) . The major determined operat ing f a c t o r f o r

these act ions i s the operating temperature i n the in te r face .

In order t o understand the mechanisms o f boundary lubr ica t ion , the

physico-chemical processes of i n t e r f a c i a l f i lm formation must be considered.

160

The l u b r i c a n t / s o l i d i n t e r a c t i o n s which l e a d t o the genera t i on o f a p ro tec -

t i v e boundary f i l m can be c l a s s i f i e d i n t o t h r e e mechanisms (Ref. 4.156,

4.157) :

( a ) PHYSICAL ADSORPTION (PHY SISORPTION)

I n a boundary - lub r i ca t i on system, phys i ca l adso rp t i on occurs when t h e mole-

cu les o f t he l u b r i c a n t a re h e l d t o the su r face by van d e r Waals su r face

fo rces ( i . e . , d i p o l e - d i p o l e i n t e r a c t i o n s , see Sec t ion 4.2.2). The molecules

a re weakly bonded, and the f i l m f o rma t ion i s cha rac te r i zed by r e v e r s i b i l i t y

and monomolecular o r mu1 t i m o l e c u l a r l aye rs . P o l a r molecules, p a r t i c u l a r l y

l o n g cha in hydrocarbons, adsorb w i t h p re fe r red v e r t i c a l o r i e n t a t i o n , see

F igu re 4.53. (Fo r i ns tance : adsorbed s t e a r i c a c i d molecules a re 19 R h igh ,

Ref. 4.158.)

u n r e a c t i v e m e t a l

F igu re 4.53 Schematic r e p r e s e n t a t i o n o f p h y s i s o r p t i o n .

The p o l a r a d d i t i v e s condense on t h e su r face t o fo rm a s o l i d f i l m . Many mole-

cu les pack i n as c l o s e l y as p o s s i b l e and s t reng then t h e f i l m w i t h l a t e r a l

cohesive fo rces . Th is s o l i d f i l m , adher ing t o the su r face and w i t h t h e mole-

cu les coher ing t o each o ther , then has the a b i l i t y t o r e s i s t p e n e t r a t i o n o f

a s p e r i t i e s and thus i n h i b i t meta l - to -meta l con tac t . I n a d d i t i o n , a zone o f

low shear s t r e n g t h i s formed between the outermost sur faces o f two monolayers

adsorbed on opposing metal sur faces . A boundary l u b r i c a t e d system w i t h phy-

s i c a l adso rp t i on o f the f i l m i s temperature s e n s i t i v e because hea t causes

161

desorp t i on , d i s o r i e n t a t i o n , o r m e l t i n g o f t h e f i l m . Thus, boundary l u b r i c a -

t i o n dependent upon p h y s i c a l adso rp t i on i s l i m i t e d t o low b u l k temperatures

and c o n d i t i o n s o f low f r i c t i o n a l hea t genera t ion , i . e . , low loads and low

s l i d i n g v e l o c i t i e s .

( b ) CHEMICAL ADSORPTION (CHEMISORPTION)

I n a b o u n d a r y - l u b r i c a t i o n system, chemisorp t ion occurs when t h e molecules

o f t h e l u b r i c a n t a r e h e l d t o t h e su r face by chemical bonds, i . e . , s h o r t -

range su r face fo rces . Compared w i t h phys i so rp t i on , i t i s g e n e r a l l y n o t com-

p l e t e l y r e v e r s i b l e and shows h i g h e r heats o f adso rp t i on (Phys i so rp t i on :

2,000 t o 10,000 cal /mole; Chemisorpt ion: 10,000 t o 100,000 ca l /mo le) . A

w e l l known example o f chemisorp t ion i n boundary l u b r i c a t i o n i s t he r e a c t i o n

o f s t e a r i c a c i d w i t h i r o n ox ide i n the presence o f wa te r t o fo rm a "metal

soap" f i l m o f i r o n s t e a r a t e on the su r face , as i n F i g u r e 4.54.

/ / i i \ \ \ \

/ / / /

\ \ \ \

/ / / /

H - C - H H - C - H H - C - H H-C-H

H - C - H H - C - H H - C - H H - C - H

H - C - H H - C - H H - C - H H - C - H

H - C - H H - C - H H - C - H H - C - H a d h e s i o n

F igu re 4.54 Schematic r e p r e s e n t a t i o n o f chemisorp t ion .

These metal soaps n o t o n l y have d e s i r a b l e shear p r o p e r t i e s , they a l s o have

m e l t i n g p o i n t s cons ide rab ly h i g h e r than those o f t h e o r i g i n a l f a t t y ac id .

Fo r example, t he m e l t i n g p o i n t o f s t e a r i c a c i d i s 69OC; o f i t s metal soaps,

i t i s about 120°C. Chemisorbed f i l m s l u b r i c a t e e f f e c t i v e l y up t o t h e i r

m e l t i n g p o i n t , whether t h e f i l m i s formed " i n s i t u " on a r e a c t i v e su r face

o r spread on an u n r e a c t i v e sur face . Boundary chemisorbed f i l m s p r o v i d e l u -

b r i c a t i o n a t moderate loads, temperatures and s l i d i n g v e l o c i t i e s and f a i l

162

under severe o p e r a t i n g c o n d i t i o n s . The f a i l u r e t o l u b r i c a t e i s a r e s u l t o f

t h e d i s o r i e n t a t i o n , so f ten ing o r m e l t i n g o f t h e f i l m under the combined ac-

t i o n o f t h e o p e r a t i n g v a r i a b l e s and the energy t ransac t i ons .

( c ) CHEMICAL REACTION

I n a boundary - lub r i ca t i on system, chemical r e a c t i o n between t h e s o l i d su r -

faces and t h e l u b r i c a n t molecules occurs when t h e r e i s an exchange of va-

l ence e l e c t r o n s and a new chemical compound i s formed as i l l u s t r a t e d i n

F i g u r e 4.55.

S S S S

S S S S S

F igu re 4.55 Schematic r e p r e s e n t a t i o n o f a boundary f i l m formed by chemical r e a c t i o n .

The boundary f i l m s a re u n l i m i t e d i n th i ckness (governed by d i f f u s i o n p ro -

cesses through t h e c r y s t a l l i n e l a t t i c e s ) and cha rac te r i zed by h i g h a c t i v a -

t i o n and bonding energ ies and i r r e v e r s i b i l i t y . Most o f t h e chemica l l y reac-

t i v e boundary l u b r i c a n t s c o n t a i n su lphur , c h l o r i n e and phosphorus atoms i n

t h e molecule. They a re b e l i e v e d t o f u n c t i o n by fo rm ing m e t a l - s a l t f i l m s o f

low shear s t r e n g t h b u t o f h igh m e l t i n g p o i n t , such as s u l f i d e , c h l o r i d e o r

phosphide, a t t h e i n t e r f a c e . These f i l m s a r e more s t a b l e than any p h y s i c a l l y

o r chemica l l y adsorbed f i l m . Boundary l u b r i c a n t s dependent upon chemical

r e a c t i o n a re s u i t a b l e f o r h i g h load, h i g h temperatures, and h i g h s M d i n g

speeds and l i m i t e d t o r e a c t i v e meta ls . These cond i t i ons a r e commonly r e f e r -

r e d t o as "extreme-pressure" c o n d i t i o n s , a1 though t h e g r e a t e s t s e v e r i t y

a r i s e s f rom h i g h temperatures. A1 though "EP" a d d i t i v e s f u n c t i o n by r e a c t i n g

w i t h the sur faces they must n o t be t o o r e a c t i v e , o the rw ise t r i bo -chemica l

wear may reach very h i g h ra tes .

163

Concerning the t r ibo logica l behaviour of a boundary-lubrication system,

s ince the boundary f i lms may be considered t o be s o l i d and t o behave “as a r i g i d continuation of the s o l i d body” (Ref. 4.159), the contact , f r i c t i o n and wear processes a s discussed in Sections 4.2, 4.3 and 4.4 a r e va l id i n

pr inc ip le . I n order t o descr ibe the f r i c t i o n a l behaviour of the various

boundary f i lms , s t y l i z e d diagrams have been used (Ref. 4.160, 4.161) as in Figure 4.56.

Figure 4.56 Fr ic t ion behaviour o f boundary-lubrication systems (schema t i c ) .

I n t h i s diagram, the coef f ic ien t o f f r i c t i o n f i s plot ted aga ins t the tem- perature T. Curve I i s f o r a system lubr ica ted w i t h a non-polar base o i l .

I t shows t h a t the f r i c t i o n is i n i t i a l l y r e l a t i v e l y high and increases with increasing temperature as the weak physical adsorption bonds are loosened.

Curve I1 i s f o r a f a t t y acid dissolved i n the base o i l . This lubr icant re- a c t s w i t h the metal sur face forming a meta l l ic soap which i s e a s i l y sheared

a t the area of real contact . Up t o Tm, the melting point of the metal soap,

the f r i c t i o n i s low and constant b u t above t h i s point r i s e s s teeply. Curve 111 is representat ive of an EP addi t ive dissolved in the base o i l . The ad- d i t i v e reac ts very slowly below a c e r t a i n react ion temperature Tr. When Tr i s reached, the chemical react ion s t a r t s and the f r i c t i o n c o e f f i c i e n t de- creases as the r a t e of f i lm formation permits a s o l i d f i lm t o carry the load. In t h i s case e f f e c t i v e lubr ica t ion i s provided up t o high temperature.

Curve IV i s a hypothetical curve f o r an e f f e c t i v e combination of I1 and 111.

Good l u b r i c a t i o n i s p rov ided by t he f a t t y a c i d below Tr, w h i l e above t h i s

temperature t h e g r e a t e r p a r t o f t he l u b r i c a t i o n i s due t o t h e EP a d d i t i v e .

I f t h e wear behav iour o f t h e d i f f e r e n t bounda ry - l ub r i ca t i on systems i s

t o be descr ibed i n t h e fo rm o f s t y l i z e d diagrams, t he c h a r a c t e r i s t i c s shown

i n F igu re 4.57 r e s u l t .

Wear

r a t e

K '

F O c r i t Load FN

F igu re 4.57 Wear behav iour o f bounda ry - l ub r i ca t i on systems (schemat ic ) .

I n t h i s diagram, t h e wear c o e f f i c i e n t K ' (wear volume x load- ' x s l i d i n g

d is tance- ' ) on a l o g sca le i s p l o t t e d versus the l oad FN.

Curve ( a ) represents t h e wear behav iour o f a d r y meta l /meta l s l i d i n g

system. As a r e s u l t o f t he wear processes desc r i bed i n Sec t i on 4.4 occur -

r i n g i n i t i a l l y a t t he "ou te r " su r face l a y e r s (see F igu re 4.5) a c e r t a i n

wear r a t e K', r e s u l t s . I f t h e l o a d i s r e l a t i v e l y low, t h e su r face l a y e r s

worn o f f may be rep laced under t h e a c t i o n o f t h e gaseous environment

( " m i l d wear" regime). I f however, t h e l o a d reaches a c e r t a i n l i m i t , FOcrit,

t h e wear process may pene t ra te t o t h e " i n n e r " sur face l a y e r s l e a d i n g t o

"severe wear" and t o an i nc rease o f t he wear r a t e over severa l o rde rs o f

magnitude.

Curve ( b ) i s f o r a system l u b r i c a t e d w i t h a base o i l . The i n f l u e n c e

o f chemical a d d i t i v e s i n a base o i l may l e a d t o two d i f f e r e n t e f f e c t s :

166

( i )

( i i )

a r e d u c t i o n o f t h e wear r a t e K' by a c e r t a i n amount A KO,

an i nc rease o f t he l o a d - c a r r y i n g c a p a c i t y Fcrit by a c e r t a i n

amount A F.

I f the a c t i o n of an a d d i t i v e leads p r i m a r i l y t o t h e e f f e c t ( i ) , as shown

i n curve ( c ) , i t i s c a l l e d "an t i -wear " (AW) a d d i t i v e . The most common types

o f AW a d d i t i v e s a r e those c o n t a i n i n g phosphorus, l i k e m e t a l - d i a l k y l d i t h i o -

phosphate, t r i c r e s y l phosphate o r d i a l k y l phosph i te . Organic c a r b o x y l i c

ac ids , l i k e s t e a r i c ac ids and o l e i c ac ids and t h e i r e s t e r s have a l s o good

AW p r o p e r t i e s . I f the a c t i o n o f an a d d i t i v e l eads p r i m a r i l y t o t h e e f f e c t

( i i ) , as shown i n curve ( d ) o f F igu re 4.57, i t i s termed "extreme pressure

( E P ) " a d d i t i v e . As mentioned above, t he most common t ype o f EP a d d i t i v e s

a re those c o n t a i n i n g s u l f u r and/or c h l o r i n e . Typ ica l s u l f u r - c o n t a i n i n g ad-

d i t i v e s a r e s u l f u r i z e d f a t t y es te rs , terpenes and o l e f i n s o r d ibenzy l d i -

s u l f i d e . The most common c h l o r i n e - c o n t a i n i n g EP a d d i t i v e s a re c h l o r i n a t e d

p a r a f f i n s , c o n t a i n i n g up t o 70% C 1 .

A l though i t i s c l e a r t h a t t h e a d d i t i v e s under boundary c o n d i t i o n s fo rm

p r o t e c t i v e su r face l a y e r s by the physico-chemical processes exp la ined above,

the chemical d e t a i l s and t h e k i n e t i c s o f t he f i l m f o rma t ion and i t s d i s p e r -

s a l a re s t i l l under d i scuss ion . C l e a r l y , i n t h e d i scuss ion o f a d d i t i v e per -

formance bes ides the p r o p e r t i e s o f t h e l u b r i c a n t a l s o t h e p r o p e r t i e s of t h e

metal s u b s t r a t e must be cons idered (Ref. 4.162). The l i t e r a t u r e on boundary

l u b r i c a t i o n p r o p e r t i e s o f a d d i t i v e s and t h e i r va r ious combinat ions i s enor-

mous and cannot be d iscussed i n d e t a i l i n t h e scope o f t h i s volume. F o r

recen t rev iews, see t h e a r t i c l e s by Godfrey (Ref . 4.156, 4.157), Campbell

(Ref. 4.161), F e i n (Ref . 4.163).

shou ld n o t be c losed w i t h o u t a c o m p i l a t i o n o f t he main i n f l u e n c i n g parame-

t e r s o f t h i s most complex f i e l d . Some o f these parameters a re conta ined i n

a fo rmula proposed by C.N. Rowe (Ref. 4.164, 4.165) f o r the r a t e o f adhesive

wear o f a boundary l u b r i c a t e d system. The fo rmula con ta ins two d imens ion less

groups, one o f which i s d e s c r i p t i v e o f t h e s l i d i n g meta l coup le and t h e

o t h e r i s o f t h e e f f e c t i v e n e s s o f t he l u b r i c a n t f i l m a t t he su r face , cons id -

e r i n g t h a t t h e hea t o f adso rp t i on may be t h e c o n t r o l l i n g f a c t o r i n t h e e f -

The t r e a t i s e on t h e b o u n d a r y - l u b r i c a t i o n mode o f a t r i b o l o g i c a l system

fec t i veness o f t h e boundary l u b r i c a n t . The model leads t o t h e express ion :

166

The parameters i n v o l v e d i n t h i s r e l a t i o n may be c l a s s i f i e d under t h e f o l l o w - i n g headings:

Opera t ing v a r i a b l e s :

FN : load

v : v e l o c i t y

1 : s l i d i n g d i s tance

TS : abso lu te temperature o f t h e s l i d i n g su r face

M a t e r i a l s parameters:

p, : f l o w pressure o f t he s o f t e r metal

Q : hea t o f adso rp t i on

Rc : molar gas cons tan t

I n t e r a c t i o n c h a r a c t e r i s t i c s :

da to : fundamental o s c i l l a t i o n t ime o f an adsorbed molecu le

f : f r i c t i o n c o e f f i c i e n t

K, : wear c o e f f i c i e n t o f t h e s l i d i n g metal sur faces

V : wear volume o f t h e boundary l u b r i c a t i o n system

The g r e a t number o f i n f l u e n c i n g f a c t o r s o f a boundary - lub r i ca t i on system

urges t h e need f o r a sys temat ic parameter c o m p i l a t i o n o f t r i b o l o g i c a l sys-

tems as at tempted i n Chapter 8.

: d iameter o f t h e area assoc ia ted w i t h an adsorbed molecu le

4,5,6 THE LIMITS OF LUBRICATION

The surveys presented i n t h e fo rego ing sec t i ons show t h a t l u b r i c a t i o n i s t h e

most impor tan t means o f i n f l u e n c i n g the t r a n s a c t i o n s o f energy and m a t e r i a l s

i n t r i b o l o g i c a l systems and reduc ing f r i c t i o n and m i t i g a t i n g wear. Conse-

quent ly , any d i s tu rbance o r f a i l u r e o f l u b r i c a t i o n has de t r imen ta l conse-

quences f o r t h e t r i b o l o g i c a l behav iour o f t he system. Besides an understand-

i n g o f t h e mechanisms o f p roper l u b r i c a t i o n , i t i s t h e r e f o r e necessary t o

ga in some i n s i g h t i n t o t h e processes and f a c t o r s which de termine a f a i l u r e

o f l u b r i c a t i o n , i . e . , t h e p o s s i b l e " l i m i t s " o f l u b r i c a t i o n .

S t a r t i n g f rom cond i t i ons o f f u l l - f l u i d - f i l m l u b r i c a t i o n and f o l l o w i n g

the course o f t he S t r i b e c k curve e i t h e r t o t h e r i g h t o r t o t h e l e f t , two

d i f f e r e n t types o f t he l i m i t s o f l u b r i c a t i o n a r e met:

167

( a )

( b )

To t h e r i g h t , as f o r i ns tance w i t h i n c r e a s i n g v e l o c i t y , t h e c o n d i t i o n s

o f l am ina r f l u i d f l o w may change t o t u r b u l e n t f l o w .

To t h e l e f t , f o r i ns tance w i t h decreas ing v e l o c i t y , runn ing th rough

t h e va r ious non-hydrodynamic l u b r i c a t i o n regimes, t h e l u b r i c a n t f i l m

may e v e n t u a l l y break down l e a d i n g t o c a t a s t r o p h i c f a i l u r e i n t h e fo rm

o f " s c u f f i n g " o r " se i zu re " (Ref. 4.166).

I n f l u i d mechanics, cons ide r ing a f l u i d o f v i s c o s i t y T and d e n s i t y p f l o w i n g

w i t h a v e l o c i t y v p a s t a l o n g c y l i n d e r o f d iameter d, t h e change f rom lam i -

n a r t o t u r b u l e n t f l o w i s d iscussed i n terms o f t h e Reynolds number

P rl

Re = - v d

Fo r Re < 1 a lam ina r f l u i d f l o w mode i s found. Fo r Re > 1 var ious e f f e c t s

o f d i s tu rbances and tu rbu lences occur , l i k e t h e "KBrmln v o r t e x s t r e e t " ap-

pea r ing f o r Re > 40 (Ref . 4.167).

I n j o u r n a l bea r ings o f t h e t y p i c a l c lea rance r a t i o s 0.001 < c r / r <

0.01, " T a y l o r v o r t e x f l ow" w i l l develop i n t h e l u b r i c a n t f i l m b e f o r e t h e

onset o f t u rbu lence . I n s t u d y i n g the f l o w between c o n c e n t r i c c y l i n d e r s i n a

c l a s s i c a l i n v e s t i g a t i o n (Ref. 4.168), T a y l o r found t h a t t h e t r a n s i t i o n t o

v o r t e x f l o w occurs i f the T a y l o r number

For non-concent r i c c y l i n d e r s , i . e . , bear ings , t h e s i t u a t i o n i s l e s s c l e a r .

A t heo ry f o r p r e d i c t i n g t h e t r a n s i t i o n t o v o r t e x f l o w f o r non-concent r i c

c y l i n d e r s has been developed by d i Prima (Ref . 4.169). As t h e r o t a t i o n a l

v e l o c i t y o f a j o u r n a l b e a r i n g i s inc reased above t h e onset o f v o r t i c e s ,

f u l l t u rbu lence may occur a t a Reynolds number o f about Re z 2500. Th is

regime has been ana lyzed by Constan t inescu (Ref . 4.170). Fo r a rev iew o f

f u r t h e r s tud ies see (Ref. 4.171).

s i d e o f t he S t r i b e c k curve, t h e reg ions o f t h e va r ious l u b r i c a t i o n modes

can be s p e c i f i e d i f t h e S t r i b e c k cu rve i s expressed i n terms o f t h e f i l m

t h i ckness t o roughness r a t i o X and combined w i t h t h e no -con tac t t ime f r a c -

t i o n 5 determined w i t h t h e e l e c t r i c a l - c o n t a c t - r e s i s t a n c e measur ing tech-

n ique (Ref . 4.172, 4.173). (The no-contac t t ime f r a c t i o n < i s d e f i n e d as

Turn ing now t o t h e l i m i t s o f f u l l - f l u i d l u b r i c a t i o n on t h e l e f t - h a n d

168

t he percentage o f t i m e d u r i n g which the e l e c t r i c a l c o n t a c t res i s tance Rc

o f a con tac t i s h i g h e r than a c e r t a i n Rc- leve l i n d i c a t i n g complete separa-

t i o n o f t he sur faces , see Sec t ion 7.2.3.) The v a r i a t i o n s o f t h e f r i c t i o n

c o e f f i c i e n t f and t h e no-contac t t ime f r a c t i o n as f u n c t i o n o f t he f i l m -

th ickness t o roughness r a t i o A a r e shown schemat i ca l l y i n F i g u r e 4.58.

u- 0.3 c, C aJ u

u-

u

.C

Gz 0.2

8

s 0.1 '7 c, u L .C

100

P ao .I- -

60 u u m c 40

0 c, 20 i m

c,

W O c .r

u u O L z +

I I I I I I

- - - -

I

1 2 3 4 5 6

F i l m th i ckness t o roughness r a t i o h

F igu re 4.58 S t r i b e c k curve and no-contac t t ime f r a c t i o n (schemat ic ) .

With the diagram shown i n F igu re 4.58, two t r a n s i t i o n s can be s p e c i f i e d :

( a ) The t r a n s i t i o n f rom f u l l f l u i d - f i l m l u b r i c a t i o n t o mixed l u b r i c a t i o n

o r p a r t i a l EHD l u b r i c a t i o n , i n d i c a t e d by

5 < 100% and h i a 3

( b ) The onset o f cont inuous a s p e r i t y c o n t a c t w i t h i n t h e i n t e r f a c e , i n d i c a t e d

by

5 = 0% and A c z l

169

The d e s c r i p t i o n o f t he t r a n s i t i o n s ( a ) and ( b

the f i lm- th i ckness - to - roughness r a t i o h . The

the o p e r a t i n g v a r i a b l e s and t h e m a t e r i a l and

c r i b e d i n Sec t i on 4.5.3.

has been g i ven i n terms o f

va lue o f h i n t u r n depends on

u b r i c a n t p r o p e r t i e s as des-

Another way o f d e s c r i b i n g t h e t r a n s i t i o n s between t h e va r ious l u b r i c a -

t i o n modes i s t o s tudy t h e change o f A as f u n c t i o n o f t h e o p e r a t i n g va r iab -

l e s f o r a g i ven s l i d i n g system. I n t h e f o l l o w i n g , a s i m p l i f i e d p h y s i c a l p i c -

t u r e o f t h e d i f f e r e n t t r a n s i t i o n s f rom a f u l l - f l u i d EHD l u b r i c a t i o n t o t h e

breakdown o f boundary - lub r i ca t i on f i l m s i s o u t l i n e d (Ref. 4.174). The s i t u a -

t i o n i s i l l u s t r a t e d i n t h e schematic diagram o f F igu re 4.59. On t h e l e f t t h e

v a r i a t i o n o f h w i t h i n c r e a s i n g c o n t a c t p ressure , p, i s shown f o r a g i ven

s l i d i n g system o f l u b r i c a t e d p o i n t o r l i n e con tac t , s p e c i f i e d by t h e mate-

r i a l s parameters (E, r, R, l o , a ) and the o p e r a t i n g v a r i a b l e s (FN, v, T ) .

On the r i g h t , t he d i f f e r e n t p o r t i o n s o f t h e c o n t a c t p ressure a r e desc r ibed

schemat i ca l l y .

pI f lu id pressure p o asperity contact pressure

pcrr l criticol failure pressure

-Ap Pl'O -I 1-P = PI 'Po

F igu re 4.59 Schematic r e p r e s e n t a t i o n of dynamic EHD c o n t a c t and f a i l u r e c o n d i t i o n s .

The A, curve represents t h e v a r i a t i o n o f A w i t h i n c r e a s i n g c o n t a c t p ressure

i n which ho i s c a l c u l a t e d on t h e b a s i s o f i so the rma l smooth-surface EHD

theo ry and i n which Ro represents the i n i t i a l su r face roughness. I n t h e

lower Adyn curve, two dynamic i n f l uences a r e taken i n t o account:

170

( i 1

( i i )

From

The increase o f t h e i n t e r f a c i a l temperature AT, es t ima ted on t h e

b a s i s o f B l o k ' s theory , see Sec t ion 4.3.4, (The assumption t h a t t h e

i n t e r f a c i a l temperature r i s e , A T , i n s l i d i n g EHD con tac ts can be e s t i -

mated on t h e b a s i s o f B l o k ' s theo ry i s supported by t h e d i r e c t I R -

temperature measurements performed by Winer and co-workers, Ref. 4.147,

see a l s o F i g u r e 4.51.)

The increase i n su r face roughness d u r i n g the s l i d i n g process. (The

ac tua l "dynamic" su r face topography has been measured i n separa t i ng

t h e s l i d i n g su r faces r a p i d l y a t d i f f e r e n t stages o f t h e t e s t . )

the values o f ( i ) , t h e v i s c o s i t y 7 = -q ( T + A T ) and t h e v i s c o s i t y -

p ressure c o e f f i c i e n t a = a ( T + A T ) a r e es t ima ted and used i n re -ca l cu -

l a t i n g t h e "dynamic" EHD f i l m t h i ckness h. I f t h i s (reduced) f i l m t h i ckness

i s d i v i d e d by t h e a c t u a l dynamic su r face roughness values ( i i ) , t he Adyn

curve o f F igu re 4.59 i s ob ta ined. The whole cha in o f events which leads t o

l u b r i c a n t f a i l u r e can now be d iscussed on the b a s i s o f t h e schematic d i a -

gram o f F igu re 4.59:

i n i t i a l f i lm- th ickness- to - roughness r a t i o o f h > 3 t o 4, c a l c u l a t e d on t h e

b a s i s o f convent iona l smooth-surface i so the rma l EHD theory , i t cou ld be ex-

pec ted t h a t t h e system operates under f u l l f l u i d - f i l m cond i t i ons . However,

depending on t h e va lues o f t he o p e r a t i n g v a r i a b l e s (F,,,, v, TV) and t h e ma-

t e r i a l data, a c e r t a i n amount o f i n t e r f a c i a l v iscous h e a t i n g must be taken

i n t o account, which then lowers t h e v i s c o s i t y qo and the p r e s s u r e - v i s c o s i t y

c o e f f i c i e n t a , l e a d i n g t o a decrease i n t h e nominal values o f h . I f then h

f a l l s below a c e r t a i n va lue ( A c 3, say), t h e f i r s t a s p e r i t y con tac ts occu r

and t h e reg ion o f p a r t i a l EHD i s reached. I n t h i s reg ion , t h e Adyn curve

r a t h e r than t h e ho curve i s v a l i d . The c o n t a c t p ressure i s then made up o f

t h e f l u i d p ressure pf and t h e a s p e r i t y p ressure pa. Through t h e a c t i o n o f

i n t e r f a c i a l v iscous h e a t i n g and a s p e r i t y c o l l i s i o n heat ing , as w e l l as con-

t a c t topography changes, A decreases s t e e p l y w i t h i n c r e a s i n g p u n t i l a

va lue o f h i s reached a t which t h e a c t i o n o f an EHD f i l m ends, i .e . ,

pf = 0. Now, t h e whole con tac t p ressure i s c a r r i e d by a s p e r i t y con tac t , i .e . ,

p = pa. I n t h e r e g i o n o f f u l l a s p e r i t y con tac t , t h e onset o f " i n c i p i e n t

s c u f f i n g " i s determined, o f course, by t h e s t a b i l i t y o f t h e a s p e r i t y su r face

f i l m s , which i n t u r n a r e a f f e c t e d by t h e metal/lubricant/atmosphere i n t e r -

a c t i o n s and the genera t i on o f f r i c t i o n a l heat i n t h e i n t e r f a c e . F a i l u r e oc-

curs , i f , f rom t h e p o i n t a t which pf = 0 and onwards, t he c o n t a c t p ressure

i s inc reased by more than an amount A p , t h e l o a d - c a r r y i n g c a p a c i t y o f t h e

I f i n s l i d i n g EHD con tac ts t h e exper imenta l c o n d i t i o n s l e a d t o an

dyn

171

su r face f i l m s (see S e c t i o n 4.5.5). The break through o f t h e s u r f a c e layer;

i n i t s e l f may a l s o occur as another s tepwise process i n which f i r s t t h e

"ou te r " su r face f i l m s (phys i - o r chemisorbed l a y e r s ) and t h e n t h e " i n n e r "

su r face l a y e r s (ox ide l a y e r s and t h e c o l d worked l a y e r s ) a r e broken o r

t he rma l l y desorbed. I t f o l l o w s t h a t t h e mechanisms o f f a i l u r e o f t h i n - f i l m

l u b r i c a t i o n of s l i d i n g concent ra ted con tac ts a r e determined by t h e p h y s i c a l

and chemical na tu re o f p r o t e c t i n g su r face l a y e r s as w e l l as t h e EHD and

a s p e r i t y c o n t a c t c o n d i t i o n s as a f u n c t i o n o f t h e o p e r a t i n g v a r i a b l e s and t h e

dynamic i n t e r f a c i a l changes.

F i g u r e 4.60 F r i c t i o n c o e f f i c i e n t and c o n t a c t topograph ies a t d i f f e r e n t stages o f f a i l u r e ( s t a t i o n a r y b a l l o f f o u r - b a l l system).

An e m p i r i c a l c h a r a c t e r i z a t i o n o f t h e c r i t i c a l values o f t h e o p e r a t i n g v a r i -

ab les a t t he f a i l u r e t r a n s i t i o n can now be ob ta ined as f o l l o w s :

I f d u r i n g a g i ven change o f o p e r a t i n g v a r i a b l e s t h e f r i c t i o n c o e f f i -

c i e n t f and the wear c o e f f i c i e n t K ' (wear volume x load- ' x s l i d i n g d i s -

tance-') a r e recorded, t h e f a i l u r e t r a n s i t i o n i n d i c a t i n g " i n c i p i e n t scu f -

f i n g " man i fes ts i n sharp jumps o f b o t h t h e f r i c t i o n c o e f f i c i e n t and t h e

wear c o e f f i c i e n t (Ref. 4.175, 4.176, 4.177). F o r t h e case o f l u b r i c a t e d

s l i d i n g concen t ra ted con tac ts , t h e onset o f i n c i p i e n t s c u f f i n g i s charac-

t e r i z e d by t h e t r a n s i t i o n s

f < 0 . 1 - f > 0.3

112

An exper imenta l example of the f r i c t i o n t r a n s i t i o n , i n

te r fe rograms o f t h e s l i d i n g sur faces a t t h e d i f f e r e n t

connect ion w i t h i n -

tages o f f i l m f a i l u r e

as descr ibed above, i s shown i n F igu re 4.60 (Ref . 4.174).

s p e c i f y the c r i t i c a l l o a d FN ( o r p ressure p ) determined f o r a g i ven cons tan t

s l i d i n g v e l o c i t y v and a g i ven b u l k o i l temperature TV d u r i n g a g i ven t e s t

d u r a t i o n t. I f n e x t t he c r i t i c a l f a i l u r e l oad i s determined f o r va r ious v a l -

ues o f v and TV, w i t h i n a g i ven t ime t, i t has been found exper imen ta l l y

t h a t t h e c r i t i c a l l o a d FN decreases w i t h bo th i n c r e a s i n g s l i d i n g v e l o c i t y v

and b u l k o i l temperature TV as i l l u s t r a t e d i n F igu re 4.61, (Ref. 4.178,

4.179). I n combining these diagrams, i t i s then p o s s i b l e t o desc r ibe the

l i m i t s of l u b r i c a t i o n i n a three-dimensional l oad -ve loc i t y - tempera tu re d i a -

gram, rep resen t ing the c r i t i c a l values o f a l l t he opera t i ng v a r i a b l e s

(FN, v, T V ) a t t h e f a i l u r e t r a n s i t i o n . Th is diagram has been termed " f a i l u r e

surface" (Ref. 4.180) and i s shown i n F igu re 4.62.

The f a i l u r e su r face separates the reg ion o f e f f e c t i v e l u b r i c a t i o n

(below the su r face ) f rom t h a t o f i n e f f e c t i v e l u b r i c a t i o n (above t h e su r face )

and shows the i n t e r r e l a t i o n o f t he values o f o p e r a t i n g v a r i a b l e s a t t he

f a i l u r e t r a n s i t i o n . ( I t should be mentioned t h a t beyond the f a i l u r e t r a n s i -

t i o n shown i n F igu res 4.60 t o 4.62, i n the r e g i o n o f i n e f f e c t i v e l u b r i c a t i o n ,

o t h e r f r i c t i o n and wear t r a n s i t i o n s may occur which a re assoc ia ted w i t h me-

t a l l u r g i c a l t rans fo rma t ions i n t h e s l i d i n g sur faces , Ref. 4.179. The d i f -

f e r e n t f r i c t i o n and wear t r a n s i t i o n s have been discussed i n d e t a i l by G.

Salomon, Ref. 4.181.)

Besides the dependence o f f a i l u r e on t h e opera t i ng v a r i a b l e s , t he i n -

f l uence o f t he l u b r i c a n t p r o p e r t i e s i s o f g r e a t i n t e r e s t . From t h e schematic

diagram o f F igu re 4.59, i t i s c l e a r t h a t bo th v i s c o s i t y and the su r face re -

a c t i v i t y o f l u b r i c a n t a d d i t i v e s i n f l u e n c e the f a i l u r e t r a n s i t i o n and the

l o c a t i o n and shape o f t h e f a i l u r e sur face . Both i n f l uences s h i f t t he c r i t i -

c a l f a i l u r e l oad t o h i g h e r values. I t has been found exper imen ta l l y t h a t

t h e i n f l u e n c e o f v i s c o s i t y on f a i l u r e i s most pronounced a t low s l i d i n g ve-

l o c i t i e s and low temperatures, whereas the i n f l u e n c e o f su r face r e a c t i v e

agents i s most pronounced a t h i g h s l i d i n g v e l o c i t i e s and h i g h temperatures

(Ref. 4.182). The i n f l u e n c e of l u b r i c a n t v i s c o s i t y on t h e l o c a t i o n and t h e

The above t r a n s i t i o n s o f f and K' can then be used as a c r i t e r i o n t o

173

.-. 800 z

LL

m 0

v z

'cI 600

400 - L 3 7

2 200

i n e f f i c i e n t

1 u b r i c a t i o n 1 u b r i c a t i o n

v = cons t .

(0.05 m / s )

30 60 90 120 0.03 0.05 0.1 0.3 0.5 1.0

Bu lk o i l temperature TV(OC) S l i d i n g v e l o c i t y v(m/s)

F i g u r e 4.61 F a i l u r e l o a d or nominal i n i t i a l mean Her t z p ressure as a f u n c t i o n o f ( a ) b u l k o i l temperature and ( b ) s l i d i n g v e l o c i t y .

s t e e l A I S I 52100

l u b r i c a n t SAE 10 W

( 7 = 33 CP/37OC)

0.05

F i g u r e 4.62 The f a i l u r e su r face : dependence o f f a i l u r e on l o a d FN, v e l o c i t y v, and temperature TV.

174

shape o f the f a i l u r e surface can be seen from Figure 4.63. The in f l uence

o f l u b r i c a n t add i t i ves on the f a i l u r e t r a n s i t i o n s has been stud ied exten-

siveFy by Sakurai and co-workers, (Ref. 4.183, 4.184, 4.185).

s tee l AISI 52100 - base o i l ( 7 = 460 cP/37OC)

6\\ --- base o i l ( T = 33 cP/37OC)

Figure 4.63 I n f l uence o f l u b r i c a n t v i s c o s i t y on the shape and l o c a t i o n o f the f a i l u r e surface.

F ina l l y , i t should be mentioned t h a t besides the in f luence o f the l u b r i -

can t ' s v i s c o s i t y and chemical r e a c t i v i t y , the contact geometry, i.e., the

type o f Her tz ian contact, l i k e "po in t " contact o r " l i n e " contact and the

r a d i i o f curvature in f luence the f a i l u r e l i m i t s (Ref. 4.186, 4.187). I n

addi t ion, t he type o f motion, e.g., t he s l i d e / r o l l r a t i o i s a lso o f great

importance i n t h a t f o r pure s l i d i n g the f a i l u r e phenomena are most pro-

nounced whereas under pure r o l l i n g condi t ions s c u f f i n g f a i l u r e i s u n l i k e l y

t o occur.

f i n g ) f a i l u r e t o occur f o r a tribo-mechanical system which operates i n i -

t i a l l y i n the regimes o f f u l l hydrodynamic o r elastohydrodynamic l u b r i c a t i o n :

I n conclusion, i t appears t h a t three condi t ions must be met f o r ( scu f -

176

( A ) The breakdown o f t h e f u l l - f l u i d hydrodynamic o r elastohydrodynamic

f i l m .

(B ) The break through o f ( p r o t e c t i v e ) su r face l a y e r s .

( C ) The occur rence o f s t r o n g metal-metal adhesion bonds.

Depending on t h e t ype o f t r ibo-mechan ica l system and o p e r a t i n g c o n d i t i o n s ,

t he sequence o f events ( A ) , ( B ) , ( C ) l e a d i n g t o f a i l u r e may occu r as a

"s tepwise" process, as exp la ined i n F i g u r e 4.59 f o r p o i n t c o n t a c t cond i -

t i o n s and r e l a t i v e l y low s l i d i n g v e l o c i t i e s . On t h e o t h e r hand, f o r o t h e r

exper imenta l c o n d i t i o n s , e.g., h i g h e r s l i d i n g v e l o c i t i e s , t h e t h r e e con-

d i t i o n s ( A ) , ( B ) , ( C ) , may apparan t l y c o i n c i d e i n a " c o l l a p s e " t y p e o f

1 u b r i c a n t f a i l u r e .

I t f o l l o w s t h a t f rom a systems p o i n t o f v iew t h e f a i l u r e l i m i t s depend

on t h e o p e r a t i n g v a r i a b l e s ( l o a d FN, v e l o c i t y v, temperature T, t i m e t )

as w e l l as on t h e s t r u c t u r e o f t h e system (elements of t h e system A, p ro -

p e r t i e s o f elements P, i n t e r r e l a t i o n s between t h e elements R) c h a r a c t e r i z e d

s y m b o l i c a l l y as:

f a i l u r e l i m i t s = f ( o p e r a t i n g v a r i a b l e s ; system's s t r u c t u r e )

f a i l u r e l i m i t s = f ( X ; S )

where X = [ FN, v , T, t }

S = { A , P, R }

Wi th the diagrams presented i n t h i s sec t i on , a p h y s i c a l p i c t u r e o f t h e

f a i l u r e o f l u b r i c a n t f i l m as w e l l as a b a s i s f o r a c o m p i l a t i o n o f t h e i m -

p o r t a n t system's parameters t h a t govern t h e l i m i t s o f l u b r i c a t i o n i s ob-

ta ined. Together w i t h t h e r e s u l t s o f t h e fo rego ing sec t i ons d e s c r i b i n g t h e

va r ious t r i b o l o g i c a l processes, these d a t a w i l l be used i n s t u d y i n g t h e

i n f l u e n c e o f t h e t r i b o l o g i c a l processes on t h e s t r u c t u r e and f u n c t i o n o f

mechanical systems.

176

5 Influence of

tri bological processes on structure of mechanical

the systems

5 , 1 GENERAL CONSIDERATIONS

Having s t u d i e d i n some d e t a i l t h e va r ious t r i b o l o g i c a l processes, i .e . , t h e

con tac t , f r i c t i o n , wear and l u b r i c a t i o n processes, we a r e now i n a p o s i t i o n

t o d iscuss t h e i n f l u e n c e s o f these processes on t h e behav iour o f whole

t r ibo-mechan ica l systems. According t o t h e systems concept o u t l i n e d i n

Chapters 2 and 3, t h e d e s c r i p t i o n o f a t r ibo-mechan ica l system must i nc lude :

( I ) The s t r u c t u r e o f t h e system, cha rac te r i zed f o r m a l l y by t h e s e t

S = ( A , P, R] , where

( A ] : t h e elements, i .e . , t h e m a t e r i a l components o f t h e system,

(PI : t h e r e l e v a n t p r o p e r t i e s o f t h e elements o f t h e system,

{ R) : t h e i n t e r r e l a t i o n s between t h e elements.

(11) The f u n c t i o n o f t h e system, c o n s i s t i n g o f :

{ X I : t h e i n p u t s o f t h e system,

{ Y } : the ou tpu ts o f t h e system,

T : the f u n c t i o n a l t rans fo rma t ion o f t h e i n p u t s i n t o t h e ou tpu ts .

I n eng inee r ing a p p l i c a t i o n s , t h e i n t e r e s t i s o f t e n ma in l y concent ra ted on

the f u n c t i o n a l behav iour o f t h e system under cons ide ra t i on . I n t h i s connec-

t i o n a t t e n t i o n shou ld be drawn t o t h e g r e a t i n f l u e n c e o f t h e system's

s t r u c t u r e on t h e f u n c t i o n a l performance o f a system. I t was exp la ined i n Chapters 2 and 3 t h a t i t i s o n l y p e r m i t t e d t o concent ra te e x c l u s i v e l y on

t h e f u n c t i o n a l aspect o f a g i ven system i f t h i s system possesses a cons tan t

177

i n v a r i a b l e s t r u c t u r e . Only i n these cases - which, f o r i ns tance , a r e o f t e n

g i ven f o r e l e c t r o n i c systems - i s i t p o s s i b l e t o desc r ibe t h e behav iour o f

t he whole system i n terms o f { X ) - { Y ) i n p u t - o u t p u t r e l a t i o n s and t o model

t h e behav iour o f t h e system by mathematical o r symbol ic means, l i k e t h e

network techniques o f system mode l l i ng . Most t r ibo-mechan ica l systems, how-

ever, possess s t r u c t u r e s which may change d u r i n g t h e f u n c t i o n a l performance

o f t he system due t o the t r i b o l o g i c a l processes descr ibed i n t h e fo rego ing

chapter . Therefore, i n t h e d e s c r i p t i o n o f t r ibo-mechan ica l systems i t must

be taken i n t o account t h a t these systems g e n e r a l l y possess a dynamic sys-

tem's s t r u c t u r e as w e l l as a dynamic sys tem's f u n c t i o n .

Accord ing t o t h e d e f i n i t i o n o f t h e s t r u c t u r e o f a system, t h e changes

i n a t r ibo-mechan ica l system's s t r u c t u r e may i n v o l v e :

( i ) The c r e a t i o n o r a n n i h i l a t i o n o f elements o f t h e system.

Examples a r e t h e genera t i on o f " t h i r d bod ies" i n t h e t r i b o l o g i c a l

c o n t a c t o f d r y sur faces i n the fo rm o f " f r i c t i o n polymers" o r r e a c t i o n

produc ts o r , on t h e con t ra ry , t h e d e s t r u c t i o n o f l u b r i c a n t f i l m s .

( i i ) Changes i n t h e i n t e r r e l a t i o n s o f t h e elements.

Examples a r e the v a r i a t i o n o f l u b r i c a t i o n modes i n f o l l o w i n g the

c o n d i t i o n s o f t h e S t r i b e c k curve, o r changes i n wear mechanisms.

( i i i ) Changes i n t h e p r o p e r t i e s o f t h e system's elements.

Examples a r e t h e t r i b o - i n d u c e d changes i n su r face topography o r i n

t h e hardness and s t r e n g t h p r o p e r t i e s o f s l i d i n g o r r o l l i n g sur faces .

These aspects a r e n o t o n l y impor tan t i n t h e a n a l y s i s o f e x i s t i n g t r i b o -

mechanical systems, they shou ld a l s o be cons idered c a r e f u l l y i n t h e des ign

o f new systems (see Sect ions 5 .4 and 6 . 6 ) . C l e a r l y , t h e d e t a i l s o f t h e

dynamic changes o f t h e sys tem's s t r u c t u r e depend on t h e t ype o f t r i b o -

mechanical system under c o n s i d e r a t i o n as w e l l as i t s f u n c t i o n a l purpose and

i t s o p e r a t i o n a l v a r i a b l e s . A1 though t r ibo-mechan ica l systems d i f f e r ve ry

b road ly i n des ign and f u n c t i o n (as can be seen f rom t h e c o m p i l a t i o n o f

t r ibo-mechan ica l systems g i ven i n t h e Appendix A ) , i t shou ld be a t tempted

t o s tudy t h e bas i c phenomena o f t h e t r i b o - i n d u c e d changes o f t h e s t r u c t u r e

o f t r ibo-mechan ica l systems which a re o f general importance. The main

fea tu res o f t h e above aspects ( i ) and ( i i ) have a l ready been d iscussed i n

Sec t ions 4.4 and 4 . 5 . 6 under t h e headings o f "wear processes" and " t h e

l i m i t s o f l u b r i c a t i o n " . I n t h e f o l l o w i n g t h e b a s i c aspects o f c l a s s ( i i i )

o f t h e t r i b o - i n d u c e d changes o f t h e s t r u c t u r e o f mechanical systems a re s tud ied .

178

5 2 CHANGES IN SYSTEM'S ELEMENTS PROPERTIES

I n cons ide r ing t h e p o s s i b l e t r i b o - i n d u c e d changes o f t h e p r o p e r t i e s o f t h e

elements o f a t r ibo-mechan ica l system i t shou ld be borne i n mind t h a t a l l

i n t e r a c t i n g components o f a system may change t h e i r r e l e v a n t p r o p e r t i e s t o

some e x t e n t d u r i n g t h e f u n c t i o n a l performance o f t h e system. I n Chapters 2

and 3 i t has been descr ibed t h a t t h e c e n t r a l p a r t o f t r ibo-mechan ica l sys-

tems cons is t s , i n genera l , o f f o u r components as i n d i c a t e d schemat i ca l l y

i n F i g u r e 5.1 (see a l s o Appendix B ) :

(1) The f i r s t machine element

( 2 ) A second machine element

(3 ) The l u b r i c a n t

(4 ) The atmospher ic environment

( f r i c t i o n and wear coup le)

t r i b o l o g i c a l processes (see Chapter 4 )

system envelope

F i g u r e 5 .1 Schematic r e p r e s e n t a t i o n of t h e main components o f t r ibo-mechan ica l systems.

The p o s s i b l e changes o f t h e l u b r i c a n t (3 ) and i t s i n f l u e n c e s on t h e s t r u c -

t u r e and f u n c t i o n o f t r ibo-mechan ica l systems were d iscussed i n some d e t a i l

i n t h e s e c t i o n on t h e l i m i t s o f l u b r i c a t i o n (Sec t i on 4.5.6). The i n f l u e n c e s

o f t h e element (4 ) , t h e atmospher ic environment and i t s changes, have i n

the p a s t o f t e n n o t been p a i d t h e a t t e n t i o n t h e y deserve. These changes,

which may i n c l u d e v a r i a t i o n s o f t h e chemical compos i t ion o f t h e environment

and i t s humid i ty , have a s t r o n g i n f l u e n c e on a1 1 t r i bo -chemica l processes

(see Sect ions 4.4.5 and 4.5.5). I n these processes a l s o t h e i n t e r a c t i o n s

between t h e environmental atmosphere ( 4 ) and the l u b r i c a n t ( 3 ) must be taken

i n t o cons ide ra t i on .

179

The t r i b o - i n d u c e d changes o f t h e p r o p e r t i e s o f t h e elements ( 1 ) and

( 2 ) - t h e main elements i n v o l v e d i n t h e t ransmiss ion o f t h e f u n c t i o n a l sys-

tem's i n p u t s and ou tpu ts - may be c l a s s i f i e d , accord ing t o t h e r e s u l t s o f

Chapter 4, b r o a d l y i n t o t h e f o l l o w i n g groups:

( a ) changes i n su r face topography,

( b ) changes i n su r face composi t ion,

( c )

I n t h e f o l l o w i n g , some o f t h e main f e a t u r e s o f these t r i b o - i n d u c e d changes

o f t he p r o p e r t i e s o f elements (1 ) and ( 2 ) o f mechanical systems w i l l be

discussed. As i n Chapter 4, t h e d i scuss ion i s r e s t r i c t e d t o t h e b a s i c phys-

i c a l phenomena o f t h e s u b j e c t ma t te r .

changes i n su r face s t r e n g t h p r o p e r t i e s .

5,2 1 SURFACE TOPOGRAPHY CHANGES

I n a l l t r ibo-mechan ica l systems i n which s o l i d - s o l i d c o n t a c t o f su r faces i n

r e l a t i v e mot ion occurs, i t must be expected t h a t t h e su r face topography may

undergo some changes d u r i n g t h e f u n c t i o n a l o p e r a t i o n o f t h e system. These

changes may be due t o two e f f e c t s :

( i ) p l a s t i c c o n t a c t deformat ion,

( i i ) wear processes.

Consider f i r s t t h e su r face topography changes due t o p l a s t i c c o n t a c t d e f o r -

mat ion. Accord ing t o Sec t i on 4.2.1 t h e t ype o f c o n t a c t de format ion can be

d i s t i n g u i s h e d by t h e p l a s t i c i t y index 4:

E : Combined e l a s t i c modulus

H : Hardness

6' : Standard d e v i a t i o n o f peak h e i g h t d i s t r i b u t i o n

p : Mean r a d i u s o f a s p e r i t i e s

If f o r a g i ven system, t h e c a l c u l a t i o n o f JI l eads t o a va lue o f

t h e p r o b a b i l i t y o f p l a s t i c c o n t a c t de fo rma t ion i s very smal l . I f on t h e

o t h e r hand,

a s p e r i t y f l o w must be expected. The p l a s t i c c o n t a c t de fo rma t ion changes t h e

su r face roughness data, such as Ra o r RZ (see Sec t ion 4.2.1) and m o d i f i e s

t h e shape and the c h a r a c t e r i s t i c s o f t h e a s p e r i t y h e i g h t d i s t r i b u t i o n curve

and the a u t o - c o r r e l a t i o n f u n c t i o n o f t h e su r face p r o f i l e .

JI -= 0.6

JI > 1, permanent su r face topography changes due t o p l a s t i c

180

40

35

- 30 - 25 5

.," 20 + r

a I

15

10

5 -

It i s w e l l e s t a b l i s h e d t h a t many eng ineer ing sur faces have a Gaussian

h e i g h t d i s t r i b u t i o n . I f t h e i n i t i a l sur face p r e p a r a t i o n techn ique i n v o l v e s

a l a r g e number o f repeated events which occur randomly over t h e sur face , i t

f o l l o w s immediately f rom the Cen t ra l L i m i t Theorem o f s t a t i s t i c s (Ref. 5.1)

t h a t t he topography o f t h e su r face w i l l tend towards a Gaussian h e i g h t

d i s t r i b u t i o n . Consequently, any p l a s t i c c o n t a c t de format ion changes t h e

i n i t i a l h e i g h t d i s t r i b u t i o n curve. The e f f e c t o f p l a s t i c c o n t a c t deforma-

t i o n on t h e changes o f t h e su r face con tac t topography i s i l l u s t r a t e d i n

F igu re 5 . 2 .

- - - - - - -

500 pn

O-O-O-

L I I I I I I I I

1 5 20 50 80 95 99 99.9

Cumulat ive h e i g h t d i s t r i b u t i o n ( W )

F igu re 5 .2 Cumulat ive h e i g h t d i s t r i b u t i o n s showing e f f e c t o f p ress ing an i n i t i a l l y rough su r face (Ref. 5.1).

I n t h i s diagram, t h e cumula t ive h e i g h t d i s t r i b u t i o n curves o f t h e i n i t i a l

and t h e p l a s t i c a l l y deformed sur faces a re p l o t t e d on p r o b a b i l i t y paper

(Ref. 5.1). ( I n t h i s diagram paper, a Gaussian d i s t r i b u t i o n i s represented

as a s t r a i g h t l i n e . ) I t can be seen t h a t t he i n i t i a l Gaussian h e i g h t d i s -

t r i b u t i o n ( A ) i s i n c r e a s i n g l y d i s t u r b e d w i t h i nc reas ing s e v e r i t y o f t he

c o n t a c t de format ion process (B) , ( C ) . Since most eng inee r ing su r faces i n i -

t i a l l y possess a Gaussian su r face h e i g h t d i s t r i b u t i o n , t he curves shown i n

F igu re 5.2 appear t o rep resen t b a s i c fea tu res o f t h e su r face topography

changes due t o p l a s t i c de format ion .

t o wear processes. The appearance o f worn su r faces has been descr ibed i n

The o t h e r group o f t r i b o - i n d u c e d su r face changes a re t h e changes due

181

Sec t ion 4.4 (see Table 4.3). F o r t h e changes o f t h e su r face topography due

t o wear, depending on t h e i n i t i a l su r face f i n i s h t h e r e a r e two p o s s i b i l i t i e s :

( i ) ( i i ) t h e wear processes may smooth o u t rough sur faces .

There i s a general consensus t h a t t he su r faces o f moving machine p a r t s

shou ld n o t be too "smooth". F o r example, f o r t h e des ign o f p i s t o n s , a s u i t -

ab le su r face f i n i s h f o r t h e c y l i n d e r bores o f Ra = 0.4 t o 0.6 pm has been

suggested (Ref. 5 . 2 ) . (These f i g u r e s shou ld n o t be genera l i zed because they

depend on t h e system under c o n s i d e r a t i o n ) .

o f su r face topography can be conven ien t l y i l l u s t r a t e d by cons ide r ing t h e

cumula t ive h e i g h t d i s t r i b u t i o n o f su r face a s p e r i t i e s (Ref. 5 .3 ) . I n F i g u r e

5 .3 the e f f e c t o f wear on the i n i t i a l l y Gaussian h e i g h t d i s t r i b u t i o n i s

shown (Ref . 5 .1 ) .

t h e wear processes may roughen smooth sur faces ,

As i n t h e case o f p l a s t i c c o n t a c t de format ion , t h e wear-induced changes

1 5 20 50 80 95 99 99.9

Cumulat ive h e i g h t d i s t r i b u t i o n ( % )

F igu re 5.3 Cumulat ive h e i g h t d i s t r i b u t i o n s showing t h e e f f e c t o f wear on t h e i n i t i a l l y Gaussian h e i g h t d i s t r i b u t i o n o f a bead- b l a s t e d su r face (Ref. 5.1).

The s i x non-Gaussian d i s t r i b u t i o n s represent , f rom (A) t o (C), p rog ress i ve

stages i n t h e wear ing process. I t can be seen t h a t a lmost immedia te ly t h e

top 20% o f t h e su r face was a l t e r e d , t h e r e s t remained comple te ly una f fec ted .

Th is ben t d i s t r i b u t i o n , and t h e cor respond ing changes i n bea r ing curve a re

t y p i c a l l y assoc ia ted w i t h l i g h t l y worn sur faces . As wearing progressed, t h e

182

t r a n s i t i o n p e r c e n t i l e between t h e new topography c rea ted by the wear p ro -

cess and t h e i n i t i a l su r face topography moved s t e a d i l y l ower u n t i l t h e

o r i g i n a l t e x t u r e had been almost t o t a l l y rep laced.

changes o f su r face topography a r e cons idered t o be o f g r e a t importance f o r

t h e f u n c t i o n a l performance o f moving mechanical components (Ref. 5.4, 5.5,

5.6). Genera l l y speaking, t h e wear-induced changes o f su r face topography

may have an i n d i f f e r e n t , b e n e f i c i a l , de t r imen ta l o r c a t a s t r o p h i c i n f l u e n c e

on t h e f u n c t i o n a l behav iour o f t h e whole t r ibo-mechan ica l system. Some as-

pec ts o f t he de t r imen ta l i n f l u e n c e o f su r face topography changes have been

discussed i n connect ion w i t h t h e l i m i t s o f l u b r i c a t i o n (Sec t i on 4.5.6). The

b e n e f i c i a l aspects o f su r face topography changes l e a d t o t h e w e l l known

runn ing - in e f f e c t o f bea r ing sur faces (Ref. 5.7, 5.8, 5 .9 ) .

Consider, as an example o f t he r u n n i n g - i n e f f e c t , a s imp le t r i b o -

mechanical d isc-on-plane s l i d i n g system. The i n f l u e n c e o f a r u n n i n g - i n

process on the t r i b o l o g i c a l behav iour has been s t u d i e d i n two steps. F i r s t l y ,

t h e S t r i b e c k curve o f t h e s l i d i n g system l u b r i c a t e d w i t h a pure p a r a f f i n i c

minera l o i l has been measured t o g e t h e r w i t h t h e no-contac t t ime f r a c t i o n

determined by e l e c t r i c a l c o n t a c t - r e s i stance measurement techn iques . These

curves, v a l i d f o r t h e i n i t i a l su r face roughness, were determined f o r con-

s t a n t values o f l o a d and temperature by v a r y i n g t h e s l i d i n g v e l o c i t y f rom

h igh t o low values w i t h i n a few seconds. (W i th t h i s procedure, S t r i b e c k l s

curve i s run th rough f rom r i g h t t o l e f t w i t h n e g l i b l e surface-roughness

changes. ) Secondly, a f t e r a " runn ing - in " process has been performed under

cond i t i ons o f boundary l u b r i c a t i o n , t h e S t r i b e c k curve and t h e no -con tac t

t ime f r a c t i o n have been determined again. The r e s u l t s o f these measurements

a re shown i n F i g u r e 5.4. I n a d d i t i o n , t h e surface-roughness c h a r a c t e r i s t i c s

be fo re and a f t e r t h e r u n - i n procedure a re compi led i n F i g u r e 5.5.

I n comparing t h e curves f o r t h e system w i t h t h e i n i t i a l su r face rough-

ness da ta ( a ) , w i t h those o f t he r u n - i n system ( b ) , t h e f o l l o w i n g main con-

sequences o f t h e r u n n i n g - i n process can be no ted :

( i )

I n mechanical eng ineer ing , t h e su r face f i n i s h and t h e wear-induced

A reduc t i on o f t h e h e i g h t o f t h e h i g h e s t a s p e r i t y peaks i n d i c a t i n g

a g r e a t e r con fo rm i t y o f t h e s l i d i n g su r faces and consequent ly, an

inc rease o f t h e l u b r i c a n t gap between t h e s l i d i n g sur faces .

( i i ) A s h i f t o f t h e minimum o f t h e S t r i b e c k cu rve t o the l e f t , i . e . , an

ex tens ion o f t h e regime o f hydrodynapic l u b r i c a t i o n .

( i i i ) A l ower ing o f t h e f r i c t i o n va lue a t t h e minimum o f t h e S t r i b e c k

curve.

183

-0.14

-

Y- -0.12 c 0

C I - V

L l t

Y- O

c , - c W

V

Y- 01 0 v -

.r

.r

-0.10

.- -0.08

-0.06

S l i d i n g v e l o c i t y v (cm/s)

F i g u r e 5.4 S t r i b e c k cu rve and no-contac t t i m e f r a c t i o n b e f o r e ( a ) and a f t e r ( b ) runn ing - in .

184

Rt = 3.00 pm Ra = 0.49 pm

Bearing-area curve Peak d i s tr i bu ti on

nr -c,

0 20 40 60 80 100 0 50 100 150 Bear ing percentage Peak number

( a ) : Before runn ing - in

100 pm - Rt = 2.20 pin Ra = 0.34 pm

I Bear ina-area curve Peak d i s t r i b u t i o n

Bear ing percentage Peak number

( b ) A f t e r runn ing - in

F igu re 5.5 Surface roughness data be fo re ( a ) and a f t e r ( b ) runn i ng - i n.

186

C l e a r l y , t he ex tens ion o f t h e hydrodynamic regime as a consequence o f

I n mechanical eng ineer ing , owing t o t h e g r e a t importance o f r u n n i n g - i n

t h e runn ing - in process enhances t h e " o p e r a t i n g s e c u r i t y " o f t h e system.

procedures f o r t h e f u n c t i o n a l behav iour o f moving machine elements, i t i s

a t tempted t o o p t i m i z e t h e r u n n i n g - i n procedure i n o r d e r t o o b t a i n p r o p e r l y

r u n - i n su r faces w i t h i n a minimum o f r u n n i n g - i n d u r a t i o n . F o r example, i n t h e

de te rm ina t ion o f r u n n i n g - i n schedules f o r D iese l engines, t h e schedules have

been op t im ized w i t h respec t t o bo th r e l i a b i l i t y and economy th rough measur ing

t h e amount o f wear d u r i n g t h e r u n n i n g - i n procedure by means o f s e n s i t i v e

r a d i o n u c l i d e measur ing methods (Ref . 5.10). D e t a i l e d s t u d i e s were made on t h e

i n f l u e n c e s o f o p e r a t i n g c o n d i t i o n s , l i k e l o a d and speed, on c r i t e r i a l i k e

engine power, s p e c i f i c f u e l and o i l consumption and su r face s t a t e o f p i s t o n

r i n g and l i n e r . As a t y p i c a l 'example, i n F i g u r e 5.6 t h e b e a r i n g area curves

o f t h e c y l i n d e r l i n e r o f a D iese l engine a t d i f f e r e n t stages o f r u n n i n g - i n

a re shown.

l a-• t = 30 h +- t = 90 min 0- t = 15 min x - x t = 0

W m 2 100 - S W

W 2 80 -

.r

W m

20 - I I I I I I I I

0 1 2 3 4 5 6 7 8 9

Sur face p r o f i l e depth (pm)

F igu re 5.6 Bear ing area curves o f t h e c y l i n d e r l i n e r o f a D iese l eng ine a t d i f f e r e n t stages o f runn ing - in (Ref. 5.10).

The su r faces a r e p r o p e r l y r u n - i n i f a c e r t a i n bear ing-area percentage a t a

c e r t a i n p r o f i l e depth i s ob ta ined and a s t a b i l i z e d (minimum) wear r a t e i s

reached. The marked i n f l u e n c e o f t h e o p e r a t i n g c o n d i t i o n s on r u n n i n g - i n a r e

i l l u s t r a t e d i n F i g u r e 5.7.

186

- 0- t = 2 h (op t im ized ) M t =16 h - t = O

$ 100 - +l

V L

5 8 0 -

60 - m .: 40 - m

2 0 -

L

0 1 2 3 4 5 6 7 8

Surface p r o f i l e depth (pn )

F igu re 5.7 Bear ing area curves o f t h e c y l i n d e r l i n e r o f a D iese l eng ine a f t e r d i f f e r e n t r u n n i n g - i n procedures (Ref. 5.10).

It can be seen t h a t w i t h an op t im ized r u n n i n g - i n schedule t h e r e q u i r e d su r -

face q u a l i t y was reached a f t e r a runn ing - in d u r a t i o n o f 2 hours, whereas i n

a convent iona l non-opt imized r u n n i n g - i n procedure f o r a comparable su r face

q u a l i t y a r u n n i n g - i n d u r a t i o n o f more than 16 hours was needed.

5 , 2 , 2 SURFACE COMPOSITION CHANGES

Th is aspect o f t h e t r i bo - induced changes o f t h e s t r u c t u r e o f a mechanical

system i s ex t remely compl ica ted b o t h f rom t h e t h e o r e t i c a l and exper imenta l

p o i n t o f view. T h e o r e t i c a l l y , owing t o t h e n a t u r e o f su r faces (see F i g u r e

4.5) and t h e complex i ty o f t h e t r i b o l o g i c a l ma te r ia l s - l ub r i can t -a tmosphere

i n t e r a c t i o n s as discussed i n Chapter 4, i t appears ex t remely d i f f i c u l t t o

develop models f o r t h e ac tua l dynamic compos i t ion o f t r i b o l o g i c a l l y s t ressed

sur faces . Exper imenta l l y , owing t o t h e i n a c c e s s i b l e c o n t a c t i n t e r f a c e , i t i s

n o t g e n e r a l l y p o s s i b l e t o s tudy " i n s i t u " t h e ac tua l compos i t ion o f su r faces

ir : con tac t . Nevertheless, some progress has been made i n r e c e n t years i n

app ly ing t h e new p h y s i c a l s u r f a c e - a n a l y t i c a l t o o l s , 1 i ke Auger e l e c t r o n

spectroscopy o r ESCA (see S e c t i o n 7.6), i n connect ion w i t h s o p h i s t i c a t e d

su r face -p repara t i on techniques. I n t h e f o l l o w i n g , some o f t h e b a s i c aspects

o f t r i b o - i n d u c e d changes o f su r face compos i t ion a r e d iscussed f o r systems of

i n c r e a s i n g complex i ty .

( a ) Before contact

187

( C ) After 5 passes ( d ) After

severe

,h 2 . 4 .r v1

2.0

'- 1.6

4J r:

L a m 2 1.2 0

c, o 0.8

1045 steel v=O.2 m/min mild transfer T=23 OC; Torr

I 1 I I I , (13 n P a ) 4 8 12 16 20 24

Number of r ider passes

20 passes

Figure 5.8 Aluminium adhesive transfer t o steel surface during sliding (Ref. 5.11).

iaa

(a ) SURFACE-COMPOSITION CHANGES OF A SLIDING SYSTEM UNDER

ULTRA-HIGH-VACUUM CONDITIONS.

I n t h i s case, the t r i b o l o g i c a l system consists o f on ly two par tners and the tr ibo-induced surface composition changes are mainly the ma te r ia l t r a n s f e r

from one par tner t o the other and v ice versa. The physical causes f o r t h i s

mater ia l t rans fe r , i . e . , the adhesion mechanisms, have been explained i n

Sections 4.2.2 and 4.4.4. As mentioned there, i n adhesion experiments of

metal-metal pa i rs , i t has been observed t h a t under the ac t i on o f pure normal

contact and separation forces the cohesively weaker mater ia l t rans fe rs t o

the cohesively stronger. With r e l a t i v e tangent ia l motion between the surfaces,

as i n s l i d i n g , r o l l i n g , o r o s c i l l a t i n g , i n t e r f a c i a l ma te r ia l s t ranspor t be-

comes more complex. Under such condit ions, p l a s t i c deformation, shear and

h igh surface temperatures due t o f r i c t i o n a l heat ing are some fac to rs which

must be given a t t e n t i o n .

changes i n the composition o f the uppermost l aye rs o f surfaces by means o f

Auger e lec t ron Spectroscopy (AES). As an example, the changes o f the compo-

s i t i o n o f a s tee l surface s l i d i n g against an aluminium counterface w i l l be

discussed (Ref. 5.11). Before s l i d i n g contact, i r o n and carbon peaks were

detected from the s tee l surface by means o f AES. I n s l i d i n g , i t was found

t h a t the aluminium t rans fe rs t o the s tee l surfaces. The degree o f the "con-

tamination" o f the s tee l surface w i t h A1 was detected by measuring the r a t i o

o f t he aluminium t o carbon AES peak i n t e n s i t i e s . This r a t i o , as a func t i on

o f the number o f passes o f the A 1 r i d e r over the s tee l surface, i s shown i n

F igure 5.8. I t can be seen t h a t a m i l d t r a n s f e r regime i s fo l lowed by a

severe t r a n s f e r regime. This example shows the importance o f surface-compo-

s i t i o n changes on the behaviour o f tribo-mechanical systems: i t i s the severe

adhesive wear, i nd i ca ted i n the r ight-hand s ide o f the graph o f Figure 5.8,

which o f t e n causes the catast rophic f a i l u r e o f components o f mechanical

sys terns.

I n the l a s t few years i t has become poss ib le t o study the t r ibo- induced

( b ) SURFACE COMPOSITION CHANGES OF A SLIDING SYSTEM UNDER

ATMOSPHERIC CONDITIONS.

I n these cases, surface composition changes due n o t on l y t o mater ia ls t rans-

f e r b u t a lso t o the i n t e r a c t i o n o f the atmospheric environment w i t h the

s l i d i n g surfaces ac t i va ted by the f r i c t i o n a l energy, take place. Important

examples are the tr ibochemical ox ida t i on processes i n dry s l i d i n g o f s tee l

surfaces. The corresponding changes i n surface composition have o f t e n been

inves t i ga ted i n studying the chemical composition o f the surface debris.

189

F i n k and Hoffmann observed i n 1932 i n a c l a s s i c paper t h a t under

c o n d i t i o n s o f r o l l i n g w i t h s l i p , t h e su r face d e b r i s c o n s i s t e d o f Fe, Fe203

and Fe304; FeO was n o t de tec tab le (Ref. 5.12). I n another fundamental

paper, Dies i n 1939 s t u d i e d the connect ions between t h e compos i t ion o f t h e

d e b r i s and t h e wear o f a s t e e l specimen (0.04% C ) s l i d i n g under atmospher ic

c o n d i t i o n s a t v = lm/s a g a i n s t a hardened s t e e l (0.86% C , 1.64% Cr ) d i s c

(Ref. 5.13). I n F igu re 5.9, t h e r e s u l t s ob ta ined by Dies as a f u n c t i o n o f

t he c o n t a c t p ressure a re shown

70

60

50

40

30

20

10

50 100 150 200

Contac t p ressure ( N/cmL)

F igu re 5.9 Composi t ion o f wear d e b r i s as f u n c t i o n o f c o n t a c t p ressure (Ref . 5.13).

The broken curves rep resen t t h e measured wear r a t e i n r e l a t i v e u n i t s . (The

c h a r a c t e r i s t i c shape o f t h e wear cu rve i s d iscussed i n t h e n e x t sec t i on ,

i n connect ion w i t h t h e t r i b o - i n d u c e d changes o f su r face s t r e n g t h p roper -

t i e s . ) The f u l l curves o f F i g u r e 5.9 show t h e v a r i a t i o n o f t h e compos i t ion

o f t h e d e b r i s w i t h i n c r e a s i n g c o n t a c t pressure. I t can be seen t h a t a t t h e

minimum o f t he wear r a t e , d e b r i s con ta ined ma in l y a- Fe203 whereas a t t h e

maximum o f wear, t h e d e b r i s cons is ted ma in l y o f m e t a l l i c i r o n .

S i m i l a r changes have been r e p o r t e d t o occur a l s o as a f u n c t i o n o f t h e

s l i d i n g v e l o c i t y (Ref . 5.14, 5.15). From t h i s work i t may be concluded t h a t

a t r i bo -chemica l wear mechanism opera tes a t low c o n t a c t p ressures and low

190

s l i d i n g v e l o c i t i e s whereas a t h i g h e r values o f t h i s o p e r a t i n g v a r i a b l e s

metal -metal adhesion becomes t h e dominant Near process. Qu inn and Wooley

(Ref. 5.16) were ab le t o show t h a t under m i l d cond i t i ons , t h e ox ide Fe203

was generated b u t t h a t a t r a n s i t i o n t o Fe304 occur red as t h e l o a d o r ve-

l o c i t y was inc reased above c e r t a i n l e v e l s .

( c ) SURFACE COMPOSITION CHANGES OF A SLIDING SYSTEM UNDER

LUBRICATED CONDITIONS.

I n these s i t u a t i o n s , t h e whole complex o f so l i d -so l i d - l ub r i can t -a tmosphere

i n t e r a c t i o n s must be taken i n t o cons ide ra t i on . Some o f t h e main phys ico-

chemical aspects o f these processes have a l ready been d iscussed i n connec-

t i o n w i t h the boundary l u b r i c a t i o n mode (see Sec t ion 4.5.5) . One o f t h e

advantages o f t he presence o f a l u b r i c a n t i n a t r ibo-mechan ica l system i s

the p o s s i b i l i t y o f i n f l u e n c i n g t h e ac tua l compos i t ion o f t h e s l i d i n g sur -

face by l u b r i c a n t a d d i t i v e s . Through t h e i n t e r f a c i a l t r i bo -chemica l reac-

t i o n s , b e n e f i c i a l su r face l a y e r s may be b u i l d up.

Obviously, as i n d ry s l i d i n g , oxygen and water p l a y ex t remely impor-

t a n t r o l e s f o r t h e " i n s i t u " compos i t ion o f t r i b o l o g i c a l l y s t ressed su r -

faces and, consequent ly, f o r t h e i r f u n c t i o n a l behaviour. I n c r e a s i n g oxygen

concen t ra t i ons seem t o have a favo rab le e f f e c t on t h e amount o f wear, as

w e l l as on t h e l oad -ca r ry ing c a p a c i t y o f s l i d i n g sur faces . F o r systems

l u b r i c a t e d w i t h p l a i n hydrocarbon l u b r i c a n t s , as t h e oxygen a v a i l a b i l i t y i n -

creases, t h e i n o r g a n i c wear p roduc ts f rom the s l i d i n g sur faces change f rom

i r o n and i r o n ca rb ide FeC t o the i r o n ox ides Fe304 and a - Fe203. I f t he

l u b r i c a n t con ta ins " l u b r i c i t y " agents, l i k e f a t t y ac ids , ca rboxy la te "soaps"

a re formed when oxygen o r water i s p resent . The ino rgan ic f i l m s formed " i n

s i t u " f rom extreme pressure agents on metal sur faces , such as s u l f i d e s ,

c h l o r i d e s , and phosphides, p rov ide l u b r i c a t i o n a t very h i g h temperatures

(see also Sec t ion 4.5.5). These t r i b o - c h e m i c a l l y formed su r face f i l m s a r e

more s t a b l e than any p h y s i c a l l y o r chemica l l y adsorbed f i l m . Reacted f i l m s

need n o t t o be t r i bo -chemica l , b u t t he r a t e o f r e a c t i o n can be enhanced by

the exposure o f su r face and t h e rubb ing temperature.

The ac tua l su r face compos i t ion i s n o t w e l l known, and a s tudy o f t h e

l i t e r a t u r e shows t h a t o n l y i n a few cases have t h e ac tua l compounds been

i d e n t i f i e d on worn sur faces . T h i s i n a b i l i t y t o d e f i n e t h e chemical n a t u r e

o f t h e su r face spec ies has been due ma in l y t o t h e f a c t s t h a t t h e l a y e r s a r e

ex t remely t h i n (about 10-3pm) and a re f r e q u e n t l y amorphous. Recent ly, i n

a p p l y i n g the newly developed sens i t i v e X-ray pho toe lec t ron spectroscopy

techn ique (ESCA o r XPS, see Sec t ion 7 .6 ) examinat ions o f s t e e l sur faces

191

before and a f t e r wear t e s t i n g have been per fo rmed (Ref. 5.17, 5.18). I n

these s tud ies , t h e su r face compos i t ion a f t e r t h e a c t i o n o f t y p i c a l a n t i -

wear (AW) a d d i t i v e s , l i k e z i n c d i a l k y l d i t h i o p h o s p h a t e (ZDDP) and t y p i c a l

extreme pressure (EP) a d d i t i v e s , l i k e d ibenzy l d i s u l p h i d e (060s) have been

s tud ied . The r e s u l t s o f these s t u d i e s i n d i c a t e t h a t o f t h e elements z inc ,

s u l f u r , phosphorus, carbon and oxygen i n t h e AW a d d i t i v e , o n l y s u l f u r under-

went a d e t e c t a b l e change i n chemical n a t u r e d u r i n g wear t e s t i n g of t h e s t e e l

su r face (Ref. 5.17). The s u l f u r su r face spec ies produced was i d e n t i f i e d as

a metal su lph ide . The r e s u l t s suggest t h a t t h i s su r face su lph ide i s assoc i -

a ted w i t h boundary l u b r i c a t i o n (see Sec t ion 4 .5 .5 ) . L ikewise , i n t h e case o f

t h e EP a d d i t i v e DBDS, t he rubbed sur faces had t h i c k d i scon t inuous l a y e r s o f

s u l p h i d e (Ref . 5.18). These f i n d i n g s a r e compat ib le w i t h those o f Coy and

Qu inn (Ref. 5.19) who a l s o observed t h i c k su lph ide l a y e r s f o r t h e h i g h EP

reg ion .

5,2,3 SURFACE STRENGTH PROPERTIES CHANGES

There a r e two p o s s i b i l i t i e s o f t r i b o - i n d u c e d changes o f t h e s t r e n g t h prop-

e r t i e s o f i n t e r a c t i n g moving su r faces :

( i ) an i nc rease i n s t r e n g t h as a consequence o f e f f e c t s l i k e " s t r a i n

hardening" due t o c o n t a c t s t resses and t h e genera t i on o f i n t e r n a l

s t r e s s f i e l d s ,

( i i ) a decrease i n s t r e n g t h due t o t h e " s o f t e n i n g " e f f e c t o f f r i c t i o n

induced hea t i n t h e c o n t a c t i n t e r f a c e .

I n t h i s connect ion t h e ques t i on o f t h e t r i b o l o g i c a l l y r e l e v a n t s t r e n g t h

p r o p e r t i e s a r i s e s . From a d i scuss ion o f t h e va r ious a t tempts t o e s t a b l i s h

c o r r e l a t i o n s between wear behav iour and mechanical p r o p e r t i e s - n e g l e c t i n g

t h e " i n t e r a c t i o n e f f e c t s " o f adhesion and t r i bo -chemica l r e a c t i o n s - i t has

been concluded t h a t many o f t h e r e l e v a n t parameters can be expressed i n

terms o f t h e r a t i o o f t h e e l a s t i c modulus E t o t h e hardness H (Ref . 5.20).

I t has a l ready been exp la ined above t h a t t h e r a t i o E/H i s p a r t o f t h e

p l a s t i c i t y i ndex J, which i s a s a t i s f a c t o r y c r i t e r i o n by which t o de termine

i n which regime a g i ven c o n t a c t de format ion process l i e s . It may t h e r e f o r e

be s u f f i c i e n t here t o r e s t r i c t t he d i scuss ion t o t h e t r i b o - i n d u c e d changes

o f E and H. The e l a s t i c modulus, E, o f a p o l y c r y s t a l l i n e metal i s p h y s i c a l l y

speaking a " s t r u c t u r e - i n s e n s i t i v e p roper t y " , and i s o n l y l i t t l e a f f e c t e d by

b o t h de fec ts and i m p u r i t i e s and temperature and s t r a i n r a t e (Ref . 5 .21 ) .

192

On t h e con t ra ry , t h e i n d e n t a t i o n hardness, H, o f m a t e r i a l s i s a markedly

"s t ruc tu re-dependent p roper t y " . It f o l l o w s t h a t t h e i n d e n t a t i o n hardness

may be the most r e l e v a n t s t r e n g t h p r o p e r t y c h a r a c t e r i z i n g t h e t r i b o - i n d u c e d

changes o f su r face s t r e n g t h p r o p e r t i e s .

Burwe l l and S t rang (Ref. 5.22) have shown t h a t s t e e l - s t e e l s l i d i n g

couples e x h i b i t a t r a n s i t i o n f rom m i l d t o severe wear when the apparent

con tac t p ressure reaches a va lue o f about o n e - t h i r d o f t h e hardness o f t h e

s o f t e r m a t e r i a l . As t h i s p ressure corresponds q u i t e c l o s e l y t o t h e u n i a x i a l

b u l k f l o w s t r e s s o f t he metal , i t was suggested t h a t t h e wear t r a n s i t i o n

was due t o t h e i n t e r a c t i o n o f p l a s t i c zones beneath c o n t a c t i n g a s p e r i t i e s

and t h e onset o f b u l k p l a s t i c de format ion . I n s tudy ing t h e t r i bo - induced

changes o f t h e hardness o f s l i d i n g surfaces, however, t h e whole s t r e s s f i e l d

o f normal and t a n g e n t i a l s t resses must be taken i n t o c o n s i d e r a t i o n (Ref.

5.23). Since t h e t a n g e n t i a l s t resses depend on t h e f r i c t i o n a l behav iour o f

the system, those p r o p e r t i e s which determine t h e f r i c t i o n ( l i k e sur face

contaminat ion, atmospher ic environment, e t c ) must a l s o be inc luded. A cha-

r a c t e r i s t i c example o f t h e changes o f t he hardness o f s l i d i n g sur faces w i t h

r e l a t i o n t o t h e va r ious i n f l u e n c i n g f a c t o r s i s g i ven i n F i g u r e 5.10. The

f i g u r e s shows c ross-sec t ions o f p i n s of pure i r o n , which have been s l i d

a g a i n s t a d i s c i n d r y s y n t h e t i c a i r o f d i f f e r e n t pressure, t oge the r w i t h

micro-hardness da ta (Ref. 5.24, 5.25). Under c o n d i t i o n s o f normal atmospher ic

p ressure through t r i bo -chemica l r e a c t i o n o f t h e i r o n w i t h t h e oxygen an ox ide

l a y e r i s formed as can be seen i n the upper p a r t o f t he micrograph o f F i g u r e

5.10. The f r i c t i o n a l shear s t resses a c t ma in l y i n t h e ox ide l a y e r s w i t h t h e

r e s u l t t h a t t h e sub-surface l a y e r s a re s t ra in -hardened o n l y t o smal l degree

( H = 2000-3000 N/mm ) . If, however, under t h e same opera t i ng c o n d i t i o n s

o f c o n t a c t p ressure , s l i d i n g v e l o c i t y , ambient temperature and s l i d i n g d i s -

tance, t he t e s t s a r e performed i n a vacuum o f

i s found. Here, a l e s s e r amount o f oxygen f o r ox ide l a y e r fo rma t ion i s

a v a i l a b l e and h i g h e r f r i c t i o n c o e f f i c i e n t va lues a r e measured. The combined

a c t i o n of t h e normal f o rces and the inc reased t a n g e n t i a l f r i c t i o n fo rces a c t ma in l y i n t h e m e t a l l i c p a r t s and l e a d t o a cons ide rab le i nc rease i n t h e sub-

su r face hardness (H = 2000-6000 N/mm ).

2

T o r r a d i f f e r e n t behav iour

2

The importance o f t h e changes o f su r face hardness and su r face composi-

t i o n on t h e wear behav iour o f a t r ibo-mechan ica l system i n d r y s l i d i n g i s

i l l u s t r a t e d i n F igu re 5.11. I n t h i s graph, t h e wear c o e f f i c i e n t K ' o f 0.52

pe rcen t carbon s t e e l as a f u n c t i o n o f t h e l o a d FN i s p l o t t e d (Ref. 5.26,

5.27). The i n i t i a l hardness o f t h e specimen was 268 DPN. A t low loads m i l d

Hardness ( G N / m 2 )

( a ) atmospher ic p ressure : p = 760 T o r r ( 0 . 1 MPa) f r i c t i o n c o e f f i c i e n t : f = 0.55 - 0.64 wear c o e f f i c i e n t : K = 0.00002

2 Hardness ( G N / m )

( b ) atmospher ic p ressure : p = T o r r (130 mPa) f r i c t i o n c o e f f i c i e n t : f = 0.81 - 0.97 wear c o e f f i c i e n t : K = 0.00058

F igu re 5.10 Tr ibo- induced hardness changes.

194

wear occurs u n t i l a t FN = 1N t h e t r a n s i t i o n T r 1 t o severe wear occurs. The

severe wear mode p e r s i s t s up t o a l oad o f about FN = 25 N. A t t h i s p o i n t , a

second t r a n s i t i o n T r 2 occurs when t h e wear mode r e v e r t s . I t was found,

f rom meta l lography and micro-hardness t e s t s , t h a t above t h e T r 2 t r a n s i t i o n

the su r face l a y e r s o f t h e specimens were hardened by a phase change. The

va lue o f t h e T r 2 t r a n s i t i o n l o a d was determined f o r a number o f s l i d i n g

v e l o c i t i e s and f o r s t e e l s o f va r ious carbon conten ts , and i n each case t h e

va lue o f t h e f l a s h temperature was ca l cu la ted . Bear ing i n mind a number o f

u n c e r t a i n t i e s i n these c a l c u l a t i o n s , t h e o v e r a l l p a t t e r n o f r e s u l t s suggests

t h a t t h e su r face harden ing i s caused by a mar tens i c t rans fo rma t ion , and t h a t

i t i s caused by t h e f l a s h temperatures and t h e i r d u r a t i o n a t t h e t r u e area

o f con tac t . The o v e r a l l e f f e c t s i l l u s t r a t e d i n F igu re 5.11 have been con-

f i r m e d by Uetz and co-workers (Ref . 5.28). The r e s u l t s c l e a r l y i n d i c a t e t h e

importance o f t he combined e f f e c t s o f su r face compos i t ion changes and su r -

face s t r e n g t h changes on t h e t r i b o l o g i c a l behav iour o f s l i d i n g systems.

10-6

- 8

5 \

m

v

a, CI 4 L

L 4 s

10-10

10-11

T r 1-

/

LTr

d=25.. mm

&.% v = l m/s m

1 10 100 Load FN ( N )

F i g u r e 5.11 Wear modes as f u n c t i o n o f l o a d (Ref. 5.26).

195

5,3 MATERIAL LOSSES

I f , i n a t r i bo -mechan ica l system i t i s n o t p o s s i b l e t o e l i m i n a t e wear

processes (see Sec t ion 5.4) o r t o m i t i g a t e these processes t o a "zero l e v e l "

(see S e c t i o n 6 . 6 ) t h e t r i b o l o g i c a l processes between two moving su r faces

g e n e r a l l y l e a d t o l osses o f m a t e r i a l f rom t h e system. Phenomenological ly,

d i f f e r e n t regimes o f m a t e r i a l losses may be d i s t i n g u i s h e d . Denot ing t h e

amount o f t h e m a t e r i a l l o s s by t h e o u t p u t symbol ZM, t h r e e s imp le t ime r e l a -

t i o n s f o r Z may be expected which a r e indeed observed exper imen ta l l y . M

F i r s t l y , t h e p r o b a b i l i t y o f t h e occur rence o f e lementary wear events

may decrease w i t h t ime. Th is case i s g iven , f o r ins tance, i f th rough changes

o f su r face topography t h e i n t e r a c t i o n r a t e o f su r face a s p e r i t y c o l l i s i o n s

decreases. I n t h i s " runn ing - in " p e r i o d t h e system self-accommodates. I n t h e

s imp les t case, t h e amount o f l oss -ou tpu ts w i l l be g i ven as a square- roo t

f u n c t i o n o f t ime

dZM - c1 _ 3 Z M ( t ) = p p ] d t ZM

Secondly,the s t r u c t u r e o f t h e system may acqu i re a r e l a t i v e l y s t a b l e behav-

i o u r under t h e a c t i o n o f t h e t r i b o l o g i c a l processes. I n t h i s case t h e proba-

b i l i t y o f wear events remains cons tan t . Th i s " s teady -s ta te " s i t u a t i o n i s

c h a r a c t e r i z e d by a constancy o f t h e m a t e r i a l - l o s s o u t p u t pe r u n i t o f t ime

w i t h o u t change i n t h e t r i b o l o g i c a l processes. I t f o l l o w s t h a t

= c2 + ZM ( t ) = C 2 t d t

T h i r d l y , when t h e amount o f m a t e r i a l - l o s s o u t p u t reaches a c e r t a i n value,

a q u a l i t a t i v e t r a n s i t i o n i n t h e s t a t e o f t h e system may occu r c o n s i s t i n g

o f a s i g n i f i c a n t change i n t h e t r i b o l o g i c a l p i c t u r e o f t h e phenomena. The

changes i n t h e s t a t e o f t h e system a r e o f a d i r e c t e d n a t u r e and t h e i n c r e -

ments i n t h e wear processes i n t h i s regime a r e m u t u a l l y dependent. Here

l a r g e increments i n one i n t e r v a l o f t ime cause even l a r g e r increments i n

the nex t t ime i n t e r v a l . I t f o l l o w s t h a t

196

I n t h i s case t h e worn m a t e r i a l - l o s s ou tpu t inc reases r a p i d l y w i th t ime.

Depending on t h e va lues o f Co and Cj s e l f - a c c e l e r a t i o n o f t h e process occur

which may l e a d t o c a t a s t r o p h i c damage o f t h e s t r u c t u r e o f t h e system and,

accord ing ly , t o " f a i l u r e " o f t h e whole system (see a l s o Sec t ion 6.4).

The t h r e e modes o f m a t e r i a l - l o s s ou tpu ts diqcussed may f o l l o w each

o t h e r i n t ime as shown i n F igu re 5.12. I n F i g u r e 5.12 ZMlim denotes a maxi-

mum l e v e l o f admiss ib le m a t e r i a l l oss -ou tpu ts . A t t h i . l e v e l , t h e s t r u c t u r e

o f t h e system has changed as a consequence o f t h e mater l .1 l oss -ou tpu ts , i n

such a way t h a t t he f u n c t i o n a l i n p u t - o u t p u t - r e l a t i o n s - which a r e performed

v i a t h e s t r u c t u r e o f t h e system - a r e seve re l y d i s t u r b e d (see Sec t ion 6.4).

L I I

Time

F i g u r e 5.12 Schematic rep resen ta t i on o f t he m a t e r i a l l oss -ou tpu t curves o f a t r ibo-mechan ica l system.

R e l a t i v e l y few workers i n t h e f i e l d o f t r i b o l o g y have at tempted t o d e r i v e

c o r r e l a t i o n s f o r wear -pa r t i c l e dimensions generated by t h e wear process.

Rabinowicz proposed a c o r r e l a t i o n between mean adhesive wear, p a r t i c l e d i a -

meter and the "surface-energy c r i t e r i o n " which i s t h e r a t i o o f t h e work o f

adhesion between two meta ls t o t h e hardness o f t h e weaker m a t e r i a l (Ref.

5.29). Th i s t h e o r e t i c a l approach has r e c e n t l y been m o d i f i e d (Ref. 5.20) and

t h e f o l l o w i n g i n e q u a l i t y has been suggested t o desc r ibe t h e mean wear-

p a r t i c l e d iameter d

E : e l a s t i c modulus

H : p e n e t r a t i o n hardness d 6 15 (E/H)' (nm)

197

C h a r a c t e r i s t i c s o f wear regimes s t u d i e d (schemat ic ) :

L u b r i c a t e d s t a t e

( S t r i beck cu rve )

Dry s t a t e

( T r a n s i t i o n s diagram)

( c ) l u b r i c a n t f i l m breakdown

( a ) quas i -

( b ) boundary - Load

Regime P a r t i c l e d e s c r i p t i o n and ma jo r dimension, d

Free metal p a r t i c l e s ; d c 5 p m

Free metal p a r t i c l e s ; d < 15 pn

Free metal p a r t i c l e s ; d c 150 pm

Red o x i d e p a r t i c l e s , a - Fe203, d UP t o 150 pm

Black ox ide p a r t i c l e s y - Fe20g, Fe304, FeO,

d up t o 150 pm

Free metal p a r t i c l e s , d up t o 1 mn

t W c, m L

( f ) severe adhesive

wear 1 ,

(severe) o x i d a t i ve wear

Load - Surface d e s c r i p t i o n

Var ies between p o l - i s h e d and ve ry rough

Stab le , smooth l a y e r w i t h a few grooves

Ploughed w i t h e v i - dence o f p l a s t i c f l o w and su r face c r a c k i n g

Ploughed w i t h areas of ox ides on t h e su r face

Ploughed w i t h areas o f ox ides on t h e su r face

Severe ly ploughed, gross p l a s t i c f l o w and smearing

Wear r a t e

+Zero

Low

H igh

- - -

High

H igh

Cata- s t r o - p h i c

F i g u r e 5.13 C h a r a c t e r i s t i c s o f wear p a r t i c l e s and t r i b o - i n d u c e d s u r f a c e f e a t u r e s (Ref. 5.30).

198

2 The dependence on (E/H) i s assumed t o be an upper bound, obeyed under

c o n d i t i o n s o f c lean sur faces . When normal l a b o r a t o r y c o n d i t i o n s o r more

contaminated environments p e r t a i n , t h e dependence f o r p a r t i c l e s i z e reduces

e m p i r i c a l l y t o (E/H) . Exper imenta l l y , t h e f o l l o w i n g f i n d i n g s on t h e chemical compos i t ion and

t h e s i z e o f t h e m a t e r i a l l o s s d e b r i s appear t o have been observed q u i t e

g e n e r a l l y f o r s l i d i n g systems o p e r a t i n g under normal atmospher ic cond i t i ons :

( i ) I n t h e so -ca l l ed m i l d wear regime, t h e worn d e b r i s c o n s i s t s o f smal l

p a r t i c l e s w i t h a d iameter o f l e s s than about 5 pm. These p a r t i c l e s a r e

formed ma in l y i n t r i b o - o x i d a t i v e wear processes and f o r s l i d i n g meta l

couples o f t e n c o n s i s t o f ox ides . Fo r example, t h e wear d e b r i s o f i r o n ,

coba l t , magnesium s l i d i n g a g a i n s t themselves under d r y c o n d i t i o n s con-

s i s t s o f II. - Fe203, COO and MgO. The fo rma t ion o f these ox ides can be

exp la ined i n accordance w i t h t h e thermodynamics o f t h e o x i d a t i o n p ro -

cesses i f t h e f r i c t i o n induced temperatures and t h e cor respond ing d a t a

o f f r e e energy o f t h e m a t e r i a l s a r e used.

( i i ) I n the s o - c a l l e d severe wear regime m e t a l l i c p a r t i c l e s rang ing i n s i z e up t o approx imate ly 1 mm a r e found. These p a r t i c l e s a r e ma in l y observed

under severe meta l1 i c adhesion processes. There i s some exper imenta l

evidence t h a t f o r l i k e m e t a l l i c s l i d i n g couples t h e s i z e o f l oose wear

p a r t i c l e s i s l a r g e r than f o r u n l i k e metal-metal p a i r s .

The d e t a i l s o f t h e c h a r a c t e r i s t i c s o f t h e wear p a r t i c l e s generated a t t h e

i n t e r f a c e o f l u b r i c a t e d and d r y s l i d i n g concent ra ted A I S I 52100 s t e e l con-

t a c t s have been s t u d i e d (Ref. 5.30) i n l a b o r a t o r y t e s t s u s i n g t h e Fer rograph

techn ique descr ibed i n Sec t i on 7.5. I n F igu re 5.13 t h e c h a r a c t e r i s t i c s o f

t h e worn m a t e r i a l loss o u t p u t and t h e wear-induced su r face changes a r e com-

p i l e d . As can be seen, each regime produced wear p a r t i c l e s o f c h a r a c t e r i s t i c

morphology and compos i t ion . S ince a l l t h e types o f p a r t i c l e s have been found

l i k e w i s e i n t h e l u b r i c a t i n g o i l o f f i e l d o p e r a t i n g machines, t h e c o m p i l a t i o n

o f F i g u r e 5.13 appears t o rep resen t a good survey o f t h e n a t u r e o f t h e wear-

induced m a t e r i a l s losses and t h e cor respond ing changes o f t h e o p e r a t i n g

sur faces o f mechanical systems. The da ta o f F i g u r e 5.13, which a r e v a l i d f o r

c o n d i t i o n of pure s l i d i n g , show t h a t f rom the s tudy o f t h e s i z e d i s t r i b u t i o n

and t h e shape and compos i t ion o f wear p a r t i c l e s impor tan t i n f o r m a t i o n on t h e

o p e r a t i n g wear modes and the a c t u a l c o n d i t i o n o f t h e s t r u c t u r e o f a t r i b o -

mechanical system can be ob ta ined (Ref. 5.31). Based on t h i s i n fo rma t ion , a

p rognos is o f t h e imminent behav iour o f machinery can then be undertaken.

199

5 , 4 SOLUTIONS FOR NO-WEAR CONDITIONS

I n t h e p rev ious sec t i ons , we s t u d i e d some o f t h e b a s i c aspects o f t h e

changes o f t h e s t r u c t u r e o f mechanical systems o c c u r r i n g as a consequence

o f t h e t r i b o l o g i c a l processes between t h e moving components o f t h e system.

Now, t u r n i n g f rom d iagnos is t o therapy , t h e ques t i on a r i s e s how t o a v o i d

de t r imen ta l e f f e c t s and how t o r e a l i z e t r ibo-mechan ica l systems w i t h un-

changing s t r u c t u r e s thus p r o v i d i n g the p r e r e q u i s i t e f o r a p roper f u n c t i o n a l

behav iour o f t h e whole system. The r e s u l t s o f t h e p rev ious sec t i ons have

shown t h a t i n almost eve ry case t h e d e t r i m e n t a l changes o f t h e system's

s t r u c t u r e a r e due t o t h e i n t e r f a c i a l wear processes. I t f o l l o w s t h a t t h e

wear-induced changes o f the sys tem's s t r u c t u r e a r e e l i m i n a t e d i f a s u i t a b l e

i n t e r f a c i a l element e n t i r e l y p reven ts t h e s o l i d - s o l i d c o n t a c t between t h e

moving components o f a mechanical system. There a r e f o u r b a s i c eng inee r ing

s o l u t i o n s t o t h i s problem, as i l l u s t r a t e d schemat i ca l l y i n F i g u r e 5.14.

,,I

( a ) F l u i d f i l m

1 - 1

( c ) Elastomers

( b ) Magnet ic f i e l d

c

( d ) F l e x u r a l means

F i g u r e 5.14 Schematic r e p r e s e n t a t i o n o f s o l u t i o n s f o r no-wear c o n d i t i o n s .

The most common method f o r t h e e l i m i n a t i o n o f wear processes f rom a t r i b o -

mechanical system ( w i t h t h e excep t ion o f s u r f a c e - f a t i g u e wear o r , perhaps,

f l u i d e ros ion o r c a v i t a t i o n ) i s by t h e use o f l i q u i d o r f l u i d l u b r i c a n t s ,

F igu re 5.14 ( a ) . I n t h e cases where a converg ing gap e x i s t s , t h e r e l a t i v e

200

mot ion o f t h e elements (1) and ( 2 ) drags t h e f l u i d i n t o t h i s gap thus gener-

a t i n g a l oad -ca r ry ing pressure w i t h i n t h e f l u i d f i l m . A l t e r n a t i v e l y , t h e

pressure may be p rov ided by an e x t e r n a l pumping system as i n a h y d r o s t a t i c

o r a e r o s t a t i c bea r ing . Another p o s s i b i l i t y , i n d i c a t e d i n F i g u r e 5.14 (b ) ,

i s t h e use o f magnet ic o r o t h e r r e p u l s i v e f o r c e f i e l d s c a r r y i n g t h e normal

l o a d and separa t i ng t h k moving sur faces ( 1 ) and ( 2 ) . I f t h e r e l a t i v e mot ion

between t h e elements ( 1 ) and ( 2 ) i s o f f a i r l y smal l ampl i tude, t h e s o l u t i o n s

shown schemat i ca l l y i n F igures 5.14 ( c ) and ( d ) may be a p p l i c a b l e . Here, t h e

moving sur faces a r e separated by an e l a s t i c a l l y deforming i n t e r f a c i a l e l e -

ment (3), and t h e r e s i s t a n c e t o a r e l a t i v e mot ion between ( 1 ) and ( 2 ) i s

g i ven by the i n t e r n a l de format ion ( i n t e r n a l f r i c t i o n ) o f e lement (3 ) .

The p r i n c i p l e s shown i n F i g u r e 5.14 have t h e advantage t h a t they e l i m -

i n a t e wear processes a1 toge the r f rom a t r ibo-mechan ica l system thus p r o v i d -

i n g an " i n v a r i a n t s t r u c t u r e " o f t h e system, Due t o t h e i r g r e a t importance,

t he main fea tu res o f t h e p r i n c i p l e s i l l u s t r a t e d i n F i g u r e 5.14 w i l l be d i s -

cussed b r i e f l y .

5 , 4 , 1 FLUID FILMS

The advantages o f hydrodynamic l u b r i c a t i o n as descr ibed i n Sec t i on 4.5.2

a re u t i l i z e d n o t o n l y i n bea r ing a p p l i c a t i q n s b u t a l s o i n o t h e r t r i b o -

mechanical systems l i k e hydrodynamic sea ls o r i n manufac tur ing processes

l i k e hydrodynamic l u b r i c a t e d w i redrawing systems. Besides t h e s e l f - a c t i n g

hydrodynamic l u b r i c a t i o n mode, h y d r o s t a t i c o r a e r o s t a t i c l u b r i c a t i o n i s ap-

p l i e d i n e x t e r n a l l y p ressu r i zed bear ings . A l though these h y d r o s t a t i c bear -

ings may r e q u i r e r e l a t i v e l y expensive and complex f l u i d supp ly equipment,

they o f f e r t he f o l l o w i n g advantages:

( i )

( i i ) ( i i i ) P r e d i c t a b l e f u n c t i o n a l performance (see Sec t ion 6.1).

I n F i g u r e 5.15 a t y p i c a l h y d r o s t a t i c t h r u s t bea r ing i s shown schemat i ca l l y .

o r pocket w i t h a depth cons ide rab ly g r e a t e r than t h e lands o r s i l l s .

(Sometimes the pad i s above, e.g., on sk ids f o r moving heavy machines on

p l a t e s l e t i n t o t h e f l o o r . ) As f l u i d i s sunp l i ed t o t h e recess a t a h igh

pressure a p ressure d i s t r i b u t i o n b u i l d s up, whose i n t e g r a l must equal t h e

No s o l i d - s o l i d contac t , i . e . no wear a t any opera t i ng v e l o c i t y

( i n c l u d i n g v = 0) o r l o a d f o r a l l types o f r e l a t i v e mot ion.

Low f r i c t i o n (determined by t h e i n t e r n a l f r i c t i o n o f t h e f l u i d ) .

The bear ing pad, i n t h i s i ns tance t h e l ower member, con ta ins a recess

201

load which i s appl ied t o the bearing. F igure 5.15 i nd i ca tes t h a t hyd ros ta t i c

bearings can operate w i t h a un i form f i l m thickness h = const ( i n con t ras t t o

hydrodynamic bearings) and a l so w i t h no r e l a t i v e tangent ia l motion. Thus, i n

the Reynolds equation, t rea ted i n Section 4.5.2, the r ight -hand s ide equals Oh zero (s ince vo, vl, may be pu t equal t o zero) . The Reynolds equation then

reduces t o

This i s Laplace's equation i n two dimensions which must be solved f o r t he

p a r t i c u l a r geometry o f the bearing under consideration.

1 and

pressure d i s t r i b u t i o n

recess '

Figure 5.15 A hydros ta t i c t h r u s t bearing.

For the con f igu ra t i on o f F igure 5.15 the f o l l o w i n g r e l a t i o n s govern the

behaviour o f the system (Ref. 5.32) . The pump pressure p i n the recess

needed f o r the support o f t he load FN i s given by P

d2 2FN

TC dml dl I n - Pp = -

202

Flow r a t e q1 and f i l m thickness are r e l a t e d v i a the equation

7 : l u b r i c a n t v i s c o s i t y

The term qlp determines the necessary power o f the pump. I f the upper p a r t

o f t he hyd ros ta t i c bearing ro ta tes w i t h an angular v e l o c i t y w, a f r i c t i o n a l

torque, MF, has t o be overcome which i s given by the i n t e r n a l f r i c t i o n o f

the l u b r i c a n t f i l m o f equal thickness h t o be ca lcu lated from the shear

s t ress. I t fol lows t h a t

P

icTwd,l

4h (d2,,, t 12) MF =

This corresponds t o a f r i c t i o n a l power MFw and a f r i c t i o n c o e f f i c i e n t

Since wear processes are e l iminated from hyd ros ta t i c bearings the t r i b o l o -

g i ca l behaviour can be described e n t i r e l y i n terms o f t h i s data and equa-

t ions. For o ther bear ing geometries the re levan t equations may be o f more

o r l ess d i f f e r e n t form (Ref. 5.33, 5.34).

5,4.2 MAGNETIC FIELDS

Tr ibo log i ca l systems employing the p r i n c i p l e s o f magnetism f o r the separa-

t i o n o f t he surfaces i n r e l a t i v e motion can be d i v ided broadly i n t o two

classes (Ref. 5.35):

( i ) Systems which u t i l i z e the e f f e c t o f a load-carry ing fo rce generated

by the flow o f conducting f l u i d s w i t h i n a magnetic f i e l d (Magnetohy-

drodynamic, MHD, bearings).

( i i ) Systems w i t h no l u b r i c a n t , d e r i v i n g t h e i r load-carry ing a b i l i t y from

the a t t r a c t i o n and repuls ion associated w i t h magnetic f i e l d s (Magnetic

supens i o n bearings ) .

203

Magnetohydrodynamic bear ings ( i ) ope ra te th rough mechanical f o r c e s produced

by magnet ic f i e l d s on a conduct ing f l u i d . From t h e laws o f e lec t romagnet ics ,

i t i s w e l l known t h a t an e l e c t r i c charge q moving w i t h a v e l o c i t y v w i t h i n

a magnet ic f i e l d B exper iences a f o r c e F, t he Lo ren tz f o r c e , a c t i n g perpen-

d i c u l a r t o t h e d i r e c t i o n o f mot ion and t h e d i r e c t i o n o f t h e magnet ic f i e l d :

A A -

F = q e ( v x B )

Fo r MHD l u b r i c a t i o n , i t f o l l o w s t h a t when an e l e c t r i c a l l y conduct ing f l u i d

f l ows across a magnet ic f i e l d t h e pressure developed i n t h e f l u i d can exceed

the o r d i n a r y hydrodynamica l l y generated pressure . The t h e o r e t i c a l t rea tmen t

o f MHD bear ings s t a r t s f rom a combina t ion o f t h e f lu id -mechan ics equat ions

and t h e e lec t romagne t i c equat ions l e a d i n g t o a magnetohydrodynamic fo rm o f

Reynolds equa t ion (Ref. 5.36). A cons ide rab le amount o f t h e o r e t i c a l work has

been undertaken i n d i c a t i n g t h e p o s s i b i l i t i e s o f MHD bear ings . However, t he

i m p r a c t i c a b i l i t i e s o f t h e magnet and assoc ia ted equipment s i z e have as y e t

r e s t r i c t e d a p p l i c a t i o n s .

The o t h e r c l a s s ( i i ) o f magnet ic bea r ings needs no l u b r i c a n t a t a l l

and d e r i v e s i t s l o a d - c a r r y i n g a b i l i t y f rom t h e a t t r a c t i o n and r e p u l s i o n as-

s o c i a t e d w i t h magnet ic f i e l d s . The mechanical f o rces produced by e i t h e r pe r -

manent magnets o r by e lec t romagnets can be used t o f r e e l y suppor t one p a r t -

n e r o f a bear ing . The p r i n c i p l e i s i l l u s t r a t e d i n F i g u r e 5.16.

F i g u r e 5.16 P r i n c i p l e of t h e suppor t o f a bea r ing s h a f t by f o u r e lec t romagnets .

204

One problem with bearings having a member freely supported i n a magnetic

f ie ld i s s tab i l i ty . This problem can be solved with a servo-control system.

If an external disturbing force acts on the "free" body, the corresponding

displacement of the body detected by non-contacting sensors thus producing

an electrical current which in turn i s fed to the electromagnets generating

an additional force compensating the disturbing displacement. Owing t o the advantageous tribological structure, (no solid-solid con-

t ac t , no lubricant, low f r i c t ion ) , magnetic bearings are able to operate under a broad spectrum of operating conditions. Charateristic data of com-

mercially available bearings are (Ref. 5.37):

l o a d capacity : 0.2 N - 15 kN

velocity : up t o 800,000 r.p.m. temperature : u p t o 800 K

The lifetime of the bearing depends on the bulk materials properties; oper-

ating lifetimes up t o 10 h have been obtained independently o f rotation

velocity. The advantages of the tribological structure of these bearings

are uti l ized in technical applications l ike the transmission of motion into

closed chambers ( fo r instance, vacuum chambers) or high-speed tracked- vehicle support.

5

5 , 4 , 3 INTERFACIAL ELASTOMERS

In th i s solution, wear processes in a tribo-mechanical system are eliminated

by replacing sliding surfaces with the internal mobility o f elastomers (Ref.

5.38). The elastomer ac t as a k i n d of lubricant and the resistance to motion

i s due t o the internal f r ic t ion of the elastomer. The most common elasto-

meric "lubricant" i s natural rubber, because of i t s excellent strength and

fatigue properties, b u t many synthetic elastomers can be used as well.

The principle of a typical elastomeric bearing i s i l lus t ra ted i n Figure 5.17. Basically, the elastomeric bearing i s comprised of alternating layers of rubber and metal laminates. The elastomer i s vulcanized and bonded t o the metal laminates as well as to the attachment metal components - inner

and outer "races". The design of an elastomers bearing depend on types of

load and motion ( rad ia l , axial, spherical, etc.). For instance, the "sand- wich-type" bearing shown in Figure 5.17 i s designed t o support high axial

loads FN while accornodating torsional ( A q ) or lateral motions ( A s ) through

the compression and shear characterist ics of the elastomer, respectively.

205

A s - laminates

races

F igu re 5.17 Typ ica l e las tomer i c a x i a l bear ing .

Th is t ype o f bea r ing i s ve ry s t i f f i n t h e a x i a l modes and s o f t i n shear.

I n genera l , t h e des ign o f e las tomer i c bea r ings must Zake i n t o c o n s i d e r a t i o n

f a c t o r s such as t h e t ype and frequency o f loads and mot ions as w e l l as

space-envelope l i m i t a t i o n s and l i f e requ i rements . The advantage o f t h e

e las tomer i c b e a r i n g i s t h a t t h e va r ious c h a r a c t e r i s t i c s o f t h e guidance o f

mot ion and t h e t ransmiss ion and d i s s i p a t i o n o f mechanical work can be de te r -

mined, a t l e a s t i n p r i n c i p l e , f rom the b u l k m a t e r i a l p r o p e r t i e s o f t h e i n t e r -

f a c i a l m a t e r i a l .

5,4,4 FLEXURAL MEANS

F o r t r ibo-mechan ica l a p p l i c a t i o n s i n which o n l y l i m i t e d t r a n s l a t o r y o r

angu lar mot ions a r e requ i red , f l e x u r a l bear ings , i .e . , bear ings wh ch f l e x

o r t w i s t i n an e l a s t i c member t o suppor t t h e load, possess a wear- r e e

i n v a r i a b l e t r i b o l o g i c a l s t r u c t u r e . These bear ings do n o t r e q u i r e a l u b r i -

can t and t h e f r i c t i o n a l r e s i s t a n c e t o mot ion i s s imp ly t h e e l a s t i c s t r e s s

i n bending o r t o r s i o n i n t e g r a t e d t o g i v e t h e f o r c e . Depending on t h e modes

o f l o a d and mot ion, d i f f e r e n t types o f f l e x u r a l bea r ings have been designed

(Ref. 5.39). As an example, a p a r a l l e l s p r i n g suppor t f o r t r a n s l a t o r y mo-

t i o n i s shown i n F i g u r e 5.18 (Ref. 5.40).

206

F S --c

7 1

F igu re 5.18 A f l e x u r a l bear ing .

The moving p a r t s o f t he bear ing , (1) and ( Z ) , a r e separated by two p a r a l l e l

f l e x u r e s t r i p s ( 3 ) which a re made o f hea t - t rea ted s t e e l o r phosphor bronze.

For a t r a n s l a t o r y mot ion, s, o f t h e upper p a r t (1) o f t h e bear ing , a f o r c e ,

FF, i s necessary which i s determined by t h e i n t e r n a l f r i c t i o n o f t h e f l e x -

u r e s t r i p s :

E : e l a s t i c moduls

FF = 2 E b h 3 s

l3

b, h, 1 : dimensions o f

t h e s t r i p s

S : displacement

The c o n t r a c t i o n pe rpend icu la r t o t h e mot ion i s g i ven by

Summing up, t he above examples show t h a t t he re a re d i f f e r e n t ways o f e l i -

m i n a t i n g s o l i d - s o l i d wear processes from mechanical systems under c e r t a i n

c i rcumstances, thus p r o v i d i n g t h e p r e r e q u i s i t e f o r a cons tan t , i n v a r i a n t

s t r u c t u r e o f t h e t r ibo-mechan ica l system. The advantages o f these s o l u t i o n s

are:

( i ) The t r i b o l o g i c a l processes i n such systems a re due t o i n t e r n a l p ro-

cesses ( i n t e r n a l f r i c t i o n and f a t i g u e ) o f t he i n t e r f a c i a l components

( f l u i d s , 1 i q u i ds , e l a s t i c m a t e r i a l s ) ,

207

( i i ) The f r i c t i o n a l losses and the l i f e t i m e p r o p e r t i e s can be es t ima ted

f rom t h e b u l k p r o p e r t i e s o f t h e i n t e r f a c i a l components.

( i i i ) The f u n c t i o n a l behav iour of these systems can be desc r ibed by

a p p l y i n g analogue models of t h e w e l l e s t a b l i s h e d t h e o r i e s o f

eng inee r ing systems a n a l y s i s (see S e c t i o n 6.1).

5 , 4 , 5 W E A R RESISTANT COATINGS

With t h e s o l u t i o n s desc r ibed i n t h e fo rego ing sec t i ons , i t i s p o s s i b l e t o

separa te comple te ly the moving sur faces o f a t r i b o - e n g i n e e r i n g system

e l i m i n a t i n g any wear process f rom the system.

s t r u c t u r e o f a t r ibo-mechan ica l system may be e s t a b l i s h e d by a p p l y i n g a

s u i t a b l e su r face t rea tment o f t h e su r faces i n o r d e r t o m i t i g a t e t r i b o -

induced changes o f su r face p r o p e r t i e s . There a re severa l d i f f e r e n t su r face

t rea tments a v a i l a b l e which a r e s u i t e d f o r t r i b o - e n g i n e e r i n g a p p l i c a t i o n s

(Ref. 5.41, 5.42). A c o m p i l a t i o n o f these methods i s g i ven i n Table 5.1.

I n t h e cho ice o f a s u i t a b l e c o a t i n g f o r a g i ven problem two b a s i c aspects

shou ld be considered, i n a d d i t i o n t o a c o s t - b e n e f i t a n a l y s i s :

( a )

( b )

I f t h e s o l u t i o n s desc r ibed above a r e n o t a p p l i c a b l e , an advantageous

The t e c h n i c a l f u n c t i o n o f t h e system under c o n s i d e r a t i o n and t h e

values o f t he o p e r a t i n g c o n d i t i o n s o f l oad , v e l o c i t y and tempera ture .

The t ype o f wear mechanism o r mechanisms expected t o a c t i n t h e

i n t e r f a c e o f t h e moving components.

Depending on t h e t ype o f t he dominant i n t e r f a c i a l wear mechanisms, d i f f e r e n t

s u i t a b l e su r face compos i t ions have been suggested. I n c o n s i d e r i n g t h i s as-

pec t f rom the view o f the"de1aminat ion theo ry o f wear" f o r low-speed d ry -

s l i d i n g wear c o n d i t i o n s , Suh and co-workers (Ref. 5.43) suggested t h a t a

s o f t metal su r face l a y e r shou ld be t h i n n e r than a c r i t i c a l t h i ckness t o

p reven t t h e accumula t ion o f d i s l o c a t i o n s i n t h e p l a t e d l a y e r and t h e forma-

t i o n o f t h e de laminated l a y e r . Th i s suggest ion was i n v e s t i g a t e d by p l a t i n g

annealed A I S I 1018 s t e e l w i t h 0.1 pm cadmium l a y e r s on bo th o f t h e contac-

t i n g sur faces . I n a s p e c i a l case t h i s has l e d t o a r e d u c t i o n o f t h e wear

r a t e o f about t h r e e o rde rs o f magnitude.

Some general adv ice f o r the des ign o f su r face coa t ings i n r e l a t i o n t o

t h e i n t e r f a c i a l wear mechanisms i s compi led i n F i g u r e 5.19 (Ref . 5 .44) :

I f i n a s l i d i n g system t h e adhesive wear mechanism i s expected t o dominate,

su r face l a y e r s o f low tendency f o r " c o l d we ld ing" and w i t h low shear s t r e n g t h

208

TREATMENT CONSTITUENTS

DEPOSITED COATIgGS

E lec t rop la t i ng

Electrochemical Co-depos i ti on

Chemical Vapour Deposit ion (CVD)

Arc Deposit ion

Powder/Wi r e Spraying

P1 asma Spraying

Detonation Gun

Spraying/Brushi ng

Sput ter ing

Porous Sintered Layers

Porous Anodic Fi lms

1 I

Cr, Rh, N i , Sn-Ni, Ag

Co/CrpC3, Pb/PTFE

T i c , T iN , WC

Co-Cr-Ni A1 loys

Ceramics, Cermets

MoSZ - Resin Bonded

MoS2 Films

Bronze/PTFE, CO/PTFE

Ti/PTFE, Al/PTFE

CHEMICAL CONVERSION COATINGS

Phosphate Ferrous A1 1 oys

Anodize

Oxal a te

D i chromate Magnesium A l l oys

T i t a n i um & A1 -A1 1 oys

Copper A1 1 oys

DIFFUSION COATINGS

Carburi z i ng

N i t r i d i n g

Sul fon i t r i d i n g

S i l i c o n i z i n g

Bor i d i ng

Chromizing

Beryl 1 i d i ng

C

N,C

N s S

S i

8, FeeB

C r

Be i n Titanium

i n Ferrous

A1 loys

~~

Table 5 . 1 Surface treatments f o r t r ibo-engineer ing app l i ca t i ons

may be appl ied. Depending on the mater ia l o f the counterpartner, t h i n sur-

face layers o f s o f t mate r ia l s w i t h a hexagonal c rys ta l log raph ic s t r u c t u r e

may f o r example be su i tab le . (Thin s o f t coat ings are a lso usefu l from the

p o i n t of the delaminat ion theory; they may a lso - i n a broader sense - p o s i t i v e l y in f luence surface f a t i g u e wear processes.) I f the abrasive wear

component dominates, very hard surface coatings, l i k e t i t a n i u m carbides,

may lead t o low wear ra tes . Hard coat ings, e.g., TiN, w i l l a lso reduce

adhesion of s tee l as w e l l as the wear ra te . I f superposi t ion o f var ious

wear processes i s t o be expected, mu l t i - l ayered surface coatings may be

bene f i c ia l (Ref. 5.45, 5.46). For c e r t a i n cases o f app l i ca t ion , the fo l low-

i n g ru les f o r the design of a t r i b o l o g i c a l l y stressed sur face as i l l u s t r a t e d

i n the lower p a r t o f F igure 5.19, may be favourable:

( i ) A t h i n outmost surface l a y e r should prevent adhesional co ld welding

effects w i t h the counterpartner.

( i i ) Below the t h i n l a y e r a hard l a y e r o f s u f f i c i e n t d u c t i l i t y should bear

the maximum o f Her tz ian contact stresses. This l a y e r should e x h i b i t a

gradient o f mechanical s t rength p roper t ies increasing from the outs ide

t o the i n s i d e o f the specimen.

( i i i ) Below the hard intermediate l a y e r the s t rength decreases progress ive ly

u n t i l t he lower values o f the base mater ia l are reached.

shear s t rength 1 p i zZzG-1

c o a t i n

mater ia l

Design of component

surface f a t i g u e

c o a t i n

mater ia l

mate r ia l

Figure 5.19 Su i tab le composition o f surface coatings.

210

These r a t h e r q u a l i t a t i v e p o i n t s shou ld be supplemented by an example

o f t h e des ign o f an ac tua l t r i b o - e n g i n e e r i n g component. Consider as a

c h a r a c t e r i s t i c example t h e design o f a bea r ing bushing (Ref. 5.47), as

shown schemat i ca l l y i n F igu re 5.20.

f l a s h Pb o r Sn o v e r l a y Pb-Sn-Cu d i f f u s i o n b a r r i e r N i

0.3-1.5 mm bear ing l a y e r bronze

s t e e l back s t e e l

F igu re 5.20 Design o f a bea r ing bushing.

I t can be seen t h a t a contemporary bea r ing may c o n s i s t o f f i v e l a y e r s t o

f u l f i l l i t s t e c h n i c a l purpose. The p r o t e c t i o n aga ins t ( c o r r o s i v e ) env i ron -

mental a t t a c k i s p rov ided by the outermost l a y e r , t he f l a s h . The t r i b o l o -

g i c a l behav iour i s determined ma in l y by t h e o v e r l a y and the bear ing l a y e r .

(Both l a y e r s a re separated by a t h i n n i c k e l l a y e r which prevents t h e d i f -

f u s i o n o f t i n f rom t h e o v e r l a y t o the copper o f t h e bear ing l a y e r which

may occur a t e leva ted temperatures. ) Whereas t h e o v e r l a y forms the s l i d i n g

sur face , t he purpose o f t h e bear ing l a y e r i s t o embed hard p a r t i c l e s and

t o rep lace the s l i d i n g su r face i f the o v e r l a y i s worn away. The purpose o f

t h e s t e e l back i s t o c a r r y the normal l o a d and t o connect t h e bushing w i t h

i t s housing. Th is example again i l l u s t r a t e s t h e importance o f a s u i t a b l e

s t r u c t u r a l design o f t h e components o f t r ibo-mechan ica l systems.

** '

211

6 Influence of tribological processes on the

function of mechanical systems

6 , 1 GENERAL CONSIDERATIONS

Whereas i n t h e preced ing chap te r t h e i n f l u e n c e o f t r i b o l o g i c a l processes on

the i n t e r n a l s t r u c t u r e o f mechanical systems has been discussed, i n t h i s

chapter t h e i n f l u e n c e o f t r i b o l o g i c a l processes on t h e e x t e r n a l f u n c t i o n

o f mechanical systems w i l l be s tud ied . It has been shown i n Chapter 3 t h a t

t he t e c h n i c a l f u n c t i o n o f t h e va r ious t r ibo-mechan ica l systems can be de-

s c r i b e d f o r m a l l y by t rans fo rma t ions o f c e r t a i n system inpu ts , such as mo t ion

and work, i n t o t h e ou tpu ts which a r e used t e c h n i c a l l y . De t r imen ta l i n f l u -

ences o f t h e f r i c t i o n and wear processes descr ibed i n Chapter 4 may then

l e a d t o d i s tu rbances o f t h e f u n c t i o n a l i n p u t - o u t p u t r e l a t i o n s , f o r example

f r i c t i o n - i n d u c e d s t i c k - s l i p e f f e c t s , un favourab le mechanical e f f i c i e n c i e s o r

even gross f u n c t i o n a l f a i l u r e s . Al though t h e d e t r i m e n t a l i n f l u e n c e s o f t h e

var ious t r i b o l o g i c a l processes on t h e m a n i f o l d mechanical systems (as com-

p i l e d i n t h e Appendix A) may be apparen t l y r a t h e r d i f f e r e n t , f rom a systems

p o i n t o f view t h e r e a r e some fea tu res which appear t o be o f genera l impor-

tance. These b a s i c aspects w i l l be s t u d i e d i n t h i s chap te r and conc lus ions

f o r a p roper f u n c t i o n a l behav iour o f t r ibo-mechan ica l systems w i l l be drawn.

To o b t a i n a s t a r t i n g p o i n t f o r a systems approach t o t h e s tudy o f t h e

main i n f l u e n c e s o f t r i b o l o g i c a l processes on t h e f u n c t i o n o f mechanical sys-

tems, f i r s t t h e f u n c t i o n a l behav iour o f mechanical systems w i t h n e g l i g i b l e

de t r imen ta l t r i b o l o g i c a l i n f l u e n c e s w i l l be d iscussed i n t h i s s e c t i o n .

I f d e t r i m e n t a l i n f l u e n c e s o f t r i b o l o g i c a l processes a re n e g l i g i b l e and

i f a mechanical system possesses a cons tan t , i n v a r i a n t s t r u c t u r e (see Sec-

t i o n 5 .4 ) , i t i s p o s s i b l e t o app ly t h e network approach o f eng inee r ing

21 2

systems a n a l y s i s t o t h e d e s c r i p t i o n o f t he f u n c t i o n a l behav iour o f t he

system. As o u t l i n e d i n Sec t i on 2.3, t h e c h a r a c t e r i z a t i o n o f t h e f u n c t i o n a l

behav iour o f a mechanical system by means o f t h e network approach o f eng i -

nee r ing systems a n a l y s i s s t a r t s w i t h t h e i d e n t i f i c a t i o n and mode l l i ng o f

t he elements o f t h e system. Next, t he i n p u t and o u t p u t v a r i a b l e s o f t h e

system a re i d e n t i f i e d and c l a s s i f i e d i n t o "across" and " th rough" v a r i a b l e s

o r " e f f o r t " and " f l o w " v a r i a b l e s . Then network graphs and s i g n a l f l o w graphs

a re drawn and the s t a t e equat ions a re fo rmula ted . For t h i s purpose, t h e

K i r c h h o f f ' s mesh and node laws a r e o f t e n u t i l i z e d . The r e s u l t i n g equat ions

are then so lved app ly ing s u i t a b l e methods, l i k e the Laplace t rans form, o r

by u t i l i z i n g d i g i t a l o r analogue computers i n o r d e r t o c h a r a c t e r i z e t h e

f u n c t i o n a l behav iour o f t h e system.

M1

F igu re 6 . 1 Simple gear t r a i n and i t s schematic rep resen ta t i on .

A mechanical system which i s f r e q u e n t l y used t o i l l u s t r a t e t h e a p p l i c a t i o n

o f t h e network techn ique i s t h e " i d e a l " gear t r a i n (no f r i c t i o n losses , no

wear e f f e c t s ) . A s imp le gear t r a i n i s shown i n F igu re 6.1. The gear t r a i n

cons is t s o f two gears w i t h r a d i i rl and r2, and t h e r a t i o o f i t s r a d i i i s

c a l l e d t h e gear r a t i o N = r2/r1. The gear t r a i n i s t r a n s m i t t i n g bo th to rque

M1-M2 and angu la r v e l o c i t y u1-u2 and i t i s sometimes c a l l e d a

mechanical-mechani c a l energy conver te r . The f u n c t i o n a l i n p u t - o u t p u t r e l a -

t i o n s o f t he g e a r - t r a i n system can be found by an e l e c t r i c a l analogue f rom

t h e genera l i zed K i r c h h o f f ' s laws (see Sec t ion 2 .3 ) :

( i ) From f o r c e e q u i l i b r i u m , t h e f o r c e e x e r t e d m u t u a l l y by t h e i n t e r a c t i n g

gear t e e t h must be equal , i . e . F2 = F1. I n t r o d u c i n g t h e gear r a t i o , N,

i t f o l l o w s t h a t t h e ou tpu t t o rque M2 i s equal t o the i n p u t t o rque M1

213

t imes t h e gear r a t i o N :

M2 = N M1

( i i ) From qeon ie t r i ca l c o m p a t i b i l i t y , t he su r face v e l o c i t i e s must be t h e same,

i . e . v2 = vl. Th i s leads t o a r e l a t i o n between t h e i n p u t and o u t p u t

angu la r v e l o c i t i e s wl, and w 2 :

1 W 2 = W 1

The r e l a t i o n s between i n p u t and o u t p u t t o rque and angu la r v e l o c i t y can be

combined u s i n g a m a t r i x rep resen ta t i on . I n p u t t o rque M1 and i n p u t angu la r

v e l o c i t y u1 a r e desc r ibed toge the r as an i n p u t v e c t o r

x = r "1 This i n p u t v e c t o r i s t rans formed i n t o t h e ou tpu t v e c t o r

by t h e t r a n s f o r m a t i o n m a t r i x

The f u n c t i o n a l behav iour o f an i d e a l gear t r a i n can be then symbol ized by

t h e r e p r e s e n t a t i o n shown i n F igu re 6 .2 .

F igu re 6 .2 Network r e p r e s e n t a t i o n o f gear t r a i n system.

214

I n p u t 1 0

0

System

s t r u c t u r e .

0

I n p u t n ---

T h i s i s t h e t y p i c a l network rep resen ta t i on o f a ( l i n e a r ) " two-por t ' '

system. I f more t h a n two i n p u t and o u t p u t v a r i a b l e s a re connected w i t h t h e

system, the g e n e r a l i z a t i o n o f t h e mode l l i ng techn ique leads t o t h e genera l

c h a r a c t e r i z a t i o n o f a n - p o r t system as shown i n F igu re 6.3.

0 ou tpu t 1 U

0

o Output m

ou tpu t

v a r i a b l e s

1,. . . ,m

System

d e s c r i p t i o n

I n p u t

1, ..., n

F igu re 6.3 Network rep resen ta t i on o f n - p o r t system.

The techn ique i l l u s t r a t e d i n F igu res 6.2 and 6 .3 o n l y works i f t h e elements

o f t h e ac tua l system can be mode l led by s imp le phys i ca l elements w i t h l i n e a r

cause-e f fec t i n t e r r e l a t i o n s h i p s between t h e i n p u t and o u t p u t v a r i a b l e s .

Moreover, t he network techn ique assumes a l o s s - f r e e s teady -s ta te f u n c t i o n

o f t h e system and a cons tan t system s t r u c t u r e . Due t o these r e s t r i c t i o n s t h e

convent iona l network technique, as i l l u s t r a t e d by t h e s imp le gear t r a i n

example, has t o be m o d i f i e d f o r t h e f u n c t i o n a l d e s c r i p t i o n o f t r ibo-mechan i -

c a l systems. An ex tens ion o f t h e network method f o r t h e s teady -s ta te case o f

power t ransmiss ion systems which takes i n t o account f r i c t i o n a l energy losses

has been proposed by Sch losser (Ref. 6.1). I n t h i s model a Coulomb-type o f

f r i c t i o n i s assumed, i n t r o d u c i n g a cons tan t c o e f f i c i e n t o f f r i c t i o n f o r a

g i ven s e t o f cond i t i ons . Wi th t h i s model t he t r a n s f e r and l o s s - c h a r a c t e r i s -

t i c s o f t h e va r ious mechanical power - t ransmiss ion systems can be descr ibed.

I n o r d e r t o s tudy t h e dynamics o f t r ibo-mechan ica l systems, v a r i a b l e f r i c -

t i o n cond i t i ons a r e t o be taken i n t o c o n s i d e r a t i o n as d iscussed i n t h e n e x t

s e c t i on .

215

6,2 TRANSMISSION OF MOTION AND STICK-SLIP EFFECTS

6,2,1 DYNAMICS OF TRIBO-MECHANICAL SYSTEMS

The f u n c t i o n a l behav iour o f any t r ibo-mechan ica l system i s connected, by

d e f i n i t i o n , w i t h r e l a t i v e mot ion o f one o r more o f t h e components o f t h e

system. As desc r ibed i n Chapter 3, t h i s mot ion may c o n s t i t u t e a t r a n s f e r

o f work, i n f o r m a t i o n o r m a t e r i a l th rough t h e t r ibo-mechan ica l system. I n

any case, t h e mot ion and t h e dynamics o f t h e whole system a r e i n f l u e n c e d

by t h e i n t e r f a c i a l f r i c t i o n processes between t h e moving components.

C lea r l y , t he d e t a i l s o f t h e i n f l u e n c e s o f t r i b o l o g i c a l processes on t h e

dynamics o f mot ion may be q u i t e d i f f e r e n t f o r t h e va r ious t r i bo -mechan ica l

systems, f o r example, b a l l bear ings (Ref . 6 .2 ) , s l ideways (Ref. 6 .3 ) o r

metal machining systems (Ref. 6 .4 ) . Cons ider ing t h e f u n c t i o n a l t ransmiss ion

o f mot ion th rough t h e va r ious types o f t r ibo-mechan ica l systems, t h e i n -

f l uences o f t h e t r i b o l o g i c a l processes desc r ibed i n Sec t i on 4 .3 may l e a d

t o unwanted v i b r a t i o n s o f t h e moving p a r t s , and t o " s t i c k - s l i p " mot ion.

These d i s t u r b i n g i n f l u e n c e s on t h e f u n c t i o n a l behav iour can be observed

i n va r ious t r ibo-mechan ica l systems: f rom t h e squea l i ng o f brakes t o the

c h a t t e r i n g o f machine t o o l s d u r i n g c u t t i n g processes. Since t h e occur rence

o f s t i c k - s l i p e f f e c t s may i n f l u e n c e t h e f u n c t i o n a l behav iour o f any t r i b o -

mechanical system, t h i s e f f e c t w i l l be s t u d i e d i n some d e t a i l .

Many tri bo-mechani c a l systems whose f u n c t i o n a l purpose i s connected

w i t h t h e t ransmiss ion o f mot ion can be mode l led i n a s i m p l i f i e d manner by

t h e c o n f i g u r a t i o n shown i n F i g u r e 6.4. The model system c o n s i s t s o f a body

( 1 ) o f mass ml, moving r e l a t i v e l y t o i t s c o u n t e r p a r t ( 2 ) o f mass m2 f i x e d

t o t h e ground v i a a s p r i n g w i t h a s p r i n g cons tan t C s 2 and a damper w i t h a

damper cons tan t Cd. The body ( 1 ) i s d r i v e n v i a t h e s p r i n g Csl a t cons tan t

v e l o c i t y vo = s / t .

body ( 2 ) o f v e l o c i t y v2 and d i s tance z i s i n f l u e n c e d by t h e f r i c t i o n f o r c e

FF a c t i n g i n t h e i n t e r f a c e ( 3 ) between body ( 1 ) and body ( 2 ) . From t h e

f o l l o w i n g s imp le q u a l i t a t i v e c o n s i d e r a t i o n (Ref . 6 .5 ) , i t f o l l o w s t h a t t h e

t ype o f mot ion i s determined by the va lue o f t h e f r i c t i o n f o r c e a t vrel = 0

and t h e dependence o f t h e f r i c t i o n f o r c e on t h e v e l o c i t y FF = f ( v ) .

L e t t h e i n i t i a l s t a t e o f t he system shown i n F i g u r e 6.4 be such t h a t t h e

sp r ings Csl and C s 2 a re uncompressed and ml and m2 a re a t r e s t . When t h e

mot ion o f v e l o c i t y vo i s i n t roduced t h e r e w i l l be no movement o f ml r e l a t i v e

The mo t ion o f body ( 1 ) o f v e l o c i t y v1 and d i s t a n c e x r e l a t i v e l y t o

216

F r i c t i o n fo rce , FF

F i g u r e 6.4 Model o f a t r ibo-mechan ica l system.

F igu re 6.5 Network rep resen ta t i on .

F i g u r e 6.6 S igna l f l o w graph.

217

Mechanical

mass

s p r i n g

damper

t o m2 ( " s t i c k " phase) u n t i l t h e d r i v i n g f o r c e on m l i s h i g h enough t o ove r -

come t h e ( s t a t i c ) f r i c t i o n f o r c e between ml and m2. I f then t h e mo t ion o f

m l r e l a t i v e t o m2 s t a r t s ( " s l i p " phase) t h e s p r i n g s decompress. Thus t h e

d r i v i n g f o r c e i s lowered by a c e r t a i n amount. I f now t h e d r i v i n g f o r c e on

ml f a l l s below t h e ( k i n e t i c ) f r i c t i o n fo rce , a second " s t i c k " phase may

evo lve .Th is i n t u r n leads t o an i nc rease o f t h e d r i v i n g f o r c e u n t i l t h e

mot ion o f t h e second s l i p phase s t a r t s , and so on.

The b a s i c equat ions which govern t h e f u n c t i o n a l behav iour o f t h e me-

chan ica l t ransmiss ion system shown i n F i g u r e 6.4 can be fo rmu la ted by

u t i l i z i n g t h e network approach o f systems a n a l y s i s (see Sec t ion 2.3).

E l e c t r i c a l

c a p a c i t o r -+'r

i n d u c t o r --- r e s i s t o r -+=-

Table 6.1 Analogue mechanical and e l e c t r i c a l system elements.

I n F i g u r e 6.5, t he netMork graph o f t he system o f F i g u r e 6.4 i s drawn. The

network graph i s based on the e lec t ro -mechan ica l analogue compi led i n Tab le

6.1. I n a p p l y i n g t h e v e l o c i t y - e f f o r t , f o r c e - f l o w analogy desc r ibed i n Sec-

t i o n 2.3, f rom a l oop p o i n t o f view t h e v e l o c i t y can be seen i n analogy t o

a " v o l t a g e d r i v e r " o f t he c i r c u i t . The fo rces F a r e then t h e " f l o w " v a r i -

ab les th rough t h e elements o f t he c i r c u i t , i . e . t h e masses ml, m 2 , t h e

sp r ings sl, s2 and the damper d. The cor respond ing s i g n a l f l o w graph o f t h e

network graph o f F i g u r e 6.5 i s shown i n F i g u r e 6.6. From t h e network and

s i g n a l - f l o w graphs, t h e equat ions d e s c r i b i n g t h e f u n c t i o n a l behav iour of

t h e t r ibo-mechan ica l system can be e a s i l y de r i ved . U t i l i z i n g K i r c h h o f f ' s

node law t h e f o l l o w i n g equat ions r e s u l t :

node 1)

node 2 )

218

( I ) Csl ( v o t - x ) = FF t m , i i

(11) -FF = Cs2z t m? t C d l

o r

For t h e s o l u t i o n o f these d i f f e r e n t i a l equat ions , d i f f e r e n t methods can be

used. (Fo r a rev iew o f a n a l y t i c a l methods see Ref. 6.5.) I n t h e f o l l o w i n g ,

these equat ions and t h e s t i c k - s l i p behav iour o f t h e t r ibo-mechan ica l system

shown i n F igu re 6.4 w i l l be s t u d i e d by means o f an analogue computer.

6 ,2 ,2 SIMULATION OF STICK-SLIP BEHAVIOUR

I f a system can be represented by d i f f e r e n t i a l equat ions , t h e behav iour o f

t h e system can be s t u d i e d w i th an analogue computer. The systems elements

can be represented w i t h reasonable accuracy by s tandard computer elements.

Whereas f o r t he t r ibo-mechan ica l system mode l led i n F igu re 6.4 the values

o f t h e sp r ings and t h e damper Csl, Cs2 and Cd, r e s p e c t i v e l y , can be e a s i l y

ad jus ted by po ten t i omete r s e t t i n g s , t h e model1 i n g o f t h e f r i c t i o n charac-

t e r i s t i c s requ i res an a p p r o p r i a t e f u n c t i o n genera tor . The above q u a l i t a t i v e

d i scuss ion o f t h e s t i c k - s l i p e f f e c t has i n d i c a t e d t h a t t h e s t i c k - s l i p mot ion

may be determined by the type o f t he dependence o f t he f r i c t i o n f o r c e FF

( o r t h e f r i c t i o n c o e f f i c i e n t f ) on t h e v e l o c i t y . I n o r d e r t o s tudy the

s t i c k - s l i p mot ion w i t h s u f f i c i e n t g e n e r a l i t y , i n t h i s study, f o r t h e f r i c -

t i o n - v e l o c i t y c h a r a c t e r i s t i c t h e shape o f t h e S t r i b e c k curve has been chosen

and t h e behav iour o f t he t r ibo-mechan ica l system a t t h e d i f f e r e n t p a r t s o f

t h e S t r i b e c k curve has been s t u d i e d (Ref. 6 .6) . The analogue computer f l o w

diagram f o r t h e system i s shown schemat i ca l l y i n F igu re 6.7.

I t can be seen t h a t t he upper and t h e l ower p a r t s o f t h e computer f l o w

diagram correspond t o t h e above d i f f e r e n t i a l equat ions ( I ) and (11) and t h a t

t he c o u p l i n g o f these d i f f e r e n t i a l equat ions v i a t h e f r i c t i o n f o r c e ( o r t h e

f r i c t i o n c o e f f i c i e n t ) i s s imu la ted by the f u n c t i o n genera to r i n t h e m idd le

219

o f F i g u r e 6 . 7 . The a p p r o p r i a t e s c a l i n g f a c t o r s a r e determined f rom t h e

des ign parameters o f a p in -on -d i sc t r i b o m e t e r mode l led by F i g u r e 6.4 .

- csl

ml X

Func t i on - genera tor

\ 1 F F b ) Z

'd ~

- - cs2

m2

8

F igu re 6 . 7 Analogue computer f l o w diagram.

Fo r g i ven cons tan t da ta of m l , m2, Csl, Cd, depending on t h e l o c a t i o n o f

t h e f r i c t i o n c o e f f i c i e n t w i t h i n t h e S t r i b e c k curve, a d i f f e r e n t dynamic

behav iour o f t h e t r ibo-mechan ica l system can be observed. W i thou t go ing

i n t o numerical d e t a i l s , t he t h r e e f o l l o w i n g d i f f e r e n t genera l p a t t e r n s o f

t h e mot ion behav iour o f t h e mode l led t r ibo-mechan ica l system o f F i g u r e 6 . 4

can be d i s t i n g u i s h e d :

( i ) Fo r t h e c o n d i t i o n o f f r i c t i o n around t h e minimum o f t he S t r i b e c k

curve, t h e system i s uns tab le and t h e mot ion f o l l o w i n g a d i s tu rbance

i s d i ve rgen t , i . e . , t he system e x c i t e s i t s e l f t o v i b r a t i o n s , as shown

i n F i g u r e 6.8 .

( i i ) F o r t h e c o n d i t i o n s o f f r i c t i o n on t h e l e f t p a r t o f t h e S t r i b e c k curve

t h e t y p i c a l s t i c k - s l i p mo t ion diagram r e s u l t s as i n F i g u r e 6.9.

( i i i ) F o r t h e c o n d i t i o n s o f f r i c t i o n on t h e r i g h t p a r t o f S t r i b e c k ' s curve

t h e system i s s t a b l e , i . e . v i b r a t i o n s i n t roduced t o t h e system a r e

damped a u t o m a t i c a l l y . Th i s behav iour can be seen i n F i g u r e 6.10 f o r

f i v e d i f f e r e n t s lopes of t h e r i g h t p a r t o f t h e S t r i b e c k curve and

f i v e o p e r a t i n g va lues o f t h e f r i c t i o n c o e f f i c i e n t f.

The r e s u l t s c o n f i r m t h e exper imenta l obse rva t i on t h a t s t i c k - s l i p e f f e c t s

a re l i k e l y t o occu r if t h e s lope of t he f r i c t i o n - v e l o c i t y curve i s n e g a t i v e

220

F r i c t i o n c h a r a c t e r i s t i c Mot ion behav iour

Y

S l i d i n g v e l o c i t y -

F i a u r e 6.8 I n s t a b l e mot ion behaviour

Time - f o r c o n d i t i o n s a t t h e minimum o f t h e

S t r i b e c k curve ( A : range o f v a r i a t i o n o f f, v ) .

F i g u r e 6.9 S t i c k - s l i p o s c i l l a t i o n s f o r c o n d i t i o n s on t h e l e f t p a r t o f t h e S t r i b e c k curve ( f0=0.6).

F igu re 6.10 S t a b l e mot ion behav iour f o r c o n d i t i o n s on t h e r i g h t p a r t o f t h e S t r i b e c k curve (f=1.0; 0.7; 0.5; 0.3; 0.02).

221

o r equal t o zero, - < 0, as i n t h e l e f t p a r t o f t h e S t r i b e c k curve. Thus,

s t i c k - s l i p e f f e c t s may occur o n l y under c o n d i t i o n s o f s o l i d f r i c t i o n o r

boundary o r mixed l u b r i c a t i o n b u t a re u n l i k e l y t o occur under c o n d i t i o n s

o f hydrodynamic 1 u b r i c a t i o n .

systems can be conven ien t l y s t u d i e d by analogue computer s i m u l a t i o n . I f an

ac tua l t r ibo-mechan ica l system i s mode l led i n t h i s way, i t i s a l s o p o s s i b l e

t o use t h i s model as a b a s i s f o r a t tempts t o e l i m i n a t e s t i c k - s l i p e f f e c t s

and t o o p t i m i z e the dynamic behav iour o f t h e system. The o p t i m i z a t i o n da ta

can be ob ta ined by v a r y i n g t h e values o f the analogue computer s e t t i n g s ,

thus s i m u l a t i n g a change i n the des ign of t h e elements o f t he system

(masses, sp r ings , dampers) o r a change o f t h e f r i c t i o n c o n d i t i o n s . Fu r the r ,

c r i t i c a l o p e r a t i n g c o n d i t i o n s o f t he mode l led system may be s tud ied . I t

f o l l o w s t h a t t h e a p p l i c a t i o n o f a combina t ion o f system mode l l i ng tech-

niques and analogue computer s t u d i e s may be o f g r e a t h e l p f o r o b t a i n i n g a

p roper f u n c t i o n a l behav iour o f a g i ven t r ibo-mechan ica l system.

d f dv

These r e s u l t s show t h a t t he s t i c k - s l i p behav iour o f t r i bo -mechan ica l

I n p u t work System - 'in s t r u c t u r e

6,3 MECHANICAL EFFICIENCY

Output work

W o u t -

I n Chapter 3 t h e f u n c t i o n a l t r a n s f e r o f mechanical work th rough a t r i b o -

mechanical system has been descr ibed as a process o f t r a n s l a t i o n and t r a n s -

fo rma t ion o f mechanical energy. Th is can be cha rac te r i zed i n a s i m p l i f i e d

manner by t h e diagram shown i n F i g u r e 6.11.

" Losses "

F igu re 6.11 Work t r a n s a c t i o n s o f a t r ibo-mechan ica l system.

222

The a b i l i t y o f a mechanical system t o t r a n s f e r work, mechanical energy

o r power i n t o a t e c h n i c a l l y u s e f u l o u t p u t i s u s u a l l y expressed by t h e e f -

f i c i e n c y -q o f t h e system de f ined as

e f f i c i e n c y =

T '

u s e f u l ou tpu t work i n p u t work

W,,t 'in

Because o f i t s economic importance, t h e e f f i c i e n c y o f a mechanical system

i s one o f i t s b a s i c eng ineer ing c h a r a c t e r i s t i c s and most s tandard books o f

mechanical eng inee r ing con ta in some data on t h e e f f i c i e n c y o f machine e l e -

ments. (See f o r i ns tance Ref. 6 .7 . ) However, due t o t h e g r e a t v a r i e t y o f

t r ibo-mechan ica l systems and t h e complex i ty o f t r i b o l o g i c a l processes,

t he re e x i s t s no genera l theory c o r r e l a t i n g t h e e f f i c i e n c y o f mechanical

systems w i t h t h e t r i b o l o g i c a l processes o c c u r r i n g w i t h i n t h e system as d i s -

cussed i n Sec t i on 4.3.4. I n t h e f o l l o w i n g , t h e i n f l u e n c e o f f r i c t i o n on t h e

e f f i c i e n c y o f a t r ibo-mechan ica l system w i l l be s t u d i e d phenomenological ly

i n d i scuss ing a s imp le techn ica l example. From the r e s u l t s o f t h i s example

some genera l conc lus ions w i l l be drawn.

F igu re 6.12. The system cons is t s o f a h o r i z o n t a l l y moving wedge (1) and a

v e r t i c a l l y moving wedge ( 2 ) . The techn ica l purpose o f t h e system i s t o

t rans fo rm t h e i n p u t mot ion, i . e . t h e i n p u t t r a n s l a t i o n x i n t o an ou tpu t

mot ion y a t a r i g h t ang le t o i t , and t o l i f t a l o a d F a t t h e o u t p u t by

i n t r o d u c i n g an i n p u t f o r c e Fx. The bas i c p r i n c i p l e o f t h e t rans fo rma t ion

o f i n p u t s o f f o r c e and mot ion (Fx, x ) i n t o t e c h n i c a l l y u s e f u l ou tpu ts o f

f o r c e and mot ion ( F

t r ibo-mechan ica l machine elements, i n c l u d i n g t r a n s l a t i o n screws, worm-wheel

d r i ves , cam-and-fol lower se ts , e t c .

c a l c u l a t e d w i t h t h e f o l l o w i n g s teps (Ref. 6 .8) :

( a )

( b )

( c )

( d )

Consider a s imp le "wedge d r i v e " as i l l u s t r a t e d i n the upper p a r t o f

Y

y ) by means o f a "wedge e f f e c t " i s u t i l i z e d i n va r ious Y'

The e f f i c i e n c y o f t he wedge d r i v e system shown i n F i g u r e 6.12 can be

draw free-body diagrams o f t h e elements o f t he system,

draw v e c t o r diagrams o f t h e fo rces a c t i n g on t h e system's elements,

determine the cond i t i ons o f f o r c e e q u i l i b r i u m ,

c a l c u l a t e t h e e f f i c i e n c y T de f i ned as 7 = Fy. y/F; x.

t Y

I

i F Y +

F3

FY

FN2

Fx

223

F igu re 6.12 C h a r a c t e r i s t i c o f "wedge d r i v e " system.

224

As i n d i c a t e d i n F igu re 6.12, t he t ransmiss ion o f t he i n p u t f o r c e Fx

i n t o t h e ou tpu t f o r c e F

( i )

( i i )

( i i i ) FF3 i s t he f r i c t i o n f o r c e a c t i n g i n t h e guides o f wedge ( 2 ) .

S p l i t t i n g up these fo rces i n t o components normal and t a n g e n t i a l t o the

surfaces, t he f o r c e vec to r diagrams shown i n t h e r i gh t -hand p a r t o f F i g u r e

6.12 can be drawn. I n these diagrams, 6 denotes t h e ang le between t h e

t a n g e n t i a l ( f r i c t i o n ) f o r c e component FT and t h e normal f o r c e component FN,

the tangent o f which i s e q u i v a l e n t t o t h e c o e f f i c i e n t o f f r i c t i o n , i . e . ,

tan 5 = FT/FN = f. From t h e p a r t i a l f o r c e v e c t o r diagrams t h e r e s u l t i n g

f o r c e vec to r diagram, d e s c r i b i n g t h e e q u i l i b r i u m c o n d i t i o n between t h e

fo rces Fx, F1, F3, Fy can be determined, see F i g u r e 6.12 below. From the

t r i g o n o m e t r i c r e l a t i o n s f o r t he two t r i a n g l e s w i t h i n t h i s diagram, i t f o l -

1 ows t h a t

i s i n f l u e n c e d by t h r e e sources o f f r i c t i o n : Y

FF1 i s t he f r i c t i o n f o r c e a c t i n g a t t h e suppor t o f wedge ( l ) ,

FF2 i s t he f r i c t i o n f o r c e a c t i n g a t t h e i n t e r f a c e between wedge ( 1 )

and wedge ( 2 ) ,

s i n p1 s i n p 2

and

F2 - - - - FX

s i n p3 s i n p4

Thus

225

I f i t i s assumed t h a t t h e c o n d i t i o n s o f f r i c t i o n ( i ) , ( i i ) , ( i i i ) a r e

equal , i .e. t h a t

fl = f * = f3 = f,

i t f o l l o w s t h a t

F 1 Y =

t a n (cp t 26) FX

Since t h e r e l a t i o n between t h e d i s tances x and y i s g i ven by

y = x tancp,

then f o r t h e e f f i c i e n c y

Fy ' Y 11 = -

Fx * x

i t f o l l o w s t h a t

t a n g

t a n ( c p t 26) 11'

This r e l a t i o n i n d i c a t e s t h a t f o r a g i ven va lue o f t h e wedge anglecp, t h e

e f f i c i e n c y i s determined by t h e f r i c t i o n c o e f f i c i e n t f = t a n 6 a t t h e t h r e e

f r i c t i o n a l i n t e r f a c e s shown i n F igu re 6.12. S i m i l a r express ions a r e a l s o

ob ta ined f o r o t h e r t r ibo-mechan ica l systems. F o r i ns tance , t h e e f f i c i e n c y

o f a t r a n s l a t i o n screw (Ref. 6.9) i s g i ven by t h e r e l a t i o n

t a n cp

t a n ( g t 6 ) T '

which i s q u i t e s i m i l a r t o t h a t o f t h e wedge-drive system. A graph o f t h e

e f f i c i e n c y o f t h e wedge-dr ive system f o r a wedge ang le c p = 30' as a func-

t i o n o f t h e c o e f f i c i e n t o f f r i c t i o n i s p l o t t e d i n F i g u r e 6.13.

226

90

80

70

F I 6o

h z

F igu re 6.13 E f f i c i e n c y o f a wedge d r i v e system as f u n c t i o n o f f r i c t i o n .

I t can be seen t h a t t h e e f f i c i e n c y v a r i e s o v e r a broad range as a f u n c t i o n

of t h e c o e f f i c i e n t of f r i c t i o n , For t y p i c a l f r i c t i o n and l u b r i c a t i o n regimes

the f o l l o w i n g ranges a r e found:

( I ) d r y s l i d i n g f r i c t i o n : 1 z 5 t o 40%

(11) boundary l u b r i c a t i o n : x 60 t o 70%

(111) hydrodynamic l u b r i c a t i o n : 1 = 90 t o 98%

( I V ) r o l l i n g f r i c t i o n : -q = 97 t o 99%

These da ta i n d i c a t e t h a t f o r s l i d i n g s i t u a t i o n s , e f f i c i e n c i e s g r e a t e r than

90 pe rcen t can o n l y be ob ta ined w i t h f u l l f l u i d l u b r i c a t i o n , and t h a t

h i g h e s t e f f i c i e n c i e s can be r e a l i z e d by s u b s t i t u t i n g s l i d i n g f r i c t i o n by

r o l l i n g elements. Al though these f i g u r e s a r e d e r i v e d f o r t h e s p e c i f i c wedge-

d r i v e system, they c h a r a c t e r i z e b road ly t h e t y p i c a l e f f i c i e n c y ranges o f

t r ibo-mechan ica l systems o p e r a t i n g under d i f f e r e n t t r i b o l o g i c a l cond i t i ons .

227

I f exac t e f f i c i e n c y da ta of a g i ven t r ibo-mechan ica l system a re needed,

exper imenta l measurements shou ld be used i n a d d i t i o n t o an a n a l y t i c a l

es t ima t ion . Fo r example, f o r t he accu ra te de te rm ina t ion o f t h e e f f i c i e n c y

o f gear systems, bo th exper imenta l measurements and mathematical model

s imu la t i ons were performed i n o rde r t o de termine t h e i n f l u e n c e o f such

f a c t o r s as d iamet ra l p i t c h , c o n t a c t r a t i o , magnitude o f t r a n s m i t t e d load,

and speed upon t h e e f f i c i e n c y (Ref. 6 .10) . I f d i f f e r e n t t r ibo-mechan ica l

systems a c t t oge the r , t h e e f f i c i e n c i e s must be m u l t i p l i e d . F o r i ns tance ,

f o r a spur gear system o f e f f i c i e n c y 11 , which i s suppor ted by two bear ings

o f e f f i c i e n c y q b t h e t o t a l e f f i c i e n c y i s g i ven by 9

I n g e n e r a l i z i n g these r e s u l t s , i t f o l l o w s t h a t a mult i -component mechanical

system o f h i g h t o t a l e f f i c i e n c y can o n l y be r e a l i z e d i f a l l i n d i v i d u a l sub-

systems a re designed w i t h e f f i c i e n c i e s as h i g h as poss ib le . Fo r t h e d e t e r -

m ina t i on o f t h e t o t a l e f f i c i e n c y o f a mult i -component system t h e procedure

o f "systems t e a r i n g " as exp la ined i n Chapter 2 may be used.

6 I 4 FUNCTIONAL FA I LURES

6,4,1 CAUSES OF FAILURE

The d i scuss ions i n the preced ing sec t i ons have shown t h a t t r i b o l o g i c a l p ro -

cesses determine the e f f i c i e n c y o f mechanical systems and may a l s o d i s t u r b

t h e f u n c t i o n a l i n p u t - o u t p u t r e l a t i o n s . If i n t h e performance o f a g i ven

system, t h e f u n c t i o n a l t r a n s f o r m a t i o n o f t h e sys tem's i n p u t s i n t o t h e tech-

n i c a l l y used ou tpu ts i s d i s t u r b e d i n such a way t h a t t h e o p e r a t i n g cond i -

t i o n s exceed c e r t a i n t o l e r a n c e l i m i t s i t i s s a i d t h a t a " f u n c t i o n a l f a i l u r e "

o f t h e system has occur red . Since i n any system, t h e i n p u t s a re t rans formed

i n t o t h e ou tpu ts v i a the s t r u c t u r e o f t h e system, i n genera l t h e e f f e c t o f

a f u n c t i o n a l f a i l u r e i s assoc ia ted w i t h , o r caused by, s i g n i f i c a n t changes

o f t h e s t r u c t u r e o f t h e system (see Chapter 5 ) . These s t r u c t u r a l changes i n

t u r n a r e i n f l u e n c e d o r caused by t h e t r i b o l o g i c a l processes o c c u r r i n g w i t h i n

t h e system d u r i n g t h e f u n c t i o n a l t r a n s f o r m a t i o n o f t h e i n p u t s i n t o t h e ou t -

pu ts . Before s tudy ing t h e r o l e o f t r i b o l o g i c a l processes i n t h e f a i l u r e o f

228

mechanical systems, some general t h e o r e t i c a l cons ide ra t i ons o f t he aspects

o f s a f e t y and f a i l u r e o f eng inee r ing systems w i l l f i r s t be made.

ven t them? According t o S tan ton (Ref. 6.11) t h e r e a re t h r e e impor tan t the-

o r i e s i n t h i s f i e l d .

Why do f a i l u r e s and acc iden ts happen and what should be done t o p re -

The f i r s t i s H e i n r i c h ' s domino sequence theory which p o s t u l a t e s t h a t

f i v e f a c t o r s , o c c u r r i n g i n sequence, l ead t o an a c c i d t i t (Ref . 6 .12 ) .

These f i v e f a c t o r s a re : (a ) persona l t r a i t s , e i t h e r i n h e . i t e d o r acqu i red

f rom t h e environment; ( b ) a persona l d e f i c i e n c y , i .e. , these t r a i t s pre-

dispose a person t o commit an unsafe a c t ( o r omiss ion) o r t o a l l o w a phys i -

ca l o r mechanical hazard t o e x i s t ; ( c ) an unsafe a c t ( o r omiss ion) o r a

phys i ca l o r mechanical hazard; i d ) t h e acc iden t ; and a t t h e end o f t he se-

quence, ( e ) t h e i n j u r y . Each f a c t o r i s l i k e a domino s tand ing on end. As

one f a l l s , i t knocks the o the rs down. To p reven t acc idents , H e i n r i c h sug-

ges ts removal o f one o f t he dominoes, p r e f e r a b l y the domino l a b e l l e d "unsafe

a c t o r mechanical o r phys i ca l hazard".

The second impor tan t t heo ry i s Haddon's abnormal energy exchange theo ry

(Ref. 6.13). Accord ing t o t h i s theory , damage occurs when a system exchanges

energy w i t h i t s environment beyond some acceptab le o r normal l e v e l . "Leve l "

can mean q u a n t i t y , q u a l i t y , o r r a t e o f t r a n s f e r . "Energy" can be o f i t s

d i f f e r e n t forms, e.g. e l e c t r i c a l , mechanical, a c o u s t i c a l , r a d i a t i o n , t h e r -

mal, e t c . App ly ing Haddon's t h e o r y t o t h e p reven t ion o f f a i l u r e r e q u i r e s

t h a t we know the l e v e l s o f energy i n p u t f rom o r t h e ou tpu t t o i t s env i ron -

ment which w i l l i n i t i a t e damage t o t h e o b j e c t under study.

a c c e p t a b i l i t y t heo ry (Ref. 6 .14) . He recogn izes t h a t t he i d e a l o f e l i m i -

n a t i n g o r n e u t r a l i z i n g a l l hazards can never be achieved i n r e a l l i f e . The

" a c c e p t a b i l i t y " o f a hazard i s determined by t h e t o l e r a b i l i t y o f t h e r i s k

assoc ia ted w i t h t h a t hazard. The magnitude o f t h e r i s k ' s t o l e r a b i l i t y i s

conceived as a th ree-d imens iona l space. The dimensions o f t h i s space a r e

( i ) s e n s i t i v i t y t o exposure, ( i i ) p r o b a b i l i t y o f occurrence, and, ( i i i )

ser iousness o f t h e e f f e c t s . S e n s i t i v i t y o f exposure i n v o l v e s such ma t te rs

as l e g a l i t y , conf idence, and e t h i c a l r e s p o n s i b i l i t y , o r values. To c o n t r o l

acc iden ts by a p p l y i n g Gr in ia ld i I s theory , we reduce t h e p r o b a b i l i t y o f oc-

cur rence by us ing f a i l - s a f e devices, reduce t h e ser iousness by exposing

fewer people f o r s h o r t e r pe r iods o f t ime, and reduce t h e s e n s i t i v i t y by

making o u r designs more acceptab le t o the changing values o f o u r s o c i e t y

(Ref. 6.11).

The t h i r d impor tan t t heo ry i n t h e f i e l d o f s a f e t y i s G r i m a l d i ' s r i s k

229

Causes o f f a i l u r e I Occurrence

bear ings

manufac tur ing f a u l t s

des ign and c a l c u l a t i o n f a u l t s

m a t e r i a l s f a u l t s o f components

s e r v i c e f a u l t s , maintenance f a u l t s , f a i l u r e o f m o n i t o r i n g equi pmen t

wear

f a i l u r e th rough e x t e r n a l causes

14.4

13.8

1.9

37.4

28.5

4.0

s l i d i n g

bear ings

10.7

9 . 1

3.6

39.1

30.5

7.0

Table 6.2 Causes o f f a i l u r e o f r o l l i n g and s l i d i n g bear ings (Ref . 6.16).

Damage types

breakages due t o o v e r s t r e s s i n g

s c u f f i n g , s e i z u r e

mechanical and c o r r o s i v e su r face damage

cracks

d e f l e c t i o n s , de format ions

Occurrence ( % )

60

18

15

5

2

Table 6.3 Types o f damage o f mechanical c l u t c h e s (Ref. 6.16).

Turn ing o u r a t t e n t i o n now t o the f i e l d o f mechanical f a u l t s , i n a d d i t i o n

t o the general t h e o r i e s o f s a f e t y and f a i l u r e , i t i s necessary t o cons ide r

the causes o f f a i l u r e observed exper imen ta l l y .

I n rev iew ing the causes o f mechanical f a i l u r e , C o l l a c o t t i n h i s recen t

book on "Mechanical f a u l t d iagnos is and c o n d i t i o n m o n i t o r i n g " (Ref. 6.15)

d i s t i n g u i s h e s between t h e f o l l o w i n g main aspec ts :

( a ) Se rv i ce f a i l u r e s

( b ) Fa t i gue

( c ) Excessive de format ion

230

(d ) Wear

( e ) Cor ros ion

( f ) Blockages

( 9 )

Th is comp i la t i on o f t he main c lasses o f f a i l u r e a l ready i n d i c a t e s t h a t

t h e r e a r e severa l n o n - t r i b o l o g i c a l causes which may lead t o f a i l u r e o f

mechanical equipment. Th i s can a l s o be seen f rom t h e da ta o f Tables 6.2

and 6.3 i n which f a i l u r e c h a r a c t e r i s t i c s o f t y p i c a l t r ibo-mechan ica l sys-

tems, namely r o l l i n g and s l i d i n g bear ings and mechanical c lu t ches , a re

l i s t e d . The da ta have been compi led by t h e insurance company ALLIANZ

(Ref. 6.16). Table 6 .2 con ta ins t h e r e s u l t s o f i n v e s t i g a t i o n s o f t h e causes

o f 1400 r o l l i n g - b e a r i n g f a i l u r e s and 530 s l i d i n g - b e a r i n g f a i l u r e s . I t can

be seen t h a t f o r these t r ibo-mechan ica l systems, about 30 pe rcen t o f t he

f u n c t i o n a l f a i l u r e s a re due t o wear processes. Table 6.3 con ta ins t h e per -

centage o f t he main types o f damage o f mechanical c lu t ches . Also i n t h i s

case t h e damage o c c u r r i n g a t t h e load- t ransmi t t i n g sur faces has been found

t o c o n s t i t u t e about 30 pe rcen t o f t he t o t a l f a i l u r e causes.

These examples show t h a t bes ides t h e t r i b o - i n d u c e d causes o f f a i l u r e ,

va r ious non- tri bo l o g i c a l causes may 1 ead t o f a i 1 u r e o f mechanical equi p-

ment. Turn ing now t o t r i b o l o g i c a l causes o f f a i l u r e , i n t h e n e x t s e c t i o n

the systems approach t o the s tudy o f t h e f a i l u r e o f mechanical systems w i l l

be o u t l i n e d by d i scuss ing an example.

Design, manufac tur ing and assembly causes o f f a i l u r e

6 ,4 ,2 A CASE STUDY: FAILURE MODES OF GEARS

I n Sec t i on 6.1, an i d e a l gear t r a i n was s t u d i e d by t h e systems a n a l y s i s

network method t o i l l u s t r a t e " i d e a l " f u n c t i o n a l behaviour. I n t h i s s e c t i o n

t h e main aspects o f t h e f a i l u r e modes o f gears w i l l be considered, as an

example o f a sys temat ic s tudy o f t h e f a i l u r e o f a t r ibo-mechan ica l system.

f a i l u r e , emphasiz ing t h e importance o f b o t h gear mechanics and gear l u b r i -

c a t i o n on gear f a i l u r e modes (Ref . 6 .17) . He p o i n t e d o u t t h a t any r a t i o n a l

approach t o gear des ign must cons ider , as a minimum, t h e impact o f t h e

va r ious modes o f gea r - too th f a i l u r e on gear performance, o p e r a t i n g l i f e ,

r e l i a b i l i t y , s ize , we igh t , and c o s t .

I t has been emphasized above t h a t f a i l u r e o f a t r ibo-mechan ica l system

occurs th rough t h e a c t i o n o f t h e o p e r a t i n g v a r i a b l e s on t h e s t r u c t u r e o f

I n a recen t rev iew, P.M. Ku o u t l i n e d t h e many f a c t o r s i n f l u e n c i n g gear

231

the system character ized by a severe d is turbance o f t he func t i ona l input -

output re la t i ons . Accordingly, a study of t he f a i l u r e o f a gear system must,

by necessity, inc lude a considerat ion o f t he t o t a l e f f e c t o f the f o l l o w i n g

p a r t i c i p a t i n g fac to rs :

I OPERATING VARIABLES

(a) type o f motion, i . e . the kinematics,

(b ) forces which may be s tud ied under steady-state condi t ions ("pseudo-

( c ) v e l o c i t i e s ,

(d ) ambient temperature,

(e ) operat ing durat ion.

I 1 STRUCTURE OF THE SYSTEM

s t a t i c s " ) and under dynamic condi t ions,

R e s t r i c t i n g the discussion t o the case o f a simple two-gears system, the

f o l l o w i n g aspects o f the system s t r u c t u r e must be taken i n t o considera-

t i o n :

(a) System components

(1) the f i r s t gear

( 2 ) the second gear

( 3 ) the l u b r i c a n t

( 4 ) the atmospheric environment

( i ) ( i i ) l u b r i c a n t ( 3 ) c h a r a c t e r i s t i c s , both phys ica l and chemical , ( i i i ) c h a r a c t e r i s t i c s o f the surrounding atmosphere (4), both phy-

( c ) I n te rac t i ons o f t he system elements The t r i b o l o g i c a l i n t e r a c t i o n s embrace the various processes d i s -

cussed i n d e t a i l i n Chapter 4, namely:

(i ) Contact processes

contact mechanics (contact deformation, t oo th de f l ec t i ons ,

t oo th misal ignment),

elastohydrodynamic l u b r i c a t i o n w i t h some specia l condi t ions,

l i k e unsteady EHD condi t ions (dynamic too th load and squeeze-

f i l m e f f e c t s ) , l u b r i c a n t s ta rva t i on , non-isothermal f l o w

condi t ions, e l l i p t i c gear-mesh conjunctions, surface-roughness

and sur face- texture e f f e c t s , non-Newtonian f l ow behaviour,

(b ) Proper t ies o f the system elements

ma te r ia l and surface c h a r a c t e r i s t i c s o f gear (1) and gear ( Z ) ,

s i c a l and chemical.

( i i ) Lub r i ca t i on modes

232

( i i i )

( i v )

boundary l u b r i c a t i o n i n c l u d i n g t h e va r ious phys i ca l and

chemical aspects o f t h e ma te r ia l - l ub r i can t -a tmosphere

i n t e r a c t i o n s .

F r i c t i o n processes

s l i d i n g / r o l l i n g f r i c t i o n o f t h e counter fo rmal gear - too th

con tac t under dynamic loads and v e l o c i t i e s .

Wear processes

gear - too th wear o c c u r r i n g th rough t h e a c t i o n o f one o r more

o f t h e b a s i c wear mechanisms, namely su r face f a t i g u e , abras ion ,

adhesion, t r i bo -chemica l reac t i ons .

The nomenclature o f t h e American Soc ie ty o f Gear Manufacturers (AGMA) c i t e s

2 1 modes o f gea r - too th f a i l u r e . According t o Ku (Ref. 6.17), i t i s thought

t o be more l o g i c a l t o c l a s s i f y t h e gear - too th f a i l u r e modes i n two b a s i c

ca tegor ies , namely, s t r e n g t h - r e l a t e d modes and l u b r i c a n t - r e l a t e d ( o r more

g e n e r a l l y t r i b o - r e l a t e d ) modes. Ma jor modes o f s t r e n g t h - r e l a t e d f a i l u r e a r e

p l a s t i c f l o w and breakage. Ma jor modes o f t r i b o - r e l a t e d f a i l u r e a re rubb ing

wear, s c u f f i n g ( o r sco r ing ) , and p i t t i n g . From a systems p o i n t o f v iew these

processes a re p r i m a r i l y connected w i t h changes i n t h e s t r u c t u r e o f t h e sys-

tem under cons ide ra t i on (see Sec t ion 5 .2) . These t r i b o - i n d u c e d changes o f

t h e system s t r u c t u r e then determine t h e f u n c t i o n a l t ransmiss ion o f power

through the system: i n t h e absence o f s t r e n g t h - r e l a t e d f a i l u r e s , t h e maximum

power t h a t can be t r a n s m i t t e d th rough a s e t o f homologous gears i s p r i m a r i l y

l i m i t e d a t low v e l o c i t i e s by rubb ing wear, a t i n te rmed ia te v e l o c i t i e s by

p i t t i n g o r s c u f f i n g and a t h i g h v e l o c i t i e s by s c u f f i n g . Some o f t h e b a s i c

aspects o f these f a i l u r e - i n d u c i n g t r i b o l o g i c a l processes have a l ready been

s t u d i e d i n Chapter 4. I n t h e f o l l o w i n g , some aspects o f t he most pronounced

g e a r - f a i l u r e mechanisms, namely p i t t i n g and s c u f f i n g w i l l be discussed.

Being a su r face f a t i g u e phenomenon, p i t t i n g i s t he consequence o f

repeated s t r e s s c y c l i n g o f t h e su r faces beyond t h e m a t e r i a l ' s endurance

l i m i t . I t takes some t ime t o develop and leads t o su r face o r subsurface

cracks and e v e n t u a l l y t o t h e detachment o f f ragments f rom and t h e fo rma t ion

o f p i t s on one o r bo th sur faces . L i k e a l l su r face f a t i g u e e f f e c t s p i t t i n g

occurs even i f t h e sur faces are comple te ly separa ted by an i n t a c t o i l f i l m .

Th is i s because the presence o f an o i l f i l m mere ly modulates t h e i n t e n s i t y

o f t h e repeated su r face s t ress ing , b u t does n o t e l i m i n a t e i t a l t o g e t h e r .

The l u b r i c a n t s does however have two s p e c i f i c i n f l uences :

( i ) i t has been observed t h a t t h e p i t t i n g l i f e i s l a r g e l y a f u n c t i o n o f

t h e r a t i o o f t h e o i l f i l m t h i ckness t o t h e composite su r face roughness

233

( i i ) t h e r e i s some evidence t h a t w i t h o i l s o f d i f f e r e n t chemical composi-

t i o n s , t h e chemical e f f e c t on p i t t i n g l i f e cannot be ignored.

From the m a t e r i a l p o i n t o f v iew, t h e s t e e l compos i t ion and t h e m e t a l l u r g i c a l

s t r u c t u r e e x e r t an i n f l u e n c e on p i t t i n g l i f e . Th i s i s i n f l u e n c e d a l s o by

l oad -sha r ing and t o o t h - p r o f i l e m o d i f i c a t i o n . The e f f e c t o f p i t t i n g occurs

w i t h gears o f low c o n t a c t r a t i o s u s u a l l y near t h e p i t c h l i n e where t h e mot ion

i s n e a r l y pure r o l l i n g b u t t h e H e r t z i a n s t r e s s i s a maximum. Fo r gears w i t h

h i g h e r c o n t a c t r a t i o s , t he l o a d s h a r i n g p a t t e r n i s q u i t e d i f f e r e n t and t h e

maximum H e r t z i a n s t r e s s may very w e l l occur i n t h e mesh c y c l e where t h e

s l i d i n g v e l o c i t y may be h igh .

o f adhesive wear which cannot occur i f an o i l f i l m o f s u f f i c i e n t t h i ckness

separates the sur faces . I n c o n t r a s t t o t h e time-dependent f a i l u r e mode o f

p i t t i n g , s c u f f i n g f a i l u r e s may occur q u i t e p r e c i p i t o u s l y . It i s b e l i e v e d

t h a t , i n o r d e r t o ensure f u l l EHD l u b r i c a t i o n t h e o p e r a t i n g c o n d i t i o n s must

be such t h a t f o r a g i ven system t h e r a t i o o f o i l f i l m t h i ckness t o composi te

su r face roughness ,h , i s i n the o rde r o f th ree . As has been exp la ined i n

Sec t i on 4.5.6, f a i l u r e o f a f u l l EHD l u b r i c a t e d systems occurs o n l y i f two

c o n d i t i o n s a re met:

( i ) ( i i ) an a d d i t i o n a l c o n d i t i o n f o r t he breakdown o f t h e su r face f i l m s .

Whereas i t appears p o s s i b l e t o t a c k l e c o n d i t i o n ( i ) f rom b a s i c E H D p r i n c i p -

l e s t a k i n g i n t o account t h e dynamic i n f l u e n c e s o f temperate and pressure-

induced v i s c o s i t y changes and su r face roughness e f f e c t s , t h e r e i s s t i l l some

d i scuss ion on t h e phys i ca l mechanism o f t h e c o n d i t i o n ( i i ) . It appears t h a t

t h e r e m igh t be a c r i t i c a l i n t e r f a c i a l " su r face temperature" o r a c r i t i c a l

"power i n p u t " o r a c r i t i c a l "power i n t e n s i t y i n p u t " t h a t a g i ven boundary

l u b r i c a t i o n f i l m may w i ths tand . C l e a r l y , t h e c r i t i c a l f a i l u r e c o n d i t i o n

depends on t h e ma te r ia l s - l ub r i can t -a tmosphere i n t e r a c t i o n under t h e a c t i o n

o f t h e s e t o f t h e o p e r a t i n g l oad -ve loc i t y - tempera tu re - t ime v a r i a b l e s .

T h i s survey on gear f a i l u r e i s based on t h e rev iew a r t i c l e by Ku (Ref. 6 .17) , and i s p resented here as an example o f t h e f a i l u r e modes o f a

t r ibo-mechan ica l system because i t c l e a r l y demonstrates t h e m u l t i p l i c i t y o f

f a i l u r e - i n d u c i n g parameters and f a i l u r e - i n d u c i n g e f f e c t s . I t a l s o i n d i c a t e s

t h e c lose i n t e r r e l a t i o n s between t r i b o - i n d u c e d changes o f t h e system's

s t r u c t u r e and t h e f u n c t i o n a l behav iour o f t h e system. A l though t h e va r ious

aspects o f f a i l u r e have been d iscussed elsewhere f o r o t h e r t r i bo -mechan ica l

S c u f f i n g i s t he o t h e r ma jor f a i l u r e mode o f gears, and i s a severe fo rm

t h e necessary c o n d i t i o n f o r t h e breakdown o f t h e EHD f i l m ,

234

systems, f o r example p l a i n bear ings (Ref. 6.18), r o l l i n g c o n t a c t bear ings

(Ref. 6.19) o r p i s t o n r i n g s (Ref. 6.20), i t i s somewhat d i f f i c u l t t o gener-

a l i z e these f i n d i n g s . An approach t o d e a l i n g w i t h the va r ious aspects o f

f a i l u r e i n a genera l i zed way i s p rov ided by t h e p r o b a b i l i s t i c r e l i a b i l i t y

e s t i m a t i o n f o r components and systems as d iscussed in t h e n e x t sec t i on .

6,5 MECHANICAL EQUIPMENT RELIABILITY

R e l i a b i l i t y i s d e f i n e d as " t h e p r o b a b i l i t y o f a dev i ce pe r fo rm ing i t s pu r -

pose adequately f o r t h e p e r i o d o f t ime in tended under t h e o p e r a t i n g con-

d i t i o n s encountered". Th i s i s t h e c l a s s i c d e f i n i t i o n o f r e l i a b i l i t y g i v e n by

t h e Radio E l e c t r o n i c s and T e l e v i s i o n Manufacturers Assoc ia t i on i n 1955.

Since t h a t t ime, t h e r e l i a b i l i t y o f e l e c t r o n i c equipment has rece ived i n -

c reas ing a t t e n t i o n , as apparatus has grown more compl ica ted and has been

a p p l i e d t o a g r e a t v a r i e t y o f impor tan t tasks . Now, t h e t h e o r y and p r a c t i c e

o f e l e c t r o n i c equipment r e l i a b i l i t y i s o f a f a i r l y h i g h s tandard and methods

f o r r e l i a b i l i t y p r e d i c t i o n and des ign ing f o r r e l i a b i l i t y have been developed

i n c l u d i n g the aspects o f redundancy (Ref. 6.21, 6.22, 6.23). Attempts of

we l l - founded cons ide ra t i ons o f mechanical equipment r e l i a b i l i t y a r e o f o n l y

r e c e n t o r i g i n (Ref. 6.24, 6.25). The d i f f e r e n c e s i n t h e s t a t e o f t h e a r t o f

r e l i a b i l i t y cons ide ra t i ons o f e l e c t r i c a l and mechanical systems may be due

t o t h e d i f f e r e n c e s i n t h e i r " i n t e r n a l s t r u c t u r e s " as d iscussed i n S e c t i o n

3 . 1 (see F igu re 3 .1 ) . Consider, as a s t a r t i n g p o i n t f o r t h e r e l i a b i l i t y

cons ide ra t i ons o f t r ibo-mechan ica l systems, t h e wear behav iour as a func-

t i o n o f t ime. I n Sec t i on 5.3 i t was exp la ined t h a t f o r t he l oss -ou tpu t wear

r a t e s o f a t r ibo-mechan ica l system t h r e e main d i f f e r e n t c h a r a c t e r i s t i c s may

be d i s t i n g u i s h e d (Ref. 6.26, 6.27):

( I ) s e l f accommodation ( " runn ing i n ' ' )

(11) steady s t a t e

(111) s e l f a c c e l e r a t i o n ( " c a t a s t r o p h i c damage")

These t h r e e modes o f change i n t h e system behav iour may f o l l o w each o t h e r

i n t ime, as i n d i c a t e d i n F igure '6 .14 . I n F igu re 6.14, ZMlim denotes a

maximum admiss ib le l e v e l o f t h e wear losses. A t t h i s l e v e l t h e system

s t r u c t u r e has changed i n such a way t h a t t h e f u n c t i o n a l i n p u t - o u t p u t r e l a -

t i o n s o f t h e system a re d i s t u r b e d severe ly . Repeated measurements show

random v a r i a t i o n s i n t h e data, as i n d i c a t e d by t h e dashed l i n e s i n F i g u r e

235

6.14. From sample functions of the wear process a distribution of the

"lifetime" of the system, i.e., a failure distribution can be derived.

failure distribution

Tine t

Figure 6.14 Wear curves and failure distribution,

In a quantitative way the reliability of a mechanical system may be charac-

terized mathematically as follows:

probabilistic function R(t) based on the following definitions:

Generally, the reliability of a mechanical system is expressed by a

F(t) : probability distribution function of

f(t) = dF0 : density function

the time to fai 1 ure

dt

A(t) = fo : failure rate (h(t)dt is a conditional probability that the system will fail during the time t + dt under the condition that the system i s safe until the time t)

1-F( t)

R(t) = 1-F(t) : reliability function

MTBF : mean time to failure (measure of reliability for repairable equipment )

236

I n some cases, the f a i l u r e ra te h ( t ) o f a component i n a system can

be estimated from the p o i n t o f view o f the physical behaviour o f the mate-

r i a l used. Empir ica l ly , and sometimes t h e o r e t i c a l l y , the fo l l ow ing proba-

b i l i t i e s are proposed (Ref. 6.28):

(a) EXPONENTIAL DISTRIBUTION

h ( t ) = constant = C

f ( t ) = C . exp (-Ct)

R ( t ) exp ( -Ct)

I n t h i s case the f a i l u r e r a t e i s constant. It means p h y s i c a l l y t h a t any

f a i l u r e occurs acc iden ta l l y wi thout any accumulation o f f a t i g u e - l i k e e f f e c t s

dur ing i t s serv ice t ime under c e r t a i n stresses. Many kinds o f e l e c t r o n i c

components fo l l ow t h i s type o f f a i l u r e . Components i n a machine break down

i n t h i s mode when the f a i l u r e i s b r i t t l e f rac tu re . As an example, i n F igure

6.15 the densi ty func t i on o f the f a i l u r e of a Diesel engine con t ro l u n i t i s

p l o t t e d showing an exponential d i s t r i b u t i o n (Ref. 6.29).

(b) RAYLEIGH DISTRIBUTION

h ( t ) = C t

f ( t ) = C t . exp (-) 2 - C t

2

I n t h i s case the f a i l u r e r a t e increases w i t h time. The constant, C , i n d i -

cates the r a t e o f d e t e r i o r a t i o n o f the component which depends upon the

s t ress l e v e l appl ied t o it.

( c ) NORMAL D I S T R I B U T I O N (TRUNCATED)

Many components of machines obey t h i s d i s t r i b u t i o n , espec ia l l y i f the

f a i l u r e occurs due t o wear processes. The f a i l u r e r a t e o f t h i s d i s t r i b u t i o n

cannot be expressed i n a simple form.

237

150 lo0l 50

1

5 10 15 20 25

Time (103h)

F igu re 6.15 Dens i t y f u n c t i o n f ( t ) o f t h e f a i l u r e o f D iese l eng ine c o n t r o l u n i t s (Exp. d i s t r i b u t i o n ) (Ref . 6 .29) .

0.95 0.90 0.80

0.50

0.20

0.10

0.05

F igu re 6.16 F a i l u r e d i s t r i b u t i o n f u n c t i o n F ( t ) o f b a l l bea r ings (Wei b u l l d i s t r i b u t i o n ) (Ref . 6 .30) .

150

f ( t ) x10 -6

100

50

5 10 15 20

Time (103h)

F igu re 6.17 Dens i t y f u n c t i o n f ( t ) o f t h e f a i l u r e o f D iese l eng ine p i s t o n s (Gamna d i s t r i b u t i o n ) (Ref . 6 .29) .

238

( d ) WEIBULL DISTRIBUTION

c c -1 t o

h ( t ) = - t

This i s a d i s t r i b u t i o n w i t h two parameters, to, t h e nominal l i f e and t h e

cons tan t C. The d i s t r i b u t i o n i s found t o rep resen t f a i l u r e o f many k inds

o f mechanical systems, such as f a t i g u e i n b a l l bear ings . As an example, i n

F igu re 6.16 the p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n o f t h e t i m e t o f a i l u r e ,

F ( t ) , as determined by t e s t i n g 500 grease l u b r i c a t e d b a l l bear ings a t 1000

r.p.m., i s shown (Ref. 6.30).

( e ) GAMMA DISTRIBUTION

where r(x) i s a Gamma f u n c t i o n . Th is i s a l s o a d i s t r i b u t i o n w i t h two para-

meters. T h e o r e t i c a l l y , t he importance o f t h i s d i s t r i b u t i o n i s a t t r i b u t e d t o

the f a c t t h a t t he equa t ion i s an x - f o l d c o n v o l u t i o n o f t he exponent ia l func-

t i o n . I t means p h y s i c a l l y t h a t a component f a i l s a t x - t h shock which occurs

as a Poisson s t a t i s t i c a l process. As an example, i n F igu re 6.17 t h e d e n s i t y

f u n c t i o n o f t he f a i l u r e o f t he p i s t o n s o f D iese l engines i s p l o t t e d showing

a Gamma d i s t r i b u t i o n w i t h x = 2 (Ref. 6.29).

process o f var ious components and systems. As a general overview, i n Table

6.4 a comp i la t i on o f t h e phenomena o f d e t e r i o r a t i o n and t h e mode o f f a i l u r e

i n connect ion w i t h t h e u n d e r l y i n g phys i ca l processes i s g iven . The t a b l e i s

due t o Yoshikawa (Ref. 6.28).

f a i l u r e processes a r e assoc ia ted w i t h d i f f e r e n t types o f f a i l u r e d i s t r i b u -

t i o n func t i ons . I t fo l l ows , t h a t i n t u r n f rom t h e exper imenta l de te rm ina t ion

o f f a i l u r e d i s t r i b u t i o n curves conc lus ions on t h e type o f f a i l u r e mechanism

may be drawn. For most t r ibo-mechan ica l systems f a i l i n g as a consequence o f

wear processes, t h e f a i l u r e behav iour i s cha rac te r i zed by t h e normal d i s t r i -

b u t i o n o r t he Weibu l l d i s t r i b u t i o n . I f f o r a g i ven t ype o f t r ibo-mechan ica l

system the f a i l u r e mode and t h e t ype o f f a i l u r e d i s t r i b u t i o n a r e known, t h i s

knowledge can be used t o improve t h e r e l i a b i l i t y o f t h e system.

These d i s t r i b u t i o n s a r e r e p r e s e n t a t i v e ones which appear i n t h e f a i l u r e

I t can be seen t h a t d i f f e r e n t f a i 1 u re modes and d i f f e r e n t e l ementary

239

S t a i n i n g

I D e t e r i o r a t i o n (Mode o f f a i l u r e ) I

0 0 Exponent ia l

Phys i c a l

Phys i ca l

process I I I I I I I

F r a c t u r e 0

Y i e l d i n g

Ray1 e i gh

Gamma

~- Rust ing

Wear Normal

Table 6.4 Phenomena o f d e t e r i o r a t i o n and mode o f f a i l u r e (Ref . 6.28).

Fo r i ns tance , t h i s approach can be used t o s e l e c t t h e type o f a b a l l o r

r o l l e r bea r ing system t o opera te under a g i ven s e t o f o p e r a t i n g c o n d i t i o n s

w i t h h i g h o p e r a t i o n a l s a f e t y (Ref . 6.31, 6 .32 ) . I n t h i s connect ion , t h e

importance o f 1 u b r i ca t i on techno1 ogy on t h e re1 i ab i 1 i ty o f tri bo-mechani c a l

system; has been emphasized (Ref. 6.33, 6 .34 ) .

To conclude t h e d i scuss ion on the f a i l u r e and r e l i a b i l i t y o f t r i b o -

mechanical systems, the dependence o f t h e f a i l u r e r a t e on t h e o p e r a t i n g

d u r a t i o n o f a system shou ld be considered. I f t h e f a i l u r e r a t e i s p l o t t e d

as f u n c t i o n o f t ime, a curve, known as t h e "ba th- tub-curve" , i s found, as

shown i n F igu re 6.18.

( b ) random f a i l u r e s , ( c ) wear-out f a i l u r e s . None o f t h e d i s t r i b u t i o n curves

d iscussed above have t h i s bath-tub-shaped f a i l u r e curve b u t an approx imat ion

may be ob ta ined by s e l e c t i n g an a p p r o p r i a t e p r o b a b i l i t y d e n s i t y f u n c t i o n f o r

each o f t h e t h r e e regimes (Ref. 6.35). Regime ( a ) descr ibes t h e r e g i o n o f

t h e " i n f a n t death" o f t h e system. Th is regime i s c h a r a c t e r i z e d by a decrease

o f t h e f a i l u r e r a t e w i t h t ime f o r example i n e f f e c t i v e r u n n i n g - i n . The r e -

gime ( b ) o f cons tan t f a i l u r e r a t e i s t h e r e g i o n o f normal runn ing . Here,

I n t h i s curve t h r e e regimes can be d i s t i n g u i s h e d : ( a ) e a r l y f a i l u r e s ,

240

f a i l u r e occurs as a consequence o f s t a t i s t i c a l l y independent f a c t o r s .

Regime ( c ) i s cha rac te r i zed by an inc rease o f t he f a i l u r e r a t e w i t h t ime.

Here f a i l u r e may be due t o ageing e f f e c t s . As descr ibed above, f o r a g r e a t

deal o f t r i bo - induced f a i l u r e s t h e f a i l u r e r a t e inc reases w i t h t ime. Thus

reg ion ( c ) o f t h e "ba th- tub curve" of F igu re 6.18 appears t o be r e l e v a n t

f o r t h e normal mode o f wear induced f a i l u r e o f mechanical systems.

( b )

Fa i 1 ure r a t e

I

I I ' Time

Figure 6.18 "Bath-tub' ' f a i l u r e r a t e curve.

6,6 REQUIREMENTS FOR PROPER FUNCTIONAL BEHAVIOUR

Having s t u d i e d i n some d e t a i 1 t h e i n f l uences o f tri bo l o g i c a l processes on

the f u n c t i o n o f mechanical systems, f i n a l l y t h e requirements f o r a p roper

f u n c t i o n a l behaviour o f t r ibo-mechan ica l systems should be considered. The

f o u r main aspects t h a t may be impor tan t i n t h i s connect ion w i l l be discussed

i n t h e f o l l o w i n g sec t i ons (see a l s o Chapter 8 ) .

6,6,1 STUDY OF ALTERNATIVE SOLUTIONS

Be fo re des ign ing a mechanical system, t h e p o s s i b i l i t y o f e l i m i n a t i n g t r i b o -

induced d i f f i c u l t i e s by us ing an a l t e r n a t i v e t e c h n i c a l s o l u t i o n shou ld f i r s t

be considered. Th is requ i res c a r e f u l c o n s i d e r a t i o n o f t h e t e c h n i c a l purpose

o f t h e system under ques t i on and t h e comp i la t i on o f t h e t e c h n i c a l l y r e q u i r e d

i n p u t s and use-outputs (see Tab le 3 .1 and 3 . 2 ) . I f t h i s a n a l y s i s shows t h a t

241

the system's inputs and o u t p u t s needed t o f u l f i l the required technical

purpose a re e s s e n t i a l l y mechanical in nature , i . e . comprise the transmis-

sion of motion, mechanical work and/or mater ia l s , the technical purpose

can, of course, be f u l f i l l e d only by a mechanical system. There a r e , how-

ever , some technical systems t h a t a r e not i n t r i n s i c a l l y mechanical in

nature b u t a re real ized by mechanical means only f o r h i s tor ica l reasons,

since mechanical methods have of ten , in the pas t , been the f i r s t means

ava i lab le f o r the solut ion of technical problems. The function of such

systems i s connected mainly with the generat ion, transmission o r repro-

duction of "information". Examples of t h i s c l a s s of (pseudo-mechanical)

systems a r e the portable mechanical clock ( t h e prototype was invented and

b u i l t by P. Henlein around 1510), the mechanical ca lcu la t ing machine ( t h e

prototype was invented by B. Pascal a n d G . W . Leibniz between 1640 and

1670), or mechanical devices f o r the control of machinery or production

processes. The technical function of these engineering systems i s essen-

t i a l l y the generation or reproduction of information. Whereas the t r a d i -

t ional mechanical rea l iza t ions of these technical systems, l i k e the clock,

a re based on the motion o f macroscopic bodies. such as gears o r l e v e r s ,

the contemporary e l e c t r o n i c rea l iza t ions of these systems a r e based on the

motion o r impulses of sub-microscopic p a r t i c l e s , namely e lec t rons . Although

in b o t h types of clock the external technical function i s i d e n t i c a l , the

internal system s t ruc tures a re e n t i r e l y d i f f e r e n t . Clear ly , the replacement

of the motion o f macroscopic bodies by the motion of sub-microscopic par-

t i c l e s not only el iminates t r ibo logica l processes b u t a l so leads t o a micro-

dimensional design and t o a f a s t and r e l i a b l e function of the system. In

the fu ture some other tribo-mechanical systems t r a d i t i o n a l l y used f o r the

generation, transmission or reproduction of information may be replaced by

technical ly more s u i t a b l e e l e c t r o n i c so lu t ions .

The replacement of conventional mechanical systems by e l e c t r o n i c sys-

tems, consis t ing of mini-chips, large sca le integrated c i r c u i t s , micropro-

cessors , e t c . , and the corresponding indus t r ia l changes have some f a r -

reaching s c i e n t i f i c , technical , economical and sociological consequences.

( I n the j o u r n a l i s t i c language t h i s has been already termed the " t h i r d

indus t r ia l revolut ion", Ref. 6 .36.) Cramer has recent ly pointed t o some

of these consequences in discussing the e l e c t r o n i c te le type as an example

for the "s t ruc tura l changes" in precision engineering (Ref. 6.37).

systems, however, in addi t ion t o the functional input-output re la t ions the

I n the study of a l t e r n a t i v e engineering so lu t ions f o r tribo-mechanical

242

i n f l uences o f d i s t u r b i n g i n p u t s f rom t h e environment shou ld be taken i n t o

account. Spec ia l ca re i s then r e q u i r e d f o r example, i n the des ign o f e l e c -

t r o n i c components s u i t e d f o r a p p l i c a t i o n s i n a v i b r a t i n g environment, as i n

a motor -car o r an a i r c r a f t . From t h i s p o i n t o f view, a robus t mechanical

s o l u t i o n may be more a p p r o p r i a t e than a f r a g i l e e l e c t r o n i c s o l u t i o n .

6,6,2 PROPER DESIGN OF SYSTEM STRUCTURE

The main aspects o f t h e approp r ia te design o f t he s t r u c t u r e o f t r i b o -

mechanical systems have a l ready been d iscussed i n Sec t i on 5.4. Some f u r t h e r

suggest ions f o r t h e design o f bea r ing systems can be found i n Ref. 6.38,

6.39, 6.40.

D iscuss ing t h e requirements o f a c o r r e c t design o f t r ibo-mechan ica l

systems, Peeken p o i n t e d o u t t h a t t he convent iona l p roduc t i on -o r ien ted and

k inemat i cs -o r ien ted design o f mechanical systems i s o f t e n n o t i n accordance

w i t h t r i b o l o g i c a l requirements (Ref. 6.41). A des igner who t r i e s t o des ign

a mechanical system i n a t r i b o l o g i c a l l y c o r r e c t manner shou ld a t tempt t o

s o l v e t h e b a s i c eng inee r ing task o f t r i b o l o g y : t o des ign i n t e r a c t i n g su r -

faces i n r e l a t i v e mot ion i n such a way t h a t f o rces can be t r a n s m i t t e d

through the i n t e r f a c e w i t h a minimum o f wear. Peeken mentioned t h r e e p o i n t s

which may be taken i n t o c o n s i d e r a t i o n i n o r d e r t o improve t h e des ign o f

tri bo-mechani c a l systems :

( i )

( i i )

I n f l u e n c e i n t e r f a c i a l b e a r i n g geometry th rough e l a s t i c and thermo-

e l a s t i c processes by changing t h e shape o f t h e moving sur faces .

Lower the fo rces t o be t ransmi t ted . Equa l i ze the f o r c e and pressure

d i s t r i b u t i o n s and i n f l u e n c e t h e v e l o c i t i e s by changing the geomet r i -

c a l design.

f a c i a l f r i c t i o n (e.g., s l i d i n g f r i c t i o n o r r o l l i n g f r i c t i o n )

t a k i n g i n t o c o n s i d e r a t i o n t h e consequences on p roduc t i on .

( i i i ) Change the k inemat ics , f o r example by changing t h e t ype o f i n t e r -

I n des ign ing t r ibo-mechan ica l systems where r e l i a b i l i t y i s a t a premium,

c e r t a i n b a s i c p r i n c i p l e s o f des ign shou ld be c a r e f u l l y taken i n t o con-

s i d e r a t i o n . These a re t h e use o f d i v e r s i t y , redundancy and des ign ing w i t h

a p r e f e r r e d mode o f f a i l u r e i n mind such as always endeavour ing t o produce

a " f a i l - s a f e " c o n d i t i o n . The p r i n c i p l e o f equipment redundancy i m p l i e s t h a t

t he system w i l l g e n e r a l l y s u r v i v e a s i n g l e equipment f a u l t and con t inue

w i th i t s in tended opera t i ona l f u n c t i o n . One method o f redundancy i s t o have

243

one system i n ope ra t i on and t h e o t h e r on standby. I f f a i l u r e o f t h e

o p e r a t i n g system takes p lace then au tomat ic change-over t o the standby

system shou ld immedia te ly take p lace . Another method o f redundancy i s t o

have two systems o p e r a t i n g " p a r a l l e l " . These p r i n c i p l e s o f redundancy which

can be e a s i l y r e a l i z e d i n e l e c t r o n i c systems are , however, n o t so e a s i l y

r e a l i z e d i n t r ibo-mechan ica l systems. An i n s t r u c t i v e example concern ing t h e

redundant des ign o f bea r ing assembl ies i s shown i n F i g u r e 6.19 (Ref . 6 . 4 2 ) .

Cent re r a c e

( a ) Standby redundancy ( b ) Para1 1 e l redundancy

F igu re 6.19 Redundant des ign o f a bea r ing assembly.

I n t h e standby case, a combina t ion of a p l a i n bea r ing and a b a l l bea r ing

a l l ows one t o f a i l b u t for o p e r a t i o n t o con t inue on the o t h e r t ype o f

bea r ing . T h i s i s an i n t e r e s t i n g example because i t a l s o b r i n g s i n the

i dea o f d i v e r s i t y which i s o f t e n used t o overcome a common f a u l t c o n d i t i o n .

I n t h e case o f t he p a r a l l e l redundant bea r ing assembly, t he l o a d can be

c a r r i e d by a s i n g l e race hence s u r v i v i n g under c e r t a i n c o n d i t i o n s a f a i l u r e

on the o t h e r race . I n t h i s case, checks shou ld be made a t maintenance,

whereas i n t h e standby arrangement i t would be u s e f u l t o have a m o n i t o r i n g

system t o sense when t h e p l a i n bea r ing i s working.

244

6,6,3 PROPER CHOICE OF OPERATING VARIABLES

I n o rde r t o o b t a i n a p roper f u n c t i o n a l behav iour o f a t r ibo-mechan ica l

system o f a g i ven design, t he o p e r a t i n g cond i t i ons ( l o a d FN o r p ressure p,

v e l o c i t y v, ope ra t i ng temperature T, o p e r a t i n g d u r a t i o n t ) shou ld n o t

exceed c e r t a i n 1 i m i t s . See a l s o Haddon's abnormal energy exchange theo ry

(Ref. 6 - 1 3 ) , d iscussed i n Sec t i on 6.4.1. These l i m i t s o f o p e r a t i n g v a r i a b l e s

may be found from the c o n d i t i o n t h a t t he a c t i o n o f the o p e r a t i n g v a r i a b l e s

may n o t l e a d t o i n t o l e r a b l e changes o f t he s t r u c t u r e o f t h e system. Al though

t h e r e i s no genera l t heo ry o f t h e l i m i t s o f o p e r a t i n g c o n d i t i o n s , f o r me-

chan ica l systems o f s imp le geometry, t h e procedure o f t h e so -ca l l ed "ze ro

wear model" (Ref. 6.43) may be a conven ien t s t a r t i n g p o i n t f o r e s t i m a t i n g

the l i m i t s o f ope ra t i ona l ' cond i t ions f o r a quas i -cons tan t s t r u c t u r e o f a

t r ibo-mechan ica l system.

"Zero wear" i s taken t o be wear o f such a magnitude t h a t t he su r face

roughness i n t h e wear t r a c k i s n o t s i g n i f i c a n t l y d i f f e r e n t f rom the i n i t i a l

su r face f i n i s h i n the unworn p a r t o f t h e sur face . To q u a n t i f y t h i s s t a t e -

ment, the zero wear l i m i t i s assumed when t h e depth o f t h e wear t r a c k equals

one-ha l f o f t he peak - to -va l l ey su r face roughness. The model s t a t e s t h a t wear

can be c o n t r o l l e d by l i m i t i n g t h e maximum ( H e r t z i a n ) shear s t r e s s T,,,~~

a c t i n g i n the c o n t a c t reg ion . D e f i n i n g one "pass" as a d i s tance 1 o f s l i d i n g

equal t o the l e n g t h o f t h e geomet r ic con tac t a rea i n the d i r e c t i o n o f s l i d -

i ng , then as an example, f o r 2000 passes su r face topography changes shou ld

be o f a " ze ro l e v e l " i f the o p e r a t i n g c o n d i t i o n s l e a d t o

ty : y i e l d s t r e s s i n shear

The va lue o f y R depends on the m a t e r i a l s i n c o n t a c t and t h e degree o f

1 u b r i c a t i o n .

For quasi-hydrodynamic l u b r i c a t i o n i t i s p o s t u l a t e d t h a t

0.54 < y R Q 1

For boundary l u b r i c a t i o n o r d r y s l i d i n g the f o l l o w i n g values

y R = 0.54 i f t h e system has a low s u s c e p t i b i l

o r y R = 0.20 i f t h e system has a h i g h s u s c e p t i b i

a re se lec ted :

ty f o r t r a n s f e r

i t y f o r t r a n s f e r

245

For i z= 2000 passes the "ze ro wear c o n d i t i o n " i s g i ven by

From t h i s r e l a t i o n , f o r a g i ven t r ibo-mechan ica l system o f known values

o f y R and t

shear s t resses t m a x ) o r t he a l l o w a b l e o p e r a t i n g shear s t resses ( f o r a

g i ven number o f passes i ) may be es t imated . Since t h i s model i s based

almost e n t i r e l y on s t r e s s cons ide ra t i ons i t may be n o t a p p l i c a b l e f o r

wear process i n c l u d i n g a cons ide rab le adhesive wear component (Ref . 6 .44) .

Indeed, the fo rm o f t he above equat ion , i . e . , t h e one-ninth-power depen-

dence, i m p l i e s t h a t t he model may be a p p l i c a b l e o n l y f o r f a t i g u e wear s i t u -

a t i o n s (see Sec t ion 4.4.2).

may be a p p l i e d i n c h a r a c t e r i z i n g t h e a l l o w a b l e l i m i t s o f o p e r a t i n g v a r i a b l e s

(Ref. 6.45). Vogelpohl found t h a t t o a reasonab le degree o f accuracy t h e f o l -

l ow ing r e l a t i o n c h a r a c t e r i z e t h e c o n d i t i o n s a t t h e t r a n s i t i o n f rom f u l l f l u i d

f i l m l u b r i c a t i o n t o mixed l u b r i c a t i o n a t t h e minimum o f t h e S t r i b e c k curve :

t he a l l owab le number o f s l i d i n g passes ( f o r g i ven o p e r a t i n g Y'

For hydrodynamica l l y l u b r i c a t e d j o u r n a l bear ings , Voge lpoh l ' s method

5 2 where : mean bear ing pressure (10 N/m )

: v i s c o s i t y ( 1 0 - ~ ~ a s = CP)

v : s u r f a c e v e l o c i t y (m/s)

From t h i s c o n d i t i o n , f o r two g i ven values o f t h e s e t ( p , ~ , v ) t h e c r i t i c a l

t r a n s i t i o n va lue o f t h e t h i r d one may be es t imated.

F i n a l l y , f o r a l u b r i c a t e d system o p e r a t i n g i n t h e low speed, h i g h

l o a d p a r t o f t h e S t r i b e c k curve , under c o n d i t i o n s o f mixed o r boundary

l u b r i c a t i o n , t h e o p e r a t i o n a l l i m i t s o f t he system may be c h a r a c t e r i z e d by

de te rm in ing e x p e r i m e n t a l l y t he " f a i l u r e su r face" f o r t h e g i ven system

(see S e c t i o n 4.5.6, F i g u r e 4 .62) .

246

6,6,4 MONITORING THE FUNCTION OF THE SYSTEM

The p r imary method o f r e l a t i n g d e t e r i o r a t i o n o f a system t o consequence

i s t h e m o n i t o r i n g o f t he performance o f t he system. The s i m p l e s t fo rm o f

such mon i to r i ng i s t he r e g u l a r reco rd ing o f r e l e v a n t parameters i n a l o g -

book. Regular l o g g i n g o r au tomat ic r e g i s t e r i n g o f impor tan t parameters and

t h e i r d e r i v a t i v e s , i n comparison w i t h re fe rence in fo rma t ion , p rov ides t h e

bas i s f o r performance-trend mon i to r i ng . In t r y i n g t o mon i to r t h e p e r f o r -

mance o f a system, i t i s necessary t o decide wh ich r e l e v a n t parameters t o

mon i to r . From a systems p o i n t o f v iew two c lasses o f parameters may be

d i s t i n g u i s h e d :

( I ) I n p u t and o u t p u t v a r i a b l e s o f t he system.

(11) Relevant parameters o f t he system s t r u c t u r e .

I n r e c e n t years, seve ra l techn iques have been developed which can be used

f o r t h e o n - l i n e m o n i t o r i n g o f o p e r a t i n g t r ibo-mechan ica l systems. I n a

feed-back loop, t h e s i g n a l s f rom the m o n i t o r i n g dev i ce may then be used

t o i n f l u e n c e o r c o n t r o l t he sys tem's i n p u t o p e r a t i n g v a r i a b l e s i n o rde r

t o o b t a i n a p roper f u n c t i o n a l behav iour o f t h e system. The main techniques

a p p l i c a b l e t o the m o n i t o r i n g o f t r ibo-mechan ica l system a r e t o be d iscussed

i n d e t a i l i n Sec t i on 7.5.

Th i s chapter on t h e f u n c t i o n a l behaviour o f tr i bo-mechanical systems

may be b e s t concluded by c i t i n g some i n t e r e s t i n g remarks o f t he g r e a t

mathematic ian John von Neumann concern ing t h e f u n c t i o n and m a l f u n c t i o n o f

eng inee r ing and l i v i n g systems. I n a l e c t u r e a t t h e Hixon Symposium, Sep-

tember, 1948, i n Pasadena, C a l i f o r n i a , e n t i t l e d "The genera l and l o g i c a l

t heo ry o f automata'' von Neumann made t h e f o l l o w i n g remarks (Ref. 6.46):

" I n l i v i n g organisms ma l func t i ons o f components occur. The organism

obv ious l y has a way t o d e t e c t them and render them harmless. The system

must, t he re fo re , c o n t a i n the necessary arrangements t o diagnose e r r o r s as

they occur, t o r e a d j u s t t h e organisms so as t o min imize t h e e f f e c t s o f t h e

e r r o r s , and f i n a l l y t o c o r r e c t o r t o b l o c k permanent ly the f a u l t y compo-

nents. Our modus procedendi wi th respec t t o ma l func t i ons i n o u r a r t i f i c a l

automata i s e n t i r e l y d i f f e r e n t . Every e f f o r t i s made t o d e t e c t every e r r o r

as soon as i t occurs. Then an a t tempt i s made t o i s o l a t e t h e component

t h a t caused the e r r o r as r a p i d l y as f e a s i b l e . Th i s may be done p a r t l y au to-

m a t i c a l l y , b u t i n any case a s i g n i f i c a n t p a r t o f t h i s d iagnos is must be

e f f e c t e d by i n t e r v e n t i o n f rom t h e ou ts ide . Once t h e f a u l t y component has

241

been i d e n t i f i e d , i t i s immedia te ly c o r r e c t e d o r rep laced. Note t h e d i f -

ferences i n these two a t t i t u d e s . The b a s i c p r i n c i p l e o f d e a l i n g w i t h mal-

f u n c t i o n s i n n a t u r e i s t o make t h e i r e f f e c t as un impor tan t as p o s s i b l e and

t o app ly c o r r e c t i v e s , i f they a r e necessary a t a l l , a t l e i s u r e . I n ou r

dea l i ngs w i t h a r t i f i c i a l automata, on t h e o t h e r hand, we r e q u i r e an imme-

d i a t e d iagnos is . There fore , we a re t r y i n g t o arrange t h e automata i n such

a manner t h a t e r r o r s w i l l become as consp ic ious as p o s s i b l e , and i n t e r v e n -

t i o n and c o r r e c t i o n f o l l o w immedia te ly . The r a t i o n a l e o f t h i s d i f f e r e n c e i s

n o t f a r t o seek. Na tu ra l organisms a r e s u f f i c i e n t l y w e l l conceived t o be

ab le t o opera te even when ma l func t i ons have s e t i n . They can opera te i n

s p i t e o f ma l func t i ons , and t h e i r subsequent tendency i s t o remove these

ma l func t i ons . An a r t i f i c i a l automaton cou ld c e r t a i n l y be designed so as

t o be a b l e t o opera te no rma l l y i n s p i t e o f a l i m i t e d number o f m a l f u n c t i o n s

i n c e r t a i n l i m i t e d areas. Any ma l func t i on , however, represents a cons id -

e r a b l e r i s k t h a t some g e n e r a l l y degenera t ing process has a l r e a d y s e t i n

w i t h i n t h e machine. I t i s , t h e r e f o r e , necessary t o i n t e r v e n e immedia te ly ,

because a machine which has begun t o m a l f u n c t i o n has o n l y r a r e l y a ten-

dency t o r e s t o r e i t s e l f , and w i l l more p robab ly go f rom bad t o worse."

248

7 Tribometry: test, simulation, and control methods

7 , 1 I NTRODUCTI ON

I t i s obvious t h a t i n a m u l t i d i s c i p l i n a r y s u b j e c t l i k e t r i b o l o g y , t h e

exper imenta l techn iques o f i n v e s t i g a t i n g and t e s t i n g p l a y an impor tan t

r o l e . I n f o l l o w i n g t h e te rmino logy o f Coulomb, who descr ibed h i s f r i c t i o n -

measuring dev ice as a " t r i bomete r " , t h e whole f i e l d o f exper imenta l s tudy

i n t r i b o l o g y i s c a l l e d " t r i b o m e t r y " . Th i s t o p i c i s very broad, rang ing

f rom f r i c t i o n and wear measurements, t h e t e s t i n g o f l u b r i c a n t s and evalua-

t i o n o f t r i b o - t e c h n i c a l components t o machinery c o n d i t i o n m o n i t o r i n g and

re1 i a b i l i t y t e s t i n g . A1 though a t f i r s t g lance t h e exper imenta l determina-

t i o n o f t he t r i b o l o g i c a l behav iour of m a t e r i a l s o r l u b r i c a n t s seems easy,

inasmuch as f r i c t i o n and wear a r e apparen t l y n o t d i f f i c u l t t o measure, t h e

d i f f i c u l t i e s l i e i n t h e i n t e r p r e t a t i o n o f t h e t e s t r e s u l t s i n connect ion

w i t h t h e var ious t r i b o - t e c h n i c a l a p p l i c a t i o n s o f m a t e r i a l s and l u b r i c a n t s

(Ref. 7 .1) .

i n t o ex i s tence w i t h some fea tu res i n common:

Dur ing t h e f i r s t h a l f o f t h i s cen tu ry a number o f t r i bomete rs came

( i ) s imp le geometry,

(ii) cheap t e s t p ieces ,

( i i i ) used f o r "acce le ra ted" t e s t i n g ,

( i v ) a t b e s t o f moderate accuracy,

( v ) y i e l d i n g r e s u l t s t h a t can n o t be i n t e r p r e t e d i n a s imp le way.

The te rm " h y b r i d t e s t e r s " was proposed, s ince s e r v i c e c o n d i t i o n s were n o t

accu ra te l y reproduced no r were phys i ca l parameters w e l l de f i ned (Ref. 7 . 2 ) .

249

Today the same equipment i s s t i l l popu la r i n I n d u s t r i a l Labora to r ies ,

because i t i s conven ien t f o r acceptance t e s t i n g and p r o d u c t i o n c o n t r o l .

However, i f t h e r e s u l t s a r e i n t e r p r e t e d as models o f r e a l tri bo-eng ineer ing

events, grave. q u a n t i t a t i v e e r r o r s may be made (Ref . 7 . 2 ) . Recent ly research

l a b o r a t o r i e s , t a k i n g advantage o f modern i ns t rumen ta t i on , have developed

var ious general-purpose t r i bomete rs . Equipped w i t h s e n s i t i v e reco rde rs and

ana lyzers , such s o p h i s t i c a t e d ins t ruments p e r m i t t he s tudy o f a g r e a t many

v a r i a b l e s (Ref. 7 . 3 ) .

These few p o i n t s i n d i c a t e t h e g r e a t v a r i e t y o f t r i b o m e t r i c techn iques

and imp ly t h a t t h e i r a p p l i c a t i o n and the i n t e r p r e t a t i o n o f r e s u l t s r e q u i r e s

g r e a t care . I n t h e f i e l d of t r i b o m e t r y i t i s aga in found t h a t t h e systems

approach can be used as a conven ien t g u i d e - l i n e f o r t h e d e s c r i p t i o n o f t h e

var ious t r i b o m e t r i c methods and t h e i r p o s s i b i l i t i e s . I t has been emphasized

i n t h e f o r g o i n g chapters t h a t bo th s t r u c t u r a l and f u n c t i o n a l aspects o f a

t r i b o l o g i c a l system must be s tud ied , and t h i s leads t o t h e f o l l o w i n g c l a s -

s i f i c a t i o n o f tri bomet r ic techniques :

( I ) S t r u c t u r a l aspects \

t e s t i n g o f system component p r o p e r t i e s

processes

( a ) elements

( b ) p r o p e r t i e s o f elements

( c ) interaction o f elements ,investigation o f t r i b o l o g i c a l

(11) Func t i ona l aspects

Func t i ona l behav iour o f t he system

-simul a t i ve tr i bo- t e s t i n g

-machinery c o n d i t i o n m o n i t o r i n g

Cons idera t ion o f t h e va r ious aspects o f t r i b o m e t r y f rom a systems p o i n t

o f view shows t h a t t h e t r i b o m e t r i c techn iques can be c l a s s i f i e d i n t o f o u r

b a s i c a l l y d i f f e r e n t groups. I t shou ld be no ted aga in t h a t each group has

i t s own (and l i m i t e d ) t e c h n i c a l purpose and p r e d i c t i v e value. Great care

i s needed f o r a mutual comparison o f t h e r e s u l t s ob ta ined by methods be-

l o n g i n g t o d i f f e r e n t groups. I n t h e f o l l o w i n g , t h e f o u r main groups o f

t r i b o m e t r y w i l l be s t u d i e d by d i scuss ing t h e main f e a t u r e s o f these tech -

niques and rev iew ing t h e i r requ i rements and p o s s i b i l i t i e s . The t rea tmen t

s t a r t s w i t h l a b o r a t o r y methods, i . e . , t he t r i b o m e t r i c techn iques f o r t h e

i n v e s t i g a t i o n o f f r i c t i o n and wear processes and s i m u l a t i v e t r i b o - t e s t i n g ,

and then t u r n s t o t h e more i n d u s t r i a l aspects o f t r i b o - t e s t i n g , namely

t r i b o - t e c h n i c a l component t e s t i n g and mach ine ry -cond i t i on mon i to r i ng .

260

7,2 FRICTION AND WEAR TEST METHODS

One o f t h e main aspects o f t r i b o m e t r y i s t h e i n v e s t i g a t i o n o f f r i c t i o n

and wear processes by means o f l a b o r a t o r y t r i b o - t e s t i n g dev ices . Reviewing

the r e s u l t s o f wear t e s t s pub l i shed i n t h e i n t e r n a t i o n a l p e r i o d i c a l WEAR

ove r a p e r i o d o f 13 years, i t has been found t h a t approx imate ly 50% o f t h e

r e p o r t e d wear t e s t s were ob ta ined w i t h l a b o r a t o r y t e s t r i g s and t h a t o n l y

17% o f t h e wear t e s t s were performed w i t h a c t u a l machine elements (Ref. 7 .4 )

These da ta c l e a r l y i l l u s t r a t e t h e g r e a t importance o f l a b o r a t o r y t r i b o -

t e s t i n g devices. I t was i n d i c a t e d p r e v i o u s l y t h a t i n r e c e n t years accura te

general-purpose t r i b o m e t e r s equipped w i t h s e n s i t i v e reco rde rs and ana lyzers

have been developed i n research l a b o r a t o r i e s . I n combining such t r i bomete rs

w i th the new power fu l su r face a n a l y t i c a l t o o l s , i t i s p o s s i b l e t o s tudy the

elementary f r i c t i o n and wear processes i n d e t a i l . It shou ld be emphasized,

however, t h a t t he a p p l i c a t i o n o f these t r i bomete rs i s u s e f u l ma in l y f o r

i n v e s t i g a t i o n s o f t h e system s t r u c t u r e - as f o r i ns tance t h e changes i n the

p r o p e r t i e s o f t h e system components due t o wear processes. As a consequence

o f t h e concen t ra t i on on t h e s t r u c t u r a l aspects, f rom a systems p o i n t o f

v iew the eng ineer ing "use - func t i on " i s f r e q u e n t l y degenerate i n t r i b o m e t r i c

models .

p i l e d (Ref. 7 .5 ) . I n t h e c e n t r a l p a r t o f t h e f i g u r e the elements, i . e . ,

t he m a t e r i a l components o f t h e t e s t system a r e sketched. I n most cases t h e

t e s t system c o n s i s t s o f two s o l i d specimens ( l ) , ( 2 ) t oge the r w i t h t h e

l u b r i c a n t ( 3 ) and t h e atmosphere ( 4 ) . The i n p u t s o f the tes t -sys tem a r e

g i ven by t h e o p e r a t i n g v a r i a b l e s compi led on t h e l e f t - h a n d s i d e o f F i g u r e

7.1. Through t h e a c t i o n o f t h e opera t i ng v a r i a b l e s on t h e tes t - sys tem

elements, f r i c t i o n and wear processes occur . For the d e s c r i p t i o n o f these

t r i b o l o g i c a l processes t h e t r i b o m e t r i c c h a r a c t e r i s t i c s compi led on t h e

r i g h t o f F igu re 7.1 have t o be measured. Supplementing these t r i b o m e t r i c

c h a r a c t e r i s t i c s , su r face c h a r a c t e r i s t i c s o f t h e specimens (1) and ( 2 ) have

t o be determined. I n t h e f o l l o w i n g sec t i ons t h e main fea tu res o f t h e para-

meters and c h a r a c t e r i s t i c s shown i n F igu re 7 .1 w i l l be d iscussed b r i e f l y .

(The measuring techniques d iscussed i n t h i s s e c t i o n i n connect ion w i t h l a -

b o r a t o r y t e s t r i g s may be adequate ly used a l s o i n t h e t e s t i n g o f t r i b o - t e c h -

n i c a l components, see Sec t ion 7.4, and i n machinery c o n d i t i o n mon i to r i ng ,

see Sec t ion 7 .5 . )

I n F igu re 7 .1 t he main parameters r e l e v a n t t o t r i b o - t e s t i n g a r e com-

251

- c-

Operating

var iables

Fr ic t ion force FF

Fr ic t ion coeff . f

Type of motion u

Duration

Tri bometer

t e s t system

( 2 ) Tribo-element

( 3 ) Lubricant

Tri bometric

c h a r a c t e r i s t i c s

I

I 1 I

Temperature TtA;

Wear r a t e

Contact condi t ions \- t Surface c h a r a c t e r i s t i c s

Figure 7 . 1 Charac te r i s t ics and parameters re levant t o t r ibo- tes t ing .

252

7 , 2 , 1 TRIBOMETER TEST SYSTEM TYPES

As exp la ined above, i n most t r i bomete rs used i n the l abo ra to ry , t e s t

specimens o f s imp le geometry a re u t i l i z e d i n o rde r t o s t a r t t h e t e s t s w i t h

t e s t cond i t i ons as w e l l de f i ned as poss ib le . Usua l l y one o f t h e moving

specimens cons is t s o f a r o t a t i n g c y l i n d e r o r d i s c aga ins t which another

s o l i d specimen o f d i f f e r e n t cu rva tu re i s pressed thus l e a d i n g t o nominal

p o i n t , l i n e o r f l a t c o n t a c t . I n a comp i la t i on o f f r i c t i o n and wear dev ices

e d i t e d by t h e American Soc ie ty o f L u b r i c a t i o n Engineers (ASLE) which i n -

c ludes 234 t e s t r i g s (Ref. 7 . 6 ) , t h e va r ious t e s t devices a r e c l a s s i f i e d

accord ing t o t h e i r geometry i n t o t h e f o l l o w i n g groups:

1.

2.

3.

4.

5.

6 .

7 . 8.

9.

10.

11.

12.

M u l t i p l e sphere

Crossed c y l i n d e r s

P i n on f l a t ( r e c i p r o c a t i n g o r 1 i n e a r mot ion)

( a ) Moving p i n

( b ) Moving f l a t

( c ) M u l t i p l e con tac t

F l a t on f l a t ( r e c i p r o c a t i n g o r l i n e a r mot ion)

Ro ta t i ng p ins on d i s c ( f a c e loaded)

P i n on r o t a t i n g d i s c ( face loaded)

Cy l i nde r on c y l i n d e r ( f a c e loaded)

Cy l i nde r o r p i n on r o t a t i n g c y l i n d e r (edge loaded)

Rectangular f l a t on r o t a t i n g c y l i n d e r (edge loaded)

D isc on d i s c (edge loaded)

Mu1 t i p l e specimens

M i sce l 1 aneous

Besides the c h a r a c t e r i z a t i o n o f t he t e s t systems geometry, t h e o t h e r

r e l e v a n t p r o p e r t i e s o f t he elements o f t he t e s t system must be s p e c i f i e d

as c l o s e l y as poss ib le . For t h i s purpose, P a r t I 1 1 o f t h e " T r i b o l o g i c a l

Systems Data Sheet" developed i n Sec t ion 8.2 can be conven ien t l y used (see

F igu re 8.5). Table 7 . 1 con ta ins the r e l e v a n t parameters t o be s p e c i f i e d i n

o r d e r t o c h a r a c t e r i z e the s t r u c t u r e o f t h e t e s t system. I n a d d i t i o n , t h e

c lean ing and su r face p repara t i on techn ique a p p l i e d t o the t e s t specimens

(1) and ( 2 ) shou ld be s p e c i f i e d .

253

T r i b o - element Tribo - elemen t Lubricant Atmosphere

Geametry/Oimensi ons/ Volume

Chemical composition

8 Hardness

other 8 vlscscosity qlbpl

11 12) 131

Other d a t a

Tribologicol in teract ions 111 - c 121

I4 )

Table 7.1 Parameters t o be s p e c i f i e d t o c h a r a c t e r i z e t h e s t r u c t u r e o f a t r i b o - t e s t i n g system.

A ve ry i m p o r t a n t aspec t o f t h e d e s c r i p t i o n o f t h e s t r u c t u r e o f t h e t e s t

system concerns t h e " i n t e r a c t i o n c h a r a c t e r i s t i c s " , i n c l u d i n g f o r i ns tance

( i )

( i i )

( i i i ) t h e r a t i o o f t h e area o f c o n t a c t t o t h e whole wear t r a c k

( i v )

t h e i n i t i a l c o n t a c t area and i t s changes d u r i n g t h e t e s t

(Ref. 7 . 7 ) ,

t h e i n i t i a l c o n t a c t p ressure and i t s changes d u r i n g t h e t e s t

(Ref. 7 . 7 ) ,

(Ref . 7.8),

t h e r e l a t i v e volumes and s u r f a c e areas o f t h e t e s t specimens

(Ref. 7 .9 ) .

These p o i n t s a r e impor tan t f o r t he t ransmiss ion , t r a n s l a t i o n and d i s s i p a -

t i o n o f mechanical work i n t roduced t o t h e t e s t system. For example, as

exp la ined i n Chapter 3 and 4 the t ransmiss ion o f mechanical work occurs

v i a t h e c o n t a c t a rea whereas f o r t h e emiss ion o f f r i c t i o n - i n d u c e d a c o u s t i c

o r thermal energy i n t o the environment, t h e sur faces n o t a c t u a l l y i n con-

t a c t p l a y an impor tan t r o l e . These p o i n t s a r e d iscussed i n Sec t i on 7.3 i n

connect ion w i t h s imu l a t i ve tr i bo- t e s t i ng .

254

7,2,2 CONTROL OF OPERATING VARIABLES

The o p e r a t i n g v a r i a b l e s o f a f r i c t i o n and wear t e s t shou ld be se lec ted t o

be c o n s i s t e n t w i t h t h e na tu re o f t h e i n v e s t i g a t i o n . As shown on t h e l e f t

of F i g u r e 7.1, t h e opera t i ng v a r i a b l e s o f a t r i b o m e t e r a re g i ven by the

f o l l ow ing q u a n t i t i e s :

- t ype o f mot ion

- l o a d FN

- v e l o c i t y v

- (ambien t ) temperature T

- t e s t d u r a t i o n t

The t y p e of mot ion i s connected w i t h the geometry o f t h e t e s t system and

i s g i ven by one o f t h e four b a s i c mot ion types , namely:

- s l i d i n g

- r o l l i n g

- s p i n

- impact

o r by a superpos i t i on o f these b a s i c types (see Sec t ion 8.2.2).

( a ) LOAD

The l o a d can be a p p l i e d by va r ious means t o t h e t e s t system, e.g. as a

mass (dead load ) , by a spr ing , by h y d r a u l i c means o r by e lec t romagne t i c

means.

256

I n F igu re 7.2 t h e d i f f e r e n t p o s s i b i l i t i e s f o r t h e a p p l i c a t i o n o f t h e

l o a d a r e shown schemat i ca l l y f o r t h e example o f a p i n - o n - c y l i n d e r t e s t

sy s tern.

t o t h e same va lue o f t h e l o a d f o r c e FN. I n dynamic l oad ing , however, owing

t o t h e d i f f e r e n t mass-spring-damper combinat ions i n e v i t a b l y i n v o l v e d i n

t h e d i f f e r e n t l o a d i n g p r i n c i p l e s , d i f f e r e n t l oad - t ime behav iour may r e s u l t .

There fore t h e dynamic F N ( t ) behav iour may be d i f f e r e n t f rom t h e i n i t i a l

s t a t i c l o a d FN, (Ref. 7.10).

F o r t h e measurement o f t h e load, f o r c e t ransducers based on s t r a i n

gauges, i n d u c t i v e elements or pressure-sens i t i v e d e t e c t o r s evapora ted on

t h e su r face o f t h e specimen i n t h e c o n t a c t zone a r e a v a i l a b l e . The mea-

surement o f t h e l o a d by means o f an e lec t ro -mechan ica l f o r c e t ransducer

has the g r e a t advantage t h a t t h e FN-s igna l t o g e t h e r w i t h t h e s i g n a l o f t h e

f r i c t i o n f o r c e FF can be f e d t o an e l e c t r o n i c d i v i d e r which c a l c u l a t e s d i -

r e c t l y t h e a c t u a l va lue o f t h e f r i c t i o n c o e f f i c i e n t f = FF/FN d u r i n g t h e

t e s t , Th i s aspec t i s d iscussed i n more d e t a i l i n t h e n e x t s e c t i o n .

I n s t a t i c l o a d i n g t h e d i f f e r e n t p r i n c i p l e s o f l o a d a p p l i c a t i o n l e a d

The l o a d FN a p p l i e d t o t h e t e s t system determines, i n connec t ion w i t h

the area o f c o n t a c t A , t h e c o n t a c t p ressure p = FN/A. S ince t h e va lue o f A

may change duc-ts wear dur ing-- the t e s t t h e va lue-o f p may a l s o undergo some

changes as f u n c t i o n o f t ime, as i n d i c a t e d i n t h e fo rego ing s e c t i o n (Ref.

7.7).

(b ) VELOCITY

For t h e c h a r a c t e r i z a t i o n and c o n t r o l o f t h e v e l o c i t y between t h e t e s t

specimens o f a t r i b o t e s t i n g system, t h e same cons ide ra t i ons as i n t h e case

o f t h e l o a d r e l a t e t o t h e dynamic behav iour . F o r t h e c o n t r o l o f t h e ve lo -

c i t y , e l e c t r o n i c o r o p t o - e l e c t r o n i c t ransducers a r e commerc ia l l y a v a i l a b l e .

The v e l o c i t y i s an impor tan t parameter i n t r i b o t e s t i n g i n as much as i t

determines t h e l u b r i c a t i o n regime w i t h i n t h e S t r i b e c k cu rve (see Sec t ion

4.5.1). I t i s a l s o t h e independent v a r i a b l e i n t h e p roduc t FFv wh ich g i ves

t h e f r i c t i o n - i n d u c e d power l o s s o f a t r i b o - t e s t i n g system.

( c ) TEMPERATURE

The (ambient) tempera ture o f t h e t e s t system i s another impor tan t o p e r a t i n g

v a r i a b l e s i n c e i t determines t h e thermal s t a t e o f t h e system - a t l e a s t a t

t h e i n i t i a l s tage o f t h e t e s t . (The problem o f t h e f r i c t i o n - i n d u c e d temper-

a t u r e i s d iscussed i n t h e n e x t s e c t i o n . ) F o r t h e c o n t r o l o f t h e tempera ture ,

t h e f o l l o w i n g two techn iques a r e u t i l i z e d most o. f ten:

256

( i ) thermocouple techniques

( i i ) in f ra red-pyrometer techniques

The c h a r a c t e r i s t i c s o f these techniques a re discussed i n t h e nex t sec t i on ,

( d ) TEST DURATION

The s e t o f t he o p e r a t i n g v a r i a b l e s ( l o a d FN, v e l o c i t y v , temperature T ) ac ts on t h e t r i b o t e s t i n g system as f u n c t i o n o f t ime o r d u r a t i o n t. As f o r

t he s e t (FN, v, t ) t he t e s t d u r a t i o n t a l s o shou ld be s e l e c t e d t o be con-

s i s t e n t w i t h the n a t u r e o f t h e i n v e s t i g a t i o n . Attempts a r e f r e q u e n t l y made

t o sho r ten t h e t e s t d u r a t i o n i n so -ca l l ed "acce le ra ted t e s t s " by i n c r e a s i n g

the s e v e r i t y o f t h e o p e r a t i n g c o n d i t i o n s o f FN, v, T. Th is procedure, how-

ever, i s o n l y p e r m i s s i b l e i f t h e n a t u r e o f t h e t r i b o l o g i c a l processes i s

n o t changed. Consider, f o r example, a c e r t a i n t e s t system runn ing under

g i ven opera t i ng v a r i a b l e s (FN, v, T) w i t h t r i b o l o g i c a l processes o c c u r r i n g

w i t h i n t h e "ou te r " su r face l a y e r s (see F igu re 4.5) o f t h e t e s t specimens,

thus g i v i n g a very low wear r a t e . Consequently, i n o r d e r t o c b t a i n s u f f i -

c i e n t removal o f m a t e r i a l f o r an accura te wear measurement, a l ong t e s t

d u r a t i o n i s needed. If, i n o r d e r t o shor ten t h e t e s t d u r a t i o n , t he s e v e r i t y

o f t h e t e s t i s now increased, e.g., by i n c r e a s i n g t h e l o a d FN, a h ighe r

wear r a t e may indeed r e s u l t . However, t he t r i b o l o g i c a l processes may now

a c t w i t h i n the " i n n e r " su r face l a y e r s thus changing e n t i r e l y the f r i c t i o n

and wear mechanisms and i n c r e a s i n g t h e p o s s i b i l i t y o f c a t a s t r o p h i c f a i l u r e

due t o s c u f f i n g or se izure . Th is s imp le example i n d i c a t e s the importance o f

t h e p roper cho ice o f o p e r a t i n g c o n d i t i o n s o f FN, v, T i n connect ion w i t h

the t e s t d u r a t i o n t f o r a g i ven t e s t s i t u a t i o n . I ns tead o f i n c r e a s i n g t h e

s e v e r i t y o f t he o p e r a t i n g c o n d i t i o n s i t m a y be more approp r ia te t o i n -

crease, where poss ib le , t he s e n s i t i v i t y o f t h e de tec to rs and ana lyzers i n

o rde r t o o b t a i n t h e necessary q u a n t i t i e s w i t h i n a c e r t a i n t e s t du ra t i on .

The t r i b o - t e s t i n g o p e r a t i n g v a r i a b l e s d iscussed h i t h e r t o r e f e r t o t e s t

systems o f a " c l o s e d s t r u c t u r e " , g i ven f o r example by t e s t systems i n which

the elements ( l ) , ( 2 ) , (3), ( 4 ) o f t h e t r i b o - t e s t i n g system a r e e n t i r e l y

w i t h i n a c losed s p e c i i e n chamber as i n d i c a t e d i n F igu re 7.1. I f , on t h e

o t h e r hand, the t e s t system s t r u c t u r e i s "open" w i t h respec t t o l u b r i c a n t

( 3 ) and environmental atmosphere ( 4 ) , t h e f l o w r a t e s o f ( 3 ) and ( 4 ) a re

a l s o impor tan t o p e r a t i n g v a r i a b l e s . Where, f o r i ns tance , a 1 i q u i d l u b r i c a n t

c i r c u l a t i n g system i s used, t h e l u b r i c a n t f l o w r a t e and the res idence t ime

o f t h e l u b r i c a n t f i l m on t h e t e s t specimens shou ld be c o n t r o l l e d , i n add i -

t i o n t o t h e o p e r a t i n g v a r i a b l e s discussed above. Another group o f systems

257

w i t h an open system's s t r u c t u r e concerns t e s t systems r e l a t e d t o i n d u s t r i a l

processes as i n a g r i c u l t u r e , mining, e a r t h moving, d r i l l i n g , d redg ing , e t c .

The o p e r a t i n g " i n p u t " o f these systems i s v a r i a b l e due t o t h e n a t u r e o f

s o i l s , rocks , s ledges, e t c . Spec ia l care i s needed i n t h e t e s t i n g o f such

systems w i t h an " i n t r i n s i c a l l y open system s t r u c t u r e " (Ref. 7.11).

7 I 2 , 3 TRI BOMETR I c CHARACTERISTICS

The t r i b o m e t r i c c h a r a c t e r i s t i c s t o be measured i n t r i b o - t e s t i n g shou ld

a l l o w p roper c h a r a c t e r i z a t i o n o f t h e f r i c t i o n and wear processes. Accord ing

t o t h e genera l scheme developed i n Chapter 3 these c h a r a c t e r i s t i c s can be

c l a s s i f i e d i n t o t h r e e groups:

( i ) Mechanical q u a n t i t i e s : F r i c t i o n f o r c e ,

f r i c t i o n c o e f f i c i e n t ,

n o i s e and v i b r a t i o n .

( i i ) Thermal q u a n t i t i e s : F r i c t i o n - induced temperatures

( i i i ) M a t e r i a l q u a n t i t i e s : Wear r a t e s .

Besides these t r i b o m e t r i c c h a r a c t e r i s t i c s , i n f o r m a t i o n on the c o n t a c t

cond i t i ons , such as t h e l u b r i c a n t f i l m t h i ckness o r t h e amount o f m e t a l l i c

con tac t , shou ld be ob ta ined.

( a ) FRICTION FORCE AND FRICTION COEFFICIENT

F igu re 7.3 Schematic diagram o f a two-component f o r c e t ransducer , t o t h e r i g h t d e t a i l s o f t h e des ign o f t h e f o u r rods a r e shown.

258

For t h e measurement o f t he f r i c t i o n fo rce , e lec t ro -mechan ica l f o r c e

t ransducers based ma in l y on s t ra in -gauge techn iques o r i n d u c t i v e e f f e c t s

a r e a v a i l a b l e commercial ly. As i n d i c a t e d i n t h e fo rego ing sec t ion , i t i s

advantageous t o measure bo th f r i c t i o n f o r c e FF and l o a d FN and t o c a l c u l a t e

t h e f r i c t i o n c o e f f i c i e n t d i r e c t l y d u r i n g t h e t e s t . A f o r c e t ransducer f o r

t he s imultaneous measurement o f FN and FF independent ly f rom each o t h e r i s

shown i n F igu re 7.3.

pe rpend icu la r t o each o t h e r (Ref. 7.12). I n t h e cen t re o f symmetry o f t h e

f o u r bars one o f t h e specimens o f a t r i b o m e t e r - f o r i ns tance t h e p i n o f a

p in -on-d isc t r i bomete r - i s i n s e r t e d . I n each no tch a s t r a i n gauge i s

f i x e d , d e t e c t i n g t h e s t r a i n s as func t i ons o f FN and FF. The s e n s i t i v i t y and

the eigenfrequency o f t he f o r c e t ransducer can be v a r i e d th rough t h e dimen-

s ions o f t h e bars and t h e l o c a t i o n s and dimensions o f t he notches. The

b l o c k diagram o f t h e de te rm ina t ion o f t he f r i c t i o n c o e f f i c i e n t f rom t h e

s i g n a l s o f FF and FN by means o f an e l e c t r o n i c d i v i d e r i s shown i n F igu re

7.4. With t h e h e l p o f t h i s measuring dev ice i t i s p o s s i b l e t o o b t a i n a l l

necessary i n f o r m a t i o n on t h e mechanics o f a t r i b o - t e s t i n g system as a func-

t i o n o f t ime. Moreover, w i t h t h e use o f a d i s c r i m i n a t o r i t i s p o s s i b l e t o

s top the t e s t i f c e r t a i n ( a d j u s t a b l e ) l e v e l s o f t h e f r i c t i o n c o e f f i c i e n t

The f o r c e t ransducer i s a dev i ce c o n t a i n i n g f o u r bars w i t h notches

are passed.

r - - - - - - - - - - - - 1 I Tribome ter I

F igu re 7.4 B lock diagram o f s i g n a l f l o w .

(b ) N O I S E AND VIBRATION

As o t h e r "mechanical" c a p a b i l i t i e s o f a t r i b o - t e s t i n g device, measurements

o f no i se and v i b r a t i o n s shou ld be mentioned (Ref. 7.13). A l though impor tan t

i n f o r m a t i o n on t h e c o n t a c t s i t u a t i o n o f t h e t e s t system may be deduced f rom

259

such measurements, they have n o t usua l l y been repor ted i n connection w i t h

l abo ra to ry f r i c t i o n and wear t e s t r i g s . These techniques are, however, o f ten

used i n moni tor ing the func t i ona l behaviour o f complete t r ibo-engineer ing

systems, such as b a l l bearings o r gear t r a i n s (see Section 7.5).

( c ) TEMPERATURE

I metal 1p 1 FN ~ yUt\, 4 " ' s To

metal 2

V C J t, dynamic thermocouple thermoel ement

P

t i n f r a r e d pyrometer

F igure 7.5 Temperature measuring methods.

The main techniques f o r the measurement o f f r i c t i o n - i n d u c e d temperatures

are i l l u s t r a t e d i n F igure 7.5. As can be seen, i n most cases thermocouples

o f d i f f e r e n t types or o p t i c a l i n f r a r e d pyrometer techniques are u t i l i z e d .

The techniques may be d i f f i c u l t t o handle o r the r e s u l t s d i f f i c u l t t o i n t e r -

pret , so t h a t i t i s s t i l l no t easy t o perform accurate and meaningful mea-

surements o f f r i c t i o n - i n d u c e d temperatures. The thermoelements commercially

ava i l ab le have t ime reponses from 10 sec t o 10 msec, depending on the s i z e

and the thermocouple mater ia ls . I n using thermocouples two methods may be

applied:

( i )

( i i ) one o r more complete thermocouples are i nse r ted i n one o r both o f t he

one ( o r both) o f the actual t e s t specimens forms p a r t o f t he thermo-

couple ( "na tu ra l thermocouple"),

t e s t specimens.

260

f o r c e t ransducer

i n f r a r e d camera

Representa t ion o f i so therms

Loca t ion

F igu re 7.6 Measurement o f f r i c t i o n - i n d u c e d temperature w i t h i n f r a r e d camera.

26 1

I n case ( i ) i t i s possible, i n p r i n c i p l e , t o ob ta in in format ion d i r e c t l y

from the f r i c t i o n a l i n t e r f a c e . This in format ion, however, may be in f luenced

by i n t e r f a c i a l e lect romot ive forces r e s u l t i n g , f o r example, from the ac t i on

of l u b r i c a n t add i t i ves . Also c i r c u l a t i n g currents i n m u l t i p l e contacts may

be of in f luence. I n case ( i i ) i t i s n o t poss ib le t o ob ta in the temperature

information d i r e c t l y from the f r i c t i o n a l i n te r face . Therefore, attempts have

sometimes been made t o determine temperature gradients by i n s e r t i n g several

thermocouples a t d i f f e r e n t distances from the i n t e r f a c e and ex t rapo la t i ng

from these measurements t o an estimated value a t the f r i c t i o n a l in ter face.

(For a discussion o f the theor ies o f f r i c t i o n - i n d u c e d temperatures see Sec-

t i o n 4.3.4).

from the surrounding o f the f r i c t i o n a l i n t e r f a c e o f o p t i c a l l y non-transpar-

ent specimen i s detected o r one pa r tne r has t o be made o p t i c a l l y t ransparent

i n the i n f r a r e d region. I n both instances the o p t i c a l e m i s s i v i t y as a func-

t i o n o f temperature and wavelength o f the r a d i a t i o n i s the c r u c i a l po in t .

An experimental example o f the app l i ca t i on o f the IR-technique t o the deter-

mination o f f r i c t i on - induced temperatures by measuring the r a d i a t i o n from

the back o f a t h i n f o i l (d-70 pm) s l i d i n g against a r o t a t i n g s h a f t i s il-

l u s t r a t e d i n F igure 7.6 (Ref. 7.14). I n a s i m i l a r way, by us ing an o p t i c a l l y

transparent pa r tne r Winer and co-workers determined the actual temperatures

w i t h i n a s l i d i n g EHD contact (see F igure 4.51). I n comparing these exper i -

menta l ly determined data w i t h temperature ca l cu la t i ons from the Blok- theory

a good c o r r e l a t i o n between the experimental and the theo re t i ca l values has

been found (Ref. 7.15).

With pyrometric techniques, e i t h e r the temperature r a d i a t i o n emi t ted

( d ) WEAR

Also f o r the determination o f wear, d i f f e r e n t measuring techniques may be

u t i l i z e d (Ref. 7.16, 7.17). According t o the German standard DIN 50321,

"Wear-quanti t i e s " , wear may be detected by measuring " d i r e c t " wear-quanti-

t i e s , such as

(a) changes o f geometry o f the specimens:

(i) changes i n l i n e a r dimensions

( i i ) changes i n cross-sections

( i i i ) changes i n volume

changes o f the mass of the specimens

the amount of worn ma te r ia l - l oss ( b )

( c )

o r " r e l a t i v e " wear-quanti t ies, i .e . , wear ra tes such as

262

( d ) t h e wear - t ime- ra t i o (wear v e l o c i t y )

( e ) t h e wear-di s t a n c e - r a t i o

o r t h e wear c o e f f i c i e n t , d e f i n e d as

wear volume mm 1 o a d - d i stance Nm ( f ) K ' = (-1

o r t h e dimensionless Archard 's wear c o e f f i c i e n t

wear vo1ume.hardnes.s loaded is tance ( 9 ) K =

For each type o f wear measurement ( a ) , (b ) , ( c ) , a p p r o p r i a t e de tec to rs a r e

commercial ly a v a i l a b l e . Some o f t he b a s i c wear-measuring techn iques a r e

d iscussed i n r e l a t i o n t o the c o n d i t i o n - m o n i t o r i n g o f machines, see Sec t ion

7.5. The type o f t h e measuring techn ique shou ld be chosen t o be c o n s i s t e n t

w i t h t h e na tu re o f t h e i n v e s t i g a t i o n , and t h e wear da ta ob ta ined shou ld be

r e p o r t e d i n terms t h a t a re u s e f u l f o r eng inee r ing a p p l i c a t i o n s (Ref . 7.18).

I n t h i s connect ion i t shou ld aga in be emphasized t h a t t he wear-quant i -

t i e s must n o t be m i s i n t e r p r e t e d as i n t r i n s i c m a t e r i a l cons tan ts b u t must be

t r e a t e d as system-dependent q u a n t i t i e s which depend on b o t h t h e o p e r a t i n g

v a r i a b l e s and t h e s t r u c t u r e o f t h e wear ing system under cons ide ra t i on . A

c h e c k - l i s t t o a s s i s t i n t h e c o m p i l a t i o n o f r e l e v a n t da ta i n connect ion w i t h

wear measurements i s developed i n Chapter 8.

Supplementing the measurement o f t he mechanical , thermal and m a t e r i a l s

c h a r a c t e r i s t i c s , i n f o r m a t i o n on the con tac t c o n d i t i o n w i t h i n a t r i b o m e t e r

may be u s e f u l . Here two groups o f c h a r a c t e r i s t i c s a r e o f i n t e r e s t :

( i ) t he e x t e n t o f r e a l s o l i d - s o l i d con tac t ( i n c l u d i n g t h e r e a l area

( i i ) t h e l u b r i c a n t f i l m t h i ckness

For t h e measurements ( i ) , t h e techniques o f o p t i c a l microscopy, desc r ibed

i n Sec t i on 7.6, and the e l e c t r i c a l c o n t a c t r e s i s t a n c e (ECR) measuring tech -

n iques have been a p p l i e d (Ref. 7.19). The p r i n c i p l e o f t h e ECR techn ique i s

i l l u s t r a t e d i n t h e b lock diagram i n F igu re 7.7 (Ref. 7.20). A smal l e l e c -

t r i c a l vo l tage (10-100 mV)' i s a p p l i e d t o the specimens and t h e t ime depen-

dence o f t h e vo l tage drop on a s e r i e s r e s i s t a n c e i s de tec ted . Usua l l y t h e

vo l tage drop f l u c t u a t e s ove r severa l o rde rs o f magnitude ( < 0.1R up t o

> 100 k R ) w i t h impulse du ra t i ons down t o the psec range as i l l u s t r a t e d i n

F i g u r e 7.8. By r a p i d e l e c t r o n i c means ( d i s c r i m i n a t o r s , a m p l i f i e r s , coun te rs )

o f c o n t a c t )

263

Figure 7 . 7 Block diagram o f ECR signal processing.

Figure 7.8 Typical ECR oscillogram o f system ( a ) , Figure 7.9.

I I I 8

100 101 102 103 lo4 lo5

Contact resistance Rc ( Q )

(a ) hexadecane

( b ) hexadecane + ole ic acid ( c ) hexadecane + ZDDP ( d ) hexadecane + DBDS

(additive concentrations: 0.03 mole/l)

Figure 7.9 ECR fluctuation rates (lubricate sliding AISI 52180 steel cylinders, r=2.5mn, poH=0.67GN/me, v=1.5cm/s, T=25 C ) .

264

i t i s p o s s i b l e t o c a l c u l a t e c h a r a c t e r i s t i c s such as the "no-contac t - t ime

f r a c t i o n " (see F igu re 4.58) o r impu ls i ve f l u c t u a t i o n r a t e s as shown i n

F igu re 7.9. Al though these r e s u l t s pe rm i t conc lus ions on t h e e x t e n t o f

m e t a l l i c con tac t o r on t h e a c t i o n o f l u b r i c a n t a d d i t i v e s t o be drawn, g r e a t

care i s needed i n t h e i r i n t e r p r e t a t i o n because o f t he e f f e c t s o f m u l t i p l e

c o n t a c t o r i n t e r f a c i a l e l e c t r o m o t i v e fo rces .

microscopy (see Sec t ion 7 .6 ) , by the capac i tance method, o r by an X-ray

technique. A d e t a i l e d d i scuss ion o f t he va r ious methods f o r measuring l u b r i -

can t f i l m th ickness i s p rov ided i n Ref. 7.21.

and wear t e s t i n g i t i s now p o s s i b l e t o supplement t h e comp i la t i on o f t he

r e l e v a n t t e s t parameters l i s t e d i n F igu re 7.1 by t h e cor respond ing measuring

techniques. Al though i n t r i b o t e s t i n g a p p l i c a t i o n s i t may n o t be p o s s i b l e t o

measure a l l o f t he parameters l i s t e d i n F i g u r e 7.1 i t shou ld be emphasized

once more t h a t every parameter can in f luen lce markedly t h e r e s u l t s o f a f r i c -

t i o n and wear t e s t .

Lub r i can t f i l m th i ckness ( i i ) may a l s o be s t u d i e d by means o f o p t i c a l

Having d iscussed t h e va r ious measuring techn iques r e l e v a n t t o f r i c t i o n

7 I 3 SIMULATIVE TRIBO-TEST I NG

I n s i m u l a t i v e t r i b o - t e s t i n g an a t tempt i s made t o s imu la te t h e t r i b o l o g i c a l

behav iour o f a p r a c t i c a l t r i b o - e n g i n e e r i n g system, or the behav iour o f some

p a r t o f i t , by means o f a l a b o r a t o r y t e s t system. Obviously, t h i s f i e l d o f

t r i b o m e t r y i s ex t remely d i f f i c u l t due t o the comp lex i t y o f t r i b o l o g i c a l p ro -

cesses, i t s numerous i n f l u e n c i n g f a c t o r s and t h e a d d i t i o n a l requirement o f

an approp r ia te " s i m u l a t i o n c r i t e r i o n " (Ref. 7.22, 7.23).

The s t a r t i n g p o i n t i n s i m u l a t i v e t r i b o - t e s t i n g shou ld be t h e c o l l e c t i o n

o f a v a i l a b l e da ta on t h e p r a c t i c a l system (PS) and t h e t e s t system (TS). For

the c o l l e c t i o n o f these da ta and "caseh is to r i es " , t he da ta sheet developed

i n Sec t i on 8.2 can be conven ien t l y used. Based on these da ta , t he c o n d i t i o n s

f o r s i m u l a t i v e t e s t i n g may then be s p e c i f i e d . From a fo rmal systems p o i n t o f

view, the procedure o f s i m u l a t i v e t r i b o - t e s t i n g requ i res :

( a ) A s i m i l a r i t y o f t h e f u n c t i o n s o f PS and TS, i . e . :

( i ) ( i i ) s i m i l a r i t y o f t he f u n c t i o n a l i npu t -ou tpu t r e l a t i o n s

A s i m i l a r i t y o f t he s t r u c t u r e s o f PS and TS, i . e . :

( i ) s i m i l a r i t y o f system elements

s i m i l a r i t y o f t h e i n p u t s and the ou tpu ts

( b )

265

( i i ) s i m i l a r i t y o f system element p r o p e r t i e s

( i i i ) s i m i l a r i t y o f t r i b o l o g i c a l i n t e r a c t i o n s

I n t r y i n g t o f u l f i l these c o n d i t i o n s , f i r s t t he m a t e r i a l s , t h e l u b r i c a n t s

and t h e atmospher ic environment shou ld be chosen t o be i d e n t i c a l i n b o t h

PS and TS. Then t h e geomet r ica l and c o n t a c t c o n d i t i o n s o f t h e t e s t system

shou ld be ad jus ted t o those o f t h e p r a c t i c a l system, t a k i n g i n t o account

the problem o f a p p r o p r i a t e sca le f a c t o r s . F i n a l l y , t h e o p e r a t i n g v a r i a b l e s

shou ld be ad jus ted i n o rde r t o o b t a i n the same t r i b o l o g i c a l i n t e r a c t i o n s

i n t h e t e s t system as i n t h e p r a c t i c a l system. C l e a r l y , s i m u l a t i v e t r i b o -

t e s t i n g as o u t l i n e d i n these few sentences i s an ex t remely d i f f i c u l t t ask

and a g e n e r a l l y accepted procedure i s n o t y e t a v a i l a b l e . I n o r d e r t o ob-

t a i n a t l e a s t a k i n d o f gu ide l i ne , some o f t h e main aspects o f s i m u l a t i v e

t r i b o t e s t i n g , w i l l be d iscussed b r i e f l y here, cons ide r ing as a s t a r t i n g

p o i n t a p in -on-d isc t r i b o m e t e r t e s t system, shown i n F igu re 7.10.

A. - AW2 /--

F igu re 7.10 Geometr ical c h a r a c t e r i s t i c s o f a t r i b o t e s t i n g model system.

Fo r t h e task o f s i m u l a t i v e t r i b o - t e s t i n g , t he t e s t system shown may be

app l icab l 'e f o r pure cont inuous s l i d i n g w i t h t h e m a t e r i a l s ( l ) , ( 2 ) iden-

t i c a l w i t h those o f t h e p r a c t i c a l system. The c o n d i t i o n s o f d r y o r l u b r i -

ca ted s l i d i n g shou ld be r e a l i z e d w i t h the atmosphere and l u b r i c a n t i d e n t i c a l

t o those i n t h e p r a c t i c a l system. Then the impor tan t "system-independent' '

p r o p e r t i e s o f t h e elements, i n c l u d i n g chemical compos i t ion , e l a s t i c modulus,

hardness, v i s c o s i t y , e t c . w i l l i n h e r e n t l y be i d e n t i c a l i n PS and TS. A f t e r

266

Mant le su r face

Contac t area (geom. )

t he cho ice o f t he elements o f t h e system and t h e i r sys,tem-independent

p r o p e r t i e s , t he geomet r ica l and c o n t a c t c o n d i t i o n s o f the t e s t system shou ld

be compared w i t h those o f t he p r a c t i c a l system. I n t h i s connect ion t h e

q u a n t i t i e s l i s t e d i n Table 7.2 a r e impor tan t .

Am1 I Am2 - An

Geometric o r con tac t p rope rt i es

Aml-Ao No-contact area

Wear t r a c k area

I v1 I v2 I I Volume

Am2-A0

AW2

T r i b o l og i c a l process

I I 1 Contac t area ( r e a l )

Relevant geomet r ica l q u a n t i t y

Table 7.2 Geometric c h a r a c t e r i s t i c s o f t e s t specimens.

The c h a r a c t e r i s t i c s compi led i n Tab le 7.2 a re n o t o n l y impor tan t f o r t he

con tac t pressures po = FN/Ao and pr = FN/Ar they a r e a l s o r e l e v a n t t o t h e

processes o f t h e t ransmiss ion and d i s s i p a t i o n o f mechanical work i n the

system, as exp la ined i n Table 7.3.

Generat ion o f f r i c t i o n a l Contact a rea (Ao, Ar) 1 hea t

Absorp t ion o f f r i c t i o n a l Volume (Vl, V2) I hea t

LEG o f f r i c t i o n a l I No-contact a rea

Table 7.3 Relevance o f geomet r ica l q u a n t i t i e s f o r t r i b o l o g i c a l processes

Besides these geomet r ic c h a r a c t e r i s t i c s , r e l a t i v e q u a n t i t i e s may a l s o be

impor tan t , f o r example t h e r a t i o o f t h e h e a t - e m i t t i n g area t o t h e heat -

absorb ing volume o f each o f t h e elements ( 1 ) and ( 2 ) :

26 I

C h a r a c t e r i s t i c s o f elements f o r which E = 1

hea t e m i t t i n g area hea t absorb ing volume

0 = r a t i o :

C h a r a c t e r i s t i c s o f elements f o r which ~ < l

Am1,2 -

"1,2 1,2 - 0

Another impor tan t r e l a t i v e q u a n t i t y i s g i ven by:

c o n t a c t area wear t r a c k area

E = r a t i o :

For the example o f t h e p in -on -d i sc t r i b o m e t e r , i t f o l l o w s t h a t

f o r t h e p i n : E~ = 1

f o r t he d i s c : E~ < 1

C h a r a c t e r i s t i c s r e l a t e d t o t h e va lue o f E a r e compi led i n Tab le 7.4.

permanent c o n t a c t

permanent f r i c t i o n h e a t i n g

no d i r e c t i n f l uence o f atmospher ic environment on wear area

no macroscopic c y c l i c s t r e s s i ng

i n t e r m i t t e n t c o n t a c t

i n t e r m i t t e n t f r i c t i o n h e a t i n g

i n f l u e n c e o f atmospher ic en- v i ronment on t h e area AM - A.

c y c l i c s t r e s s i n g

Table 7.4 Dependence o f t r i b o l o g i c a l processes on t h e c o n t a c t a rea t o wear - t rack-area r a t i o E .

The d i scuss ion o f t h e geomet r ic and c o n t a c t c o n d i t i o n s show t h a t t h e prob-

lem o f a p p r o p r i a t e " s c a l e f a c t o r s " f o r t h e s i m u l a t i o n o f these q u a n t i t i e s

shou ld be p a i d g r e a t a t t e n t i o n . An example o f t h e de te rm ina t ion o f s c a l e

268

f a c t o r s based on s i m i l a r i t y t heo ry and dimensional ana lys i s f o r t h e simu-

l a t i v e t e s t i n g o f a drum brake was r e p o r t e d by Pogosian (Ref. 7.22).

An impor tan t p o i n t i n s i m u l a t i v e t r i b o - t e s t i n g i s t h e r e a l i z a t i o n o f

the same t r i b o l o g i c a l processes as i n the p r a c t i c a l system. For t h i s pur -

pose, t h e opera t i ng v a r i a b l e s shou ld be ad jus ted i n connect ion w i t h t h e

geometr ic and con tac t cond i t i ons i n o rde r t o o b t a i n t h e same f r i c t i o n and

wear processes i n TS and PS. A s i m u l a t i o n procedure f o r t h e design o f h igh -

performance d r y bear ings , suggested by P lay and Godet (Ref. 7 - 2 4 ) , i s based

on t h e assumption t h a t i d e n t i c a l c o e f f i c i e n t s o f f r i c t i o n and even wear

r a t e s i n the TS and the PS a re ob ta ined f o r equal average pressures , ve-

l o c i t i e s , con tac t temperatures and i d e n t i c a l c o n t a c t types. I n an i t e r a t i v e

procedure, convergence between two temperatures i s sought i n t h i s method.

F i r s t an exper imenta l s i m u l a t i o n o f p ressure and v e l o c i t i e s found i n t h e

mechanism t o be designed i s s e t up and temperatures a re measured. The t h e r -

mal pa th o f t h e s i m u l a t o r can be mod i f i ed by d i f f e r e n t degrees o f coo l i ng .

Second, temperatures i n t h e a c t u a l mechanism a r e c a l c u l a t e d by f i n i t e -

element techniques f o r t h e c o e f f i c i e n t o f f r i c t i o n found exper imenta l ly .

The t h e o r e t i c a l and exper imental temperatures a r e compared and t h e simul a-

t o r c o o l i n g c o n d i t i o n s a r e m o d i f i e d u n t i l bo th temperatures a r e equal . The

problem i s cons idered t o be so lved when pressures, v e l o c i t i e s and tempera-

tu res a re c o r r e c t l y s imu la ted .

o f bea r ing m a t e r i a l s t o be used i n o i l l u b r i c a t e d bear ings has been proposed

by de Gee (Ref. 7.25). Th is procedure s t a r t s f rom a cons ide ra t i on o f t h e

f r i c t i o n and l u b r i c a t i o n s t a t e i n the S t r i beck curves o f bo th t h e p r a c t i c a l

system ( j o u r n a l bea r ing ) and the t e s t system (p in -on - r i ng t r i bomete r ) .

Another procedure f o r s i m u l a t i v e t e s t i n g o f t h e t r i b o l o g i c a l behav iour

I I

C o e f f i c i e n t o f fri c t i on f

/P

hydrodynamic

1 u b r i c a t i on

m i xed

1 ubr i c a t i on

boundary

1 u b r i c a t i on

F igu re 7.11 S i m p l i f i e d form o f t h e curve o f f r i c t i o n c o e f f i c i e n t f vs bea r ing c h a r a c t e r i s t i c number q w / p .

269

I n Figure 7.11, a s i m p l i f i e d form o f the curve o f c o e f f i c i e n t o f f r i c -

t i o n f versus bearing c h a r a c t e r i s t i c number w i s shown, i .e., the S t r i beck

curve, discussed i n Section 4.5.1, ( 7 i s the dynamic v i s c o s i t y o f the l u b r i -

cant, w t h e angular v e l o c i t y and p the l oad per u n i t p ro jec ted area). I n the

s imu la t i ve t r i b o t e s t i n g procedure suggested by de Gee, the same l u b r i c a t i o n

s t a t e i n the t e s t system as i n the p r a c t i c a l system i s establ ished, as f a r

as poss ib le , by ad jus t i ng the operat ing condi t ions i n the t e s t system u n t i l

f becomes independent o f the parameter 2. This imp l i es boundary l u b r i c a t i o n

only and i s done i n the fo l l ow ing steps:

(i)

(ii)

P

P

Use the same mater ia ls , l u b r i c a n t s and atmospheres i n TS and PS.

Choose an appropr ia te surface roughness o f t he t e s t specimens. To a

f i r s t approximation i t may be assumed t h a t the Ra value o f a machined

sur face increases w i t h increas ing rad ius o f curvature o f the j ou rna l ,

rps, according t o

R~ :: 1.2 [rPsI1" Ra i n pm and

rPS i n m

( i i i ) Apply a r e a l i s t i c normal load F N ~ ~ t o the t e s t system. The most widely

acceptable compromise i s t o make the force per u n i t p ro jec ted p i n area

i n the TS equal t o the force per u n i t pro jected bear ing area of the PS.

Choose a temperature TTS o f the l u b r i c a n t bath o f the TS corresponding

t o t h a t o f the PS. Because o f f r i c t i o n heat ing the se lec t i on o f a

r e a l i s t i c temperature may be d i f f i c u l t . I n such cases i t may be wise

t o in t roduce the t e s t temperature as an independent parameter, per-

forming t e s t s a t d i f f e r e n t temperatures and present ing separate re-

s u l t s f o r each temperature l e v e l .

Es tab l i sh f o r a l l ma te r ia l s o r m a t e r i a l - l u b r i c a n t combinations t o be

tested, the lower l i m i t o f the angular v e l o c i t y Q f o r which the

f r i c t i o n c o e f f i c i e n t f becomes independent o f w. I f the lowest Q value thus establ ished i s B a t a constant wvalue, wtest < Omin.

A t the condi t ions o f

load FN = F N ~ ~ angular v e l o c i t y w = uTS

= TTS temperature T

subsequent experiments are performed

270

perform experiments with a l l mater ia l - lubricant combinations t o be

tes ted. Measure f r i c t i o n during the e n t i r e t e s t period and measure

wear of the s ta t ionary specimen during or a f t e r termination of the

t e s t . The t e s t duration t should be long enough t o allow f o r deter-

mination of the t o t a l amount of wear by weight-loss measurement.

By applying t h i s simulative t r ibo- tes t ing procedure, de Gee obtained a

f ina l ranking of candidate bearing al loys t o be used in lubricated journal

bearings,

In the simulative t r ibo- tes t ing procedure proposed by de Gee, the

f r i c t i o n a n d lubricat ion s t a t e o f the system (spec i f ied as location within the Stribeck curve) served as "simulation c r i te r ion" . As other "simulation

c r i t e r i a " which ind ica te a s i m i l a r i t y of t r ibo logica l processes within the t e s t system and the pract ical system the appearance of worn surfaces or

vibrat ion c h a r a c t e r i s t i c s may be used.

Load FN ~

- Velocity v

"Ambient" Temperature T

Test duration t

1. Collect data of practical system (PSI and test system (TS)

2. Choose conditions and parameters of test system

- I I I adjust parameters

to influence inter-

actionsbetween I the elements

- *

I out identical 1 I (A) Ooeratina variables I

h u t i d e n G I 1 to data of PS

(8) Structure of the test system

Material properties of elements ( 1 I , (21, (31, (4)

Contact conditions between ( 1 ) and (2) L - - h

interactions between elements:

(1 1 + adhesion, abrasion, fatigue + (2) 4 lubrication, tribochem. react& 4

(31 solution, diffusion (4)

\

-- ., -

L - - to data of PS Type of motion I

until similar

I tribologicai

characteristics 1 of TS and PS result I I

r---1

- L h o o z p p r o ]

priate simula-

I i t e r i a I

(C) Tribological characteristics

Appearance of worn surfaces - Thermal parameters

Frictional parameters data of TS Wear parameters I andPS J

F o m p a r e l

I measu red

-

Figure 7.12 Schematic ou t l ine for simulative t r ibo- tes t ing .

Vibrational Darameters

271

In summarizing t h e va r ious aspects o f s i m u l a t i v e t r i b o - t e s t i n g , f rom

a systems p o i n t o f view, a g u i d e - l i n e as o u t l i n e d i n F igu re 7.12 may be

recommended. Accord ing t o F i g u r e 7.12 we may proceed th rough the f o l l o w i n g

steps i n choosing t h e c o n d i t i o n s o f a t e s t system i n an a t tempt a t s imu la-

t i v e t e s t i n g :

( i ) make t h e type o f mot ion and t h e m a t e r i a l p r o p e r t i e s o f t h e elements

(l), ( 2 ) , ( 3 ) , ( 4 ) i d e n t i c a l i n bo th TS and PS.

choose an a p p r o p r i a t e s i m u l a t i o n c r i t e r i o n o r s i m u l a t i o n c r i t e r i a , ( i i )

( i i i ) a d j u s t t h e o p e r a t i n g v a r i a b l e s (FN, v, T , t ) as w e l l as the c o n t a c t

c o n d i t i o n s u n t i l s i m i l a r t r i b o l o g i c a l c h a r a c t e r i s t i c s o f TS and PS

a r e observed.

Al though i t i s c l e a r , t h a t a procedure as i n d i c a t e d i n F igu re 7.12 can o n l y

be regarded as a ve ry rough o u t l i n e , success fu l s i m u l a t i v e t r i b o t e s t i n g has,

i n f a c t , been based on p r i n c i p l e s s i m i l a r t o t h e g u i d e - l i n e o f F i g u r e 7.12,

see S e c t i o n 8.5. Fo r example, Heinke has r e p o r t e d a s i m u l a t i o n o f t h e t r i b o -

l o g i c a l behav iour o f a vane pump (PS) by means o f a p in -on -d i sc apparatus

( T S ) (Ref . 7.26). I n t h i s ins tance, t he appearance o f t h e worn su r faces o f

PS and TS, s t u d i e d by means o f a scanning e l e c t r o n microscope (SEM), served

as a s i m u l a t i o n c r i t e r i o n . I f He inke ' s s tudy i s represented i n t h e manner

o f F igu re 7.12, a schematic diagram f o r h i s procedure appears as shown i n

F igu re 7.13.

Test system

Materials properties

v I

Adjustment of operating variables FN. v. T, t until similar appearance of worn Result of simulative

testing: surfaces result

Different tribotech

nical materials

i

t o m H -

worn cylinder surface disc surface

F igu re 7.13 An example o f s i m u l a t i v e t r i h o - t e s t i n g (Ref . 7.26).

212

I t can be seen t h a t , as a f i r s t step, t h e m a t e r i a l s and the t ype o f

mot ion were made i d e n t i c a l . Then, t h e values o f t h e o p e r a t i n g v a r i a b l e s

(FN, v, T, t ) were ad jus ted u n t i l t he SEM p i c t u r e s o f t h e worn sur faces i n

the TS and the PS were t h e same. The r e s u l t o f t he s i m u l a t i v e t e s t i n g i n

t h i s case was t h e p l a c i n g o f d i f f e r e n t t r i b o - t e c h n i c a l m a t e r i a l s i n an o rde r

o f m e r i t .

7 ,4 TESTING OF TRIBO-TECHNICAL COMPONENTS

The c h a r a c t e r i z a t i o n o f t h e performance o f a g i v e n t r i b o - e n g i n e e r i n g system

r e q u i r e s i t s p r a c t i c e - o r i e n t e d t e s t i n g . These t e s t s should be performed w i t h

the ac tua l components o f - t h e t r i b o - e n g i n e e r i n g system. Due t o the g r e a t va-

r i e t y o f t r ibo-mechan ica l systems (see Appendix A ) and t h e i r components (see

Appendix B) t h e t e s t procedures may vary w i d e l y i n scope and performance.

Therefore, i n t h i s s e c t i o n o n l y some general remarks w i l l be made.

i n t o ( a ) t h e t e s t i n g o f t r i b o - t e c h n i c a l machine elements and ( b ) t h e t e s t i n g

o f 1 ub r i can ts .

The t e s t i n g o f t r i b o - t e c h n i c a l components can be b road ly c l a s s i f i e d

( a ) TESTING OF TRIBO-TECHNICAL MACHINE ELEMENTS

I n t h e t e s t i n g o f a c t u a l t r i b o - t e c h n i c a l machine elements some o f t he f r i c -

t i o n and wear measur ing techn iques descr ibed i n Sec t ion 7.2 may be a p p l i -

cab le . For the measurement o f mechanical and thermal q u a n t i t i e s (such as

c o n t a c t pressures, f r i c t i o n fo rces o r f r i c t i o n - i n d u c e d temperatures) f o r c e -

d e t e c t i n g t ransducers, i n c l u d i n g s t r a i n gauges o r pressure- o r temperature-

s e n s i t i v e coat ings , may be f i x e d d i r e c t l y on t h e machine element t o be i n -

ves ti gated.

t e s t i n g o f machine components i s performed. Consider, as an example o f t h i s

type o f t r i b o - t e s t i n g , t h e t e s t i n g o f gears. A number o f t e s t machines have

been developed which employ gears as t e s t specimens. A l though ac tua l gears

a re used as t e s t specimens, t h e c o r r e l a t i o n o f t e s t performance w i t h s e r v i c e

performance requ i res c a r e f u l c o n t r o l o f t h e t e s t parameters. For i ns tance ,

i f t h e g e a r - t e e t h - r a t i o o f t h e gear t e s t system i s d i f f e r e n t f rom t h a t o f

t h e p r a c t i c a l gear system t h e f requenc ies o f t h e con tac t o f a gear t o o t h o f

one gear w i t h a g i ven gear t o o t h o f t h e o t h e r gear may be d i f f e r e n t , thus

l e a d i n g t o d i f f e r e n t runn ing - in behav iour o f t h e two systems.

I n some cases, i n o r d e r t o avo id f u l l - s c a l e t e s t i n g a semi -p rac t i ca l

273

drive

Max speed

Max load ( k N per mm width)

Load applied while running

(rpm)

4.5 30 30 40 40 40

6000 12000 12000 30000 15000 30000

2.29 0.89 0.75 1.26 0.89 1.07

no no yes yes yes no

Table 7.5 Characteristics of some spur gear rigs (Ref. 7 .27) .

The most widely used gear t e s t machines employ spur gears. I t i s n o t pos-

s ib le here to go into the de ta i l s of the various types, b u t the charac-

t e r i s t i c s of s ix common spur-gear t e s t machines are presented in Table 7.5

as compiled by Brown (Ref. 7 .27) . These test-machines a l l employ the power-

circulating or “four-square’‘ principle. The application of t h i s principle to gear testing was suggested f i r s t by Kutzbach i n 1926 (Ref. 7.28). He al-

so showed tha t i t has the advantage that power i s needed only t o overcome

the f r ic t ion in the t e s t and slave gears and the i r support bearings, see

Figure 7.14.

are determined in order t o describe the tribological behaviour o f a gear se t :

( a ) f r ic t ion losses

( b ) wear resistance

( c ) surface fatigue ( d ) scuff load (load-carrying capacity)

With gear t e s t machines, the following main tribometric characterist ics

274

Lz L4 L2

Losses: L electrical ; L bearing-friction; L air-friction; L gear-friction 1 2 3 4

Figure 7.14 Power transmission and power circulating principles (Ref. 7 . 2 8 ) .

These tribometric characteristics are in most cases also determined i n the testing of other tribo-technical components, for example ball and roller

bearings. As mentioned above, these tribometri c characteristics concentrate, however, on the loss-output function and the wear-induced change of the sys-

tem's structure. In addition to this type of testing o f tribo-technical com-

ponents, for the characterization of the performance of actual machinery the

control and monitoring of the use-function of the tribo-engineering system

is needed. This aspects of tribometry is discussed in the next section.

(b) TESTING OF LUBRICANTS

A l s o for the testing o f the other group o f tribo-technical components,

namely the lubricants, several aspects must be considered. As in the charac-

terization of every component of a tribological system, the testing and

characterization of system-independent and system-dependent properties of

276

1 ubr icants shoul d be d i s ti ngui shed. The sys tem-independent 1 ub r i can t char-

a c t e r i s t i c s describe the p roper t i es "per se" o f t he l u b r i c a n t , independently

o f the t r ibo-engineer ing a p p l i c a t i o n o f the l ub r i can t . The main l u b r i c a n t

c h a r a c t e r i s t i c s fa1 1 i n g i n t o t h i s category are:

1.

2.

3. dens i t y and s p e c i f i c g r a v i t y

4. s p e c i f i c heat and thermal conduc t i v i t y

5. d i e l e c t r i c constant

6. a c i d i t y , b a s i c i t y , n e u t r a l i z a t i o n number

7. a n i l i n e p o i n t

8. f lash and f i r e p o i n t

9. cloud, pour and f l o c k po in ts

10. h y d r o l y t i c s t a b i l i t y

11. ox ida t i on c h a r a c t e r i s t i c s

12. evaporation and v o l a t i l i t y

13. i n t e r f a c i a l tens ion

14. emulsion c h a r a c t e r i s t i c

15. foaming

16. v i s c o s i t y

17. v i scos i ty-temperature c h a r a c t e r i s t i c

18. v i scos i ty-pressure c h a r a c t e r i s t i c

For the t e s t i n g and s p e c i f i c a t i o n o f these system-independent l u b r i c a n t

p roper t i es and cha rac te r i s t i cs , well-known t e s t s have been worked ou t and

standardized. This has been done, f o r instance, i n the USA by the American

Society f o r Test ing and Ma te r ia l s , Committee on Standards on Petrolem Pro-

ducts and Lubr icants (ASTM-DZ), i n England by the I n s t i t u t e o f Petroleum

(IP) and i n the Federal Republic o f Germany by the FachausschuR M ine ra lo l -

und Brennstoffnormung i m Deutschen I n s t i t u t f u r Normung (FAM-DIN). The

d e t a i l s o f the various t e s t s can be found i n the o f f i c i a l pub l i ca t i ons o f

these i n s t i t u t i o n s ; f o r general compilat ions o f these t e s t s the reader i s r e f e r r e d t o R e f s . 7.29 t o 7.31.

I n con t ras t t o the standardized t e s t s f o r the system-independent phy-

s i c a l , chemical and technologica l p roper t i es o f l ub r i can ts , the t e s t i n g of

the func t i ona l behaviour o f l u b r i c a n t s should be performed i n connection

w i t h the technica l f unc t i on o f the actual t r ibo-engineer ing system i n which

the l u b r i c a n t i s used. These tests , assess predominantly the o v e r a l l a b i l -

i t y o f a l u b r i c a n t t o permi t rubbing surfaces t o operate w i thou t s c u f f i n g

chemical composition ( i n c l u d i n g content o f S, P, C1, H20)

d i r t content ( i n c l u d i n g ash content)

216

s e i z i n g o r o t h e r m a n i f e s t a t i o n o f m a t e r i a l d e s t r u c t i o n . They can be b road ly

c l a s s i f i e d i n t h r e e groups (Ref. 7 .32) :

( i )

I n these t e s t s , t h e performance o f l u b r i c a n t s i s t e s t e d w i t h s i m p l i f i e d

t e s t geometries l e a d i n g t o p o i n t , l i n e o r f l a t con tac t . The more f a m i l i a r

t e s t s o f t h i s type a r e the Four B a l l , Timken, SAE o r Amsler, Fa lex and

Almen. Most o f these t e s t s were devised t o d i f f e r e n t i a t e between EP and

non-EP o i l s , and t h e i r accuracy i s sometimes n o t good enough t o grade d i f -

f e r e n t l e v e l s o f EP a c t i v i t y . E r r a t i c r e s u l t s can occur i f o p e r a t i n g v a r i -

ab les (e.g. t he temperature o f t h e l u b r i c a n t ) a re n o t c l o s e l y c o n t r o l l e d .

As ment ioned above, t h e term " h y b r i d t e s t e r s " was proposed as n e i t h e r se r -

v i c e cond i t i ons n o r p h y s i c a l l y w e l l de f i ned parameters were reproduced

(Ref. 7 . 2 ) . P r e d i c t i n g t h e performance o f l u b r i c a n t s on t h e b a s i s o f these

t e s t s a lone i s a lmost imposs ib le . On the o t h e r hand, they a re conven ien t

f o r acceptance t e s t i n g , p roduc t i on c o n t r o l and they a re good i n d i c a t o r s o f

ba tch v a r i a t i o n s o f 1 ub r i can ts .

T e s t i n g o f l u b r i c a n t s i n s i m p l i f i e d bench t e s t s .

( i i ) T e s t i n g o f l u b r i c a n t s w i th t r i b o - t e c h n i c a l components.

Because o f t he above shortcomings, a d i f f e r e n t type o f l u b r i c a n t t e s t i n g

i s r e q u i r e d t o p e r m i t c o n t r o l o f as many v a r i a b l e s as p o s s i b l e w h i l e simu-

l a t i n g a c t u a l performance requirements. A conven ien t way o f do ing t h i s i s

t o t e s t l u b r i c a n t s i n t h e l abo ra to ry , where o p e r a t i n g c o n d i t i o n s can be

c o n t r o l l e d , t h e p a r t s under t e s t be ing those used i n t h e complete t r i b o -

eng ineer ing u n i t . The b e s t known examples o f t h i s type o f l u b r i c a n t t e s t i n g

a r e the l a b o r a t o r y t e s t s performed w i t h g e a r - t e s t r i g s as compi led i n Tab le

7.5. Consider, as a f u r t h e r example o f t h i s t ype o f t e s t i n g , t he t e s t i n g o f

hypo id gear l u b r i c a n t s (Ref. 7.33). I n these t e s t s , f u l l - s c a l e r e a r ax les

a r e s e t up on l a b o r a t o r y t e s t beds and d r i v e n by engines and t ransmiss ions

w h i l e l o a d (F,,,) i s a p p l i e d th rough abso rp t i on dynamometers on t h e d r i v e n

ax les a t c e r t a i n v e l o c i t i e s ( v ) and o i l temperatures ( T ) f o r a g iven p e r i o d

o f t ime ( t ) . A f t e r t h e t e s t program i s completed, gears a r e i nspec ted f o r

s igns o f s c u f f i n g , wear o r o t h e r d i s t r e s s and the l u b r i c a n t r a t e d as e i t h e r

pass o r f a i l . The t e s t procedure i s based on c o r r e l a t i o n w i t h f i e l d t e s t s

on s i m i l a r ax les i n f u l l - s c a l e veh ic les , which a l s o showed d i f f e r e n c e s be-

tween t h e l u b r i c a n t s .

211

( i i i )

There i s general agreement t h a t t h e o n l y s a t i s f a c t o r y means o f e v a l u a t i n g

t h e performance c h a r a c t e r i s t i c s o f l u b r i c a n t s i s by f u l l - s c a l e t e s t s o f i t s

a c t u a l use i n t r i b o - e n g i n e e r i n g systems. A l though these t e s t s va ry b road ly

i n scope and.procedure, they may be c l a s s i f i e d acco rd ing t o t h e broad ca te-

go r ies which account f o r t h e m a j o r i t y o f l u b r i c a n t s consumed, namely

(a ) General machinery l u b r i c a n t s

( b ) ( c ) I n t e r n a l combustion engine o i l s

( d ) Steam c y l i n d e r o i l s

( e ) Compressor o i l s

( f ) Gear o i l s

Tes t procedures f o r t he f u l l - s c a l e t e s t i n g o f these main groups o f l u b r i c a n t s

can be found i n Refs. 7.34 and 7.35.

T e s t i n g o f l u b r i c a n t s i n f u l l - s c a l e t e s t s

H y d r a u l i c f l u i d s and t u r b i n e o i l s

Al though the p r a c t i c a l va lue o f f u l l - s c a l e t e s t i n g o f l u b r i c a n t s i s

agreed, t h e c o s t o f f i e l d o r p rov ing-ground t e s t s i s cons iderab le , so t h a t

t h i s t ype o f t r i b o - t e s t i n g i s g e n e r a l l y used o n l y as f i n a l p r o o f o f t h e de-

c i s i o n s made w h i l e deve lop ing t h e des ign o f an a c t u a l t r i b o - e n g i n e e r i n g

system.

7,5 MACHINERY CONDITION MONITORING

Wi th t h e i nc rease o f s o p h i s t i c a t i o n o f contemporary machinery any d i s t u r -

bance o r f a i l u r e o f t he p roper f u n c t i o n i n g o f complex machines w i l l tend

t o have se r ious consequences. To i l l u s t r a t e t h e cos ts which can be i nvo l ved ,

i t has been r e p o r t e d t h a t a s imp le bea r ing f a i l u r e i n a f u l l y i n t e g r a t e d

s t e e l m i l l can l e a d t o shut-down which a t f u l l o u t p u t r a t e may c o s t d 150 - a 3 0 0 p e r minute. A s i m i l a r bea r ing f a i l u r e i n a modern genera tor s e t cou ld

i n v o l v e a l o s s o f 61 - d20 per minu te u n t i l t h e s e t was aga in o p e r a t i o n a l

(Ref. 7.36). I n o r d e r t o p reven t such f a i l u r e s o f t r i b o - e n g i n e e r i n g systems,

i n c r e a s i n g a t t e n t i o n i s now b e i n g g i ven t o t r i b o m e t r i c machinery c o n d i t i o n

o r " h e a l t h " m o n i t o r i n g techn iques .

I n recen t years , s e n s i t i v e d e t e c t o r s and techn iques f o r t h e d iagnos is

o f ma l func t i ons i n machinery have been developed (Ref. 7.37). Emphasis i s

be ing g i ven t o " o n - l i n e m o n i t o r i n g techn iques" as a means o f d e t e c t i n g de-

t e r i o r a t i o n so t h a t remed ia l a c t i o n can be taken b e f o r e t h e breakdown p o i n t

270

i s reached. I n add i t i on , there i s growing recogn i t i on t h a t f u tu re progress

cannot r e l y upon diagnosis alone. I t i s becoming inc reas ing l y important t o

monitor the " s t a t e o f heal th" of machinery on e i t h e r an i n t e r m i t t e n t o r

continuous basis. A prognostic approach can then be adopted and remedial

ac t i on can be taken a t a convenient t ime i n the normal cyc le o f operat ion

o f the equipment (Ref. 7.38).

ven ien t l y used f o r the c l a s s i f i c a t i o n and desc r ip t i on o f t he t r i b o m e t r i c

machinery cond i t i on moni tor ing techniques. Since the cha rac te r i za t i on o f

a t r ibo-engineer ing system requi res the desc r ip t i on o f the system func t i on

as w e l l as i t s s t ruc tu re , the machinery cond i t i on moni tor ing techniques can

be broadly c l a s s i f i e d i n (a) t r i b o m e t r i c techniques f o r the moni tor ing o f

the system function, and (b ) t r i b o m e t r i c techniques f o r the moni tor ing o f

the system s t ruc tu re .

The systems approach as appl ied throughout t h i s volume can be con-

(a ) MONITORING OF THE FUNCTION OF TRIBO-MECHANICAL SYSTEMS

The moni tor ing o f the system's use-function would requ i re the con t ro l o f

operating i npu t var iab les and i t s corresponding use-outputs, namely:

- the type o f motion,

- the i n p u t and output forces, o r contact pressures,

- the i n p u t and output ve loc i t i es ,

- the temperatures a t the i n p u t and the output.

A1 though the use-function o f t r ibo-engineer ing systems i s connected w i t h

the above quan t i t i es , in format ion on the proper funct ion o f a given t r i b o -

engineering system i s o f t e n i n d i r e c t l y obtained by moni tor ing the loss-

outputs corresponding t o the use-input and use-output q u a n t i t i e s (Ref.

7.39). For the movement from diagnosis towards prognosis the s ignals from

the loss-outputs i n d i c a t i n g the ai lments o f machinery may be fed back by

means o f servo-control equipments o r microprocessors t o the input , thus

in f luenc ing the operational inputs i n order t o es tab l i sh a proper func-

t i o n i n g o f the whole system.

of mechanical work w i t h i n a tribo-mechanical system as i l l u s t r a t e d i n F igure

3.4, the fo l l ow ing loss-output q u a n t i t i e s should be monitored:

(i) F r i c t i o n force and f r i c t i o n a l changes

An increase o r decrease i n the f r i c t i o n o f t r ibo-engineer ing systems l i k e

bearings, gears etc. can be a po in te r towards decreased performance and

i n c i p i e n t f a i l u r e (see Section 4.5.6).

According t o the general scheme o f the transmission and t ransformat ion

279

(ii) Noise and v i b r a t i o n

Changes i n the noise spectrum associated w i t h p a r t i c u l a r t r ibo-engineer ing

components operat ing under normal condi t ions i n known environments can

i n d i c a t e i n c i p i e n t f a i l u r e . Two types o f acoust ic s igna ls may be d i s t i n -

guished: - noise f i e l d s due t o v ib ra t i ons , impacts o r aerodynamic processes emi t ted

i n a r e l a t i v e l y low frequency range (10 t o 20 kHz),

impu ls - l i ke acoust ic s ignals o f low amplitude due t o m ic ros t ruc tu ra l

changes, l i k e micro-cracking, emi t ted i n a frequency range o f about

50 kHz t o 1.5 MHz (acoust ic emission) (Ref. 7.40).

-

Area C

2

I I I 1 1 I , I 10 25 50 100 250 500 1000 2500 5000

Frequency (Hz)

Figure 7.15 Noise diagram o f submarine engine (Ref. 7.41).

As a p r a c t i c a l example o f the noise-analys is o f t r ibo-engineer ing systems,

i n F igure 7.15 a noise diagram i s shown which i s used as maintenance indi-

ca to r f o r t he moni tor ing o f submarine engines. The d i f f e r e n t frequency

ranges A t o D correspond t o d i f f e r e n t types o f mechanical f a u l t s (Ref. 7.41).

( i i i ) Heat emission and temperature changes Tribo-induced heat and temperature r i s e may lead t o thermal d i s t o r t i o n and

thermal stresses and may both adversely a f f e c t the mechanical s t reng th o f

the machine components and the p roper t i es o f t he l u b r i c a n t , thus i n f l u e n c i n g

the performance and sa fe ty o f the machine. I n the cond i t i on moni tor ing o f

r o l l i n g element bearings and s l i d i n g bearings, t he temperature l e v e l s com-

p i l e d i n Table 7.6 are recommended as thresholds f o r t h e alarm o r t h e stop-

page of the bear ing (Ref. 7.42).

280

Location

1. housing

2. r i n g s

3. bearing bushinc (2mm below m i - nimum o i l gap)

4. l u b r i c a n t w i t h i n bearing

5. l u b r i c a n t o u t l e t

Temperature l e v e l (OC)

l o l l i n a element bearinu 1 S l i d i n a bearina

%l arm stop I alarm stop

70

90

80

80

Table 7.6 Temperate data re levan t t o the moni tor ing o f r o l l i n g element bearings and s l i d i n g bearings.

For the moni tor ing of c h a r a c t e r i s t i c s (i), (ii), (iii) a hos t o f sensing

devices i s ava i l ab le today, based on the measuring techniques described i n

d e t a i l i n Section 7.2.

( b ) MONITORING OF THE STRUCTURE OF TRIBO-MECHANICAL SYSTEMS

Besides the moni tor ing o f the i n p u t and output parameters o f a t r i bo -eng i -

neering system i n d i c a t i n g the (momentary) f unc t i ona l behaviour o f the sys-

tem, the moni tor ing o f parameters character iz ing the s ta te o f the system's

s t r u c t u r e i s required. I n t h i s connection a t t e n t i o n should be drawn t o the

important d i f f e rence between the in format ion and the conclusions t h a t f o l -

low from the moni tor ing o f f unc t i ona l and s t r u c t u r a l parameters. These d i f -

ferences can be e a s i l y explained i n considering the conceptual tr ibo-process

diagram o f a given tribo-mechanical system, see F igure 3.4. I f on ly the

func t i ona l parameters on the conceptual f unc t i ona l plane o f a given t r i b o -

engineering system are monitored, t he system s t r u c t u r e may undergo unper-

ceived gradual changes , f o r example on the conceptual mater ia l planes, 1 ead-

i n g a f t e r a c e r t a i n operat ing du ra t i on t o an unexpected f a i l u r e although

du r ing the whole t ime the func t i ona l parameters remained i n t h e i r proper

range. If, on the other hand, the moni tor ing o f t he re levan t parameters o f

the s t r u c t u r e o f the system i n d i c a t e a constancy o f the system s t ruc tu re

and if, i n addi t ion, the func t i ona l inputs are w i t h i n t h e i r proper range,

281

the occurrence o f a sudden f a i l u r e i s r a t h e r u n l i k e l y . Although the on - l i ne

moni tor ing o f the c h a r a c t e r i s t i c s o f the system s t r u c t u r e i s , i n general,

more d i f f i c u l t than the moni tor ing o f the c h a r a c t e r i s t i c s o f the func t i ona l

inputs and outputs, convenient detectors have been developed f o r t h i s pur-

pose a l so i n recent years.

actua l s t a t e o f the s t r u c t u r e o f a t r ibo-engineer ing system:

(i) Lubr icant supply and l u b r i c a t i o n mode I f the volume o f l u b r i c a n t t o the component i s inadequate o r i f the phys ica l

and chemical p roper t i es o f the l u b r i c a n t change i n service, the l u b r i c a t i o n

mode may change leading t o a d e t e r i o r a t i o n o f the performance o f the whole

system. Methods o f moni tor ing o i l supply o f a machine a re we l l known and

have long been pract iced. The techniques invo lved range from the v i sua l

checking o f the o i l l e v e l i n the sump o r o i l tank using a s i g h t glass, t o

the i n s e r t i o n o f o i l pressure gauges and o i l f l ow meters. These detectors

are o f t e n connected t o an automatic alarm system so t h a t the o i l f l ow i s

monitored continuously. Further, the l u b r i c a n t q u a l i t y should be monitored

by tak ing samples o f the used o i l s a t i n t e r v a l s and sub jec t i ng them t o l a -

boratory t e s t s t o determine whether re levan t l u b r i c a n t p roper t i es have

changed.

(ii) Surface condi t ions o f machine components Changes i n sur face roughness o r the appearance o f p i t s o r cracks are a

powerful i n d i c a t o r o f i n c i p i e n t f a i l u r e , p a r t i c u l a r l y i n r o l l i n g elements

and gears. The techniques f o r the i n v e s t i g a t i o n o f surfaces are discussed

i n some d e t a i l i n Section 7.6. The app l i ca t i on o f these techniques i n ma-

ch inery cond i t i on moni tor ing i s hindered by the f a c t t h a t moving surfaces

have t o be invest igated. To overcome these d i f f i c u l t i e s attempts have been

made t o use l ase rs f o r the i n s i t u de tec t i on o f surface roughness charac-

t e r i s t i c s . Another p o s s i b i l i t y i s t o make a r e p l i c a o f the surface t o be

monitored. It has been reported, f o r example, t h a t the surface examination

o f a hypoid gear may be c a r r i e d ou t by such methods w i thou t removing i t

from i t s housing (Ref. 7.43).

( i i i ) As c h a r a c t e r i s t i c s o f the wear-induced changes o f the s t r u c t u r e o f t r i b o -

mechanical systems, (a ) geometrical changes o f t he moving components o r (b)

worn ma te r ia l loss ra tes may be monitored. As an example o f c lass (a) i n

F igure 7.16 a method f o r p i s t o n r i n g cond i t i on moni tor ing i s shown.

The fo l l ow ing c h a r a c t e r i s t i c s may be monitored as an i n d i c a t i o n o f t he

Wear behaviour o f the system

282

I proximi ty transducer

F igure 7.16 Schematic representat ion o f p i s ton - r i ng -cond i t i on moni tor ing technique.

The p i s t o n r i n g cond i t i on i s sensed by means o f p rox im i t y transducers,

which are mounted f l u s h w i t h the running Qur face o f the cy l inders. The

transducer detects r i n g s n o t i n proper coti tact w i t h the cy l i nde r , as w e l l

as broken p i s ton r i ngs . From the e l e c t r o n i c signal-processing equipment

shown i n Figure 7.16, in format ion can be CJbtained about the p i s ton r i n g

condi t ion.

Various techniques are a l so ava i l ab lq f o r the moni tor ing o f wear out-

p u t rates. Careful examination o f debr is q r l u b r i c a n t contaminants can i n -

d i ca te t h e i r o r i g i n and a l l ow conclusion go be drawn about t h e i r formation,

and hence the cond i t i on o f inaccess ib le moving par ts . For example, i t i s

n o t poss ib le t o examine i n s i t u the workirlg p a r t s o f a j e t engine, b u t each

drop o f l u b r i c a n t which c i r c u l a t e s through the moving p a r t s c a r r i e s w i t h i t

evidence o f i t s experience i n passage. Careful examination o f the o i l and

any p a r t i c l e s i t may conta in a l lows i n t e r i r e t a t i o n o f the condi t ions. The

wear debris contained i n the l u b r i c a n t s i n operat ing mechanisms may be

monitored by the f o l l o w i n g methods:

(a) Spectrographic o i 1 analys is procedure (SOAP) Very small concentrat ions o f m e t a l l i c wear products (1-2 p a r t / m i l l i o n )

suspended i n used l u b r i c a t i n g o i l can be i d e n t i f i e d by spectrographic

analys is (Ref. 7.44). Using the in format ion thus obtained together w i t h

283

a knowledge o f chemical compos i t ion o f o i l - w e t t e d p a r t s , i t i s p o s s i b l e t o

determine which components a r e wear ing. Fo r example, abnormal l e v e l s o f

i r o n i n the sump o i l o f a D iese l eng ine can i n d i c a t e excess ive c y l i n d e r

bore wear.

l 4 O I 120

f 100

- 80

262 mg/h a t 221h 32min

887 mg/h a t 221h 58min

1 I I I I I

100 120 140 160 180 200 220

Engine runn ing t ime ( h )

F igu re 7.17 Spec t romet r i c a n a l y s i s - Olympus eng ine 59332 i n Concorde p r o t o t y p e a i r c r a f t (Ref. 7 .45) .

As an example o f t he a p p l i c a t i o n o f t h e SOAP techn ique i n F i g u r e 7.17 a

t y p i c a l p l o t o f t h e Fe - ra te i n an Olympus eng ine i n s t a l l e d i n t h e concorde

p ro to type a i r c r a f t i s shown (Ref. 7 .45) . The r a p i d i nc rease a t 220 hours

was found t o a r i s e f rom heavy f r e t t i n g wear on the beve l s p l i n e l o c a t i o n

on t h e l a y s h a f t d r i v e n by the p o r t gear box.

(0) Magnet ic c h i p d e t e c t o r s

The use o f a magnet i n a l u b r i c a t i o n system p rov ides a s imp le and e f f e c t i v e

method f o r m o n i t o r i n g t h e contaminat ion o f l i q u i d s . A s t r o n g magnet w i l l

a t t r a c t p a r t i c l e s i n an o i l stream. as f o r i ns tance metal f l a k e s such as

a r i s e f rom f a t i g u e f ragmenta t ion . Use o f t h i s d e t e c t o r i n v o l v e s removal o f

t he magnet ic probe a t r e g u l a r i n t e r v a l s and t h e i n s e r t i o n o f a f r e s h probe

w h i l e t h e o r i g i n a l i s r e t a i n e d f o r t h e assessment o f t h e p a r t i c l e s adher ing

t o it.

(y) Rad ioac t i ve t r a c e r methods

The use o f rad io i so topes , a r t i f i c a l l y produced by neu t ron i r r a d i a t i o n o f -

f e r s a p a r t i c u l a r l y conven ien t method f o r f o l l o w i n g t h e movement o f m a t e r i a l

284

d u r i n g de fwmat ion , t r a n s f e r , o r t he forniat ion o f wear deb r i s . I n r e c e n t

years , a g r e a t r e d u c t i o n i n background r a d i a t i o n by i m p l a n t i n g r a d i o a c t i v e

i ons i ns tead o f a c t i v a t e the whole sample has been ob ta ined. I n u s i n g a

t h i n - l a y e r a c t i v a t i o n techn ique i t i s p o s s i b l e t o d i f f e r e n t i a t e between

t h e wear f rom d i f f e r e n t p a r t s of moving Machine elements.

6

5

m 4 - E v

$ 3 x

2

1

1 2 3 4 5

Running t ime (h )

F igu re 7.18 Three-component wear measurement w i t h rad io i so topes (Ref . 7.46).

As an example (Ref. 7 -46) , i n F i g u r e 7.18 wear curves f rom the d i f f e r e n t

p a r t s o f a D iese l engine, namely the c y l i n d e r l i n e r , t h e runn ing su r face

and t h e f l a n k s o f t h e p i s t o n r i n g s a re shown. The p o s s i b i l i t i e s o f t h e

a p p l i c a t i o n o f r a d i o a c t i v e t r a c e r i n machSnery c o n d i t i o n m o n i t o r i n g have

been reviewed i n d e t a i l by GervZ? (Ref. 7.46).

(6) Ferrography

Ferrography i s a techn ique developed t o separa te wear d e b r i s f rom t h e

l u b r i c a n t and spread i t accord ing t o s i z e on a t ransparen t subs t ra te f o r

examinat ion i n an o p t i c a l o r scanning e l e t t r o n microscope (Ref. 7.47). The

Ferrograph ana lyze r c o n s i s t s o f a pump t o d e l i v e r a sample a t low r a t e , a

magnet t o p rov ide a h i g h - g r a d i e n t magnet ic f i e l d near i t s po les and a

t r e a t e d t ransparen t subs t ra te (Ferrogram s l i d e ) on which t h e p a r t i c l e s a re

depos i ted . The o i l sample, d i l u t e d w i t h a spec ia l s o l v e n t t o promote t h e

285

1 I ------ r I I operating

4 I L - 4 tribo-mechanical system +--I

I -J

Figure 7.19 I l l u s t r a t i o n of the Ferrography technique: ( a ) schematic representat ion of Ferrograph analyzer, ( b ) SEM micrograph o f deposited wear p a r t i c l e s (Ref. 7 .48) .

286

p r e c i p i t a t i o n o f t h e wear p a r t i c l e s , i s pumped across a transparent sub-

s t r a t e which i s mounted a t a s l i g h t i n c l i n e , the magnetic p a r t i c l e s adhere

t o the substrate, d i s t r i b u t e d approximately according t o s ize. The q u a n t i t y

o f wear p a r t i c l e s and t h e i r s i z e d i s t r i b u t i o n can be determined by o p t i c a l

densi ty measurement. I n Figure 7.19 the app l i ca t i on o f the Ferrograph tech-

nique (Ref. 7.48) i s i l l u s t r a t e d .

The moni tor ing techniques described i n t h i s sect ion are appl ied i n

various types o f machinery as f o r instance i n the f a i l u r e e a r l y warning

system f o r a i r c r a f t engines. I t may be concluded t h a t machinery condi t ion-

moni tor ing techniques, i n a d d i t i o n t o enabl ing a prognost ic approach t o

f a i l u r e prevent ion can be an a i d t o the design o f advanced machinery f o r

immediate maintenance and f a i l u r e f r e e serv ice wi thout c o s t l y r e p a i r work.

7,6 SURFACE INVESTIGATION TECHNIQUES

Since f r i c t i o n and wear processes occur p r i m a r i l y a t surfaces, surface i n -

ves t i ga t i on techniques p lay an important r o l e f o r l abo ra to ry t r i b o - t e s t i n g

as we1 1 as f o r the pract ice-or iented t e s t i n g o f t r ibo-engineer ing equipment

(Ref. 7.49). For a complete i n v e s t i g a t i o n both the topography and the com-

p o s i t i o n o f surfaces have t o be studied.

(a ) INVESTIGATION OF SURFACE TOPOGRAPHY

Surfaces can be s tud ied i n a q u a l i t a t i v e manner by microscopic techniques.

For plane surfaces, the usual o p t i c a l microscopy can be u t l l i z e d . With the

use o f Nomarski lenses i t becomes poss ib le t o study surfaces w i t h a r e -

s o l u t i o n i n depth o f about 50 A (Ref. 7.50). For example wi th t h i s tech-

nique i t i s poss ib le t o detect s l i p bands around wear t racks as w e l l as t o

estimate the thickness o f t h i n polymer f i l m s (thickness l ess than 200 1) t r ans fe r red t o m e t a l l i c counterfaces i n the s l i d i n g o f polymer-metal couples

(Ref. 7.51), as shown i n Figures 7.20 and 7.21. Q u a n t i t a t i v e measurements o f surface i r r e g u l a r i t i e s , such as steps,

scratches, o r grooves, can be made on smooth surfaces w i t h an o p t i c a l i n t e r -

ference microscope o r i n apply ing mu1 t i p l e beam in te r fe rence microscopy

(Ref. 7.52). Peak-to-valley sur face roughness values down t o 0.015 pm can

be measured (7.53) . The technique can be improved f u r t h e r by applying the

method o f equidensit ies, which s p l i t s up every i n te r fe rence l i n e i n t o two

l i nes , thus improving the s e n s i t i v i t y and p rov id ing a 3-dimensional p i c t u r e

207

F i g u r e 7.20 Nomarski o p t i c a l micrograph o f an A1 su r face a f t e r s l i d i n g con tac t w i t h a g lass b a l l .

( b ) ( a ) - 50 pm

F igu re 7.21 Nomarski o p t i c a l micrographs: ( a ) PTFE t r a n s f e r on g lass , (b) s t e p o f evaporated g o l d f o r comparison, h.230 w.

F i g u r e 7.22 I n te r fe rog ram (a ) and cor respond ing e q u i d e n s i t i e s ( b ) o f a c i r c u l a r wear sca r on a p lane (spac ing o f i n t e r - fe rence 1 ines : h/2 = 0.27 pm).

289

o f t h e su r face roughness, see F i g u r e 7.22. By f o l l o w i n g an i n d i v i d u a l i n -

t e r f e r e n c e l i n e w i t h a p lan imeter , su r face roughness data, such as t h e Ra

( cen te r -1 ine-average) va lue can be determined f o r t h e va r ious c ross -sec t i ons

o f t h e p r o f i l e .

worn su r faces i s l i m i t e d t o t h e s tudy o f r e l a t i v e l y p lane and smooth su r -

faces because o f t h e very poor depth o f focus o f o p t i c a l techniques, be ing

o n l y 0 . 1 pin a t a m a g n i f i c a t i o n o f say 500 t imes. There fo re t h e i n t r o d u c t i o n

o f t h e scanning e l e c t r o n microscope (SEM) t o t h e s tudy o f worn su r faces has

been very advantageous (Ref. 7.54). Due t o t h e ex t remely s h o r t wavelength

o f t h e e l e c t r o n beam, bo th h i g h m a g n i f i c a t i o n and h i g h dep th o f focus can

be ob ta ined. Fo r example, a t a m a g n i f i c a t i o n o f 5000 t imes t h e depth o f

focus i s s t i l l h i g h e r than 10 pm. There fore , t h i s techn ique can be conve-

n i e n t l y used i n t h e s tudy o f r e l a t i v e l y rough su r faces as i l l u s t r a t e d by

the examples shown i n Sec t i on 4.4, demonst ra t ing t h e d i f f e r e n t appearance

o f worn sur faces . The SEM can a l s o be used t o d e t e c t t h e s t a t e o f deforma-

t i o n below the su r face w i t h t h e " e l e c t r o n channel 1 i n g p a t t e r n (ECP)" tech-

nique. I n t i l t i n g t h e e l e c t r o n beam w i t h respec t t o t h e su r face s p o t under

study, t h e d i f f r a c t i o n o f t h e e l e c t r o n beam a t t h e d i f f e r e n t c r y s t a l lograph-

i c planes leads t o c h a r a c t e r i s t i c ECP l i n e s (Ref . 7.55). Under optimum ex-

per imenta l c o n d i t i o n s , w i t h t h e ECP technique, which i s analogous t o t h e

K i kuch i techn ique o f t h e t ransmiss ion e l e c t r o n microscopy, i n f o r m a t i o n on

d i s l o c a t i o n d e n s i t i e s can be es t ima ted f rom t h e w id th , w, o f t h e ECP l i n e s

(Ref. 7.56). I n F i g u r e 7.23 examples o f ECP diagrams a r e shown (Ref. 7.57).

o f t he s u r f a c e topography. A smal l diamond need le w i t h a t i p r a d i u s o f about

5 pin i s moved across t h e su r face and t h e d e r a t i o n o f t h e need le i s a m p l i f i e d

by e l e c t r o n i c means. The v e r t i c a l r e s o l u t i o n has a va lue o f about 0.01 pm

whereas t h e h o r i z o n t a l r e s o l u t i o n i s determined by t h e r a d i u s o f t h e t i p o f

t he needle. Feeding t h e e l e c t r o n i c o u t p u t o f t h e p r o f i l e m e t e r t o a computer

i t i s p o s s i b l e t o c a l c u l a t e t h e va r ious su r face roughness measures desc r ibed

i n S e c t i o n 4.2.1.

The a p p l i c a t i o n o f o p t i c a l m ic roscop ic techn iques t o i n v e s t i g a t i o n s o f

P r o f i l o m e t e r methods a r e p r e f e r r e d f o r t h e q u a n t i t a t i v e de te rm ina t ion

Moreover, c h a r a c t e r i s t i c s such as t h e F o u r i e r a n a l y s i s , t h e au tocor re-

l a t i o n f u n c t i o n and r e l a t e d q u a n t i t i e s can be ob ta ined. Wi th t h e h e l p o f a

specimen s tage (x -y -mot ion i n s teps ) su r face p r o f i l e maps can be ob ta ined.

The a p p l i c a t i o n o f su r face p r o f i l o m e t r y t o t h e s tudy o f t r i b o - i n d u c e d su r -

face topography changes can be seen f rom t h e examples d iscussed i n Sec t ion

5.2.1. A su r face con tou r map o f an A1 su r face b e f o r e and a f t e r a c o n t a c t de-

fo rma t ion process i s shown i n F i g u r e 7.24 (Ref. 7.58).

290

SEM micrographs

/

W 3

F igu re 7.23 ECP diagrams near t h e end o f a wear t r a c k on an A l -sur face , i n d i c a t i n g an i nc rease o f sub-sur face d i s l o c a t i o n d e n s i t y o f about two o rde rs o f magnitude f rom l o c a t i o n 1 t o l o c a t i o n 3.

291

Figure 7.24 Surface contour map before and a f t e r contact deformation (Ref. 7.58).

(b ) INVESTIGATION OF SURFACE COMPOSITION

For the i n v e s t i g a t i o n o f the composition o f surfaces several powerful t o o l s

are ava i l ab le today.

I n the e l e c t r o n probe microanalyzer (EPMA) an e l e c t r o n beam i s scanned

across the surface and the X-ray r a d i a t i o n emi t ted i s analyzed by means o f

a spectrometer. The concentrat ion o f the chemical elements belonging t o the

c h a r a c t e r i s t i c X-ray r a d i a t i o n i s reg i s te red on a screen. Since the X-ray

emission o r i g i n a t e s from the topmost sur face atoms as well as f r o m atoms

some pm below the surface one resolved spot on the screen i s r e l a t e d t o a 3 specimen volume o f about 1 pm (Ref. 7.59). Therefore, the EPMA can be used

only f o r the study o f the sur face composition o f r e l a t i v e l y t h i c k sur face

layers. I n Figure 7.25 the i d e n t i f i c a t i o n o f the chemical nature o f a wear

p a r t i c l e on a copper p i n which has been s l i d against an i r o n d i sc i s shown.

The comparison o f the p o s i t i v e images from the Cu-Karadiat ion and the Fe-K,

r a d i a t i o n i n d i c a t e t h a t the wear p a r t i c l e consis ts mainly o f i r on .

Sur face- invest igat ion techniques f o r the analys is o f the topmost sur-

face l aye rs have been developed on ly i n recent years. The main p r i n c i p l e o f

these techniques i s t h a t t he surface is bombarded w i t h photons, e lect rons,

292

Figure 7.25 Example o f an EPMA identification of the chemical nature of a wear particle.

293

Photons hv

E lec t rons e

ions , e t c . and the e m i t t e d p a r t i c l e s which c a r r y some i n f o r m a t i o n about

t h e i r h i s t o r y , a r e analyzed. I n F i g u r e 7.26 a genera l scheme o f t h e va r ious

phys i ca l processes u t i l i z e d i n su r face a n a l y z i n g techn iques i s shown (Ref.

7.60).

ESCA AES,LEED

Photons Photons

E lec t rons E lec t rons

Ions Ions

Neu t ra l p a r t i c l e s Neu t ra l p a r t i c l e s

E l e c t r i c f i e l d

S o l i d su r face

SIMS

Photons E lec t rons fi FIM I Ions i l

Neu t ra l s N

Ions N e u t r a l s Heat E l e c t r i c f i e l d

i I N I k T I E

F igu re 7.26 Methods f o r su r face a n a l y s i s i n t h e monolayer range.

The main techn iques which have been a p p l i e d a l ready i n t r i b o l o g i c a l s tud ies

are :

( e -eA) : AES : Auger e l e c t r o n spectroscopy

( e -eg) : LEE0 : Low energy e l e c t r o n d i f f r a c t i o n

(hv-e) : ESCA : E l e c t r o n s c a t t e r i n g f o r chemical a n a l y s i s

( i -i ) : SIMS : Secondary i o n mass spectroscopy

(E - i ) : FIM : F i e l d i o n microscopy

S

The a p p l i c a t i o n o f these new power fu l s u r f a c e - i n v e s t i g a t i o n techn iques t o

t r i b o l o g i c a l problems i s s t i l l i n i t s beg inn ings . I n t h e f o l l o w i n g , b r i e f

d e s c r i p t i o n s o f t he b a s i c phys i ca l p r i n c i p l e s o f these techn iques toge the r

w i t h re fe rence t o some examples o f t h e i r a p p l i c a t i o n w i l l be g iven. For

294

I ,,noble metal

Copper

S i 1 ver

S t r u c t u r a l arrangement

I ' i r o n and , noble metal

Go1 d

F igure 7.27 L E E D photographs o f i r o n (011) s u r f a c e a f t e r adhesion of noble meta ls (Ref. 7 .61) .

295

more d e t a i l s t h e reader i s r e f e r r e d t o t h e rev iew a r t i c l e s , Ref. 7.61,

7.62, 7.63.

I n t h e AES techn ique, t h e sur face t o be i n v e s t i g a t e d i s bombarded by

a monoenerget ic e l e c t r o n beam ( E =: 3 keV) and t h e energy d i s t r i b u t i o n o f

t he eini t t e d secondary e l e c t r o n s (Auger-el e c t r o n s ) i s measured. The energy

o f t h e Auger e l e c t r o n s i s a f u n c t i o n o f t h e su r face m a t e r i a l . I n t h i s way,

t he cnemical elements a t t h e su r face can be de tec ted , w i t h t h e excep t ion o f

l i g h t chemical elements (hydrogen t o n i t r o g e n ) . Wi th AES a s e m i q u a n t i t a t i v e

a n a l y s i s w i t h a r e s o l u t i o n o f 1/1000 o f a monolayer i s p o s s i b l e . An example

o f t h e a p p l i c a t i o n o f t he AES techn ique i s shown i n F i g u r e 5.7.

I n t h e LEED techn ique, an e l e c t r o n beam o f low energy ( E - 2 0 ... 2000eV)

i s d i f f r a c t e d a t a s i n g l e c r y s t a l su r face . Measured q u a n t i t i e s a re : l o c a -

t i o n , ampl i tude, shape and i n t e n s i t y o f d i f f r a c t i o n spots g i v e n by t h e e l a s -

t i c a l l y d i f f r a c t e d e l e c t r o n s . From t h i s techn ique, i n f o r m a t i o n can be ob-

t a i n e d on the geomet r ic c o n f i g u r a t i o n o f t h e topmost su r face atoms, b u t n o t

on t h e i r chemical na tu re . F i g u r e 7.27 presents LEED p a t t e r n s f o r t h e i r o n

(011) su r face a f t e r adhesive c o n t a c t w i t h nob le meta ls . The s t r u c t u r a l a r -

rangement o f t h e adherent nob le metal on t h e i r o n a f t e r f r a c t u r e o f adhesive

con tac t i s e s s e n t i a l l y t h e same (Ref . 7.61).

FeS04 FeS

170 165 160 155 B ind ing energy (eV)

( a ) Before s p u t t e r i n g

Severe wear sca r

M i l d wear sca r

Unworn su r face

FeS

- 170 165 160 155 B ind ing energy (eV)

( b ) A f t e r 30 s s p u t t e r i n g

F igu re 7.28 S u l f u r (2p) XPS f e a t u r e s f rom wear scars and unworn sur face (Ref. 7.64).

296

The ESCA technique u t i l i z e s the e f f e c t o f p h o t o e l e c t r i c emission o f

surfaces. Oepending on the energy o f t he i n c i d e n t r a d i a t i o n t h e techniques

o f u l t r a v i o l e t pho toe lec t ron spectroscopy (UPS) , extreme UPS (XUPS) and

X-ray photoelect ron spectroscopy (XPS) can be d i s t i ngu ished . The spectrum

o f t he photoelect rons g ives a p i c t u r e o f t he e l e c t r o n i c s t r u c t u r e o f the

su r face l aye rs thus a l l o w i n g conclus ions about t h e i r chemical composi t ion.

With t h i s technique i t i s a l s o p o s s i b l e t o determine the s t a t e o f chemical

bonding o f t he su r face atoms. An example o f t h e a p p l i c a t i o n o f t he ESCA

technique f o r the s tudy o f t he a c t i o n o f t h e l u b r i c a n t a d d i t i v e d ibenzy l -

d i su lph ide under m i l d and severe wear cond i t i ons i s shown i n F igu re 7.28

(Ref. 7.64) (see a l s o Sect ion 5.2.2).

through the bombardement w i t h argon ions ( E :: 3 keV). The i o n s a re then

analyzed by means o f mass spectroscopy. With t h i s technique a l l chemical

elements can be detected. The r e s o l u t i o n o f t h e technique has been repo r ted

t o be b e t t e r than

used t o s tudy the composi t ion o f sur face l a y e r s formed on t h e runn ing sur-

faces o f bo th a p in-on-d isc t r i bomete r and an i n t e r n a l combustion engine

l u b r i c a t e d w i t h a commercial engine o i l (Ref. 7.66). I n t h i s study, t he

spec t ra o f p o s i t i v e and nega t i ve secondary i o n s were measured be fo re and

a f t e r the t e s t runs and the r a t i o o f t he measured i o n i n t e n s i t i e s a f t e r and

be fo re the t e s t runs were determined.

I n the SIMS technique an emission o f i ons f rom the su r face i s obta ined

o f d monolayer (Ref. 7.65). The SIMS technique was

0

c, .r

2 1 10 20 30 40 50 60 70 80 90 100

Mass number

F igu re 7.29 Spectra o f nega t i ve i ons detected w i t h the SIMS technique (Ref. 7.66).

297

Figure 7 .30 FIM micrographs o f tungsten prior and after contact with gold (Ref. 7 . 6 1 ) .

298

Figure 7.31 FIM micrographs o f tungsten p r i o r and a f t e r contact with PTFE (Ref.7.61).

299

With the FIM technique i t i s poss ib le t o get a p i c t u r e o f the atomic

arrangement o f surfaces (Ref. 7.67). As specimen an extremely t h i n t i p o f a

metal w i t h h igh me l t i ng p o i n t ( W , N i , P t ) i s used. This i s subjected t o an

e l e c t r i c f i e l d o f h igh strength, as a r e s u l t o f which p a r t i c l e s are emi t ted

and become v i s i b l e on a f luorescent screen. This microscope i s t r u l y unique

i n t h a t i t i s the on ly device ava i l ab le today which w i l l a l l ow the examina-

t i o n o f i n d i v i d u a l atom s i t e s and surface s t ruc tu res i n atomic d e t a i l . I t

has an atomic r e s o l u t i o n o f 2.5 8. I n Figures 7.30 and 7.31, FIM micrographs

o f a tungsten sur face before and a f t e r contact w i t h the metal gold, and the

polymer po l y te t ra f l uo re thy lene are shown (Ref. 7.61). I t can be seen t h a t i n

a l l cases ma te r ia l from the counterpartner adheres on the tungsten surface.

This then i s the d i r e c t p roo f o f the occurrence o f adhesion on an atomic

scale!

The techniques and a p p l i c a t i o n examples discussed i n t h i s sec t i on i n d i -

cate t h a t very powerful t oo l s f o r surface i nves t i ga t i ons are a v a i l a b l e to-

day. I n combining these techniques w i t h the o the r t r i b o m e t r i c techniques and

the t h e o r e t i c a l t r i b o a n a l y s i s methods and check1 i s t s described i n the next

chapter some f u r t h e r progress i n the d i f f i c u l t f i e l d o f t r i b o t e s t i n g may be

an t i c ipa ted .

300

8 Practical systems methodology

8 , 1 INTRODUCTION

The discussions in the preceding chapters have amply i l l u s t r a t e d the multi-

d i sc ip l inary nature and the tremendous inherent complexity of t r ibology.

I t has been shown, among other things, t h a t f r i c t i o n and wear of material

pa i r s a re n o t i n t r i n s i c material propert ies b u t system-dependent interac-

t ion c h a r a c t e r i s t i c s . I t follows t h a t :

( i )

( i i )

( i i i )

I t i s not possible t o deal with the subject o f t r ibology in simple

terms.

Any proper analysis and solut ion of t r ibological problems require

the consideration of numerous parameters and influencing fac tors

(Ref. 8.1).

Consequently, "monistic" s implif ied approaches t o t r ibo logica l

problems may lead t o grave e r rors in t h a t important parameters or influencing fac tors may be neglected or overlooked (Ref. 7 . 2 ) .

Although most workers in the f i e l d of t r ibology are well aware of these

f a c t s , i t i s a common experience t h a t in publications dealing with f r i c t i o n ,

lubricat ion and wear important parameters a r e often omitted or a re reported

in a manner or in uni t s unsuitable f o r comparison with other r e s u l t s or f o r

fur ther appl icat ions. I f , f o r instance, wear r a t e s a re given in mass uni t s

i t i s often impossible t o ca lcu la te from these data wear r a t e s in terms of

length uni t s required f o r engineering appl icat ions. Other typical omissions

concern the character izat ion of important c h a r a c t e r i s t i c s of system compo-

nents , such as surface roughness data , o r the descr ipt ion of the atmospheric

301

o r env i ronmenta l c o n d i t i o n s . These omissions and shortcomings are , o f

course, n o t i n t e n t i o n a l b u t a r e consequences o f t he mu1 t i d i s c i p l i n a r y na-

t u r e o f t r i b o l o g y . I t i s c l e a r t h a t a p h y s i c i s t o r chemist , who pub l i shes

exper imenta l r e s u l t s o f i n v e s t i g a t i o n s o f f r i c t i o n o r wear processes, i s

main l y i n t e r e s t e d i n d e s c r i b i n g t h e p h y s i c a l o r chemical con ten t o f h i s

i n v e s t i g a t i o n r a t h e r than i n t h i n k i n g o f p o s s i b l e l i n k s o f h i s f i n d i n g s

w i t h eng inee r ing a p p l i c a t i o n s . On t h e o t h e r hand, i t i s o f t e n n o t p o s s i b l e

t o draw b a s i c genera l i zed conc lus ions f rom t h e r e s u l t s o f eng inee r ing i n -

v e s t i g a t i o n s o f t r i b o - t e c h n i c a l components o f machinery. Th is i n t u r n ne-

c e s s i t a t e s the r e p e t i t i o n o f s tud ies a l ready performed b u t i ncomp le te l y

descr ibed iil t h e l i t e r a t u r e and p a r t l y e x p l a i n s the vas t number o f p u b l i -

c a t i o n s produced eve ry y e a r i n t h e f i e l d o f t r i b o l o g y . (As ment ioned i n

Sec t i on 1.3, about 8000 t r i b o l o g i c a l papers a re c u r r e n t l y pub l i shed every

y e a r . ) From a l l t h i s i t f o l l o w s t h a t bo th t h e l a c k o f a conven ien t frame-

work f o r t h e d e s c r i p t i o n o f t r i b o l o g i c a l r e s u l t s and t h e l a c k o f a conve-

n i e n t methodology f o r t he s o l u t i o n of t r i b o l o g i c a l problems fo rm severe

obs tac les t o p rogress . D iscuss ion o f t he m u l t i f a r i o u s aspects o f t r i b o l o g y

f rom a systems p o i n t o f view as presented i n t h e fo rego ing chapters has

p rov ided t h e bas i s f o r a systems approach t o these problems. Fo r t h i s pur -

pose, t he general t h e o r e t i c a l framework as presented i n the t r i b o - p r o c e s s

diagram, F i g u r e 3.4, shou ld be brought i n t o a fo rm s u i t a b l e f o r eng inee r ing

a p p l i c a t i o n s . I n t h e f o l l o w i n g , t he development o f a "da ta sheet" s u i t a b l e

f o r t h e a n a l y s i s and s o l u t i o n o f t r i b o l o g i c a l problems w i l l be desc r ibed

and examples o f t h e a p p l i c a t i o n o f systems methodology w i l l be g i ven (Ref.

8 .2 ) .

8,2 A TRIBOLOGICAL SYSTEMS DATA SHEET

As a s t a r t i n g p o i n t f o r an eng ineer ing systems approach t o t h e a n a l y s i s o f

t r i b o l o g i c a l problems, cons ide r a t y p i c a l t r i b o - t e c h n i c a l system, namely

the gear-box as shown i n F igu re 8.1.

As desc r ibed i n Chapters 2 and 3, t h e two p a r t n e r s which fo rm t h e

" t r i b o l o g i c a l l y i n t e r a c t i n g su r faces " , i . e . , gear 1 and gear 2, can be

h y p o t h e t i c a l l y separa ted f rom t h e i r environment by t h e p roper cho ice o f a

system's envelope. A l l components o f t h e system a r e w i t h i n t h i s envelope

and a r e p a r t o f t h e s t r u c t u r e o f t h e system. The s t r u c t u r e c o n s i s t s o f t h e

elements o f t h e system, t h e i r r e l e v a n t p r o p e r t i e s and t h e i r i n t e r r e l a t i o n s ,

descr ibed f o r m a l l y by t h e s e t S = [ A, P , R 1 .

302

The inputs o f the operat ing var iab les a re transformed through the

s t ruc tu re o f the system i n t o outputs which are used techn ica l l y : the use-

outputs. Sirnul taneously, as a consequence o f the t r i b o l o g i c a l i n t e r a c t i o n s

between the elements, loss-outputs occur, denoted i n summary by the terms

f r i c t i o n and wear losses. The way i n which the inputs are transformed i n t o

outputs determines the technica l funct ion o f the system.

I s = {A, eli ’ Operating

A: Variables n. n--

Use -Outputs ‘t

System‘s Envelope

Loss- Outputs

Figure 8.1 Analysis and desc r ip t i on o f a t r i bo techn ica l system.

From the discussion o f the t r ibo-engineer ing system i l l u s t r a t e d i n F igure

8.1, as wel l as the theo re t i ca l considerations of Chapters 2 and 3, i t

fo l lows t h a t the re levant t r i b o l o g i c a l parameters can be d i v ided i n t o the

fo l l ow ing fou r groups as compiled i n Table 8.1.

I n the next f o u r sections, the main features o f the re levan t para-

meters of these groups w i l l be discussed. Since most o f the various sys-

tems aspects have been already t rea ted i n some d e t a i l i n t he preceding

chapters, the fo l l ow ing considerations w i l l be summarizing i n nature.

303

I I Technical function of the tribo-system I ~~ ~

Transmission of motion, information. energy. materiols

Il7 Operating variables I Type of motion Load. Velocity. Temperature Time Materials flow

Im Structure of the tribo-system I a) Elements

I l l Tribo-element (3) Lubricont I.?) Tribo- element (41 Atmosphere

Relevant geometrical and materials properties of ~1~,121,13),141 b) Properties of elements

cl Relations between elements

Ill7 Tribological characteristics I a1 Tribo- induced chonges of system’s structure

b) Tribo-induced energy losses c) Tribo- induced moterials losses

Table 8.1 Fundamentals o f a systems analys is check l i s t f o r t r i b o - mechanical systems.

8,2,1 TECHNICAL FUNCTION OF THE SYSTEM

I n Section 3 .2 i t was explained t h a t the technica l f unc t i on o f t r i b o l o g i -

ca l systems i s connected w i t h the transmission o r t ransformat ion o f the

bas ic q u a n t i t i e s

- motion

- in format ion

- work

- ma te r ia l s

I n us ing these fou r bas ic q u a n t i t i e s o r r e l a t e d q u a n t i t i e s , the techn ica l

f unc t i on o f the various t r i b o l o g i c a l systems may be c l a s s i f i e d i n terms o f

the input-output r e l a t i o n s o f these q u a n t i t i e s . The p r i n c i p l e s o f the method

o f c l a s s i f y i n g tribo-mechanical systems according t o t h e i r f unc t i on were

i l l u s t r a t e d i n Table 3.2. A more d e t a i l e d c l a s s i f i c a t i o n i s given i n the

Appendix ( A ) .

304

S l i d i n g

.C.p p7

Spin

8,2,2 OPERATING VARIABLES

R o l l i n g

(J$$ Impact

The most c h a r a c t e r i s t i c operat ing va r iab le o f a t r ibo-mcf ian ica l system i s

the type o f r e l a t i v e motion between tr ibo-element (1) and tr ibo-element

( 2 ) . The basic types o f motion are

- s l i d i n g

- r o l l i n g

- sp in

- impact

as i l l u s t r a t e d i n F igure 8.2 f o r the simple case o f the r e l a t i v e motion o f

a b a l l (1) against a plane ( 2 ) .

F igure 8.2 Basic types o f r e l a t i v e motion,

It can be shown t h a t every type o f r e l a t i v e motion between two s o l i d

bodies can be expressed as a superposi t ion o f these f o u r bas ic types o f

motion. I n add i t i on t o the cha rac te r i za t i on o f the type o f motion, i t s

dependence on t ime should be speci f ied, being f o r example:

- continuous

- o s c i l l a t i n g

305

- r e c i p r o c a t i n g

- i n t e r m i t t e n t

The o t h e r o p e r a t i n g v a r i a b l e s a r e t h e f o l l o w i n g q u a n t i t i e s :

- l o a d FN

- v e l o c i t y v

- temperature T

- d i s tance o f mot ion s

- o p e r a t i n g d u r a t i o n t

For some t r i b o l o g i c a l systems, these phys i c 1 o p e r a t i n g v a r i a b l e s r e ac-

companied by m a t e r i a l i n p u t s , e.g., t h e f l o w r a t e o f t h e l u b r i c a n t . Some

d i s t u r b i n g i n p u t s may a l s o be present , e.g., v i b r a t i o n and r a d i a t i o n .

8,2,3 STRUCTURE OF THE SYSTEM

As compi led i n Table 8.1, t h e s t r b c t u r e o f a system i s g i ven by t h e sys-

tem's elements, t h e i r r e l e v a n t p r o p e r t i e s and t h e i r i n t e r r e l a t i o n s , des-

c r i b e d f o r m a l l y by t h e s e t S = [ A , P , R } .

( a ) ELEMENTS OF THE SYSTEM, A = [ ai ]

I f t h e sys tem's envelope ( f o r d e f i n i t i o n , see Sec t ion 2 . 2 ) i s l o c a t e d as

c l o s e l y as p o s s i b l e around t h e " i n t e r a c t i n g su r faces i n r e l a t i v e mot ion" ,

i t appears t h a t i n most t r i b o l o g i c a l systems f o u r d i f f e r e n t b a s i c elements

a r e i n v o l v e d i n t h e f r i c t i o n and wear processes.

I (4) (1) Tr ibo-e lement (moving)

( 2 ) T r ibo-e lement ( s t a t i o n a r y

( 3 ) I n t e r f a c i a l e lement ( l u b r

( 4 ) Environment (atmosphere)

System envelope

cant ,e tc . 1

F igu re 8.3 Bas ic elements o f a t r ibo-mechan ica l system.

306

As i l l u s t r a t e d i n F igu re 8.3, t h e components t h a t fo rm t h e p a i r of t he

" i n t e r a c t i n g sur faces i n r e l a t i v e mot ion" a r e named " t r i bo -e lemen t (1)" and

" t r i bo -e lemen t ( 2 ) " . The o t h e r two b a s i c elements a re t h e l u b r i c a n t ( 3 ) and

t h e environment ( 4 ) .

( b ) PROPERTIES OF THE ELEMENTS, P = ( P(ai))

Any t r i b o l o g i c a l process i s i n f l u e n c e d by many p r o p e r t i e s o f t he bas i c e l e -

ments ( l ) , ( 2 ) , (3), ( 4 ) . Owing t o t h e g r e a t v a r i e t y o f t r ibo-mechan ica l

systems and t r i b o l o g i c a l processes, i t i s v e r y d i f f i c u l t t o p r o v i d e a com-

prehens ive general comp i la t i on o f t h e t r i b o l o g i c a l l y r e l e v a n t p r o p e r t i e s o f

t he systems elements. The f o l l o w i n g p r o p e r t i e s o f t h e elements have been

found t o be o f p r imary concern f o r t he t r i b o l o g i c a l behav iour o f t h e system:

( i ) P r o p e r t i e s o f t h e t r i bo -e lemen ts (1) and ( 2 )

The t r i b o l o g i c a l l y r e l e v a n t p r o p e r t i e s o f t he elements (1) and ( 2 )

can be sub-d iv ided i n t o "volume" p r o p e r t i e s and "su r face" p r o p e r t i e s .

The s tudy o f t h e t r i b o l o g i c a l processes, as d iscussed i n Chapter 4,

has shown t h a t t h e f o l l o w i n g main p r o p e r t i e s o f t h e elements (1) and

( 2 ) a re r e l e v a n t f o r t h e t r i b o l o g i c a l behav iour o f t h e system:

and m e t a l l u r g i c a l

us, hardness,

- Volume p r o p e r t i e s : geometry, chemical compos i t ion

s t r u c t u r e ; m a t e r i a l s da ta , i n c l u d i n g e l a s t i c modu

dens i t y , thermal c o n d u c t i v i t y .

- Sur face p r o p e r t i e s : su r face roughness and su r face

P roper t i es o f t h e l u b r i c a n t ( 3 ) ( i i )

composi ti on.

The main r e l e v a n t p r o p e r t i e s o f t h e l u b r i c a n t a re t h e v i s c o s i t y and

i t s dependence upon temperature and pressure, t oge the r w i t h t h e che-

m ica l compos i t ion o f t h e l u b r i c a n t .

( i i i ) P r o p e r t i e s o f t he environmental atmosphere ( 4 )

The main r e l e v a n t p r o p e r t i e s o f t h e atmosphere are i t s chemical com-

p o s i t i o n and t h e amount and pressure o f i t s components, e s p e c i a l l y

water vapour.

( c ) INTERRELATIONS BETWEEN THE ELEMENTS, R = { R(ai, a j ) )

The t r i b o l o g i c a l i n t e r a c t i o n s between the elements o f a t r i b o l o g i c a l system

were s t u d i e d i n d e t a i l i n Chapter 4 under t h e headings of

- c o n t a c t processes

- f r i c t i o n processes

- wear processes

- l u b r i c a t i o n modes

307

I n F igu re 8.4 t h e b a s i c t r i b o l o g i c a l processes a r e expressed i n the

fo rm o f schematic diagrams f o r systems o f i n c r e a s i n g complex i ty , i.e., i n -

c reas ing number o f i n t e r a c t i n g system's elements (Ref . 7 .16) .

System i n vacuum

c o n t a c t de fo rma t ion - ( 2 ) (1) -surface f a t i g u e

ab ras ion adhesion

I System i n a i r I

t r i bochemica l r e i c t i o n s

de fo rma t ion

ab ras ion -(2) ( 1) J -surface f a t i g u e

adhesion

System l u b r i c a t e d I I I

de fo rmat ion su r face f a t i g u e

(1)- abras ion -(2) adhesion

t r i bochemica l r e a c t i o n s

F igu re 8.4 Schematic r e p r e s e n t a t i o n o f t r i b o l o g i c a l i n t e r a c t i o n s ,

I n t h i s connect ion i t shou ld be emphasized t h a t bes ides t h e f r i c t i o n and

wear processes between the sys tem's elements (1) and ( 2 ) t h e processes o f

d i f f u s i o n and e f f u s i o n between t h e elements ( 3 ) , t h e l u b r i c a n t , and ( 4 ) ,

t he environment, a r e of g r e a t importance f o r t he behav iour of t r i b o l o g i c a l

systems. (The in f l uence o f d i f f u s i o n processes (4)-(3) i s i l l u s t r a t e d

i n F igu re 8.8; f o r an i n s t r u c t i v e example o f e f f u s i o n processes (3)-(4)

see Ref. 8 .3 . )

308

8,2,4 TRIBOLOGICAL CHARACTERISTICS

The t r i b o l o g i c a l c h a r a c t e r i s t i c s may be d i v i d e d i n t o the f o l l o w i n g t h r e e

groups :

( a ) ( b ) Tr ibo- induced energy losses

( c ) Tr ibo- induced m a t e r i a l losses

According t o Chapter 5, t r i b o - i n d u c e d changes o f a system's s t r u c t u r e ( a )

may concern:

( i )

( i i )

( i i i ) changes i n t h e i n t e r r e l a t i o n s between t h e elements, as f o r i ns tance ,

Tr ibo- induced changes o f sys tem's s t r u c t u r e

the d e s t r u c t i o n o f elements o r t he c r e a t i o n o f new elements i n a

t r ibo-sys tem,

changes i n t h e p r o p e r t i e s o f t he elements, f o r ins tance, changes i n

con tac t topography and su r face composi t ion,

changes o f t h e wear mechanisms under t h e a c t i o n o f t h e opera t i ng

va r iab les .

The o t h e r two mairi t r i b o l o g i c a l c h a r a c t e r i s t i c s ( b ) and ( c ) l i s t e d i n Tab le

8.1, i . e . , t h e f r i c t i o n - i n d u c e d energy losses and the wear-induced m a t e r i a l s

losses , may be expressed f o r m a l l y as:

f r i c t i o n losses = f ( o p e r a t i n g v a r i a b l e s ; system's s t r u c t u r e )

wear losses = f ( o p e r a t i n g v a r i a b l e s ; system's s t r u c t u r e )

Consequently, f r i c t i o n c o e f f i c i e n t , f, and wear r a t e , w, o f a t r ibo-mechan i -

c a l system may be expressed f o r m a l l y as:

m f = f ( X ; S )

where X : Opera t ing v a r i a b l e s

S : ( A , P, R ) : System's s t r u c t u r e

Al though the parameter groups X, S , a re n o t independent v a r i a b l e s s ince they

a re connected w i t h each o t h e r th rough t h e t r i b o l o g i c a l i n t e r r e l a t i o n s R , t h e

above symbol ic rep resen ta t i on o f f r i c t i o n and wear c h a r a c t e r i s t i c s can be

conven ien t l y used as s t a r t i n g p o i n t f o r t he p r a c t i c a l a p p l i c a t i o n o f t h e

systems methodology, see Sect ion 8.5.

Summarizing t h e var ious parameters o f t r ibo-mechan ica l systems, a da ta

sheet r e s u l t s as shown i n F igu re 8.5. On t h e b a s i s o f t he general explana-

t i o n s g iven i n t h e l a s t sec t i ons , t he da ta sheet should be s e l f - e x p l a n a t o r y .

309

I 'her op variobles

I Technical function of the tribo-system

Locotion

l7 Operating variables 'pe of motion'J IDurotion of operotion t i 1

Tri bo - element Tri bo - element o ert ies of elements L u bricont Atmosphere 1 4 ) initiol/finall Il l

resignation of element tnd moteriol I

(21 ( 3 )

ianges in properties of the ements6' lvs time t or distonce sl

Friction doto Wear dato Ivs time t or distonce s)

l l e g sliding, roll!ng. oscilloting, reciprocoting.etc 2)the contact pressure p is given by p =%/A 3)velocity of tr ibo-elementl l) relative to tr ibo-elernent/2/ Lltemperature ot stoted location 5)eg density, thermol conductivity, Youngs modulus etc 61eg changes in hordness of lIll2). rhonges in viscosity of/3/, changes in humidity of /Ll,etc

F i g u r e 8.5 T r i b o l o g i c a l systems data sheet .

I

ther characterist icsleg contoct resistonce. vibrotions. noise, etc) Appearonce of worn surfaces

310

8 , 3 THE DESCRIPTION OF TRIBO-ENGINEERING SYSTEMS

With the h e l p o f t he t r i b o l o g i c a l systems da ta sheet, t h e r e l e v a n t parame-

t e r s o f t r i b o - e n g i n e e r i n g systems can be e a s i l y compi led i n a comprehensive

manner. As a t y p i c a l a p p l i c a t i o n example, i n F i g u r e 8.6 t h e c h a r a c t e r i s t i c s

o f a j o u r n a l b e a r i n g opera t i ng a t t h e minimum o f t h e S t r i b e c k curve a r e com-

p i l e d w i t h da ta taken f rom t h e l i t e r a t u r e (Ref . 8.4). The main reason f o r

choosing t h i s example was the f a c t t h a t most o f t he impor tan t parameters o f

t h i s t r i b o - e n g i n e e r i n g system have been r e p o r t e d by t h e i n v e s t i g a t o r o f

Ref. 8.4. I n d i scuss ing t h i s example, o n l y t h e procedure o f comp i l i ng t h e

da ta sheet i s r e a l l y r e l e v a n t here, n o t t he a p p l i e d measuring techniques o r

r e s u l t per se o f t h e quoted i n v e s t i g a t i o n . There fore , o n l y some main fea tu res

o f t h e example a re p o i n t e d ou t .

t r i b o l o g i c a l system:

The da ta sheet c l e a r l y i n d i c a t e s t h e main fea tu res o f t h i s most t y p i c a l

The t e c h n i c a l f u n c t i o n (I) o f t h e system can be descr ibed as "guidance

o f mot ion" .

The opera t i ng v a r i a b l e s (11) are g iven by t h e type o f mot ion, namely

"cont inuous s l i d i n g " o f a d u r a t i o n o f 40 min toge the r w i t h t h e g i ven values

o f l o a d FN, v e l o c i t y v, and b u l k o i l temperature T.

The s t r u c t u r e (111) o f t h e system i s descr ibed by the elements o f t h e

system, t h e i r r e l e v a n t p r o p e r t i e s and i n t e r r e l a t i o n s . I n t h i s case, t r i b o -

element (1) i s g i ven by a bea r ing bushing c o n s i s t i n g o f a l ead - t i n -b ronze

and t r i bo -e lemen t ( 2 ) i s a s t e e l s h a f t . As l u b r i c a n t ( 3 ) a m ine ra l o i l of

t he type SAE 2OW-20 i s used and t h e atmosphere ( 4 ) i s l a b o r a t o r y a i r . To-

ge ther w i t h the des igna t ion o f t h e elements and m a t e r i a l s the da ta sheet

con ta ins a l l impor tan t p r o p e r t i e s o f t h e elements. The da ta sheet a l s o i n -

d i c a t e s the t r i b o l o g i c a l i n t e r a c t i o n s between t h e elements o f t h e system which

can be cha rac te r i zed as a " runn ing - in " p e r i o d l e a d i n g t o topograph ica l chan-

ges which a re w i t h i n t h e i n i t i a l roughness o f t he bear ing bush element ( 2 ) .

t e r i z a t i o n o f wear r a t e s . A l though t h e o r i g i n a l wear r a t e s a r e g i ven i n mass

u n i t s , s ince t h e dimensions o f t h e bear ing a re given, i t i s p o s s i b l e t o es-

t i m a t e wear- t ime r a t e s and wear -d is tance ra tes . Because t h e wear measurements

have been performed by means o f r a d i o - t r a c e r techniques, i t i s p o s s i b l e t o

d i s t i n g u i s h between the wear r a t e s o f t r i bo -e lemen t ( l ) , t h e bear ing bushing,

and t r i bo -e lemen t (Z), t h e bear ing s h a f t .

As t r i b o l o g i c a l c h a r a c t e r i s t i c s ( I V ) emphasis i s l a i d i n t h e charac-

311

. o o d 2 ’ 6 ( t ) [ N 1

FNrj 7000

0 20 40 t (min)

I Technical function of the tribo-svstem

~ e l o c t ty v(t)[m/sl Temperature” T ( t ) [ O C /

v 1 F l 0 20 40 0 20 40

t ( m i n l t (min)

Journa l bear ing : guidance o f mot ion

ll Operating variables IDurotton of operotton t 40 min ‘pe Of motton” cont inuous s l i d i n g

o erttes of dements tntttal/kndrC

lestgnotton of element md moteriol

Trlbo-element Tribo-element (11 (21

bush ing s h a f t bronze s t e e l

m ine ra l o i l SAE 20 W 20

a i r

91

other5’ (thermal c o n d u c t i v i t y I 45 kcal/mh°C I 3 kcal/mh°C

d = 65 mm Geometry/Dtrnenstons/ / d = o. Volume

Chemical composition 15 Pb; 7 Sn 0.2 C ; 0.8 Mo 78 Cu 0.2 C r ; 0.4 V

VI Topography descriptors 2 I (c /o . ,e tc) R, (p) I 2 .5 - 3 .0 1 0.5

k Phys.-mech. doto: 2 Hardness (N/mm ) Viscosity q(T,pl

g Surface layer doto glSf different from volume1 I ~

H=700 H=2630

I -

ianges /n properties of the ements6’

Lubricant I Atmosphere

briction doto Ivs Itme t or distance sl

~ I - T =130 cP/20°C 7 =17. 5cP/8O0C

dens i t y :

Other do t o : r a d i a1 c lea rance

ratio:shaft r a d i u s (Jr= 0.2 %

erocttons

up iuortcarion moae qua> I -riyur uuyridiii I L 1 rj/-14/

Minimum o f S t r i b e c k curve

rher characteristics /eg contact reststonce, vtbrotions, noise, etcl

Wear dato

Appeorance of worn surfoces

( 1 ) : r u n - i n

( 2 ) : s l i g h t l y roughened

F igu re 8.6 D e s c r i p t i o n o f a j o u r n a l bea r ing .

312

I n a s i m i l a r manner as t h e example descr ibed i n F igu re 8.6, t h e char -

a c t e r i s t i c s o f o t h e r t r i b o - e n g i n e e r i n g systems can be descr ibed w i t h t h e

he lp o f t he t r i b o l o g i c a l systems data sheet. F o r an adequate d e s c r i p t i o n

o f t h e var ious t r i b o - e n g i n e e r i n g systems, t h e da ta sheet may be i n d i v i d u a l l y

mod i f i ed , .i .e. shortened, extended o r grouped i n another o rde r . However, i n

a l l a p p l i c a t i o n s , t h e t o t a l o f t h e f o u r groups o f parameters as compi led i n

Table 8.1 shou ld be taken i n t o account i n any case.

8 ,4 THE PRESENTATION OF FRICTION AND WEAR RESEARCH DATA

The i n t r o d u c t o r y remarks o f t h i s chapter have amply demonstrated t h e need

f o r a use fu l framework f o r t he r e p r e s e n t a t i o n o f f r i c t i o n and wear research

data. I t i s impor tan t t h a t r e s u l t s be presented i n a fo rm s u i t a b l e f o r sub-

sequent independent e v a l u a t i o n and, i f poss ib le , c o r r e l a t i o n w i t h r e s u l t s

ob ta ined from o t h e r sources. The va lue o f a l l work, whether bas i c o r app l i ed ,

would be g r e a t l y inc reased i f some bas ic standards o f r e p o r t i n g exper imenta l

v a r i a b l e s would be accepted. I n the f o l l o w i n g , t he a p p l i c a t i o n o f t h e tri-

b o l o g i c a l systems da ta sheet t o the p r e s e n t a t i o n o f f r i c t i o n and wear re -

search da ta w i l l be i l l u s t r a t e d i n d i scuss ing two examples.

I n F igu re 8.7, t h e r e l e v a n t parameters and da ta o f an i n v e s t i g a t i o n o f

a s l i d i n g c o b a l t - c o b a l t couple under c o n d i t i o n s o f h i g h vacuum a re l i s t e d

(Ref. 8.5). I n t h i s case, t he t r ibo-sys tem, a p in -on-d isc apparatus, con-

s i s t s o f o n l y the two elements (1) and ( 2 ) . The t r i b o l o g i c a l systems data

sheet c l e a r l y shows the main fea tu res o f t h i s t r ibo-system, namely:

( i )

( i i )

t he inc rease o f t h e sys tem's temperature w i t h i n c r e a s i n g s l i d i n g

ve l o c i ty , t h e d i f f e r e n c e s i n the r a t i o o f c o n t a c t area t o t o t a l wear t r a c k , E , f o r t h e t r i bo -e lemen t (1) and t r i bo -e lemen t ( 2 ) l e a d i n g t o d i f f e r e n -

ces i n t h e thermal s i t u a t i o n s o f (1) and ( 2 ) ,

( i i i ) t h e t rans fo rma t ion o f t h e c r y s t a l s t r u c t u r e o f t he p i n a t a c e r t a i n

( i v )

temperature,

t h e changes o f f r i c t i o n and wear behav iour w i t h i n c r e a s i n g s l i d i n g

v e l o c i t y as a consequence o f ( i ) , ( i i ) , ( i i i ) .

I n another example, shown i n F igu re 8.8, t h e da ta o f a research s tudy w i t h

a b a l l - o n - c y l i n d e r t r i b o - t e s t i n g system a r e compi led (Ref. 8.6). By c o n t r a s t

w i t h t h e fo rego ing example, i n t h i s example t h e t r i b o l o g i c a l system c o n s i s t s

o f f o u r elements, i .e . , a s l i d i n g s t e e l - s t e e l coup le ( l ) , ( 2 ) , t oge the r w i t h

Figure 8.7 Example o f the representat ion o f f r i c t i o n and wear research data.

I Technical function of the tribo-system F r i c t i o n and wear t e s t w i t h pin-on-disc apparatus

Il Operating variables Type of motion": continuous s l i d i n g Durotion of operotion t l h 1. 7 h run - in t ime

~ o a d " G ( t ) [ N ] ~ e l o c r t ~ ~ ' v ( t ) l m / J ~ e m ~ e r a t u r e " TTI~I[OC I

FN=10 N = const.

(10 steps) ,' 8.6

Other op variables: from contact surface

lU Structure of the tribo-system Properties, of dements

l ~ n r t i o l / k ~ b ~ Desrgnation of element ond material

I Trrbg-element 1 171

p i n CO (polycryst:

Tribo-element (21

d isc CO ( p o l y c r y s t )

Lubricant (31

Atmosphere (4)

Figure 8.8 Example o f the representat ion o f f r i c t i o n and wear research data.

I T e c h n i c a l function of t h e tribo-system F r i c t i o n and wear t e s t w i t h ba l l -on -cy l inder apparatus

II O p e r a t i n g v a r i a b l e s Type Of motion"' continuous s l i d i n g Duration of operation t 100 min

~ o o d " % ( f ) [ N / velocity3' v/t)[m/ 4 Temperature" TTlt)lOc I

1 lot (min)loO 1 t1° (min) 100 1 lot (minfoO

Other op voriobles: A

Locotion: ambj en t

lU Structure of the t r i b o - s y s t e m Tribo-element

111 b a l l 52100 steel

d=12.7

0.98 C 1.50 C r

Rc= 61

0.02 - 0.05

-

Pro erties, of elements L i t i a / / ~

Designation of element and rnoteriol

Atmosphere 14 1

(A):Ar, 1 (B ) :a ic d ry 1 dry

100 ~ r i 80 N2 , 20 0,

-

Tribo-element

c y l i nder 52100 s tee l

d=44.4 mn

0.98 C 1.50 Cr

Rc' 20

al.S 5' E H

4

3 .: U L 2 $,O '40

Contact area ~ l m d Tribological interactions: (A): (0):

App. lubrication mode: mixed 1 u b r i ca t ion (3)-

ll? T r i b o l o g i c a l characteristics Friction doto Wear doto

Formation and rubbing away o f

t (min)

Lubricant

base o i l (Bay01 35)

- hydrocarbon (h igh ly r e f . )

7 /25Oc=2.5 CP

Geometry/Dimensions/ Volume

Chemical composition

Phys.-mech. dato: Hardness (Rockwell ) Viscosity qlT.pl otherS'

Topography descriptors ic.l.o..etclcl a (pm) Surface layer data Cf different from volume)

Other characteristics(e.g.: contact resrstonce, vibrations. noise, etcl:

0.25 - 0.33

-

Appearance of worn surfaces:

Corrosive wear phenomena

other doto: impur i t i es i n ( 4 ) : (A): 5 ppm water

20 ppm 0 (B): 20 ppm w%ter

315

a l u b r i c a n t ( 3 ) and the atmosphere (4). I n t h i s i nves t i ga t i on , the i n f l uence

o f d i f f e r e n t atmospheric environments on the t r i b o l o g i c a l behaviour o f l u -

b r i c a t e d s tee l - s tee l contacts was studied. Also i n t h i s case, the compila-

t i o n o f the experimental data i n the form o f a t r i b o l o g i c a l data sheet has

the advantage t h a t a l l r e levan t parameters are reg is tered. The main features

o f t h i s f r i c t i o n and wear t e s t , which was run under a constant s e t o f operat-

i n g var iab les (F,,,, v, T), are given by the d i f f e rences i n the t r i b o l o g i c a l

i n t e r a c t i o n s between the f o u r elements ( l ) , ( 2 ) , ( 3 ) , (4) . I f d ry argon i s

used as atmosphere, the element (4) i s an " i n e r t " one. If, i n contrast , d r y

a i r i s used as atmosphere (4), the d i f f u s i o n o f atmospheric oxygen i n t o the

l u b r i c a n t (4)-(3) connected w i t h tr ibo-chemical processes (4), (3)---( 1),

( 2 ) d i s t i n c t l y in f luences the f r i c t i o n and wear mechanisms. This leads t o

remarkable d i f f e rences i n the f r i c t i o n and wear data o f t he systems (A) and

( 6 ) . These examples - which could e a s i l y be supplemented by examples from

o the r s tud ies - c l e a r l y i l l u s t r a t e the advantages o f a compi la t ion o f the

re levan t t r i b o l o g i c a l parameters i n the form o f t r i b o l o g i c a l systems data

sheets. The pub l i ca t i ons quoted here are excep t iona l l y deta i led. Neverthe-

less, two items on the data sheets had t o be estimated. However, t r i b o l o -

g i s t s w i l l be f a m i l i a r w i t h the problem o f comparing the work o f d i f f e r e n t

authors. As mentioned above, i t i s u s u a l l y found t h a t some important para-

meters, requi red f o r comparative s tud ies o r f o r the a p p l i c a t i o n o f t he study

t o pract ice, are missing. I f, i n f u t u r e publ icat ions, authors would add such

a t r i b o l o g i c a l systems data sheet no re levan t parameter would be omi t ted and

the usefulness of the pub l i ca t i ons would be much enhanced (Ref. 8.7). Another

major p r a c t i c a l aspect i s t h a t data banks are being compiled f o r many as-

pects o f technology. A f i r s t step f o r t r i b o l o g y would be the use o f standard

data c h e c k l i s t s as developed here.

8.5 APPLICATION OF SYSTEMS METHODOLOGY TO THE SOLUTION OF

TR I BOLOG I CAL PROBLEMS : SOME CASE STUD I ES

I n concluding t h i s t r e a t i s e on t r i bo logy , the app l i ca t i on o f systems tech-

niques t o the s o l u t i o n o f p r a c t i c a l t r i b o l o g i c a l problems should be ou t l i ned .

AS emphasized throughout t h i s volume, i n attempts t o reach a systematic so lu-

t i o n o f t r i b o l o g i c a l problems, the whole s e t o f the fou r bas ic groups o f sys-

tems parameters discussed i n Section 8.2 and t h e i r interdependencies must be

taken i n t o considerat ion under the headings:

316

I Technical f u n c t i o n o f t h e system

I 1 Opera t ing v a r i a b l e s

111 S t r u c t u r e o f t h e system

I V T r i bo l o g i ca l c h a r a c t e r i s t i c s

Again, t he e s s e n t i a l p o i n t i s t h a t o n l y by sys temat i c c o n s i d e r a t i o n of a l l

main v a r i a b l e s o f t h e f o u r bas i c groups o f parameters can o v e r s i g h t o f i m -

p o r t a n t i n f l u e n c i n g f a c t o r s be avoided. Once t h i s "systems t h i n k i n g " i s

adopted, t h e a p p l i c a t i o n o f systems methodology t o t h e s o l u t i o n o f t r i b o l o -

g i c a l problems appears t o be a q u i t e s t r a i g h t f o r w a r d a p p l i c a t i o n o f " t ech -

n o l o g i c a l common sense" on a broad sca le .

l u s t r a t e sys temat ic approaches t o the s o l u t i o n o f t r i b o l o g i c a l problems f rom

d i f f e r e n t c lasses o f t r i b o - e n g i n e e r i n g systems, components and processes as

w e l l as t o i l l u s t r a t e m a t e r i a l - s e l e c t i o n procedures, wear - reduc t ion a t tempts

and f a i l u r e analyses. I n most cases, t he s o l u t i o n o f t he problem has been

ob ta ined by a combinat ion o f systems methodology and l a b o r a t o r y t r i b o - t e s t i n g

(see Sect ions 7 . 2 and 7 .3) . Whi le t h e t r i b o l o g i c a l da ta sheet developed i n

Sec t i on 8.2 served as a conven ien t " c h e c k - l i s t " f o r t he c o n s i d e r a t i o n o f per -

t i n e n t parameters, f o r t h e sake o f b r e v i t y , i n the case s t u d i e s o n l y the main

r e l e v a n t parameters a r e i n d i v i d u a l l y compi led and o n l y t h e main s teps o f t h e

s o l u t i o n o f t he problem a re o u t l i n e d . The examples presented i n t h e f o l l o w i n g

i n d i c a t e t h a t p roper s o l u t i o n s of t r i b o l o g i c a l problems can be ob ta ined by

d i f f e r e n t means, f o r example change o f design (see Sect ion 8.5.5), app rop r i -

a te m a t e r i a l and l u b r i c a n t s e l e c t i o n (see Sec t ion 8.5.2, 8.5.3 and 8.5.4)

app rop r ia te i n t e r f a c i a l and environmental c o n d i t i o n s (see Sec t ion 8.5.6 and

8.5.8), app rop r ia te ope ra t i ona l ranges o f load , v e l o c i t y o r temperature (see

Sec t ion 8.5.1 and 8.5.7) i n connect ion w i t h t h e o t h e r systems parameters o f

t he problem under d iscuss ion .

The case s t u d i e s discussed i n b r i e f i n t h e f o l l o w i n g a r e chosen t o il-

8 , 5 , 1 I N V E S T I G A T I O N OF THE VALIDITY OF "COULOMB-FRICTION"

FOR POLYMER-STEEL SLIDING PAIRS

( a ) PROBLEM

Polymer-steel p a i r s t o be used i n a p r e c i s i o n eng ineer ing a p p l i c a t i o n under

d ry s l i d i n g c o n d i t i o n s should e x h i b i t a ( l o w ) f r i c t i o n c o e f f i c i e n t wh ich

must be cons tan t under va ry ing opera t i ng cond i t i ons . The c o n d i t i o n s f o r con-

s t a n t "Cou lomb- f r i c t i on " o f s u i t e d po lymer -s tee l p a i r s a r e t o be s p e c i f i e d .

317

( b ) APPROACH

The "Amontons-Coulomb l a w " o f d r y s l i d i n g f r i c t i o n s t a t e s t h a t t h e f r i c t i o n

c o e f f i c i e n t f i s i n d e p e n d e n t o f l o a d FN and g e o m e t r i c a l a r e a o f c o n t a c t A.

and t h u s i n d e p e n d e n t o f t h e nomina l c o n t a c t p r e s s u r e po = FN/Ao ( s e e Sec-

t i o n 4 . 3 . 2 ) . I n a d d i t i o n , f o r l o w s l i d i n g v e l o c i t i e s v, i t i s o f t e n assumed

t h a t t h e f r i c t i o n c o e f f i c i e n t i s a l s o i n d e p e n d e n t o f t h e s l i d i n g v e l o c i t y v .

I n c o n t r a s t , many " d e v i a t i o n s f r o m C o u l o m b - f r i c t i o n ' ' have been r e p o r t e d i n

t h e l i t e r a t u r e , so t h a t a s y s t e m a t i c s t u d y o f t h e dependence o f t h e f r i c t i o n

c o e f f i c i e n t on t h e v a r i o u s sys tem p a r a m e t e r s has t o be p e r f o r m e d .

T h e o r e t i c a l l y , f r o m a systems v i e w p o i n t , t h e f r i c t i o n o f a g i v e n s l i d -

i n g p a i r depends on b o t h t h e s e t o f o p e r a t i n g v a r i a b l e s and t h e s y s t e m ' s

s t r u c t u r e . As d e s c r i b e d i n S e c t i o n 8 .2 .4 t h i s can be e x p r e s s e d f o r m a l l y as:

f r i c t i o n c o e f f i c i e n t = f ( o p e r a t i n g v a r i a b l e s ; s y s t e m ' s s t r u c t u r e )

o r f = f ( X ; S )

T h e r e f o r e , t h e f o l l o w i n g p a r a m e t e r s , a t l e a s t , mus t be c o n s i d e r e d as p o t e n -

t i a l i n f l u e n c i n g v a r i a b l e s :

O p e r a t i n g v a r i a b l e s , [ X ] :

FN : l o a d , o r c o n t a c t p r e s s u r e

v : s l i d i n g v e l o c i t y

T : t e m p e r a t u r e

s : s l i d i n g d i s t a n c e

S y s t e m ' s s t r u c t u r e S = [ A , P, R ] : { A ] : e l e m e n t s o f t h e sys tem

(1) p o l y m e r ( t o be s p e c i f i e d )

( 2 ) s t e e l ( A I S I 52100)

( 3 ) a i r

{ P I : r e l e v a n t p r o p e r t i e s o f (I), ( Z ) , ( 3 )

( R } : f r i c t i o n a l i n t e r r e l a t i o n s between (l), ( Z ) , ( 3 )

C l e a r l y , t h e i n f l u e n c e s o f t h e many p o t e n t i a l p a r a m e t e r s can be s t u d i e d o n l y

i n c a r e f u l l y c o n t r o l l e d l a b o r a t o r y t e s t s . A l i t e r a t u r e s e a r c h shows ( s e e f o r

example Ref . 8 . 8 and 8 . 9 ) t h a t f r o m t h e m a t e r i a l s c o m m e r c i a l l y a v a i l a b l e a t

p r e s e n t , t h e f o l l o w i n g p o l y m e r s may e x h i b i t a l o w c o e f f i c i e n t o f f r i c t i o n

( f = 0.1) i f s l i d i n g a g a i n s t s t e e l :

p o l y t e t r a f l u o r e t h y l e n e (PTFE)

h i g h d e n s i t y p o l y e t h y l e n e (HDPE)

I n us ing these mate r ia l s i n connection w i t h t h e ranges o f operat ing v a r i -

ables given by the engineering a p p l i c a t i o n condit ions, f r i c t i o n t e s t s were

performed w i t h a pin-on-disc t r ibometer u t i l i z i n g the two-component fo rce

transducer described i n Sect ion 7.2.3. (For fu r the r d e t a i l s o f the tribome-

te r , see Ref. 8.10.) I n Table 8.2, the t e s t condi t ions are l i s t e d .

Table 8.2 Conditions o f f r i c t i o n tes ts .

319

( c ) RESULTS

I n F igu re 8.9 t h e v a r i a t i o n o f f r i c t i o n c o e f f i c i e n t o f t h e PTFE-steel and

HDPE-steel s l i d i n g p a i r s as a f u n c t i o n o f bo th c o n t a c t p ressure p and s l i d -

i n g v e l o c i t y v and an ambient temperature o f T = 23OC i s shown. I n a d d i t i o n ,

f o r PTFE-steel t h e f ( p , v ) curves f o r an ambient temperature o f T = 7OoC

a r e a l s o p l o t t e d (b roken l i n e s ) . The exper imenta l r e s u l t s show t h a t two

f r i c t i o n regimes can be d i s t i n g u i s h e d :

( i ) a l o w - f r i c t i o n regime w i t h an approx imate ly cons tan t c o e f f i c i e n t o f

f r i c t i o n , i . e . ,

f = 0.04 2 0.01 PTFE-steel

f = 0.12 0.02 HDPE-steel

f o r 2 p = 0.6 - 6 N/mm

v = 0.01 - 1 mm/min

( i i ) a h i g h - f r i c t i o n regime w i t h an i n c r e a s i n g c o e f f i c i e n t o f f r i c t i o n ,

i .e.,

f = 0.05 - 0.35 PTFE-steel

f = 0.10 - 0.35 HDPE-steel

f o r p = 0.6 - 6 N/mL

v = 1 mm/min - 10 m/min

I n t h e two d i f f e r e n t f r i c t i o n regimes, d i f f e r e n t appearances o f t h e s l i d i n g

su r faces a r e a l s o found w i t h repeated s l i d i n g , as shown i n F i g u r e 8.10. I n

t h e l o w - f r i c t i o n regime (i) a t h i n o r i e n t e d f i l m , t h i ckness d = 20 nm, i s

observed, whereas i n t h e h i g h - f r i c t i o n regime ( i i ) t h e polymer t r a n s f e r r e d

t o the s l i d i n g s t e e l coun te r face c o n s i s t s o f lumps o f polymers o f a t h i c k -

ness up t o severa l pm. (Fo r a d i scuss ion o f t h e p h y s i c a l mechanisms o f t h e

d i f f e r e n t s l i d i n g behav iour i n regimes ( i ) and ( i i ) see Ref. 8.10 and 8.11.)

( d ) FOLLOW-UP

The r e s u l t s o f t h i s s tudy c o n f i r m t h e w e l l known f a c t t h a t v e r y l ow c o e f f i -

c i e n t s o f f r i c t i o n f o r d r y PTFE-steel s l i d i n g p a i r s can be ob ta ined. How-

ever, “Cou lomb- f r i c t i on ” , i .e., a cons tan t f r i c t i o n c o e f f i c i e n t independent

o f c o n t a c t p ressure and s l i d i n g v e l o c i t y i s found approx imate ly o n l y under

very l i m i t e d c o n d i t i o n s : i n t h e genera l case, t h e dependence o f t h e f r i c t i o n

c o e f f i c i e n t on b o t h t h e s e t o f o p e r a t i n g v a r i a b l e s (FN, v, T, s ) as w e l l as

on t h e system’s s t r u c t u r e S = { A , P, R ] must be taken i n t o cons ide ra t i on .

For t h e eng ineer ing a p p l i c a t i o n under ques t i on , t h e o p e r a t i n g c o n d i t i o n s

320

Figure 8.9 Friction coefficient of polymer-steel sl iding pairs as a function of velocity v and pressure p.

2 p = 6 .2 N/INII

v = 0.01 m/min

T = 70 OC

2 p 0.6 N/mm

v = 10 m/min

T = 70 O C

Figure 8.10 Appearance of steel surface a f t e r sliding against PTFE.

321

shou ld be w i t h i n t h e l i m i t s o f t h e above regime ( i ) i n o rde r t o o b t a i n a

low f r i c t i o n c o e f f i c i e n t o f an approx imate ly cons tan t va lue .

8,5,2 CHARACTERIZATION O F THE TRIBOLOGICAL BEHAVIOUR OF WEAR-RESISTANT DIFFUSION SURFACE COATINGS

A c h a r a c t e r i z a t i o n o f t h e wear r e s i s t a n c e o f newly developed su r face t r e a t -

ments ( b o r i d i n g , vanad iz ing) i n comparison w i t h su r face t rea tments a l ready

used i n p r a c t i c a l t r i b o - e n g i n e e r i n g a p p l i c a t i o n s ( c a r b u r i z i n g , n i t r i d i n g )

i s t o be made.

( b ) APPROACH

Wear - res i s tan t su r face coa t ings a r e used i n d i f f e r e n t t r i b o - e n g i n e e r i n g

a p p l i c a t i o n s under b road ly v a r y i n g cond i t i ons . Since a t t h e development

stage o f new su r face t rea tments , s u i t a b l e eng ineer ing a p p l i c a t i o n c o n d i t i o n s

a re u s u a l l y s t i l l n o t s p e c i f i e d , a c h a r a c t e r i z a t i o n o f t h e wear behav iour o f

these coa t ings i n general terms i s necessary. I n Sec t i on 4.4 i t was empha-

s-ized t h a t wear i s n o t a s i n g l e process b u t a v a r i e t y o f processes. To char -

a c t e r i z e ( o r c o n t r o l ) wear, each o f these processes must be i s o l a t e d and

s t u d i e d independent ly . From a systems v iewpo in t , t h e wear o f a g i v e n s l i d i n g

p a i r depends - l i k e f r i c t i o n - on bo th t h e s e t o f o p e r a t i n g v a r i a b l e s and

the sys tem's s t r u c t u r e . As descr ibed i n Sec t i on 8.2.4, t h i s can be expressed

f o r m a l l y as:

wear r a t e = f ( 0 p e r a t i n g va r iab les ; System's s t r u c t u r e )

w = f ( X ; S )

Therefore, t o c h a r a c t e r i z e the wear r e s i s t a n c e o f t h e su r face coa t ings the

f o l l o w i n g parameters must be cons idered:

Opera t ing v a r i a b l e s , ( X ] :

FN : load ,o r c o n t a c t p ressure p

v : s l i d i n g v e l o c i t y

T : tempera ture

s : s l i d i n g d i s tance

System's s t r u c t u r e , S = { A , P, R } :

( A ] : elements o f t h e system ( t o be s p e c i f i e d below)

( P ) : p r o p e r t i e s o f t h e elements ( t o be s p e c i f i e d below)

322

Hardness o f base mater ia l H ( load 100N)

"C N/mm2)

[ R ) : wear mechanisms:

- sur face fa t i gue

- abrasion

- adhesion

- tri bo-oxidation

It fo l lows t h a t i n order t o character ize the t r i b o l o g i c a l behaviour o f

wear- res is tant surface coatings, the mater ia ls should be s tud ied succes-

s i v e l y under d i f f e r e n t condi t ions i n which on ly one o f the fou r basic wear

mechanisms p reva i l s . I n the fo l lowing, on ly the adhesive and the abrasive

wear resistance o f some d i f f u s i o n surface coatings w i l l be characterized.

I n Table 8.3 the mater ia ls , surface treatments and re levant mater ia l pro-

p e r t i e s are l i s t e d .

6 100 3480 2740 2780

Surface roughness R, (PI

Table 8.3 Proper t ies of surface coatings.

The adhesive wear res is tance o f the surface-treated ma te r ia l s ( A ) - ( D )

s l i d i n g against themselves has been tested i n vacuum where the formation o f

p r o t e c t i v e t r i bochemica l l y formed i n t e r f a c i a l l aye rs i s reduced and thus the

adhesion component i s the dominating wear process. The abrasive wear res i s -

tance has been stud ied w i t h a disc-on-abrasive-paper technique where the

abrasive "micro-cutt ing" process i s the dominating wear process. (For f u r t h e r

d e t a i l s see Ref. 8.12.)

323

I

lo4

lo3

: lo2 W u 5 m

.r v) W L

L 1 m 10

W > .tJ

W (Y

.c

a 1 7

10-1

lo2

.," lo1

W U c 4 * ul W L

L

3

W >

3 1

.r-

2 10-1 7

W CT

-9 p in -on -d i sc ; vacuum 10 b a r

FN= 10 N ; v= 0.1 m/s

T = 23 C; s = 1 km 0

( A ) ( 6 ) ( C ) ( i ) adhes ive wear behav iour

abrasive-paper-on-disc; corundum paper grade 220

p = 1.9 N/cm2; n = 125 rpm 0 T = 23 C ; t = 6 rnin

c m w bul d EO v u

N O

( A ) ( 5 ) ( C ) (D) ( i i ) ab ras i ve wear behav iour

F i g u r e 8.11 Wear r e s i s t a n c e o f s u r f a c e coa t ings t e s t e d under (i) adhesive and ( i i ) ab ras i ve wear cond i t i ons .

324

vacuum: lo-’ bar

FN = 10 N; v = 0.1 m/s; T = 23 C; s = 1 km - 10 pm

0

Figure 8.12 Appearance o f wear surfaces o f pins a f t e r t e s t i n g i n vacuum.

325

( d ) RESULTS

I n F igu re 8.11 t h e r e l a t i v e wear r e s i s t a n c e o f t h e su r face coa t ings under

c o n d i t i o n s o f adhesive wear and ab ras i ve wear t o g e t h e r w i t h t h e a p p l i e d t e s t

c o n d i t i o n s i s shown w i t h t y p i c a l r e s u l t s .

cor respond ing appearance o f worn sur faces , shown i n F i g u r e 8.12 i n d i c a t e

t h a t t h e n i t r i d e d su r face coa t ings e x h i b i t t h e b e s t wear - res is tance behav-

i o u r . The poores t wear r e s i s t a n c e has been found f o r t he ( v e r y ha rd ) vana-

d i zed s t e e l . I n t h i s case, t h e su r face -coa t ing l a y e r was pene t ra ted so t h a t

t h e adhesive wear a c t i o n extended t o the ( s o f t ) base m a t e r i a l . I t shou ld be

ment ioned t h a t t h e adhesive wear r e s i s t a n c e o f t h e b o r i d e d coa t ing , which

a l s o shows a r e l a t i v e l y poor behav iour accord ing t o F i g u r e 8.11, i s markedly

improved i f oxygen i s a v a i l a b l e . I n t h i s case, t h e adhesive wear r e s i s t a n c e

of bo r ided s t e e l i s c l e a r l y b e t t e r than t h a t o f case-hardened s t e e l .

I n t h e adhesive-wear s i t u a t i o n , t he measured wear r e s i s t a n c e and t h e

I n c o n t r a s t , i n t h e abrasive-wear s i t u a t i o n , t h e b e s t w e a r - r e s i s t a n t

behav iour i s found f o r t h e vanadized su r face coa t ing . As desc r ibed i n Sec t i on

4.4.3, t h i s behav iour can be exp la ined i n terms o f t h e hardness o f t h e t e s t e d

m a t e r i a l s and the abras ive . Since corundum, which was used as an ab ras i ve

(hardness HV = 17000 N/mm ) , i s cons ide rab le ha rde r than bo th t h e case-hard-

ened s t e e l ( A ) and t h e n i t r i d e d s t e e l ( B ) , bo th m a t e r i a l s ( A ) , ( B ) a r e i n t h e

"severe wear" regime, whereas the bo r ided s t e e l ( C ) and t h e vanadized s t e e l

( 0 ) a r e s t i l l i n t h e " m i l d wear" regime due t o t h e i r h igh hardness. I f t h e

t e s t s were performed w i t h a s i l i c o n ca rb ide ab ras i ve paper (HV = 27000 N / m m ) ,

t h e b o r i d e d s t e e l a l s o changes t o the severe wear regime, whereas t h e vana-

d i zed s t e e l remains i n t h e m i l d wear regime.

of some d i f f u s i o n su r face coa t ings show t h a t under t h e choosen t e s t cond i -

t i o n s a q u i t e d i f f e r e n t ( i n f a c t , a reve rse ) r a n k i n g o f t h e su r face coa t ings

i n o r d e r o f m e r i t i s found i n t h e two cases:

( i ) adhesive wear r e s i s t a n c e : 1. n i t r i d i n g

2

2

I n summary, t h e s t u d i e s on t h e adhesive and t h e ab ras i ve wear r e s i s t a n c e

2. case harden ing

3. b o r i d i ng

4. vanad iz ing

( i i ) ab ras i ve wear r e s i s t a n c e : 1. vanad iz ing 2. b o r i d i n g

3. case harden ing

4. n i t r i d i n g

326

( d ) FOLLOW-UP

The r e s u l t s o f t h i s s tudy c o n f i r m t h a t f o r a p r e - c h a r a c t e r i z a t i o n o f t h e

wear behav iour o f su r face coa t ings besides t h e opera t i ng c o n d i t i o n s the

dominat ing wear mechanism must be known. It fo l l ows t h a t d i f f e r e n t su r face

t rea tments may be suggested t o be used i n d i f f e r e n t t r i b o - e n g i n e e r i n g appl i-

cat ions . For example, f o r t he p reven t ion o f severe adhesive wear ( o r scu f -

f i n g ) o f gears, n i t r i d i n g may be s u i t a b l e whereas f o r t h e m i t i g a t i o n o f

ab ras i ve wear a t t a c k , as i n dredge pumps, vanad iz ing may be bes t .

8,5 ,3 MATERIAL SELECTION FOR OFF-SHORE B E A R I N G APPLICATION

(a ) PROBLEM

A m a t e r i a l s e l e c t i o n f o r a j o u r n a l bea r ing o p e r a t i n g a t 30 m below sea l e v e l

(component o f anchor-buoy) has t o be made. Accord ing t o the dimensions o f

the j o u r n a l bear ing , a l i n e a r wear r a t e o f 0.6 pm/h o f t h e bear ing bush ing

corresponds t o a s p e c i f i c wear r a t e o f approx imate ly 4 mm /Nm. Because

o f s t r e n g t h cons ide ra t i ons , t he wear r a t e o f t h e j o u r n a l i s t o be sma l le r

than 0.1 * loe6 mm /Nm. The o b j e c t i v e was t o f i n d a m a t e r i a l combina t ion t h a t

meets these requirements. Moreover, a t t a c k ( s c r a t c h i n g ) o f t h e j o u r n a l su r -

face shou ld be as m i l d as p o s s i b l e i n o rde r t o min imize the chance o f sc ra tch -

induced f a t i g u e e f f e c t s occu r r i ng .

3

3

( b ) APPROACH

The t r i b o l o g i c a l systems parameters which have t o be taken i n t o cons idera-

t i o n i n the m a t e r i a l - s e l e c t i o n process can be seen from the t r i b o l o g i c a l

da ta sheet o f a j o u r n a l bear ing , F igu re 8.6. For m a t e r i a l s e l e c t i o n a simu-

l a t i v e t r i b o - t e s t i n g procedure w i t h a p in -and- r i ng t e s t r i g was app l i ed . A

diagrammatic p r e s e n t a t i o n o f t h i s r i g i s shown i n F igu re 8.13. The specimen

assembly cons is t s o f a p i n (1) and a r i n g ( 2 ) . The p in , made f rom t h e bear-

i n g m a t e r i a l t o be tes ted , i s pressed under a known normal f o r c e a g a i n s t t h e

curved su r face o f t h e r o t a t i n g r i n g , made f rom the j o u r n a l m a t e r i a l t o be

tes ted . The con tac t su r face o f t h e p i n i s preshaped t o f i t t h e r a d i u s o f

cu rva tu re o f t he r i n g . Diameter r i n g : 50 mm; dimensions p i n ( rec tangu la r

cross sec t i on ) : 12.0 x 8.0 mm; o v e r l a p percentage E = 7.6%. The specimens

were surrounded by a box, f i l l e d w i t h a r t i f i c i a l sea water o f 2loC. The

specimens were comple te ly submerged.

327

I I I 1. I ,' I lever

-L pressurized

r - air

F igu re 8.13 Diagrammatic p r e s e n t a t i o n o f p in -and- r i ng t e s t r i g .

Type o f mot ion s l i d i n g

Load F, ( N )

( r e c i p r o c a t i n g )

To ta l s l i d i n g

__-__

Geometry and d i men s i on s

Environment

Journa l d iameter 0.42 m

Seawater ( 5 - 3 5 ' ~ )

P in -and- r ing t e s t r i g

s l i d i n g ( con t inuous )

3.85 * 10'

4.0 . lo7

v = 0.05

18 I Ring d iameter 50 mm P i n c ross s e c t i o n 12 x 8 mm

A r t i f i c i a l seawater (21OC) I

Table 8.4 Cond i t i ons i n p r a c t i c e and i n s i m u l a t i v e t r i b o - t e s t i n g .

328

(i) Opera t ing va r iab les :

A l l exper iments were performed under a normal f o r c e FN = 3850 N and a t a

s l i d i n g speed o f v = 0.05 m/s (con t inuous r o t a t i o n ) . A t FN = 3850 N , t h e

p r o j e c t e d pressure p = 4.0 - 10 N/m, i . e . equal t o p i n p r a c t i c e . The s l i d -

i n g speed v was s e t a t 0.05 m/s ( i . e . 5 t imes vmax i n p r a c t i c e ) . For an ex-

per iment d u r a t i o n t = 100 hrs , t h e t o t a l s l i d i n g d i s tance s i n one e x p e r i -

ment was 100 x 3600 x 0.05 x 0.001 = 18 km.

Table 8.4 compares t h e c o n d i t i o n s i n p r a c t i c e w i t h those i n s i m u l a t i v e

t e s t i n g . I t can be seen t h a t t h e r e a re some d i f f e r e n c e s between the prac-

t i c a l s i t u a t i o n and t h e t e s t s i t u a t i o n , assoc ia ted w i t h FN, v and s . As t o

FN, t h e cho ice o f a much lower va lue i n l a b o r a t o r y t e s t i n g was j u s t i f i e d

p r i m a r i l y by cons ide r ing t h a t by e q u a l i z i n g t h e pressure p, t h e amount o f

deformat ion i n v o l v e d i n the l a b o r a t o r y t e s t w i l l be equal t o t h a t i n prac-

t i c e . As t o v, t he reason ing was t h a t t h e main e f f e c t o f an i nc rease i n v

i s t o i nc rease the temperature i n t h e con junc t i on area due t o f r i c t i o n a l

heat ing . Al though t h i s w i l l c e r t a i n l y be t h e case i n t h e p resen t s i t u a t i o n ,

even a t v = 0.05 m/s t h e above temperature r i s e was so l ow (o rde r o f mag-

n i t u d e : a few degrees K) t h a t i t cou ld p robab ly be neg lec ted (no te t h a t t he

sea-water p resen t i n p r a c t i c e as w e l l as i n t h e l a b o r a t o r y t e s t coo ls t h e

rubb ing sur faces q u i t e e f f e c t i v e l y ) . As regards s , t he acceptance o f 18 km

i n s t e a d o f 1000 km was based on t h e assumption t h a t t he wear process would

r a p i d l y reach a s teady -s ta te c o n d i t i o n . Again, by v i r t u e o f t h e f a c t t h a t

thermal e f f e c t s a r e v i r t u a l l y n e g l i g i b l e , t h i s assumption seemed r e a l i s t i c .

7

(ii) M a t e r i a l s

M a t e r i a l s f o r p i n and r i n g were p rese lec ted on t h e bas i s o f a number o f

n o n - t r i b o l o g i c a l c r i t e r i a , f o r ins tance, r e s i s t a n c e t o sea-water c o r r o s i o n

and p r i c e , as w e l l as t r i b o - t e c h n i c a l exper ience and handbook data. Even-

t u a l l y i t was decided t o make t h e t e s t specimens f rom t h e m a t e r i a l s des-

c r i b e d i n Table 8.5. Because o f r e s t r i c t e d t ime, o n l y a l i m i t e d number o f

combinat ions o f p i n and r i n g m a t e r i a l s was tes ted .

( c ) RESULTS

A summary o f r e s u l t s i s g i ven i n Table 8.6. T h i s shows t h a t , f rom t h e two

bronzes w i t h MoS2, t ype (a ) d i d n o t come up t o expec ta t i ons . However t y p e

(b ) , combined w i th r i n g m a t e r i a l s ( C ) and (E), met t h e requirements as r e -

gards wear r a t e . However, even w i t h m a t e r i a l (b ) t h e r i n g s were s l i g h t l y

damaged, see F i g u r e 8.14. Combinations o f d i f f e r e n t coba l t - t ype a l l o y s ,

329

M a t e r i a1

P i n

(bush ing)

(1)

i .e . , m a t e r i a l combinat ions (cD), (cE), (cF) and (dF), were success fu l as

fa r as t h e wear r a t e o f t h e p i n (bush ing) m a t e r i a l was concerned. However,

i n a l l cases an unacceptab ly h i g h wear r a t e o f t h e r i n g s was observed, rang-

i n g f rom 0.5 u n i t s f o r combina t ion (cF) t o 1.5 u n i t s f o r combina t ion (dF) .

Code Type Hardness 1 eve1

(lo7 N I ~ )

c a s t bronze w i t h MoS2 150-250 . - - - - - - -

5 00 - 6 00 C cobal t-chromium a l l o y s - I- _ _ - - _ _ - _ ----

e

Ring

( j o u r n a l )

( 2 )

30-40 f pheno l i c r e s i n s + f i l l e r s 9 t s o l i d l u b r i c a n t h

A Cr-Ni a l l o y 200

B Cu-Ni a l l o y 200

C Fe-Ni a l l o y 250

- - - - - --- _-- - - - - _ --- - - ~ - ---

5 00 -6 00

Table 8.5 Types o f p rese lec ted m a t e r i a l s .

F i n a l l y , a l l combinat ions i n v o l v i n g res in -based p i n s were success fu l i n

t h a t wear r a t e o f t he p i n s never exceeded 4 u n i t s . M inor damage o f t he r i n g s

o f t h e type shown i n F igu re 8.14 occur red w i t h m a t e r i a l combinat ions (eA),

( f E ) and (hB). However, i f used i n combina t ion w i t h p i n m a t e r i a l s (e ) and

( g ) , r i n g s o f m a t e r i a l (B) remained comp le te l y undamaged, see example i n

F igu re .8.15.

(d ) FOLLOW-UP

On t h e b a s i s o f t h e above r e s u l t s , a p p l i c a t i o n o f m a t e r i a l s (e ) , (9 ) and (B) seemed w e l l j u s t i f i e d . Fu r the r , i t looked as i f combina t ion (bC) o r

(bE) m igh t w e l l be chosen as a p o s s i b l e back-up s o l u t i o n .

formed w i t h combinat ions (gB) and (bC) t e s t d u r a t i o n : 0.5 yea r ; t o t a l s l i d -

Since pe r fo rm ing t h e l a b o r a t o r y t e s t s , p r o t o t y p e t e s t i n g has been pe r -

330

F igu re 8.14 P r o f i l e diagram and photomicrograph o f p i n su r face a f t e r t e s t . Ma te r i a1 combina t ion : bC. Damage c l a s s i f i c a t i o n : 51 i g h t l y damaged.

F igu re 8.15 P r o f i l e diagram and photomicrograph o f p i n su r face a f t e r t e s t . M a t e r i a l combinat ion: gB. Damage c l ass i f i c a t i o n : undamaged.

331

pin r ing !

ing dis tance: 25 km). The r e s u l t s f u l l y corroborate the pin and r ing re- s u l t s and thus j u s t i f y in re t rospec t the choice of the tes t condi t ions i n

the laboratory tests.

pin

Wear r a t e

KI ( ~ o - ~ ~ ~ / N ~ ) Materi a1

(b) c a s t bronze with MoS2

( c ) cobal t-chromium a1 loy

(d) cobal t-chromium a l loy

( e ) phenolic res ins t f i l l e r s t s o l i d lubr icant

( f ) phenolic resins + f i l l e r s t s o l i d lubr icant

phenolic resins + f i l l e r s t s o l i d lubr icant

phenolic res ins t f i l l e r s t s o l i d lubr icant

( 9 )

(h)

( F j Co-Cr a l l & 6

( C ) Fe-Ni a l l o y 3 ( E ) Co-Cr a l loy 3 (F) Co-Cr a l loy 5

(0) Co-Cr a l loy 0.4 ( E ) Co-Cr a l l o y 0.5 ( F ) Co-Cr a l loy 0.1

( F ) Co-Cr a l loy 0.4

( A ) Cr-Ni a l loy

-

4 ( B ) Cu-Ni a l l o y 2

3 (B) Cu-Ni a l l o y

2 ( B ) Cu-Ni a l loy

2 ( 8 ) Cu-Ni a l loy

-

( a ) c a s t bronze with M0S2 ( A ) Cr-Ni a l loy

( 6 ) Cu-Ni a l loy ( C ) Fe-Ni a l l o y ( D ) Co-Cr a l loy f E l Co-Cr a l lov

10 9 7 6 10

ring

< O . l 0.6 0.3 0.1

< 0.1 < 0.1

< O . l < O . l c o . 1

0.8 0.8 0.5

1 . 5

< 0.1 <0.1

e o . 1

co.1

< 0.1

Table 8.6 Summary of r e s u l t s of pin and r ing t e s t i n g . (Note t h a t each f igure given i s the highest f i g u r e found in t r i pl i ca te t e s t i n g )

332

8 ,5 ,4 LUBR

( a ) PROBLEM

CANT SELECTION FOR NSTRUMENT PIVOT BEARING

I n a c o s t - b e n e f i t a n a l y s i s o f an ins t rument , t h e use o f two types o f r a t h e r

expensive spec ia l l u b r i c a n t f o r t h e l u b r i c a t i o n o f a s tee l - sapph i re p i v o t

bea r ing was c r i t i c i z e d . Al though the bear ing system worked very s a t i s f a c -

t o r i l y , f o r t h e sake o f c o s t r e d u c t i o n the spec ia l l u b r i c a n t s had t o be r e -

p laced by more convent iona l l u b r i c a n t s . The o b j e c t i v e was t o s e l e c t a s u i -

t a b l e l u b r i c a n t which meets t h e requ i rement o f c o s t r e d u c t i o n b u t ma in ta ins

p roper l u b r i c a t i o n w i t h o u t d e t e r i o r a t i o n o f t h e bear ing ' s performance. I n

p a r t i c u l a r , t he wear r a t e o f the p i v o t shou ld n o t inc rease as a consequence

o f t h e replacement o f t h e spec ia l l u b r i c a n t .

( b ) APPROACH

The problem demands a comparison o f t h e f u n c t i o n a l behav iour o f t h e p i v o t

bea r ing l u b r i c a t e d w i t h e i t h e r t h e p r a c t i c a l l y proven spec ia l l u b r i c a n t s o r

t he new l u b r i c a n t s t o be se lec ted on bo th economic and techno log ica l

grounds.

A couple o f l u b r i c a n t s (minera l o i l s ) were p rese lec ted on the bas i s o f

c r i t e r i a l i k e p r i c e , chemical c o n s t i t u t i o n , ageing behav iour and v i s c o s i t y

( v i s c o s i t y range a t room temperature: 100-300 mPas). I n Tab le 8.7 some char -

a c t e r i s t i c s o f t he p rese lec ted l u b r i c a n t s a re l i s t e d .

and l u b r i c a n t s ( C ) - (F ) a re p o t e n t i a l cand ida tes f o r t he replacement. The

f i g u r e s CA, CN, Cp c h a r a c t e r i z e t h e percentage o f carbon atoms i n a romat ic

groups, naphthenic groups o r p a r a f f i n i c groups, r e s p e c t i v e l y . (For a des-

c r i p t i o n o f these terms see Sec t ion 4.5.5. )

The t r i b o l o g i c a l performance o f t he p r a c t i c a l l y proven and t h e prese-

l e c t e d l u b r i c a n t s was t e s t e d by s i m u l a t i n g t h e behaviour o f t h e p i v o t bear-

i n g i n l a b o r a t o r y t e s t s us ing t h e i d e n t i c a l s tee l - sapph i re bea r ing m a t e r i a l s

and a d j u s t i n g t h e opera t i ona l t e s t v a r i a b l e s t o t h a t o f t h e p r a c t i c a l bear -

i n g system. The v a r i a b l e s r e l e v a n t f o r s i m u l a t i v e t r i b o - t e s t i n g have been

checked w i t h t h e h e l p o f t he t r i b o l o g i c a l systems data sheet, see F igu re

8.5. I n Table 8.8 t h e p e r t i n e n t da ta o f t h e p r a c t i c a l system and t h e t e s t

system a re l i s t e d . I t can be seen t h a t t h e l a b o r a t o r y t e s t s were performed

under s l i g h t l y i n t e n s i f i e d t e s t cond i t i ons concern ing c o n t a c t p ressure and

speed.

Lub r i can ts (A) and (B) a re t h e p r a c t i c a l l y proven spec ia l l u b r i c a n t s ,

333

Lubricant

I

Dens i &y a t 20 C

0.878

0.893

0.894

0.894

0.896

0.895

Mean molecular weight

556

779

585

574

656

595

Table 8.7 Propert ies o f preselected lubricants .

Operating var iables

Type of motion

Load FN ( N )

Pressure poH (N/m )

Speed (rpm)

Temperature ( O C )

Duration ( h )

-_____

-~ 2

~- ~

-

~-.______

Geometry

r Components o f the

systems

%CA %CN %CP

9 20 71

8 21 71

4 34 62

2 38 60

6 30 64

6 31 63

P i v o t bearing

spin (continuous)

2.6

2 . 1 . lo9

22

Test r i g I spin (continuous) 1

54 I 25 I

( 4 ) q F N , (1) AISI 52100 s t e e l bal l

E = 2 . 10 N/cm

H v = 8000 N/mm

Ra = 0.02 pm

E = 5 - l o 7 N/cm2

Ra = 0.02 pm

7 2

2

( 2 ) sapphire

( 3 ) lubr icant ( s e e Table 8 . 7 )

( 4 ) a i r .... L Table 8.8 Conditions in prac t ice and in simulative t r ibo- tes t ing .

334

( c ) RESULTS

The f u n c t i o n a l performance o f t h e p i v o t bea r ing i s determined ma in l y by

boundary l u b r i c a t i o n a t t h e s tee l - sapph i re i n t e r f a c e and t h e l i m i t s o f

p roper f u n c t i o n a l behav iour a re reached i f t h e amount o f wear o f t h e p i v o t

reaches a c e r t a i n c r i t i c a l l i m i t . Thus, t h e wear c o e f f i c i e n t o f t h e p i v o t

served as the u l t i m a t e l u b r i c a n t s e l e c t i o n c r i t e r i o n . I n Tab le 8.9, t he

measured wear c o e f f i c i e n t s f o r t h e var ious systems s t u d i e d a r e compiled.

L u b r i c a n t used

p r a c t i c a l l y proven spec ia l l u b r i c a n t s

t------- l u b r i c a n t s t o be I used

Wear c o e f f i c i e n t o f p i j o t

K ' (mm /Nm)

2.9 - 1.5 *

8.9

8.2 - 6.6 lo-'

7.8 * lo-'

Table 8.9 Resu l ts o f wear t e s t i n g .

The comparison o f these systems shows t h a t no d e t e r i o r a t i o n o f t he b e a r i n g ' s

performance i s t o be expected i f the p r a c t i c a l l y proven spec ia l l u b r i c a n t s

( A ) , (6) are rep laced by one o f t h e l u b r i c a n t s ( C ) - (F ) . Moreover, f rom t h e

da ta o f Table 8.8, i t may be concluded t h a t even an improvement i n wear be-

hav iou r o f t h e p i v o t bea r ing may be ob ta ined by us ing one o f t he l u b r i c a n t s

(C) - ( F ) .

( d ) FOLLOW-UP

On t h e bas i s o f t h e above r e s u l t s i t was suggested t h a t t he spec ia l (and

expensive) l u b r i c a n t s ( A ) and ( 5 ) shou ld be rep laced by t h e l u b r i c a n t ( E ) .

Th is has been done i n p r a c t i c e and over a p e r i o d o f t h r e e yea rs ( d u r i n g

which the proper f u n c t i o n a l behav iour o f t h e p i v o t bear ings has been

checked) a s a t i s f a c t o r y f u n c t i o n a l performance o f t h e p i v o t bea r ing was

observed.

335

8,5,5 REDUCTION OF SEVERE WEAR OF CAM-TAPPET DESIGN

( a ) PROBLEM

Cam and t a p p e t combinat ions ( p a r t s o f t e x t i l e machinery) which f u n c t i o n a t

i r r e g u l a r i n t e r v a l s t o t r a n s m i t mot ion, s u f f e r f rom severe adhesive wear,

f r e q u e n t l y w i th in 1 month a f t e r p u t t i n g i n t o use. I n p a r t i c u l a r , t h e f o l -

l ow ing ques t ions were fo rmula ted :

( i )

(ii) ( i i i ) Does t h e a p p l i c a t i o n o f resin-bonded MoS2 improve t h e s i t u a t i o n ?

I n p r a c t i c e , i f t h e system i s operated, normal f o r c e FN i s b u i l t up f rom

0 t o 500 N i n 4s, a f t e r which F,,, remains a t t h e 500 N l e v e l f o r 1s and FN

decreases aga in t o 0 i n another 4s . Thus, a f u l l con tac t c y c l e r e q u i r e s

9 s . The problem i s cons idered t o be so l ved i f t h e cam can pe r fo rm 15000

movement cyc les , i r r e g u l a r l y d i v i d e d over a p e r i o d o f 5 years , w i t h o u t

severe adhesive wear occu r r i ng . The t o t a l c o n t a c t t ime i s then equal t o

37.5 h rs .

I s f a i l u r e o f t h e phosphated sur faces force-dependent o r p ressure-

dependent?

What i s t h e maximum a l l owab le f o r c e o r p ressure?

( b ) APPROACH

Since, f rom a systems p o i n t o f view, wear o f a g i ven t r i b o - e n g i n e e r i n g

system i s a f u n c t i o n o f bo th the o p e r a t i n g v a r i a b l e s , X, and t h e sys tem's

s t r u c t u r e , S, i . e . ,

wear = f ( X , S ) ,

one cons iders s o l v i n g t h e problem by one o r more o f t he f o l l o w i n g c u r a t i v e

a c t i o n s :

( I ) Changing o p e r a t i n g va r iab les , X ) :

- decrease o f FNmax

(11) Changing system's s t r u c t u r e , S = ( A, P , R ) : - -

a p p l i c a t i o n o f a resin-bonded MoS2 f i l m

i nc rease i n r a d i u s o f cu rva tu re o f t h e cam ( t h u s l o w e r i n g t h e

H e r t z i a n c o n t a c t p ressure pH)

I n o r d e r t o f i n d t h e optimum s o l u t i o n , s i m u l a t i v e l a b o r a t o r y t e s t s were

performed w i t h a p in -and- r i ng t e s t r i g . Rings o f r a d i u s o f c u r v a t u r e r2 =

38mm ( r e p r e s e n t i n g t h e t a p p e t s ) and p i n s w i t h hemispher ica l t i p s w i t h

336

Opera t ing v a r i a b l e s - Type o f mot ion s l i d i n g

r a d i i rl o f 1.5, 5 and l l m m ( r e p r e s e n t i n g cams) were made f rom 15 CrNi6

s t e e l . P r i o r t o use, t he specimens were t r e a t e d i n a manganese-phosphating

ba th s i m i l a r t o the one used i n p r a c t i c e . Dur ing t e s t , t h e specimen assem-

b l y was comple te ly immersed i n 20W30 o i l of,50°C. The speed o f r o t a t i o n o f

t h e r i n g s was ad jus ted a t 200 rev./min, which y i e l d e d a l i n e a r speed i n t h e

f r i c t i o n i n t e r f a c e o f 0.8 m/s.

Tr ibo-e lement

( s t a t i o n a r y p i n ) ( 1 )

M a t e r i a l s t e e l 15 CrNi6

T r i bo-element L u b r i c a n t Atmosphere ( 2 ) (3) ( 4 )

( r o t a t i n g r i n g )

s t e e l o i 1 a i r 15 CrNi6 SAE 20W30

Load F N ( t ) (N)

Hardness (Rockwel l C)

Sur face t rea tment

I V e l o c i t v v h/s 1 I 0.8 I

- - 62 62

manganese-i ron manganese-i ran - - phosphate phosphate

Temperature T ?C

Opera t ing d u r a t i o n

I !Peter 1-14 Dimensions (mm) r a d i i 1,5; 5; 11

Table 8.10 Cond i t ions o f wear t e s t .

337

FN - r

(mm) (N)

1.5 10 50

100 250

5 100 250 500 750

Dur ing a t e s t t h e normal f o r c e FN-t ime c h a r a c t e r i s t i c was s i m i l a r t o

t h a t i n p r a c t i c e , i . e . b u i l d up o f FN f rom 0 t o maximum va lue i n 45, con-

s t a n t l e v e l FN = Fmax d u r i n g I s , fo l lowed by decrease t o 0 N i n another 4s.

Cont ra ry t o p r a c t i c e , however, t he l o a d cyc les f o l l o w e d i n immediate suc-

cess ion , 15000 cyc les thus cor respond ing t o a t e s t i n g t ime o f 37.5 h rs . I n

Table 8.10 t h e s i m u l a t i v e t e s t c o n d i t i o n s a r e l i s t e d .

___

endurance

w i t h MoS2 w i t h o u t MoS2

m i n h r s m i n h r s

217 > 2400 > 40 >2400 ’40 370 90 1 . 5 60 1

0 0

467 633 0 - 215 >2400 > 4 0 > 2400 > 40 292 1500 25 1200 20 368 110 2 70 1 422 0

> 2400 > 40 > 2400 > 40

PHer tz

(10’ N /m2)

0 - -

0 -

( c ) RESULTS

3000 4000 457

1010 17 980 16 0 0

0 0 -

-

Table 8.11 Resu l t s o f t r i b o - t e s t i n g .

Table 8.11 shows r e s u l t s , expressed i n terms o f endurance, i . e . t i m e t o

f a i l u r e by adhesive wear e f f e c t s . These r e s u l t s show t h a t t he su r faces

f a i l e d immedia te ly a t pHertz > 400 * 10

i n c r e a s i n g l y l o n g endurances were found. M ic roscop ic obse rva t i on d i r e c t l y

be fo re and a f t e r f a i l u r e i n d i c a t e d t h a t t h e occurrence o f adhesive-wear

e f f e c t s was assoc ia ted w i t h f a i l u r e o f t h e phosphate f i l m .

though d i s c e r n i b l e , has o n l y l i t t l e i n f l u e n c e on t h e endurance o f t h e phos-

phate f i l m . I n a d d i t i o n a l exper iments i t has been shown t h a t t h i s i s due t o

the 20W30 o i l r a p i d l y d i s s o l v i n g t h e r e s i n , thus d e s t r o y i n g t h e cohesive

i n t e g r i t y o f t h e s o l i d l u b r i c a n t f i l m . Under c o n d i t i o n s o f d r y rubb ing , a

resin-bonded MoS2 f i l m p r o t e c t s phosphated sur faces q u i t e e f f e c t i v e l y , b u t

i n t h e p resen t case t h i s i s o f no p r a c t i c a l va lue .

7 2 N/m . A t l ower values o f pHertz,

Table 8.11 shows t h a t t he presence o f a resin-bonded MoS2 f i l m , a l -

Clearly, fa i lure of the phosphate film is pressure-dependent rather

t h a n force-dependent. Further, the results show t h a t the endurance i s more 7 2 than 40 hrs a t pHertz G 230 - 10 N/m . A t r = 5, t o reach th i s pHertz value

would require a dras t ic decrease i n normal force, i.e. from 500 N t o some

150 N. Thus i t was recommended t o increase the radius of curvature of the cam t o 11 m instead.

( d ) FOLLOW-UP

Since performing the experiments, the radius of the cam has indeed been in-

creased, i .e. t o 10.5 mm. Since then, severe adhesive wear has n o t been re-

ported for a period which now amounts t o approximately 1 Year.

8,5,6 REDUCTION OF FRICTION-INDUCED NOISE OF

WHEEL/RA I L SYSTEM

( a ) PROBLEM

110

100

h

B 90 v

01 w 0 .r

* 80

70

I 1 I I I I I I I 1 0.06 0.12 0.25 0.5 1 2 4 8 15

Frequency (kHz)

Figure 8.16 Diagram of noise spectrum emitted by wheel-rail system.

339

City t r a i n s running through narrow curves o f t e n produce a pene t ra t i ng

squealing noise which reach noise l e v e l s up t o 120 db a t frequencies ranges

from 4000 t o 8000 Hz. As a t y p i c a l example i n F igure 8.16, a no ise diagram

i s shown measured i n s i x runs o f a ca r r i age running through a curve o f 193111

radius. The causes o f f r i c t i on - induced noise generation are t o be s tud ied

and methods f o r no ise reduct ion are t o be suggested.

(b) APPROACH

A t heo re t i ca l cons iderat ion o f the forces and movements a c t i n g between the

r a i l and a r i g i d wheel-frame running through a curve shows t h a t a t ransverse

s l i p motion between wheel and r a i l occurs i f the r a i l - t r a c k curve rad ius i s

l ess than 500 m f o r a ra i lway t rack width o f 1435 nun (Ref. 8.13). For a t r a i n

speed o f 15 m/sec and r a i l curves 200-500 m, the transverse s l i d i n g v e l o c i t y

i s i n the range o f vt = 0.1 t o 0.3 m/sec. The t ransverse s l i d i n g motion and

the i n t e r f a c i a l f r i c t i o n lead t o s t i ck -s l i p - i nduced v ib ra t i ons o f the wheel/

r a i l system which i s mani fest i n the generation o f noise.

Having discussed i n b r i e f the reason f o r the generation o f noise, the

question o f how t o m i t i g a t e t h i s " p o l l u t a n t " must be answered. I n t e r p r e t i n g

the noise emission as t r ibo- induced " loss-output" o f the t r i b o l o g i c a l wheel-

r a i l system, the general system desc r ip t i on can be used as a convenient

s t a r t i n g p o i n t f o r a systematic considerat ion o f the parameters t h a t may be

changed i n order t o r e l i e v e the noise emission.

described fo rma l l y as:

According t o Section 8.2.4, the t r ibo- induced noise emission can be

noise = f (Operating var iab les, System's s t r u c t u r e )

noise = f ( X ; S )

Thus, the main i n f l u e n c i n g fac to rs can be c l a s s i f i e d under the headings:

( I ) Operating var iab les, ( X ) :

- - - Temperature (depending on season)

Load (weight o f ca r r i age p lus passengers)

Speed ( t r a i n speed, transverse s l i p speed)

(11) System's s t ructure, S = ( A, P, R ]

{ A ) Elements:

( 1 ) Type o f wheel

(2 ) Type o f r a i l

( 3 ) Envi ronmental atmosphere

340

[ P ] P r o p e r t i e s o f elements:

- M a t e r i a l o f wheel and r a i l

- Geometric des ign o f wheel and r a i l

- Geometric des ign o f r a i l t r a c k

- Sur face p r o p e r t i e s o f wheel and r a i l

{ R) I n t e r r e l a t i o n s between elements:

T r i b o l o g i c a l i n t e r r e l a t i o n s between ( l ) , ( 2 ) , ( 3 )

C l e a r l y , t h e parameters ( I ) and a l s o most o f t h e parameters (11) a re f i x e d

f o r a g i ven commercial w h e e l - r a i l - t r a i n system. There fore , s i n c e changes i n

des ign cannot be made, an a t tempt must be made t o i n f l u e n c e d i r e c t l y t he i n -

t e r f a c i a l t r i b o l o g i c a l processes ( R ) which a re t h e o r i g i n o f t h e no ise ge-

n e r a t i o n .

E m p i r i c a l l y , i t was found t h a t i f c e r t a i n phosphate s o l u t i o n s a re

sprayed on t h e r a i l s , t he no ise vanished. T h e o r e t i c a l l y , f rom the analogue

computer s tud ies o f s t i c k - s l i p e f f e c t s (see Sec t ion 6.2.2), i t f o l l o w s t h a t

t he s t i c k - s l i p e f f e c t s depend on t h e f r i c t i o n - v e l o c i t y g rad ien t . I n o r d e r t o

c l a r i f y t h e p o s s i b i l i t i e s o f r e l i e f o f s t i c k - s l i p - i n d u c e d no ise and t o o p t i -

mize t h e c o n d i t i o n s o f an approp r ia te su r face t rea tment o f t h e r a i l s , s t i c k -

s l i p s tud ies i n t h e l a b o r a t o r y were made (Ref. 8.14). For these s tud ies , a

p in -on-d isc and a b a l l - o n - d i s c t r i b o m e t e r were used. The t e s t s were per -

formed w i t h t h e o r i g i n a l wheel - r a i 1 m a t e r i a l s under o p e r a t i n g cond i t i ons

s i m i l a r t o t h a t i n p r a c t i c e (p,, = 5 0 . 10 N/m ; v = 2 - 20 cm/s).

( c ) RESULTS

The exper imenta l s tud ies show t h a t t he s t i c k - s l i p e f f e c t s a r e markedly i n f l u -

enced by d i f f e r e n t phosphate t rea tments o f t h e sur faces . I t was found t h a t

th rough t h e su r face t rea tment , t h e s t a t i c f r i c t i o n c o e f f i c i e n t f, i s s l i g h t l y

decreased and the dynamic f r i c t i o n c o e f f i c i e n t fd i s cons ide rab le inc reased,

so t h a t the d i f f e r e n c e A f = fS - fd i s approx imate ly zero. There fore , t h e

requirement f o r van ish ing s t i c k - s l i p e f f e c t s i s g iven (see Sec t ion 6.2.2).

Indeed, i t has been found t h a t under these c o n d i t i o n s the s t i c k - s l i p ampl i -

tude i s d r a s t i c a l l y reduced. A t y p i c a l r e s u l t o f t he i n f l u e n c e o f t h e su r face

t rea tment on the s t i c k - s l i p behav iour i s shown i n F igu re 8.17.

7 2

( d ) FOLLOW-UP

On t h e bas i s o f t h e sys temat ic l a b o r a t o r y s t i c k - s l i p i n v e s t i g a t i o n s , a phos-

phate s o l u t i o n , which appeared t o be o p t i m a l l y s u i t a b l e f o r p r a c t i c a l pu r -

poses cou ld be s p e c i f i e d . By t r e a t i n g t h e r a i l s a t r e g u l a r i n t e r v a l s w i t h

341

t h i s s o l u t i o n , a s a t i s f a c t o r y r e d u c t i o n o f t h e s t i c k - s l i p - i n d u c e d n o i s e o f

t he p r a c t i c a l dheel r a i l system was ob ta ined.

= 0.47 f s t a t i c fdynarni c = 0.26 d r y s l i d i n g

V = 0 .42 = o.39 w i t h su r face t rea tmen t f s t a t i c

fdynami c

/ Time

F igu re 8.17 I n f l u e n c e o f su r face t rea tmen t on s t i c k - s l i p behav iour .

8 , 5 , 7 FAILURE INVESTIGATION OF ELECTRICAL CONTACTS

( a ) PROBLEM

E l e c t r i c a l con tac ts i n te lephone exchange u n i t s show sudden, i n e x p l i c a b l e

f a i l u r e s due t o severe adhes ive wear e f f e c t s . There i s some i n d i c a t i o n

t h a t a t low r e l a t i v e h u m i d i t y ( u n i t s l o c a t e d i n d e s e r t c o u n t r y ) t h e f a i l u r e

r a t e i s h ighe r than elsewhere. The causes o f f a i l u r e a r e t o be s t u d i e d and

methods f o r a v o i d i n g f a i l u r e a re t o be suggested.

342

Type o f mo t ion

( b ) APPROACH

From a systems v iewpo in t , f a i l u r e o f a g iven t r i b o - e n g i n e e r i n g system oc-

curs through the a c t i o n o f t h e o p e r a t i n g v a r i a b l e s on t h e s t r u c t u r e o f t h e

system i n d i c a t e d by a severe d i s tu rbance o f t h e f u n c t i o n a l i npu t -ou tpu t

r e l a t i o n s (ice Sec t ion 6.4). Checking the p o t e n t i a l i n f l u e n c e o f t h e v a r i -

ous system's parameters w i t h t h e he lp o f t h e t r i b o l o g i c a l systems da ta sheet

(see F i g u r e 8 .5 ) , i t appears t h a t t h e f a i l u r e o f t h e e l e c t r i c a l con tac ts i s

due t o a breakdown o f " p r o t e c t i v e " su r face l a y e r s i n f l u e n c e d d i f f e r e n t l y by

c o n t a c t l oad FN and atmospher ic h u m i d i t y R.H. f o r var ious con tac t -ma te r ia l

combinat ions. I n o rde r t o s tudy these f i n d i n g s f u r t h e r , l a b o r a t o r y f a i l u r e

t e s t s w i t h var ious con tac t m a t e r i a l s were performed w i t h a p in -on -d i sc tri-

bometer. I n Table 8.12 the f a i l u r e t e s t c o n d i t i o n s a re l i s t e d . (Fo r f u r t h e r

d e t a i l s see Ref. 8.15).

s l i d i n g

Load FN ( N )

V e l o c i t y v (m/s)

Temperature ( O C )

Opera t ing d u r a t i o n ( h )

0.01 - 1

0.2

18 t 1

up t o 72 -

Contact e lement ( 1 ) ( s t a t i o n a r y p i n )

Ma te r i a1

Contac t element ( 2 ) ( r o t a t i n g p i n )

70 Ag, 20 Au, 10 Cu 99.9 CU, a i r 85 Cu, 15 Zn, re1 . humi - 90 Cu, 9.5 Sn, 0.5P, d i t y : 55 Cu, 18 N i , 27 Zn 0-100%

Table 8.12 Cond i t ions o f f a i l u r e t e s t s .

Oimensions (mm)

Sur face roughness

R a t i o € ( % )

(d iamete r )

Ra (p)

2 75 -

0.1 - 0.2 0.1 - 0.2 -

__ 100 < 1

343

( c ) RESULTS

Resu l ts ob ta ined w i th t h e m a t e r i a l combina t ion Ag-Au-Cu a g a i n s t Cu-Ni-Zn

a r e g i ven i n Table 8.13. Obvious ly , a t zero humid i t y , a t r a n s i t i o n occurs

a t a l o a d FN = (8 - 1 0 ) . 10q2N. The onset o f wear i s marked c l e a r l y by a

d e f l e c t i o n i n t h e h e i g h t versus t ime reco rd ing . The f o u r t h column o f Tab le

8.13 g ives t h e t ime p e r i o d which e x p i r e s b e f o r e t h e p i n beg ins t o wear.

Th i s p e r i o d o f t ime i s c a l l e d " i n c u b a t i o n t ime" . V i sua l i n s p e c t i o n and m i -

c roscop ic obse rva t i on o f t he d i s c su r faces revea l t h a t a t 8 - 10q2N and be-

low, t h e d i s c su r face remains v i r t u a l l y undamaged.(As usual f o r con tac ts

s l i d i n g i n a i r , t he "wear t r a c k " becomes marked by a s l i g h t d i s c o l o r a t i o n ,

due t o fo rma t ion o f a t h i n ox ide f i l m . ) A t l oads o f 0 .1 N and h ighe r , no

v i s i b l e ox ide f i l m s a r e formed on the d i s c sur face , presumably because

f r e s h metal su r faces form con t inuous ly , due t o the cons tan t removal o f par -

t i c l e s i n t h e fo rm o f wear d e b r i s . The c o e f f i c i e n t o f f r i c t i o n has a con-

s t a n t va lue o f 0.8 a t loads below t r a n s i t i o n . Above t r a n s i t i o n , f r i c t i o n

r a p i d l y drops t o values cor respond ing t o f = 0.6, as soon as t h e system

s t a r t s t o wear. A t 60% r e l a t i v e humid i t y , t h e t r a n s i t i o n has s h i f t e d t o a

much h i g h e r l o a d value, v i z . between 0.4 and 0.5 N, as a r e s u l t o f i n t r o -

duc ing wa te r vapour c o n t a i n i n g a i r . F r i c t i o n i s l ower than a t 0% R.H., be-

low as w e l l as above t r a n s i t i o n .

The r e s u l t s ob ta ined a t 0% and 60% h u m i d i t y suggest t h a t t h e t r a n s i t i o n

l o a d con t inuous ly inc reases w i t h i n c r e a s i n g humid i t y . Th is was t e s t e d by

pe r fo rm ing a d d i t i o n a l exper iments a t i n t e r m e d i a t e and h i g h e r h u m i d i t y v a l -

ues. The r e s u l t s o f a l l exper iments a r e summarized i n Tab le 8.14 and show

t h a t t h e r e a r e two d i s c r e t e t r a n s i t i o n values, one o c c u r r i n g a t loads be-

tween 0.08 and 0.1 N a t h u m i d i t i e s o f 50% and lower, and t h e o t h e r occur -

r i n g a t loads between 0.4 and 0 .5 N , a t h u m i d i t i e s o f 60% and h i g h e r . Ap-

p a r e n t l y , f o r t h i s m a t e r i a l combinat ion, t he s h i f t i n t r a n s i t i o n l o a d oc-

curs a t approx imate ly 55% R.H. To de termine whether o r n o t t he c r i t i c a l

r e l a t i v e h u m i d i t y o f 55% i s s p e c i f i c f o r t h e m a t e r i a l combina t ion a t hand,

c r i t i c a l h u m i d i t y de te rm ina t ions were performed w i t h t h e o t h e r d i s c mate-

r i a l s , v i z . Cu-Zn, Cu-Sn and Cu. The r e s u l t s a r e summarized i n Tab le 8.15.

I t can be seen, t h a t t h e endurance o f t h e s l i d i n g coup le inc reases a b r u p t l y

a t a c r i t i c a l va lue o f r e l a t i v e humid i t y . Th i s c r i t i c a l va lue i s a f u n c t i o n

o f t h e a l l o y composi t ion, p robab ly be ing determined by t h e water adso rp t i on

c h a r a c t e r i s t i c s o f t h e d i f f e r e n t su r face ox ides .

The analyses c l e a r l y show t h a t t h e p roper f u n c t i o n a l behav iour o f t h e

e l e c t r i c a l c o n t a c t system i s c r i t i c a l l y i n f l u e n c e d by the r e l a t i v e h u m i d i t y

344

60

I

10 15 40 60

20 30 40 50 60 70

Relat ive humidity 1

( % I

R.H. ( % I

0 20 40 50 60 80

C r i t i c 1 load (lo-? N)

8 - 10 8 - 10 8 - 10 8 - 10

40 - 50 40 - 50

Wear r a t e o f Ag-Au-Cu p i n

um/h 1

e 0.01 < 0.01

0.7 1.8 2.4 4.1

c: 0.01 *: 0.01 < 0.01

42 50 62

Incubation t ime ( h)

> 72 ’ 72 3 1

< 0.02 0.02

> 72 > 72 > 72

9 0.5 0.5

c o e f f i c i e n t o f f r i c t i o n

f

0.8 -0.6 0.8-0.6

0.6 0.6

0.6 0.6 0.6 0.6-0.5 0.5 0.5

Table 8.13 Results obtained w i t h Ag-Au-Cu s l i d i n g against Cu-Ni-Zn.

Table 8.14 T r a n s i t i o n load as a funct ion o f r e l a t i v e humid i ty f o r Ag-Au-Cu s l i d i n g against Cu-Ni-Zn.

Table 8.15 C r i t i c a l r e l a t i v e humid i ty f o r various ma te r ia l combinations (FN = 0.4 N, p i n mater ia l Ag-Au-Cu).

345

o f the surrounding atmosphere, i .e., by a proper ty o f the element ( 3 ) o f

the t r ibo-engineer ing system under study.

(d ) FOLLOW-UP

Some telephone exchange u n i t s , operat ing i n extremely dry environments,

were provided w i t h a i r condi t ion ing. This ( r a t h e r expensive) s o l u t i o n

proved t o be e n t i r e l y s a t i s f a c t o r i l y . I n o the r cases, go ld p l a t i n g o f the

e l e c t r i c a l contacts (a l so expensive) e f f e c t i v e l y e l iminated the problem.

(With go ld p la ted contacts, adhesive mater ia l t r a n s f e r always occurs; how-

ever formation o f loose wear p a r t i c l e s i s a r e l a t i v e l y ra re event . )

F i n a l l y , i n rep lac ing exchange u n i t s w i t h mechanical contacts by f u l l y

e l e c t r o n i c un i t s , precedence was given t o rep lace un i t s , operat ing i n ex-

tremely d r y environments.

8,5,8 COMPILATION OF CHARACTERISTICS OF METAL-WORKING

PROCESSES

(a) PROBLEM

An important area o f t r i b o l o g y which has n o t been t rea ted e x p l i c i t l y i n

t h i s volume so f a r concerns the t r i b o l o g y o f manufacturing processes. Also

i n t h i s f i e l d , progress i s poss ib le on l y through a b e t t e r understanding o f

the g rea t number o f c o n t r o l l i n g var iab les. While i t i s n o t poss ib le t o en-

t e r i n t o d e t a i l s o f t h i s f i e l d w i t h i n the scope o f t h i s volume, a t l e a s t a

b r i e f o v e r a l l view o f i t s main "systems parameters" should be attempted

here.

(b ) APPROACH

I n the Appendix ( A ) , a compi la t ion o f the various manufacturing processes

i s given. Clear ly , i n a l l these processes the t r i b o l o g i c a l mechanisms, des-

c r i bed i n Chapter 4, i .e., the contact, f r i c t i o n , wear and l u b r i c a t i o n pro-

cesses, a c t a l l a t the workpiece-tool i n te r face . I n manufacturing, the tri-

bologica l processes p lay a "dual" r o l e :

( i ) On one hand, t r i b o l o g i c a l processes i n f l uence d i r e c t l y the surface

p roper t i es o f the manufactured workpiece. Thus, t r i b o l o g i c a l processes

determine t o a great extent the q u a l i t y o f the manufactured workpiece,

i .e., the q u a l i t y o f the "use-output" o f t he manufacturing system.

346

( i i ) On t h e o the r hand, t r i b o l o g i c a l processes a t t h e workp iece- too l i n t e r -

f ace a re respons ib le f o r too l -wear and too l -workp iece f r i c t i o n . Thus,

as i n any t r i b o - e n g i n e e r i n g system, t r i b o l o g i c a l processes a r e a l s o

respons ib le , o f course, f o r t h e energy and m a t e r i a l " l oss -ou tpu ts " o f

t h e manufac tur ing system.

Manufac tur ing processes can be c l a s s i f i e d b road ly i n two groups: " c u t t i n g "

o r "machining" processes, and " fo rm ing" processes. I n machining, m a t e r i a l

i s removed f rom a c rude p iece o f s tock t o l eave beh ind a p rec is ion-shaped

use fu l p a r t . Manufac tur ing by t h i s method i s , however, was te fu l o f m a t e r i a l ;

sometimes as much as 90 pe rcen t o f t h e o r i g i n a l m a t e r i a l i s removed and

d iscarded i n the process. I n f u t u r e , such waste may become i n t o l e r a b l e as a

consequence o f t he i n c r e a s i n g e f f o r t s o f conse rva t i on o f m a t e r i a l s . Thus,

the u l t i m a t e method o f manufacture i n t h e f u t u r e w i l l be " c o n s o l i d a t i v e

process ing" - the manufacture o f goods by fo rm ing o r assembl ing m a t e r i a l i n

a c o n t r o l l e d p r e c i s e manner (Ref. 8.16). One o f t he major areas o f c o n s o l i -

d a t i v e manufac tur ing processes i s t h e f i e l d o f meta l -work ing processes. I n

t h e f o l l o w i n g , t h e main systems parameters r e l e v a n t t o the t r i b o l o g y o f me-

t a l - w o r k i n g processes w i l l be s t u d i e d i n b r i e f .

( c ) RESULTS

A comprehensive rev iew o f t he t r i b o l o g y o f meta l -work ing processes was pub-

l i s h e d by Schey i n 1970 (Ref. 8 .17) . F u r t h e r rev iews o f t h e o v e r a l l f i e l d

o r spec ia l impor tan t aspects can be found i n Refs 8.18 t o 8.22. I f on t h e

bas i s o f t h i s work t h e main systems parameters o f t h e t r i b o l o g y o f meta l -

work ing processes a r e compi led w i t h the h e l p o f t h e t r i b o l o g i c a l systems

data sheet (see F igu re 8.5), t h e f o l l o w i n g c o m p i l a t i o n r e s u l t s :

1. Techn ica l f u n c t i o n o f meta l -work ing systems

Forming o f m a t e r i a l s th rough:

- drawing

- p ress ing

- r o l l i n g

- f o r g i n g

- e x t r u s i o n

11. Opera t ing v a r i a b l e s o f meta l -work ing process

- type o f mot ion a t t he workp iece-d ie i n t e r f a c e

- l o a d and/or i n t e r f a c i a l pressure, s t r a i n r a t e

- su r face and/or de format ion v e l o c i t y , v e l o c i t y d i s t r i b u t i o n

341

- work ing temperature (ambient temperature and f r i c t i o n - i n d u c e d

- o p e r a t i n g d u r a t i o n

- m a t e r i a l f l o w and/or de format ion r a t e

tempera ture)

111. S t r u c t u r e o f metal-work

( a ) Components o f meta

(1) Workpiece

( 2 ) D ie

ng system

-work ing system

( 3 ) L u b r i c a n t / c o o l a n t

( 4 ) Sur round ing atmosphere

( b ) P r o p e r t i e s o f meta l -work ing components

(1) Workpiece: m a t e r i a l , geometry and dimensions, compos i t ion ,

d u c t i l i t y , hardness, su r face roughness, p re t rea tmen t

( 2 ) D ie : m a t e r i a l , geometry and dimensions, compos i t ion ,

su r face c o a t i n g ( i f any) , hardness, su r face roughness

( 3 ) Lub r i can t : type, chemical composi t ion, v i s c o s i t y ,

T - T - and 1-p-behav iour , - q - s t r a i n o r v e l o c i t y dependence

( 4 ) Atmosphere: compos i t ion , humid i t y

( c ) T r i b o l o g i c a l processes a t t he workp iece- too l i n t e r f a c e

- c o n t a c t de fo rma t ion processes: t ype , s t a t e o f s t r e s s and

- adhesion and t r i bochemica l processes

- f r i c t i o n processes

- wear processes, w i t h respec t t o (1) workpiece and ( 2 ) d i e

- l u b r i c a t i o n modes

s t r a i n , s t a t e o f de format ion

I V . T r i b o l o g i c a l " l oss -ou tpu t ' ' c h a r a c t e r i s t i c s

- f r i c t i o n da ta ( a l s o amount o f f r i c t i o n - i n d u c e d power l o s s

o r hea t genera t i on )

wear and p i ckup da ta and su r face c o n d i t i o n o f d i e - - su r face c o n d i t i o n o f workpiece

I n a d d i t i o n t o t h i s genera l comp i la t i on o f e f f e c t s and parameters o f t h e

t r i b o l o g y o f meta l -work ing processes, t y p i c a l ranges o f t he b a s i c o p e r a t i n g

v a r i a b l e s o f p ressure , p roduc t speed and temperature a re o u t l i n e d i n Tab le

8.16 f o r t he main meta l -work ing processes.

348

Meta lwork ing process

i 4 \ a tmos uhere

I P ress ing ,

I + Forg i

I E x t r u s i o n

Bas ic o p e r a t i n g v a r i a b l e s

0.0005 ( b a r and tube)

. . .20 I

.80

20-150

30- 130

100-200

... 1 i e a v i e r w i r e )

. , ,15-30 f i n e w i r e )

0.02-0.5

5-25

( c o l d r o l l i n g )

0.1-0.5

( h o t r o l l i n g )

0.02-0.2

(hydr . presse:

. . .10

(hammers)

0.05

( I' h o t sho t I' )

0.5-5

temperature ( O C ) . .

co ld : room temperature

warm: 400-600 h o t : 800 f o r Mo,W

t AT=200-300

room o r e leva ted temperature (e.9.

f o r T i ) 500-800

room temperature o r e leva ted temperature

r o l l i ng) (400-1250, h o t

100-200 ( c o l d )

500-600 (warm )

. . .1200 ( h o t f o r g i n g )

room o r e leva ted temperature (1000-1200 h o t e x t r u s i o n : 600 non-ferroL

L

Table 8.16 Some c h a r a c t e r i s t i c s o f meta l -work ing processes.

349

( d ) FOLLOW-UP

C l e a r l y , t h e g i v e n c o m p i l a t i o n o f c h a r a c t e r i s t i c s o f m e t a l - w o r k i n g p r o c e s -

ses mus t be s p e c i f i e d and e x t e n d e d f o r a g i v e n a c t u a l s i t u a t i o n . However,

t h e s y s t e m a t i c c o m p i l a t i o n o u t l i n e d i n b r i e f may be used f o r p u r p o s e s o f

m a t e r i a l and l u b r i c a n t s e l e c t i o n as w e l l as a f ramework f o r r e p o r t i n g ex -

p e r i m e n t a l v a r i a b l e s o r p e r f o r m i n g s i m u l a t i v e t r i b o - t e s t i n g o f m e t a l - w o r k i n g

p rocesses .

350

Appendix

A compilation of basic

tribo- engineering systems

The t r e a t i s e on t h e t r i b o l o g y o f mechanical systems, p resented i n t h i s

volume i n a genera l i zed manner, a p p l i e s t o a g r e a t v a r i e t y o f ac tua l t r i b o -

eng ineer ing systems. As a supplement t o t h e genera l t r e a t i s e on t h e t r i b o -

l ogy o f mechanical systems, a comp i la t i on o f b a s i c eng inee r ing systems i n

which t r i b o l o g i c a l processes, i .e., con tac t , f r i c t i o n , l u b r i c a t i o n and wear

processes, occur i s g iven i n t h i s s e c t i o n o f t h e appendix.

I n general terms, a t r i b o - e n g i n e e r i n g system i s de f i ned as an e n t i t y

whose techn ica l f u n c t i o n i s connected w i t h " t h e i n t e r a c t i o n o f m a t e r i a l

sur faces i n r e l a t i v e mot ion". I t was descr ibed i n Chapter 3 how the tech-

n i c a l f u n c t i o n s r e a l i z e d through i n t e r a c t i n g m a t e r i a l su r faces can be

b road ly c l a s s i f i e d i n t he f o l l o w i n g groups:

( a ) Transmission o f MOTION

( b )

( c ) ( d ) T ranspor ta t i on o f MATERIALS

( e ) Forming o f MATERIALS

Using t h i s c l a s s i f i c a t i o n , a comp i la t i on o f b a s i c t r ibo-mechan ica l systems

o f technology and b i o l o g y i s g i ven i n t h e f o l l o w i n g . Most o f t h e t r i b o -

systems named can be a d d i t i o n a l l y c l a s s i f i e d . For example, t h e group o f

" s l i d i n g bear ings" can be c l a s s i f i e d f u r t h e r i n t o j o u r n a l bear ings , t h r u s t

bear ings , d r y bear ings , f l u i d bear ings , e tc . , o r t h e group o f "human j o i n t s "

can be c l a s s i f i e d f u r t h e r i n t o h i p j o i n t s , knee j o i n t s , e t c . Whi le n o t

c l a i m i n g t o be complete, t h i s l i s t i n g shows t h e ex t remely wide re levance o f

t he t r i b o l o g y o f mechanical systems. I t shou ld be emphasized t h a t t he sys-

Transmission o f WORK ( o r POWER)

Generat ion o r rep roduc t i on o f INFORMATION

361

S1 i d i n g bearings B a l l and r o l l e r bearings Needle bearings P i v o t bearings Gyros cop i c bea r i n g s Guides S1 i deways Ball-and-screw mechanisms Spindles Hinges Engineering j o i n t s Human and animal j o i n t s Shoe ( o r f o o t ) on ground

F1 anges Gear couplings Splines Cone clutches Disc clutches Band clutches

4

terns l i s t e d below are the basic, i.e., t h e "s implest" , tr ibo-mechanical

systems which may be combined t o systems o f h igher rank ing order - i.e.,

complete machines, instruments, vehicles, e tc . - as expla ined i n Chapter 2,

F igure 2.1.

Primary technica l f unc t i on I t

( a l ) Guidance o r transmission o f MOTION

~

(a2) Coupling o f MOTION

(a3) A n n i h i l a t i o n o f MOTION

I (b) Transmission o f WORK o r POWER

T r i bo-engineering system ( o r t r ibo-engineer ing processes)

I

Block brakes Band brakes Disc brakes Fastener sets Bol t sets F r i c t i o n dampers

~

Rack-and-pinions Spur gears Bevel gears Hypoid gears Planetary gears Worm gears Power screws Chain d r i ves Be1 t dr ives Rope d r i ves Crank d r i ves Cam dr ives Actuators F r i c t i o n d r i ves Hydraul ic d r i ves

352

Primary technica l f unc t i on

( c l ) Generation o f INFORMATION

(c2) Reproduction o f INFORMATION

( d l ) Transportat ion o f MATERIALS

(d2) Control o f f l ow o f MATERIALS

( e l ) Forming o f MATERIALS

(e2) Tearing o f MATERIALS

T r i bo-engineering system ( o r tri bo-engineering processes)

C1 ock-works Cam-and-fol lowers E l e c t r i c a l contacts Switches Re 1 ays P r i n t i n g u n i t s Typewriter u n i t s W r i t i n g u n i t s

Tape-recorder heads S1 i p - r i n g assemblies Audio pick-ups Video pick-ups

Wheel and r a i l Tyre and road Pipe1 ines Conveyors Earth movement u n i t s Human and animal veins

Seals Valves Packings Washers Pis ton-cy l inder assemblies

Drawing Deep drawing Pressing Ext rus ion Forging Rolling Casting I n j e c t i o n moulding Spinning Weaving

~~~ ~

M in ing Well d r i l l i n g Quarry i ng Comminution Dredging Human and animal t ee th

363

Primary technica l f unc t i on

(e3) Machining o f MATERIALS

Tribo-engineering system ( o r t r ibo-engineer ing processes

Cu t t i ng Punching Sawing F i l i n g Turning Shaping and Planing Bor ing D r i 11 i n g Grinding Abrasive c u t t i n g Chipless c u t t i n g Lapping Po l i sh ing B1 a s t i n g Brushing

Suppl emen t i ng remark:

The compi la t ion o f bas ic t r ibo-engineer ing systems shows the g rea t v a r i e t y

o f mechanical systems i n which f r i c t i o n , l u b r i c a t i o n , and wear processes

occur. While i t i s n o t poss ib le t o deal w i t h s p e c i f i c d e t a i l s o f the i n d i -

v idual t r ibo-engineer ing systems w i t h i n the scope o f t h i s volume, the tri-

bo log ica l fundamentals re levan t t o the various mechanical systems are pre-

sented i n the preceding chapters under the headings: - Contact processes, Section 4.2, page 47 - F r i c t i o n processes, Section 4.3, page 69 --Wear processes, Section 4.4, page 97 - Lubr ica t i on modes, Section 4.5, page 130

The in f luences o f f r i c t i o n and wear processes on mechanical engineering

systems are discussed i n general t e n s under the headings:

S t r u c t u r a l aspects :

--D Surface topography changes, Section 5.2.1, page 179 - Surface composition changes, Section 5.2.2, page ,186 -L Surface s t reng th p roper t i es changes, Section 5.2.3, page 191 - Solut ions f o r no-wear condi t ions, Section 5.4, page 199

- Dynamic behaviour, Section 6.2.1, page 215 - S t i c k - s l i p e f f e c t s , Section 6.2.2, page 218 -- E f f i c i ency , Section 6.3, page 221 - F a i l u r e and safety , Sect ion 6.4, page 227 - R e l i a b i l i t y , Section 6.5, page 234 - Machinery cond i t i on monitoring, Section 7.5, page 277 ----c Requirements f o r proper func t i ona l behaviour, Section 6.6, page 240

Functional aspects:

354

Appendix (B) Elements of

tri bo-engineering systems

The t r i b o - e n g i n e e r i n g systems compi led i n Appendix (A) c o n s i s t o f ( m a t e r i a l )

elements d i r e c t l y i n v o l v e d i n t h e con tac t , f r i c t i o n , l u b r i c a t i o n and wear

processes. The components fo rm ing the " i n t e r a c t i n g sur faces i n r e l a t i v e mo-

t i o n " o f a g i ven t r i b o - e n g i n e e r i n g system a re termed t r i bo -e lemen t (1) and

t r i bo -e lemen t ( 2 ) . I t was emphasized i n Chapters 4 and 5 t h a t f o r an under-

s tand ing o f f r i c t i o n , l u b r i c a t i o n and wear, t h e i n t e r a c t i o n o f a l l t he mate-

r i a l elements i n v o l v e d i n t h e i n t e r f a c i a l t r i b o l o g i c a l processes must be

taken i n t o cons ide ra t i on . Thus, t he i n t e r f a c i a l medium ( 3 ) ( i f any) between

components (1) and ( 2 ) and t h e sur round ing medium ( 4 ) a r e i n t e g r a l c o n s t i -

t u e n t o f any t r i bo -eng ineer ing system. I n t h e f o l l o w i n g , t h e elementary e l e -

ments ( l ) , ( Z ) , (3), ( 4 ) o f t r i b o - e n g i n e e r i n g systems a r e l i s t e d as examples

f rom every group o f t he b a s i c t r i b o - e n g i n e e r i n g systems compi led i n Appendix

( A ) *

356

T r i bo-engi nee r i ng

sys tern

( o r process)

( a l l S l i d i n g bear ing Human h i p j o i n t

Band c l u t c h Spline

(a21

(a3 1 Disc brake Fastener s e t

(b) dorm gear s e t 3el t d r i v e

( c l ) :am and fo l l ower P r i n t i n g u n i t

E l e c t r i c a l contaci h d i o pick-up

(c2)

id2) la1 ve ' is ton assembly

: e l ) h redrawing t o t ex t rus ion

[e2) Je l l d r i l l i n g l redgi ng

:a31 rurning k i n d i n g

1 T r i bo-element

(1) (moving o r s t a t i o n a r y )

Shaf t Femur

Shaf t Inner s p l i n e

Disc B o l t

worm Shaf t

Cam P r i nt-head

Ring Record

idheel F l u i d

P1 ug Piston r i n g

d i r e 3 i l l e t

3orer kedge

Jorkpiece lorkp iece

Elements o f the system

T r i bo-element (2)

(moving o r s t a t i o n a r y )

Bushing Acetabulum

Band Outer s p l i n e

Pad Nut

Gear Be1 t

Fol 1 ower Paper

Brush Sapphire t i p

Rai 1 Pipe

Val ve-body Cyl inder

Die Die

S o i l Earth

Cu t t i ng t o o l Gr ind ing whee

I n t e r f a c i a l medi um

( 3 )

Lubr icant Synov i a

- Grease

Contami n ant -

Gear o i l -

Lubr icant Dye

Spray -

Contaminant -

F l u i d Lub r i can t

Borax G1 ass

- -

Cut t i ng f l u i c Cu t t i ng f l u i o

Surrounding medium (4)

A i r -

A i r A i r

A i r A i r

A i r A i r

A i r A i r

Cover gas A i r

A i r -

F l u i d F l u i d

A i r A i r

- A i r

A i r A i r

356

Appendix (C)

Bibliographic work: DOCUMENTATION TRIBOLOGY

The l i te ra ture in the f ie ld of tribology i s extremely voluminous owing to

the vast number o f topics included. For example, as mentioned already in

Section 1.3, in the period 1966 t o 1977 some 55,000 papers were published

i n t h i s f ie ld . An international and comprehensive bibliography i s provided

by the DOCUMENTATION TRIBOLOGY:

- an annual systematic bibliography of t i t l e s covering the en t i re f ie ld

of wear, f r ic t ion and lubrication, including l i t e ra ture from a l l over

the world (English translations of the t i t l e s are given in brackets

wherever the t i t l e s are Non-English), - a comprehensive source material, also referring t o parallel publications,

translations and abstract material, edited and published by the

Bundesanstal t fur Materialprufung (BAM) in Berlin (West), Germany

- p r o v i d i n g d i rec t and easy access t o required re7erences from various

points of in te res t by a detailed and lpgical classification of the f i e ld , consisting o f ten main sections and more than 100 subsections,

relieving the individual sc ien t i s t o r engineer of the pains of currently scanning the l i t e r a tu re and registering the relevant t i t l e s referring to

his/her f ie ld of in te res t , - total number o f references a t present 6000-8000 t i t l e s per year, among

these are:

-

357

mate r ia l s and p a i r i n g s 650 wear- res is tant coatings 450 lub r i can ts , l u b r i c a n t t e s t i n g 600 bearings 1250 transmissions 250 manufacturing processes, t o o l s 1200

- may be ordered through a bookstore o r

BAM, Unter den Eichen 87,

D-1000 B e r l i n 45

I n the fo l lowing, a summary o f the c lass

d i r e c t l y from the publ isher :

f i c a t i o n o f main sections and sub-

sections of the DOCUMENTATION TRIBOLOGY i s given:

1. General, monographs, reviews

2. Experimental methods and equipment

3. T r i bo log i ca l fundamentals, f r i c t i o n and wear:

laws, mechanisms, e f f e c t s

3.1 Mechanical and acoust ica l phenomena

3.2 Chemical , physi co-chemical and thermal phenomena

3 .3 E l e c t r i c a l and o p t i c a l phenomena

4. Appearance o f damage

5. Wear and f r i c t i o n under s p e c i f i c s t ress ing condi t ions

5.0 Resting and p re l im ina ry displacement i n s t a t i c f r i c t i o n

5 .1 S l i d i n g , i nc lud ing s t i c k - s l i p

5.2 Ro l l i ng , r o l l i n g w i t h s l i d i n g

5.3 Spin

5.4 Impact

5.5 Grain s l i d i n g

5.6 F r e t t i n g , f r e t t i n g corros ion

5.7 Wear caused by f l ow ing media

5.8 Thermal wear, a b l a t i o n

6. Ma te r ia l s and combinations o f ma te r ia l s

( w i t h and w i thou t in termediate ma te r ia l s )

6.1 Metals

6.2 Minerals, ceramics

6.3 Polymers ( p l a s t i c s and rubber)

6.4 Composites ( g l a s s - f i b r e re in fo rced mater ia ls , cermets,

laminated ma te r ia l s e tc . )

358

6.8 T e x t i l e m a t e r i a l s , l e a t h e r

6.9 Other m a t e r i a l s and combinat ions o f m a t e r i a l s ( i n c l u d i n g wood,

paper, shoe soles, f l o o r i n g s , g r a n u l a r m a t e r i a l s , b i o l o g i c a l

m a t e r i a l s , den ta l m a t e r i a l s )

7. I n f l u e n t i a l f a c t o r s and c o n t r o l parameters

7 . 1

7.2

7.3

7.4

Ma te r i a1 -dependent f a c t o r s

7.1.1 S t reng th

7.1.2 Composition, t e x t u r e , s t r u c t u r e

7.1.9 Other m a t e r i a l c h a r a c t e r i s t i c s ( i n c l u d i n g c o m p a t i b i l i t y )

Surface-dependent f a c t o r s

7.2.1 Topography

7.2.2 Sur face l a y e r s (adsorbed f i l m s , ox ide l a y e r s )

7.2.3 Sur face t rea tment (mechanical and hea t t rea tmen t )

7.2.4 Sur face coa t ings

Opera t ing c o n d i t i o n s

7.3.1 Mot ion and v e l o c i t y

7.3.2 Shear fo rce , l o a d

7.3.3 Temperature

7.3.4 Environment

Other i n f l u e n t i a l f a c t o r s

7.4.1 E l e c t r i c p o t e n t i a l , c u r r e n t passage

7.4.2 S o l i d i n te rmed ia te p a r t i c l e s , dus t , contaminants

7.4.3 I r r a d i a t i o n

7.4.4 Geometric f a c t o r s , e f f e c t s o f des ign

8. L u b r i c a t i o n

8 .1

8.2

8.3

8.4

8.5

8.6

8.7

8 .8

8.9

T h i c k - f i l m l u b r i c a t i o n , e s p e c i a l l y hydrodynamic 1 u b r i c a t i o n

T h i n - f i l m l u b r i c a t i o n (boundary 1 u b r i c a t i o n , e l a s t o -

hydrodynamic l u b r i c a t i o n )

L u b r i c a t i o n i n spec ia l environments

L u b r i c a t i o n a t extreme temperatures

L u b r i c a t i o n under r a d i a t i o n and/or i n r e a c t o r techn ique

Extreme pressure l u b r i c a t i o n

Lubr i can ts , 1 u b r i c a n t t e s t i n g

L u b r i c a t i o n systems and methods

Hygiene and m i c r o b i o l o g i c a l problems

359

9. F i e l d s o f a p p l i c a t i o n . Techn ica l designs and processes

9 .0 L i f e , r e l i a b i l i t y and maintenance o f t e c h n i c a l systems

9 . 1 Machinery and components: s e l e c t i o n and performance

9 .1 .1 Bear ings

9.1.2 Transmissions

9.1.3 Coupl ings, c l u t c h e s and brakes

9.1.4 Seals

9.1.5 Machines, se ts . Veh ic les and vesse ls

9.1.6 Wheel and r a i l

9.1.7 Tyre and road

9.1.8 S p e c i f i c i n d u s t r i e s

9.1.9

9.2 Manufac tur ing processes. Too ls

Other machine elements and produc ts

9 .2 .1 Forming

9.2.2 Ch ip less c u t t i n g

9.2.3 Machining

9.2.4 Sur face f i n i s h i n g

9.2.5 J o i n i n g

9.2.6 Coat ing

9.3 M a t e r i a l s t e s t i n g

9.4 Rock mechanics, geomechanics

10. Bas ic i n f o r m a t i o n on s o l i d su r faces and con tac ts

10.1 S o l i d su r faces

10.1.1 Morphology

10.1.2 S t reng th , sur face tens ion and energy, chemical r e a c t i o n s ,

environmental e f f e c t s

10.2 Contacts

10.2.1 Area o f con tac t , de fo rma t ion o f con tac t , hea t t r a n s f e r

10.2.2 J o i n t cha rac te r , adhesion

360

References

CHAPTER 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1.10

1.11

1.12

1.13

R.H. Cannon, Jr., Dynamics o f Physical Systems, Mc Graw-Hill, New York, 1967.

Tribology - A Glossary o f Terms and D e f i n i t i o n s , Organisation f o r Economic Co-operation and Development, OECD, Paris, 1969.

Lub r i ca t i on (Tr ibo logy) Education and Research - A r e p o r t on the present p o s i t i o n and i n d u s t r y ' s needs, Her Majesty's Stat ionery Of f ice, London, 1966.

F.P. Bowden and D. Tabor, The F r i c t i o n and Lubr i ca t i on o f Sol ids, Clarendon Press, Oxford, 1964.

E. Rabinowicz, F r i c t i o n and Wear o f Mater ia ls , Wiley, New York, 1965.

1 . V . Krage lsk i i , F r i c t i o n and Wear, Butterworths, London, 1965.

A. Cameron, The Pr inc ip les o f Lubr icat ion, Longmans, London, 1966.

J. H a l l i n g ( E d i t o r ) , P r inc ip les o f Tribology, MacMillan, London, 1975.

G. Amontons, De l a Resistance Caus6e dans l e s Machines, H i s t o i r e Acad. Roy. Sci., Paris, 12(1699) 206.

E. Coulomb, Th'eorie des machines simples, Mem. Math. Phys., Paris , 10( 1785) 161.

J.T. Desagulier, A Course o f Experimental Philosophy, London , 1734.

L. Ret i ( E d i t o r ) , Leonardo-Kunstler, Forscher, Magier, S. Fischer Verlag, Frankfur t , 1974.

W.B. Hardy and J.K. Hardy, Note on s t a t i c f r i c t i o n and on the l u b r i c a t i n g proper t ies o f c e r t a i n chemical substances, P h i l . Mag., 6(1919) 32.

361

1.14

1.15

1.16

1.17

1.18

1.19

1.20

1.21

1.22

1.23

1.24

1.25

1.26

1.27

1.28

1.29

1.30

1.31

G.A. Tomlinson, A molecular theory o f f r i c t i o n , P h i l . Mag., 7 (1929) 905. R. Holm, Die Reibungskraft i n der wahren Kontaktf lache, Wiss. Verof f . Siemens Werke, 17(1938) 38.

H. Ernst and M.E. Merchant, Surface f r i c t i o n between metals - A basic f a c t o r i n the metal c u t t i n g process, Proc. Special Summer Conf. F r i c t i o n and Surface F in ish, M I T Press, Cambridge, Mass., 1940, p. 76.

F.P. Bowden and D. Tabor, The theory o f m e t a l l i c f r i c t i o n and the r o l e o f shearing and ploughing, Council Sci. and Ind. Research, Comm. o f Aus t ra l i a , B u l l e t i n 145, 1942.

F.P. Bowden and 0. Tabor, The F r i c t i o n and Lubr i ca t i on o f Sol ids, Clarendon Press, Oxford, 1954.

M. Fuchsel, Ober Verschle iBbarkei t der Werkstoffe be i trockener Reibung, Organ For tschr . Eisenbahnwes., 84( 1929) 413.

M. F ink und U. Hofmann, Zur Theorie der Reiboxydation, Arch iv Eisenhuttenwes., 6(1932) 161.

R. Mailander und K. Dies, Be i t rag zur Erforschung der Vorgange beim VerschleiR, Tech. M i t t . Krupp Forsch.-Ber., 5(1942) 209.

E. Siebel, Ober d i e prakt ische Bewahrung der m i t VerschleiRver- suchen gewonnenen Ergebnisse, Tagungsband VDI-VerschleiDtagung, S t u t t g a r t , 1938, 5.4.

I-Meng Feng, Metal t r a n s f e r and wear, J. Appl. Phys., 23( 1952) 1011. J.T. Burwell and C.D. Strang, On the empir ica l law o f adhesive wear, J. Appl. Phys., 23(1952) 18.

M. Kerridge, Metal t r a n s f e r and the wear process, Proc. Phys. SOC. B, London, 68(1956) 400.

J.F. Archard, Contact and rubbing o f f l a t surfaces, J . Appl. Phys. 24(1953) 24. J.F. Archard and W . H i r s t , The wear o f metals under un lubr icated condi t ions, Proc. Roy. SOC., London, A 236(1956) 397.

J.T. Burwell , Survey o f poss ib le wear mechanisms, Wear, l(1957) 119.

c i t e d i n : R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics, Vol. 11, Addison-Wesley, Reading, 1964, p. 40-3.

0. Reynolds, On the theory o f l u b r i c a t i o n and i t s app l i ca t i on t o Mr . Beauchamp Tower's experiments, i nc lud ing an experimental determination o f the v i s c o s i t y o f o l i v e o i l , P h i l . Trans., 177( 1886) 157.

R. St r ibeck, Die wesentlichen Eigenschaften der G l e i t - und Rollenlager, VDI -Ze i t sch r i f t . 46(1902) 1341, 1432, 1463.

A. Sommerfeld, Zur hydrodynamischen Theorie der Schmiermittel- reibung, Z . Math. Phys., 50(1904) 97.

C. B i e l , Die Reibung i n G le i t l age rn bei Zusatz von Vol too l zu Mineral01 und be i Veranderung der Umlaufzahl und der Temperatur, VDI -Ze i t sch r i f t , 64(1920) 449, 483.

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G. Vogelpohl , Bet r i ebss i che re G l e i t l a g e r , Sp r inge r B e r l i n , 1958.

W.B. Hardy and J. Doubleday, Boundary l u b r i c a t i o n , se r ies , Proc. Roy. SOC., London, A lOO(1922) 550.

V e r l ag ,

The p a r a f f i n

K. Kirschke, H. Czichos, K.-H. Habig, P. S tud t , T r i b o l o g i e - Forschungsber ich t zum Schwerpunktprogramm VerschleiB, Reibung, Schmierung, Franz S t e i n e r Ver lag, Wiesbaden, 1971.

The i n t r o d u c t i o n o f a new technology, Report 1966-1972 o f the Committee on T r ibo logy , Her Ma jes ty ’ s S t a t i o n e r y O f f i c e , London, 1973.

G.H. Got tner , T r i b o l o g i e - B e g r i f f , Wesen und Bedeutung, Schmiertechnik und T r i b o l o g i e , 17( 1970) 285.

P. Jos t , Some economic f a c t o r s o f t r i b o l o g y , Proc. JSLE-ASLE I n t e r n a t . Lubr . Conf. ( E d i t o r : T. Saku ra i ) , E l s e v i e r , Amsterdam, 1976, p. 2 . D. Summers-Smith, 10 years a f t e r J o s t : t h e e f f e c t on i n d u s t r y , Proc. T r i b o l o g y Convention, I n s t . Mech. Engrs, 1976, p. 21.

DOCUMENTATION TRIBOLOGY - Wear, F r i c t i o n and L u b r i c a t i o n , 11 Volumes, 1967-1974, E d i t e d by Bundesansta l t f u r M a t e r i a l p r u f u n g (BAM), Fachgruppe Rheologie und T r i b o l o g i e , D-1 B e r l i n 45.

CHAPTER 2 2.1

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2 . 3

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L. von B e r t a l a n f f y , Genetal System Theory, Penguin, Condm, 1971.

K.E. Boulding, General systems theo ry - t h e ske le ton o f science, Management Science, 2 ( 1956) 197.

G. Ropohl, Systemtechnik - Grundlagen und Anwendung, Hanser Ver lag, Munchen, 1975.

M.D. Mesarovic, Views on General Systems Theory, Wi ley, New York, 1964.

G.J. K l i r , An Approach t o General Systems Theory, Van Nostrand Reinhold, New York, 1969.

J .J . van Dixhoorn and F.J. Evans, ( E d i t o r s ) , Phys ica l S t r u c t u r e i n Systems Theory, Academic Press, London, 1974.

P . Faur re and M. Depeyrot, Elements o f System Theory, Nor th Hol land, Amsterdam, 1977.

S. Seely, An I n t r o d u c t i o n t o Eng ineer ing Systems, Pergamon, New York, 1972, p. 55.

J.U. Thoma, I n t r o d u c t i o n t o Bond Graphs and T h e i r A p p l i c a t i o n , Pergamon, Oxford, 1975, p. 167.

H.M. Paynter, Ana lys i s and Design o f Eng ineer ing Systems (Class notes f o r M.I.T. course 2.751), The M.I.T. Press, Cambridge, Mass., 1960.

0. Karnopp and R. Rosenberg, Systems Dynamics: A U n i f i e d Approach, Wi ley , New York, 1975.

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2.12 N. Wiener, Cybernet ics o r Con t ro l and Communication i n t h e Animal and t h e Machine, The M.I.T. Press, Cambridge, Mass., 1948.

2.13 A.D. H a l l , A Methodology f o r Systems Eng ineer ing , Van Nostrand, New York, 1962.

CHAPTER 3 3.1 G. F l e i s c h e r , Systembetrachtungen z u r T r i b o l o g i e ,

3.2 G. Salomon, A p p l i c a t i o n o f systems t h i n k i n g t o t r i b o l o g y ,

3.3 H. Czichos, The p r i n c i p l e s o f systems a n a l y s i s and t h e i r

3.4 H. Czichos, Systemanalyse und Physik t r i b o l o g i s c h e r Vorgange,

Wiss. Z . TH Magdeburg, 14(1970) 415.

ASLE Trans, 17(1974) 295.

a p p l i c a t i o n t o t r i b o l o g y , ASLE Trans, 17(1974) 300.

T e i l 1: Grundlagen, T e i l 2: Anwendungen, Schmier techn ik und T r i b o l o g i e , 22(1975) 126 und 23(1976) 6.

t r i b o l o g i c a l systems, Wear, 44(1977) 247.

J. Mfilgaard, The d r y wear o f meta ls as a process i n an open system, Wear, 32( 1975) 353.

W.M.J. Schlosser, A c o n t r i b u t i o n t o t h e s tudy o f ana log ies o f power t ransmiss ion i n machines, Proc. J. Mech. E. London, 188(1974) 1.

3.8 J.U. Thoma, Bondgraph des ign f o r h y d r o s t a t i c bear ings , T r ibo logy , 6(1973) 97.

3.9 J.N. Brdnsted, On t h e concept o f hea t , Det K g l . Danske Videnskabernes Selskab, Mat.- fysk. Meddelelser, 19(1941) No. 8, 79p.

3.5 H. Czichos, and J. Mdlgaard, Towards a genera l t heo ry o f

3.6

3.7

CHAPTER 4 4.1

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4.3

4.4

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A.D. de P a t e r and J.J. K a l k e r ( E d i t o r s ) , The Mechanics o f t h e Contac t between Deformable Bodies, D e l f t U n i v e r s i t y Press, D e l f t , 1975.

F.F. L ing , Sur face Mechanics, Wi ley, New York, 1973.

H. Her tz , Ober d i e Beruhrung f e s t e r e l a s t i s c h e r Korper, J. f u r d i e r e i n e u. angew. Mathem., 92(1881) 156.

M.H. Jones, R.I.L. Howel ls, and S.D. Prober t , S o l i d s i n s t a t i c c o n t a c t - a review, Wear, 12(1968) 225.

J.F. Archard, Sur face topography and t r i b o l o g y , T r ibo logy , 7(1974) 213.

D.J. Whitehouse, The measurement and a n a l y s i s o f su r faces , T r ibo logy , 7(1974) 249.

T.R. Thomas, Recent advances i n t h e measurement and a n a l y s i s o f su r face microgeometry, Wear, 33j1975) 205.

H. v. Weingraber, M o g l i c h k e i t e n f u r e i n e s t a t i s t i s c h e Auswertung techn ischer Oberf lachen, Fe inge ra te techn ik , 19(1970) 416.

J. Pek len ik , Grundlagen z u r K o r r e l a t i o n s t h e o r i e techn ischer Oberf lachen, Ind . Anz., 87(1965) 456.

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A.M. Jones, P.W. O'Cal laghan and S.D. P rober t , P r e d i c t i o n o f con tac t parameters f rom t h e topographies o f c o n t a c t i n g surfaces, Wear, 31(1975) 89.

P.T. Sura tkar , S.M. Pand i t and S.M. Wu, A s t o c h a s t i c approach t o t h e mode o f de format ion and c o n t a c t between rough surfaces, Wear, 39(1976) 239.

J.F. Archard, Contact and rubb ing o f f l a t sur faces , J. Appl . Phys., 24( 1953) 981.

J.F. Archard, E l a s t i c de format ion and t h e laws of f r i c t i o n , Proc. Roy. SOC., London, A 243(1957) 190.

J.A. Greenwood and J.H. T r ipp , The e l a s t i c con tac t o f rough spheres, Trans ASME: J . Appl . Mech., 89(3967) 153.

A. Se i reg and E.J. Wei te r , Behaviour o f f r i c t i o n a l H e r t z i a n con tac ts under impu ls i ve load ing , Wear, 8(1965) 208.

K.C. Ludema and D. Tabor, The f r i c t i o n and v i s c o - e l a s t i c p r o p e r t i e s o f po lymer ic s o l i d s , Wear, 9(1966) 329.

R. S t r i beck , Kuge l lager fur b e l i e b i g e Belastungen, V D I - Z e i t s c h r i f t , 45(1901) 73.

J.A. Greenwood and J.B.P. Wi l l iamson, The con tac t o f nomina l l y f l a t sur faces , Proc. Roy. SOC., London, A 295(1966) 300.

D.J. Whitehouse and J.F. Archard, The p r o p e r t i e s o f random sur face o f s i g n i f i c a n c e i n t h e i r con tac t , Proc. Roy. SOC., London, A 316(1970) 97.

0. Tabor, A s i m p l i f i e d account o f su r face topography and the con tac t between s o l i d s , Wear, 32(1975) 269.

J.F. N icho las , The d i s s i p a t i o n o f energy d u r i n g p l a s t i c de format ion , Acta Met., 7(1959) 544.

H.C. Gatos, S t r u c t u r e o f sur faces and t h e i r i n t e r a c t i o n s , i n : I n t e r d i s c i p l i n a r y Approach t o F r i c t i o n and Wear, ( E d i t o r : P.M. Ku), NASA SP-181, Washington, 1968, p.7.

G. Schmaltz, Technische Oberflachenkunde, Spr inger , B e r l i n , 1936.

H.B.G. Casimir , Proc. Kon ink l . Ned. Akad. Wetenshap, B 51(1948) 795.

B.J. B r i scoe and 0. Tabor, Sur face fo rces i n f r i c t i o n and adhesion, Faraday Spec. Disc. Chem. SOC., No. 2(1972) 7.

J.M. Ziman, E lec t rons i n Meta ls - A Shor t Guide t o t h e Fermi Surface, Tay lo r and Franc is , London, 1963.

J. Fe r ran te and J.R. Smith, A t heo ry o f adhesion a t a b i m e t a l l i c i n t e r f a c e : ove r lap e f f e c t s , Surface Science, 38(1973) 77.

J. Fe r ran te and J.R. Smith, Metal i n t e r f a c e s : adhesive energ ies and e l e c t r o n i c b a r r i e r s , S o l i d s t a t e comm., 20(1976) 393.

H. Czichos, The mechanism o f t he m e t a l l i c adhesion bond, J . Phys. 0: Appl . Phys., 5(1972) 1890.

D.H. Buckley, Adhesion o f var ious meta ls t o a c lean i r o n (011) su r face s t u d i e d w i t h LEED and Auger emiss ion spectroscopy, NASA TN D-7018, Washington, 1971.

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F.P. Bowden and G.W. Rowe, The adhesion o f c lean meta ls , Proc. Roy. SOC. London, A 233(1956) 429.

M.E. S i k o r s k i , C o r r e l a t i o n o f t h e c o e f f i c i e n t o f adhesion w i t h va r ious p h y s i c a l and mechanical p r o p e r t i e s o f meta ls , Trans. ASME, D 85( 1963) 279.

D.H. Buckley, The i n f l u e n c e o f c r y s t a l s t r u c t u r e , o r i e n t a t i o n and s o l u b i l i t y on t h e adhesion and s l i d i n g o f va r ious metal s i n g l e c r y s t a l s i n vacuum (10-11 T o r r ) , ASTM STP No. 431, 1967, p.248.

D.H. Buckley and R.L. Johnson, The i n f l u e n c e o f c r y s t a l s t r u c t u r e and some p r o p e r t i e s of hexagonal meta ls on f r i c t i o n and adhesion, Wear, l l ( 1 9 6 8 ) 405.

K.-H. Habig, Der E i n f l u B d e r gegense i t igen L o s l i c h k e i t von M e t a l l e n auf e i n i g e i h r e r t r i b o l o g i s c h e n Eigenschaften, Me ta l l obe r f l ache , 24(1970) 375.

D.H. Buckley, F r i c t i o n , Wear and L u b r i c a t i o n i n Vacuum, NASA SP-277, Washington, 1971, p.66.

D.H. Buck ley , The in f l uence o f t h e atomic na tu re o f c r y s t a l l i n e m a t e r i a l s on f r i c t i o n , Trans. ASLE, l l (1968) 89.

K.-H. Habig, Zur S t r u k t u r - und Orient ierungsabhangigkei t der Adhasion und de r t rockenen G l e i t r e i b u n g von Me ta l l en , Ma te r ia lp ru fung , lO(1968) 417.

D.H. Buckley, E f f e c t o f va r ious m a t e r i a l p r o p e r t i e s on t h e adhesive stage o f f r e t t i n g , AGARD Conf. Proc. NO. 161,

N. Gane, P.F. P f a e l z e r and D. Tabor, Adhesion between c lean su r faces a t l i g h t loads , Proc. Roy. SOC., London, A 340(1974) 495.

K.L. Johnson, K. Kenda l l and A.D. Roberts, Sur face energy and t h e c o n t a c t o f e l a s t i c s o l i d s , Proc. Roy. SOC., London, A 324(1971) 301.

K.N.G. F u l l e r and 0. Tabor, The e f f e c t o f su r face roughness on t h e adhesion o f e l a s t i c s o l i d s , Proc. Roy. SOC., London, A 345(1975) 327.

R.D. M i n d l i n , Compliance o f e l a s t i c bod ies i n con tac t , Trans. ASME, J . Appl. Mech., 71(1949) 259.

J . S . Mc Far lane and 0. Tabor, R e l a t i o n between f r i c t i o n and adhesion, Proc. Roy. SOC., London, A 202(1950) 244.

J .S . Cour tney -Pra t t and E. E isner , The e f f e c t o f a t a n g e n t i a l f o r c e on the c o n t a c t o f m e t a l l i c bodies, Proc. Roy. SOC., London, A 238(1957) 529.

H. Czichos, Fes tko rpe r re ibung - T e i l g e b i e t d e r T r i b o l o g i e , Umschau (1971) 116.

M. Godet, Sur face and shape e f f e c t s i n t h e measurement o f f r i c t i o n fo rces , Wear, 28(1974) 115.

R. Cour te l , Modes d ' i n t e r p r e t a t i o n de l a t r o i s i e m e dimensions dans l e s processus de f r o t t e m e n t i n t e r m g t a l l i q u e . Role du b o u r r e l e t f r o n t a l , B u l l . I n s t . Sc i . Techn. du Centre Energ ie A t . , 90(1965) 3.

1975, p. 13-1.

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L.A. M i t c h e l l and C . Osgood, A t heo ry o f f r i c t i o n and wear based on a new c h a r a c t e r i z a t i o n o f a s p e r i t y i n t e r a c t i o n s , Wear, 40( 1976) 203.

D.H. Buck ley , The meta l - to -meta l i n t e r f a c e and i t s e f f e c t on adhesiop and f r i c t i o n , J . C o l l . I n t e r f a c e Sc i . , 58(1977) 36.

D. Tabor, I n t e r a c t i o n between Surfaces: Adhesion and F r i c t i o n , i n : Sur face Physics o f M a t e r i a l s , Vol . I 1 ( E d i t o r : J.M. B l a k e l y ) Academic Press, New York, 1975, p. 475.

H. Czichos, D ie Energieverlustmechanismen der Ro l l re ibung , Schmiertechnik und T r i b o l o g i e , 16( 1969) 62.

0. Reynolds, On r o l l i n g f r i c t i o n , P h i l . Trans. Roy. SOC., London, 116( 1876) 155.

H.L. Heathcote, The b a l l bear ing , Proc. I n s t n . Automot ive Engrs, 15(1921) 1569.

F.W. Car te r , On the a c t i o n o f a locomot ive d r i v i n g wheel, Proc. Roy. Soc., London, A 112(1926) 151.

H. P o r i t s k y , Stresses and d e f l e c t i o n s o f c y l i n d r i c a l bodies i n con tac t w i t h a p p l i c a t i o n t o con tac t o f gears and o f locomot ive wheel, Trans. ASME, J. Appl . Mech., 72(1950) 191.

L. Foppl, D ie s t renge Losung f u r d i e r o l l e n d e Reibung, Munchen, 1947.

D. Tabor, The mechanism of r o l l i n g f r i c t i o n , 11, t h e e l a s t i c range, Proc. Roy. SOC., London, A 229(1955) 198.

B.G. Bro the rs and G.R. Bremble, The e f f e c t o f geomet r ic con fo rm i t y between a b a l l and i t s t r a c k on the f r e e r o l l i n g res i s tance , Wear, 20(1972) 175.

0. Tabor, The mechanism o f r o l l i n g f r i c t i o n , P h i l . Mag., 43( 1952) 1055.

D.G. Flom and A.M. Bueche, Theory o f r o l l i n g f r i c t i o n f o r spheres, J . Appl. Phys., 30(1959) 1725.

J.B. Halaunbrenner, E l a s t o - o p t i c a l i n v e s t i g a t i o n s o f r o l l i n g o f a r i g i d c y l i n d e r on a v i s c o - e l a s t i c base, Wear, 8 (1965) 30.

K.R. Eldredge and 0. Tabor, The mechanism o f r o l l i n g f r i c t i o n , I, the p l a s t i c range, Proc. Roy. SOC., London, A 229(1955) 181.

L.D. Dyer, R o l l i n g f r i c t i o n on s i n g l e c r y s t a l s o f copper i n the p l a s t i c range, Ac ta Met., 9(1961) 928.

K.L. Johnson, A rev iew o f t h e theo ry o f r o l l i n g con tac t s t resses , Wear, 9(1966) 4.

A.W. Crook, Simulated gear - too th con tac ts : some exper iments upon t h e i r l u b r i c a t i o n and subsur face deformat ions, Proc. Conf. Lubr. Wear, I , Mech. Eng., 1957, 701.

G. M. Hamil ton, P l a s t i c f l o w i n r o l l e r s loaded above the y i e l d p o i n t , Proc. I n s t . Mech. Engrs, 177(1963) 667.

J.W. Merwin and K.L. Johnson, Ana lys i s o f p l a s t i c de format ion r o l l i n g con tac t , Proc. I n s t . Mech. Engrs, 177(1963) 676.

H. Czichos, Ober den Zusammenhang zwischen Adhasion und E lek t ronen- s t r u k t u r von Me ta l l en b e i de r R o l l r e i b u n g i m e l a s t i s c h e n Bereich, Z. angew. Physik, 27(1969) 40.

367

K. Kenda l l , R o l l i n g f r i c t i o n and adhesion between smooth s o l i d s , Wear, 33(1975) 351.

B.V. Der jagu in and V.P. Smilga, E l e c t r o s t a t i c component o f t h e r o l l i n g f r i c t i o n f o r c e moment, Wear, 7(1964) 270.

J.H. Dismant, Rev iv ing t h e c l a s s i c a l t h e o r y o f f r i c t i o n by a modern d i s l o c a t i o n theo ry o f de format ion r e v i s i o n , J. Appl. Phys., 31(1960) 221.

B.J. K o s t e t s k i i and P.V. Natarenko, I n f l u e n c e o f changes o f d i s l o c a t i o n s t r u c t u r e on t h e r e l a t i o n between f r i c t i o n and normal p ressure (The Amontons-Coulomb law) , S o v i e t Phys ics - Doklady, 9( 1965) 1011.

R. Feder and P. Chaudhari, Transmission e l e c t r o n microscopy of wear t racks , Wear, 19(1972) 109.

G. E . R. Schul t z e , Metal 1 p hys i k , Akademi e - Ver l ag , Be r l i n , 1967, p. 217.

N. Gane and J. Sk inner , The genera t i on o f d i s l o c a t i o n s i n me ta l s under a s l i d i n g c o n t a c t and the d i s s i p a t i o n o f f r i c t i o n a l energy, Wear, 25(1973) 381.

G. A n d a r e l l i , D. Maugis and R . Cour te l , Observa t ion o f d i s l o c a t i o n s c r e a t e d by f r i c t i o n on aluminium t h i n f o i l s , Wear, 23(1973) 21.

J.G. B o l l i n g e r , Noise - an i n d u s t r i a l p o l l u t a n t o f i n t e r n a t i o n a l concern, C I R P Annals, 22( 1973) 197.

D.M. T o l s t o i , S i g n i f i c a n c e o f t h e normal degree o f freedom and n a t u r a l normal v i b r a t i o n s i n c o n t a c t f r i c t i o n , Wear, lO(1967) 199.

Triboluminescence, d t v -Lex i kon d e r Phys ik , Deutscher Taschenbuch- Ver lag, Munchen, 1971, Bd. 9, p. 168.

J. Fer ran te , Exoe lec t ron emiss ion f rom a clean, annealed magnesium s i n g l e c r y s t a l d u r i n g oxygen adso rp t i on , ASLE Trans., 20( 1977).

J . Wortmann, Zu r Exoelektronenemission (EEE), i n "Verhal t e n und E igenschaf ten von m e t a l l i s c h e n Oberf lachen", TU B e r l i n , Fachbereich 17 (Fachseminar WS 75/76) 1976, p. 280.

H.S. Carslaw and J.C. Jaeger, Conduct ion o f Heat i n So l i ds , Clarendon Press, Oxford, 1947, p. 56. R. Holm, C a l c u l a t i o n o f t h e tempera ture development i n a c o n t a c t heated i n t h e c o n t a c t sur face , and a p p l i c a t i o n t o t h e problem o f t h e temperature r i s e i n a s l i d i n g contac t , J. Appl. Phys., 19( 1948) 361.

H. Blok , T h e o r e t i c a l s tudy o f temperature r i s e a t sur faces o f a c t u a l c o n t a c t under o i l i n e s s l u b r i c a t i n g cond i t i ons , Proc. Gen. D isc . Lubr., I n s t . Mech. Engrs, London, 1937, v o l . 2, p. 14.

J.F. Archard, The temperature o f rubb ing sur faces , Wear, 2( 1958/59) 438.

P.S. Kounas, A.D. Dimarogonas and G.N. Sandor, The d i s t r i b u t i o n o f f r i c t i o n hea t between a s t a t i o n a r y p i n and a r o t a t i n g c y l i n d e r , Wear, 19(1972) 415.

F. Charron, Partage de l a cha leu r e n t r e deux corps f r o t t a n t s , E d i t i o n s Blonde1 l a Rougery, Pa r i s , 1943.

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J.F. Archard, Wear, i n : I n t e r d i s c i p l i n a r y Approach t o F r i c t i o n and Wear (Edi tor : P.M. Ku), NASA SP-181, Washington, 1968, p. 267.

H. Czichos und K.-H. Habig, Grundvorgange des Verschleisses metal l i s c h e r Werkstoffe - Neuere Ergebnisse der Forschung, VDI-Ber. Nr . 194, 1973, S. 23. P.A. Engel, Impact Wear o f Materials, E lsev ier , Amsterdam, 1976. O.R. Lang, Surface f a t i g u e o f p l a i n bearings, Wear, 43(1977) 25.

K.H. Kloos und E. Broszei t , Zur Frage der Dauerwalzfestigkeit, Z. f . Werkstofftechnik, 5(1974) 181.

M.J.W. Schouten, Der E in f l uB elastohydrodynamischer Schmierung auf Reibung, VerschleiB und Lebensdauer von Getrieben, Schmiertechnik und Tr ibo log ie, 20( 1973) 147.

W.E. Littmann, The mechanism o f contact fa t igue, i n : I n t e r d i s c i p l i n a r y approach t o the l u b r i c a t i o n o f concentrated contacts, NASA SP-237, Washington, 1970, p. 309. Y.P. Chiu, T.E. T a l l i a n and J . I . Mc Cool, An engineering model o f s p a l l i n g fa t igue f a i l u r e i n r o l l i n g contact, I , The subsurface model, Wear, 17(1971) 433. T.E. T a l l i a n and J.I . Mc Cool, 11, The surface model, Wear, 17(1971) 447. T.E. Ta l l i an , 111, Engineering discussion and i l l u s t r a t i v e examples, Wear, 17(1971) 463.

J . C . Ty ler , R.A. Burton and P.M. Ku, Contact f a t i gue under o s c i l l a t o r y normal load, ASLE Trans., 6(1963) 255. P. Haasen, Physi ka l ische Metal 1 kunde, Springer-Verlag, Be r l i n , 1974, p. 298.

D. Kuhlmann-Wilsdorf and C, Laird, D is loca t i on behaviour i n fat igue, Mat. Sci. Eng. , 27(1977) 137. E. Hornbogen, The r o l e o f f r a c t u r e toughness i n the wear o f metals, Wear, 33(1975) 251.

N.P. Suh, The delamination theory o f wear, Wear, 25( 1973) 111. J.P. H i r t h and D.A. Rigney, Crystal p l a s t i c i t y and the delamination theory o f wear, Wear, 39( 1976) 133. T.S. Eyre, Wear cha rac te r i s t i cs of metals, Tr ibo logy In te rna t i ona l , (1976) 203. K. Well inger und H. Uetz, Gle i tverschle iB. SpulverschleiD, St rah lverschle iD un te r Wirkung von kornigen Stoffen, VDI-Forschungsheft 449, Beilage zu Forsch. Ing. Wes. Zl(1955) 1.

K. Wellinger, H. Uetz und M. Gurleyik, GleitverschleiBuntersuchungen an Metal len und n ichtmeta l l ischen Har t s to f fen unter Wirkung korn iger Stof fe , Wear, ll(1968) 173. M.M. Khrushov, Resistance o f metals t o wear by abrasion; r e l a t e d t o hardness, Proc. Conf. Lubr. and Wear, I ns tn . Mech. Engrs, London, 1957, p. 655.

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M.M. Khrushov, P r i n c i p l e s o f ab ras i ve wear, Wear, 28(1974) 69.

R.C.D. Richardson, The wear o f me ta l s by r e l a t i v e l y s o f t abras ives , Wear, 11( 1968) 245.

P.L. Hur r i cks , Some m e t a l l u r g i c a l f a c t o r s c o n t r o l l i n g t h e adhes ive and ab ras i ve wear r e s i s t a n c e o f s t e e l , a rev iew, Wear, 26(1973) 285.

H. Uetz und J . Foh l , Versch le iD und Reibung a l s komplexe mechanisch-physikal isch-chemische Prozesse, E rzmeta l l , 23( 1970) 205.

D.H. Buckley, Wear and i n t e r f a c i a l t r a n s p o r t o f m a t e r i a l , NASA TMX-71781, 1975.

M. Cocks, Shear ing o f j u n c t i o n s between metal sur faces , Wear, 9(1966) 320.

M. A n t l e r , Stages o f wear o f a prow fo rm ing meta l , ASLE Trans. , 13( 1970) 79.

D. Landheer and J.H. Zaat, The mechanism o f meta l t r a n s f e r i n s l i d i n g f r i c t i o n , Wear, 27(1974) 129.

D.H. Buckley, E f f e c t o f va r ious m a t e r i a l p r o p e r t i e s on t h e adhesive s tage o f f r e t t i n g , NASA TMX-71582, 1974.

P.A. Thiessen, K. Meyer und G. He in icke , Grundlagen de r Tr ibochemie, Akademie-Verlag, B e r l i n , 1967.

T.F.J. Quinn, The e f f e c t o f "ho t spo t " temperatures on t h e u n l u b r i c a t e d wear o f s t e e l , ASLE Trans., lO(1967) 158.

P.L. Hur r i cks , The mechanism o f f r e t t i n g - a review, Wear, 15(1970) 389.

R.B. Waterhouse, F r e t t i n g Cor ros ion , Pergamon, Oxford, 1972

R . B . Waterhouse, Phys ics and m e t a l l u r g y o f f r e t t i n g ,

H. Czichos, D iscuss ion on t h e adhesive s tage o f f r e t t i n g ,

J. Mdlgaard, D ie Entw ick lung von VerschleiBprozeBthesen, Schmi e r t e c h n i k und T r i b o l o g i e, 23( 1976) 126.

see Ref. 1.29.

see Ref. 1.28.

see Ref. 1.27, Chapter 40.

M.D. Hersey, Theory and Research i n L u b r i c a t i o n , Wi ley , New York, 1966, p. 34.

H.C. R ippe l , 0. Decker and Z. Zudans, NASA C o n t r i b u t i o n s t o F l u i d - F i l m L u b r i c a t i o n - A Survey, NASA SP-5058, Washington , 1969.

J. Ho l l and , D ie E r m i t t l u n g de r KenngroRen f u r z y l i n d r i s c h e G l e i t l a g e r , Kons t ruk t i on , 13( 1961) 100.

G. Vogelpohl, B e t r i e b s s i c h e r e G l e i t l a g e r , Spr inger -Ver lag , B e r l i n , 1958, p. 73.

AGARD-CP-161, 1975, p. 8-1.

AGARD-CP-161, 1975, p. 13-16.

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D.F. Moore, P r inc ip les and Appl icat ions o f Tribology, Pergamon, Oxford, 1975, p. 346.

J.J. O'Connor, J . Boyd, E.A. Avallone, (Ed i to rs ) , Standard Handbook o f Lub r i ca t i on Engineering, McGraw-Hill , New York, 1968. L.D. Wedeven, What i s EHD?, Lubr. Engng, 31(1975) 291.

F.H. Theyse, Elastohydrodynami k, Schmiertechni k, 15(1967) 15.

J.W. Kannel, J.C. B e l l and C.M. A l len, Methods f o r determining pressure d i s t r i b u t i o n s i n l ub r i ca ted r o l l i n g contact, ASLE Trans., 8(1965) 250.

see Ref. 1.7, p. 203.

0. Dowson and G.R. Higginson, New r o l l e r - b e a r i n g l u b r i c a t i o n formula, Engineering, London, 192( 1961) 158.

H.S. Cheng and F.K. Orcutt, A c o r r e l a t i o n between the theo re t i ca l and experimental r e s u l t s on the elastohydrodynamic l u b r i c a t i o n o f r o l l i n g and s l i d i n g contact, Proc. I. Mech. E., London, Vol. 180, Pa r t 38, (1965/66) 158.

A.J. Petrousevitch, D.S. Kodnir, R.G. Salukvadze, D.L. Bakashvi l i and V.Sh. Schwarzman, The i n v e s t i g a t i o n o f o i l f i l m thickness i n l ub r i ca ted ba l l - race r o l l i n g contact, Wear, 19(1972) 369.

F.J. Westlake and A. Cameron, Opt ica l elastohydrodynamic f l u i d tes t i ng , ASLE Trans., 15(1972) 81.

A. Jackson, F i l m thickness i n EHL p o i n t contacts: r e v i s i o n o f Westlake and Cameron's equations, ASLE Trans., 19(1976) 48. -

J. Tevaarwerk and K.L. Johnson, A simple non- l inear c o n s t i t u t i v e equation f o r elastohydrodynamic o i l f i l m s , Wear, 35( 1975) 345.

0. Dowson, T rans i t i on t o boundary l u b r i c a t i o n from elastohydro- dynamic l u b r i c a t i o n , i n : Boundary Lubr icat ion, (Edi tors : F.F. Ling, E.E. Klaus and R.S. Fe in) , ASME, New York, 1969, p. 229.

A. Dyson, discussion in : I n t e r d i s c i p l i n a r y approach t o the l u b r i c a t i o n o f concentrated contacts, NASA SP-237, Washington, 1970, p. 58.

J.F. Archard, Elastohydrodynamic l u b r i c a t i o n o f rea l surfaces, Tribology, 6(1973) 8.

L.D. Wedeven, Tract ion and f i l m thickness measurements under s tarved elastohydrodynamic condit ions, Trans. ASME, JOLT, 97( 1975) 321.

H. Munnich, E in f l uB der Schmierung auf Lebensdauer, Reibung und VerschleiB von Walzlagern, Schmiertechnik und Tr ibo log ie, 16( 1968) 87.

V.K. Ausherman, H.S. Nagaraj, D.M. Sanborn and W.O. Winer, I n f r a r e d temperature mapping i n elastohydrodynamic l u b r i c a t i o n , Trans. ASME, F, 98(1976) 236.

L. Gumbel, Der Einf luD der Schmierung auf d i e Konstruktion, Jb. schif fbautechn. Ges., 18(1917) 299.

G. Vogelpohl , Die Stribeck-Kurve a l s Kennzeichen des allgemeinen Reibungsverhaltens geschmierter Gle i t f lPchen, VDI -Z . , 96(1954) 261.

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H. Christensen, A theory o f mixed l u b r i c a t i o n , Proc. I ns tn . Mech. Engrs, London, 186(1972) 421.

D. Berthe and M. Godet, A more general form o f Reynolds equation - app l i ca t i on t o rough surfaces, Wear, 27(1974) 345.

K.L. Johnson, J.A. Greenwood and S.Y. Poon, A simple theory o f asper i t y contact i n elastohydrodynamic l u b r i c a t i o n , Wear, 19(1972) 91.

T.E. T a l l i a n , The theory o f p a r t i a l elastohydrodynamic contacts, Wear, Zl(1972) 49.

E.S. Forbes, Antiwear and extreme pressure add i t i ves f o r l ub r i can ts , Tribology, 3(1970) 145.

P. Studt, Schmieroladdit ive f u r hohe Flachenpressung und i h r e Wirkung, VDI-Berichte, 156(1970).

D. Godfrey., Boundary l u b r i c a t i o n , i n Ref. 4.131, Chapter 2.

D. Godfrey, .Boundary l u b r i c a t i o n , i n : I n t e r d i s c i p l i n a r y Approach t o F r i c t i o n and Wear, (Ed i to r : P.M. Ku), NASA SP-181, Washington, 1968, p. 335.

J.S. Courtney-Pratt, An o p t i c a l method o f measuring the thickness o f adsorbed monolayers, Proc. Roy. SOC., London, 212(1952) 505.

R. Holm, E l e c t r i c Contacts, H. Gebers Forlag, Stockholm, 1946, p. 198.

F.P. Bowden and D. Tabor, F r i c t i o n - An In t roduc t i on t o Tr ibo logy, Heinemann, London, 1973, p. 128.

W.E. Campbell, Boundary l u b r i c a t i o n , i n : Boundary Lubr icat ion, (Edi tors : F.F. Ling, E.E. Klaus and R.S. Fein), ASME, New York, 1969, p. 87.

F.G. Rounds, I n f l uence o f s tee l composition on a d d i t i v e performance, ASLE Trans., 15(1972) 54.

R.S. Fein, Chemistry i n concentrated - conjunct ion l u b r i c a t i o n , i n : I n t e r d i s c i p l i n a r y Approach t o the Lubr i ca t i on o f Concentrated Contacts, NASA SP-237, Washington, 1970, p . 489.

C.N. Rowe, Some aspects o f the heat o f adsorpt ion i n the func t i on o f a boundary l u b r i c a n t , ASLE Trans., 9(1966) 100.

C.N. Rowe, A r e l a t i o n between adhesive wear and heat o f adsorption f o r the vapor l u b r i c a t i o n o f graphite, ASLE Trans., lO(1967) 10.

A. Dyson, Scu f f i ng - a review, Tr ibo logy, 8(1975) 77 and 117.

T.v. Mrmin, Ober den Mechanismus des Widerstandes, den e i n bewegter Korper i n e ine r F l u s s i g k e i t e r f a h r t , Nachrichten der K. Ges. d. Wissenschaften, Math-phys. Klasse, Gottingen, 1911.

G.I. Taylor, S t a b i l i t y o f a viscous l i q u i d contained between two r o t a t i n g cy l i nde rs , Trans. Roy. SOC. , London, A 223(1923) 289.

R.C. d i Prima, A note on the s t a b i l i t y o f f l ow i n loaded jou rna l bearing, ASLE Trans., 6( 1963) 249.

V.N. Constantinescu, Analysis o f bearings operat ing i n tu rbu len t regime, Trans. ASME, D, 84(1962) 139.

E. Saibel, Turbulence i n l u b r i c a t i o n , i n Ref. 1.7, p. 441.

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T.E. T a l l i a n , Y.P. Chiu, D.F. Hut ten locher , J.A. Kamenshine, L.B. S i b l e y and N.E. S ind l i nge r , L u b r i c a n t f i l m s i n r o l l i n g con tac t o f rough sur faces , ASLE Trans., 7(1964) 109.

H. Czichos, Untersuchungen uber d i e V e r t e i l u n g meta l1 i s c h e r und n i c h t m e t a l l i s c h e r K o n t a k t a n t e i l e b e i Mischreibung, Wear, 17(1971) 209.

H. Czichos, I n f l u e n c e o f a s p e r i t y c o n t a c t cond i t i ons on the f a i l u r e o f s l i d i n g elastohydrodynamic contac ts , Wear, 41(1977) 1.

R.S. Fein, C.N. Rowe and K.L. Kreuz, T r a n s i t i o n temperatures i n s l i d i n g systems, ASLE Trans., 2(1959) 50.

R.S. Fein, Opera t ing procedure e f f e c t s on c r i t i c a l temperatures, ASLE Trans., 10( 1967) 373.

H. Czichos and K. Kirschke, I n v e s t i g a t i o n s i n t o f i l m f a i l u r e ( t r a n s i t i o n p o i n t ) o f l u b r i c a t e d concent ra ted contac ts , Wear, 22( 1872) 321.

H. Czichos, F a i l u r e modes o f s l i d i n g l u b r i c a t e d concent ra ted contac ts , Wear, 28(1974) 95.

A. Bege l i nge r and A.W.J. de Gee, T h i n f i l m l u b r i c a t i o n o f s l i d i n g p o i n t con tac ts o f A I S I 52100 s t e e l , Wear, 28(1974) 103.

H. Czichos, F a i l u r e c r i t e r i a i n t h i n f i l m l u b r i c a t i o n : t h e concept o f a f a i l u r e sur face , T r ibo logy , 7(1974) 14.

G. Salomon, F a i l u r e c r i t e r i a i n t h i n f i l m l u b r i c a t i o n - t h e I R G program, Wear, 36(1976) 1.

H. Czichos, T r ibomet r i sche Untersuchung de r Versagensgrenzen von Gle i t re ibungssys temen m i t Hertzschem Kontak t i m Mischreibungs- geb ie t , Ma te r ia lp ru fung , 16(1974) 32.

A. Sethuramiah, H. Okabe, T. Sakurai , C r i t i c a l temperatures i n EP l u b r i c a t i o n , Wear, 26(1973) 187.

M. Tomaru, S. Hironaka and T . Sakura i , E f f e c t s o f oxygen on the l oad -ca r ry ing a c t i o n o f some a d d i t i v e s , Wear, 41(1977) 117.

M. Tomaru, S. Hironaka and T. Sakurai , E , f fec ts o f some chemical f a c t o r s on f i l m f a i l u r e under EP cond i t i ons , Wear, 41(1977) 141.

A . Bege l i nge r and A.W.J. de Gee, L u b r i c a t i o n o f s l i d i n g p o i n t con tac ts o f A I S I 52100 s t e e l - t h e i n f l u e n c e o f cu rva tu re , Wear, 36(1976) 7.

H. Czichos, F i l m f a i l u r e o f s l i d i n g H e r t z i a n contac ts : The i n f l u e n c e o f con tac t geometry, Proc. JSLE-ASLE I n t e r n a t . Lubr. Conf. Tokyo 1975, ( E d i t o r : T. Sakura i ) , E l s e v i e r , Amsterdam, 1976, p. 368.

CHAPTER 5 5.1 J.B.P. Wi l l iamson, J . P u l l e n and R.T. Hunt, The shape o f s o l i d

surfaces, in : Sur face Mechanics ( E d i t o r F.F. L ing) , The American SOC. o f Mech. Engrs, New York, 1969, p. 32. M.J. Neale ( E d i t o r ) , T r i b o l o g y Handbook, But te rwor ths , London, 1973, p. A31. K.J. S tou t , T.G. K ing and D.J. Whitehouse, A n a l y t i c a l techniques i n su r face topography and t h e i r a p p l i c a t i o n t o a runn ing - in experiment, Wear, 43(1977) 99.

5.2

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J.E. W i l l n , C h a r a c t e r i z a t i o n o f c y l i n d e r bore su r face f i n i s h - a rev iew o f p r o f i l e ana lys i s , Wear, 19(1972) 143.

J.C. Campbell, C y l i n d e r bore su r face roughness i n i n t e r n a l combustion engines: i t s a p p r e c i a t i o n and c o n t r o l , Wear, 19( 1972) 163.

J.R. Dowd and F.T. Ba rwe l l , T r i b o l o g i c a l i n t e r a c t i o n between p i s t o n and c y l i n d e r o f a model h i g h pressure h y d r a u l i c pump, ASLE Trans., 18(1975) 21.

R. g s t v i k and H. Chr is tensen, Changes i n su r face topography w i t h runn ing - in , Proc. I n s t n . Mech. Engrs, London, Vol . 183 P t 3P, (1968/69) 57.

G.W. Rowe, Sur face topograph ic changes a t breakdown o f t h i n - f i l m l u b r i c a t i o n ; a s h o r t account o f a c o l l a b o r a t i v e C . I . R . P . i n v e s t i g a - t i o n , Wear, 28(1974) 125.

E. Sa ibe l , A s t a t i s t i c a l approach t o r u n - i n and the dependence o f t he c o e f f i c i e n t o f f r i c t i o n on v e l o c i t y , Wear, 35(1975) 383.

J . Volz, E r s t e l l u n g o p t i m i e r t e r Einlaufprogramme von Dieselmotoren ( E i n System u n t e r Anwendung von Radionukl i den ) Kernforschungszentrum Kar ls ruhe, Labora tor ium f u r I so topen techn ik , KFK 2432, Marz 1977.

D.H. Buckley, Wear and i n t e r f a c i a l t r a n s p o r t o f m a t e r i a l , J. Vac. S c i . Technol . , 13( 1976) 88.

M. F ink and U. Hofmann, Zur Theor ie de r Reiboxydat ion, A r c h i v f . d . Eisenhuttenwesen, 6( 1932) 161.

K. Dies, D ie Vorgange beim Versch le iB b e i r e i n g l e i t e n d e r t rockener Reibung, V D I - Z . , 83(1939) 307.

T.S. Eyre and D. Maynard, Sur face aspects o f u n l u b r i c a t e d me ta l - to - metal wear, Wear, 18(1971) 301.

S. Hogmark, 0. Vingsbo and S. F r ieds t rom, Mechanisms o f d r y wear o f some m a r t e n s i t i c s t e e l s , Wear, 31(1975) 39.

T.F.J. Qu inn and J.L. Wooley, The u n l u b r i c a t e d wear o f 3% Cr-1/2% Mo s t e e l , Lubr . Eng., 26(1970) 226.

B.A. Baldwin, Chemical c h a r a c t e r i z a t i o n o f wear su r faces us ing X-ray pho toe lec t ron spectroscopy, Lubr . Engng, 32( 1976) 125.

R.J. B i r d and G.D. Ga lv in , The a p p l i c a t i o n o f pho toe lec t ron spec t ro - scopy t o t h e s tudy o f E . P . f i l m s on l u b r i c a t e d sur faces , Wear, 37( 1976) 143.

R . C . Coy and T.F.J. Quinn, The use o f p h y s i c a l methods o f a n a l y s i s t o i d e n t i f y su r face l a y e r s formed by organosulphur compounds i n wear t e s t s , ASLE Trans, 18(1975) 163.

G. Levy, R.G. L i n f o r d and L.A. M i t c h e l l , Wear behav iour and mechani- c a l p r o p e r t i e s : t h e s i m i l a r i t y o f seemingly u n r e l a t e d approaches, Wear, 21(1972) 167.

see Ref. 1.5, p. 18. J.T. Bu rwe l l and C.D. Strang, On t h e e m p i r i c a l law o f adhesive wear, J. Appl. Phys., 23(1952) 18.

R.D. A r n e l l , A.P. Herod and D.G. Teer, The e f f e c t o f combined s t resses on t h e t r a n s i t i o n f rom m i l d t o severe wear, Wear, 31(1975) 237.

374

5.24

5.25

5.26

5.27

5.28

5.29

5.30

5.31

5.32

5.33

5.34

5.35

5.36

5.37

5.38

5.39

5.40

5.41

5.42

5.43

5.44

K.-H. Habig, K. Kirschke, W . - W . Maennig, H. T ischer , Fes tkorper - g l e i t r e i b u n g und Versch le iB von Eisen, Koba l t , Kupfer, S i l b e r , Magnesium und Aluminium i n einem Sauerstoff-Stickstoff-Gemisch zwischen 760 und 2

K.-H. Habig, K. K i rschke, W . - W . Maennig, H. T ischer , Fes tkorper - g le i t re i ’ bung und Versch le iB von Eisen, Kobal t, Kupfer, S i l b e r , Magnesium und Aluminium i n einem Sauerstoff-Stickstoff-Gemisch zwischen 760 und 2 - 10-7 To r r , Wear, 22(1972) 373.

N.C. Welsh, The d r y wear o f s t e e l . I, The general p a t t e r n o f behaviour; 11. I n t e r p r e t a t i o n and spec ia l f ea tu res , P h i l . Trans. Roy. SOC., London, A 257(1965) 31.

see Ref. 4.89.

H. Uetz and J. Fohl , P r u f t e c h n i k b e i einem VerschleiBsystem a u f Grund de r VerschleiBanalyse, insbesondere d e r thermischen Analyse, VDI-Ber ichte, N r . 194, 1973, p. 57.

see Ref. 1.5, p. 151 ff.

A.A. Reda, R. Bowen and V . C . Westcott , C h a r a c t e r i s t i c s o f p a r t i c l e s generated a t t h e i n t e r f a c e between s l i d i n g s t e e l sur faces , Wear, 34( 1975) 261.

T.E. T a l l i a n , G.H. B a i l e , H. Da la l , O.G. Gustafsson, R o l l i n g Bear ing Damage - A Morpho log ica l A t l as , SKF I n d u s t r i e s , Technology Center, K ing o f Pruss ia , Pa, 1974. E.R. Bowen, V.C. Westcott , Wear P a r t i c l e A t l as , Report No N00156-74- c-1682, prepared f o r Naval A i r Eng ineer ing Center, Lakehurst , N.J., J u l y 1976.

see Ref. 4.129, p. 252 ff.

H.C. R ippe l , Des ign ing f l u i d - f i l m bear ings by computer, Mech. Engng, (1970) 30.

P.B. Davies and R.B. Howarth, H y d r o s t a t i c l u b r i c a t i o n , see Ref. 1.8, p. 308 f f .

C.M. Tay lo r , Unusual bea r ings : a i r and magnet ic suspension, Ind . L u b r i c a t i o n and T r ibo logy , 24( 1972) 234.

M . I . Anwar and C.M. Rodkiewicz, S l i d e r bea r ing w i t h segmented e l e c t r i c f i e l d , Wear, 29(1974) 173.

R. Ka t te r l ohe r , Magnet lager auch i m Maschinenbau: Aufbau, Eigen- schaf ten , Anwendungen, Maschinenmarkt, 81( 1975) 315.

J.L. Po t te r , The e las tomer i c bear ing : what i t can do f o r you, Mech. Engng, (1973) Dec, 22.

see Ref. 4.131, p. 5-110.

S. Hi ldebrand, Feinmechanische Bauelemente, VEB Ver lag Technik, B e r l i n , 1967, p. 456 f.

see Ref. 5.2, s e c t i o n C2.

M. Donovan, J.L. Sanders, R. Hazzard, G.R. B e l l , R.E. Mansford, Sur face coa t ings ( P a r t I t o I V ) , T r i bo logy , 5(1972) 205.

S. Jahanmir, N.P. Suh and E .P . Abrahamson, 11, The de lamina t ion theory o f wear and the wear o f composite surface, Wear, 32(1975) 33.

see Ref. 4.90.

10-7 To r r , BAM-Berichte N r . 13, B e r l i n , Jun i 1972.

375

5.45 see Ref. 1.6, p. 301 ff.

5.46 G. Cros and J . -L . P o l t i , E i n i g e t h e o r e t i s c h e und p r a k t i s c h e Gesichtspunkte der Reibung, Schweizer A rch i v , 36(1970) 147.

5.47 E. Roemer, Werks to f fe und Sch ich tau fbau b e i G l e i t l a g e r n , Z . f. Werks to f f t echn i k, 4( 1973) 2.

CHAPTER 6 6.1

6.2

6.3

6.4

6.5

6.6

6.7

6 .8

6.9

6.10

6 .11

6.12

6.13

6.14

6,15

6.16

6.17

W.M.J. Schlosser, A c o n t r i b u t i o n t o t h e s tudy o f ana log ies o f power t ransmiss ions i n machines, Power d r i v e s , (1974) 48 and 49.

C.T. Wal te rs , The dynamics o f b a l l bear ings , Trans ASME, JOLT, (1971) 1.

D.G. S tewar t , J.B. Hunt, Re laxa t i on o s c i l l a t i o n s on a machine t o o l s l ideway, Proc. I n s t . Mech. Engrs, London, Vol . 184 P t 3L, (1969/70) 33.

J.A. B a i l e y , F r i c t i o n i n metal machining - mechanical aspects, Wear, 31(1975) 243.

L. Eaton, F r i c t i o n i n s t a b i l i t y , i n Ref. 1.8, p.147.

H.-U. Mit tmann and H. Czichos, Analogue computer s t u d i e s o f s t i c k - s l i p e f f e c t s , BAM, Ber l in-Dahlem, (1976) unpubl ished.

G. Niemann, Maschinenelemente, Bd 1 und Bd 2, Spr inger -Ver lag , B e r l i n , 1961.

F. Sass, Ch. Bouch6, A . L e i t n e r , DUBBEL Taschenbuch f u r den Maschinenbau, Bd 1, Spr inger -Ver lag , B e r l i n , 1970, p. 232.

R.H. Creamer, Machine Design, Adison-Wesley Publ . Co. Reading, 1976, p. 281 f.

E. Radzimovsky and A. M i r a r e f i , Dynamic behav iour o f gear systems and v a r i a t i o n o f c o e f f i c i e n t o f f r i c t i o n and e f f i c i e n c y d u r i n g the engagement cyc le , Trans ASME, B, 97(1975) 1274.

G.B. Stanton, Jr., The f u t u r e o f s a f e t y and h e a l t h : a cha l l enge t o eng inee r ing managers, Trans ASME, J. o f Engng f o r I n d u s t r y , (1976) 761.

H.W. H e i n r i c h , I n d u s t r i a l acc iden t p reven t ion : a s c i e n t i f i c approach, Mc Graw-Hi l l , New York, 1950, p. 11 ff.

W. Haddon, J r , The p reven t ion o f acc iden ts , i n P reven t i ve Med ic ine ( E d i t o r s : D.M. C la rk and B. Mac Mahon) L i t t l e , Brown, Boston, 1967, chap te r 33.

J.V. Gr ima ld i , App ly ing systems a n a l y s i s techn iques i n s a f e t y s i t u a t i o n s , The Center o f Safe ty , New York U n i v e r s i t y , New York, Apr. 1968, p. 31 ff.

R.A. C o l l a c o t t , Mechanical f a u l t d iagnos is and c o n d i t i o n mon i to r i ng , Chapman and H a l l , London, 1977, chap te r 2.

A l l i a n z , Handbuch d e r Schadenverhutung, A l l i a n z Versicherungs AG, Munchen und B e r l i n , 1. Auf lage, 1972, p. 361 and p. 376; 2. e rwe i - t e r t e und u b e r a r b e i t e t e Auf lage, 1976, p. 645 and p. 695.

P.M. Ku, Gear g a i l u r e modes - importance o f l u b r i c a t i o n and mechanics, ASLE Trans, 19(1976) 239.

376

6.18

6.19

6.20

6.21

6.22

6.23

6.24

6.25

6.26

6.27

6.28

6.29

6.30

6.31

6.32

6.33

6.34

6,35

6.36

6.37

S.O. Rafique, Fai lures o f p l a i n bearings and t h e i r causes, Proc. I ns t . Mech. Engrs, London, Vol. 178, P t 3N, (1963/64) 180.

F.F. Simpson, F a i l u r e of r o l l i n g contact bearings, Proc. I ns t . Mech. Engrs, London, Vol. 178, P t 3N, (1963/64) 215.

D. Scott, A . Smith, J. T a i t , G.R. Tremain, Mater ia ls and metal- l u r g i c a l aspects o f p i s ton r i n g s c u f f i n g - a l i t e r a t u r e survey, Wear, 33(1975) 293.

E. Dombrowski , Einfuhrung i n d i e Zuverlassigkei t e lek t ron i sche r Gerate und System?, AEG-TELEFUNKEN, Ber l i n , 1970.

J.C. Cluley, E lec t ron i c equipment r e l i a b i l i t y , Mac M i l l a n Press, London, 1974.

R.A. Bones, Designing f o r r e l i a b i l i t y , Engineering, 216( 1976) 798.

W. Gerisch, Zuver lass igkei t aus phi losophischer, mathematischer und ingenieurwissenschaftlicher Sich t , Ma te r ia l und Technik, (1973) 51.

Messerschmi t t - B o l kow-Blohm (Herausgeber) , Technische Zuverlassig- k e i t , Springer-Verlag, Be r l i n , 1971.

6. Mathhai , Ober den G le i t ve rsch le ia ungeschmierter Oberflachen, Forsch. Ing. Wes., 30(1964) 1. H. Thum, Zuver lass igkei t und VerschleiR von mechanischen Baugruppen, Schmierungstechnik, 3(1972) 139.

H. Yoshikawa, Fundamentals o f mechanical r e l i a b i l i t y and i t s app l i ca t i on to'computer aided machine design, C I R P Annals, 24( 1975) 297.

G. Fleischer, P rob lem der Zuver lass igkei t von Maschinen, Wiss. 2 . TH Magdeburg, 16(1972) 289.

G. Bergl ing, Betr iebszuver lass igkei t von Walzlagern, Kugel lager-Zei tschr i f t , 51(1976) 1. P. Eschmann, Be t r i ebss i che rhe i t und Gebrauchsdauer von Walzlagern, Walzlagertechnik, 13(1974) 3.

H. P i t t r o f f , Funktionssichere Walzlagerungen f u r Elektromaschinen, Kugel l a g e r - Z e i t s c h r i f t , 51(1977) 10.

W.J. Bartz, Tr ibotechnik a l s Grundlage zur Vermeidung van Schaden an Maschinenelementen, Schmiertechni k und T r i bologie, 20(1973) 50.

G. Fleischer, Der Einf luB der Schmierungstechnik auf d i e Minderung der Ve rsch le ia in tens i ta t und d i e Sicherung e i n e r hohen Zuverlassig- k e i t , Standardisierung und Q u a l i t a t , 21( 1975) 83.

M.L. Shooman, P r o b a b i l i s t i c r e l i a b i l i t y - an engineering approach, Mc Graw-Hill , New York, 1968.

N.N., "Darunter kommt a l l e s i n s Rutschen": Moderne E lek t ron i k s c h a f f t A r b e i t s l o s i g k e i t - sowohl be i Hers te l l e r f i rmen a l s auch bei den Abnehmern, Der Spiegel, 30(1976) Nr. 51, 87.

B. Cramer, Der e lekt ron ische Fernschreiber a l s Be isp ie l f u r den Strukturwandel i n der Feinwerktechnik, Feinwerktechni k und MeBtechnik, 85(1977) 1.

311

6.38

6.39

6.40

6.41

6.42

6.43

6.44

6.45

6.46

D.F. Wi lcock and E.R . Booser, Bear ing des ign and a p p l i c a t i o n , Mc Graw-Hi 11, New York, 1957.

E . E . B isson and W.J. Anderson, Advanced b e a r i n g techno logy , NASA, SP-38, Washington, 1964.

F.E. Kennedy and H.S. Cheng ( E d i t o r s ) , Computer-aided Design o f Bear ings and Seals, The American SOC. o f Mech. Engrs, New York, 1976.

H. Peeken, D ie t r i b o l o g i s c h r i c h t i g e Kons t ruk t i on , V D I - Z . , 118( 1976) 201.

A.E. Green and A.J. Bourne, R e l i a b i l i t y , Technology, Wi ley - I n t e r s c i e n c e , London, 1972, p. 19.

R.G. Bayer and T.C. Ku, Handbook o f a n a l y t i c a l des ign f o r wear, Plenum Press, New York, 1964.

J.H. Dumbleton and S.R. Rhee, The a p p l i c a t i o n o f a zero wear model t o m e t a l l p o l y e t h y l e n e s l i d i n g p a i r s , Wear, 35( 1975) 233.

see Ref. 4.129.

J.v. Neumann, The genera l and l o g i c a l t h e o r y o f automata, i n : Modern systems research f o r t h e behav io ra l s c i e n t i s t ( E d i t o r : W . Buck ley) , A l d i n e Publ . Co, Chicago, 1968, p. 97.

CHAPTER 7 7 .1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

7.10

J . Bloue t , T r i bomi i t r i e , Le Fro t tement e t l ' U s u r e , Journkes d'Etude, 5/6 d6c 1966, 1.

G. Salornon, The s t r u c t u r e o f t r i b o l o g i c a l systems, Lubr. Engng, 32(1976) 458.

H. Czichos, Exper imen te l l e Methoden z u r Untersuchung t r i b o l o g i s c h e r E f f e k t e i m Mischre ibungsgeb ie t , VDI -Ber ich te , 156, 1970, 5 .

H. Wiegand u. E. B r o s z e i t , Zu r Frage d e r Beanspruchungszei t b e i Verschleinuntersuchungen u n t e r Mischreibungsbedingungen, Motortechn. Z e i t s c h r i f t , 34( 1973) 33.

H. Czichos, T r i b o l o g i s c h e M a t e r i a l p r u f u n g - Phys ika l i s c h e Grund- lagen und technisch-wirtschaftliche Bedeutung, Amts- u. M i t t e i l u n g s - b l a t t de r BAM 7(1977) 5.

R. Benzing, 1. G o l d b l a t t , V. Hopkins, W. Jamison, K. Mecklenburg, M. Peterson, F r i c t i o n and Wear Devices, 2nd e d i t i o n , ASLE, Park Ridge, 1976.

K.R. Mecklenburg, The e f f e c t o f wear on t h e compressive s t r e s s i n t h e sphere-on-plane c o n f i g u r a t i o n , ASLE Trans, 17( 1974) 149.

G.H. Got tner , D e f i n i t i o n und Er fassung e i n i g e r B e g r i f f e z u r Beschreibung des Geschehens i n R e i b s t e l l e n b e i Mischreibung, Schmiertechni k und T r i b o l o g i e , 20( 1973) 22.

E.D. Braun, Mode l l i e rung - e i n e o b j e k t i v e Methode z u r B e u r t e i l u n g de r Reibungseigenschaften von Werks to f fen , Schmierungstechni k, Z(1971) 12.

J.A. E lde r , J r . and N.S. Eiss , J r . , A s tudy o f t h e e f f e c t o f normal s t i f f n e s s on k i n e t i c f r i c t i o n f o r c e s between two bod ies i n s l i d i n g contac t , ASLE Trans, 12(1969) 234.

7.11

7.12

7.13

7.14

7.15

7.16

7.17

7.18

7.19

7.20

7.21

7.22

7.23

7.24

7.25

7.26

7.27

7.28

7.29

7.30

7.31

7.32

7.33

G. Salomon, The s i m u l a t i o n o f marg ina l c o n t r o l , Lubr. Engng, 32(1976) 570.

H.-U. Mittmann, N. Czaika and H. Czichos, A new dev ice f o r s imultaneous measurement o f f r i c t i o n f o r c e , normal f o r c e and f r i c t i o n c o e f f i c i e n t , Wear, 31(1975) 179.

E. B rosze i t , K.H. Kloos, F.J. Hess und E. Wagner, E in f l uB von Schwingungen a u f d i e Versch le iRe igenschaf ten e i nes Rei bsys terns, Wear, 28( 1974) 395.

H. Czichos und K. Kaffanke, Zur Bestimmung von Grenzf lachen- temperaturen b e i tri bo log ischen Vorgangen, V D I - Z . , 112( 1970) 1491 und 1643.

see Ref. 4.147.

K.-H. Habig, Mog l i chke i ten der Modell-VerschleiBprufung, Mate r ia lp ru fung , 17( 1975) 358.

R.G. Bayer ( E d i t o r ) , S e l e c t i o n and Use o f Wear Tests f o r Meta ls , ASTM Techn ica l P u b l i c a t i o n 615, Ph i l ade lph ia , 1976.

K.-H. Habig, On the de te rm ina t ion o f wear ra tes , Wear, 28(1974) 135.

R. Holm, E l e c t r i c a l con tac ts , Spr inger -Ver lag , B e r l i n , 1967.

H. Czichos, W . Grimmer and H.-U. Mittmann, Rapid measuring techniques f o r e l e c t r i c a l c o n t a c t r e s i s t a n c e a p p l i e d t o l u b r i c a n t a d d i t i v e s s tud ies , Wear, 40(1976) 265.

B.B. Seth and T. W i l l i s , Techniques f o r f i l m t h i ckness measurements i n elastohydrodynamic l u b r i c a t i o n , Trans ASME, Paper 76-Det-79.

A.K. Pogosian, Fo rcecas t i ng t h e v i a b i l i t y o f f r i c t i o n p a i r s i n acce le ra ted t e s t s , Wear, 26(1973) 175.

S .V . P ineg in , A.V. C ic inadze und E.D. Braun, Entw ick lungsr ich tungen der Mode l l i e rung zur B e u r t e i l u n g von Reibungs- und Versch le iBvor - gangen, Schmierungstechni k, 6 ( 1975) 5.

D. P lay and M. Godet, Design o f h i g h performance d ry bear ings , Wear, 41(1977) 25.

A.W.J. de Gee, S e l e c t i o n c r i t e r i a f o r l u b r i c a t e d j o u r n a l bear ings , Wear, 36(1976) 33.

G. Heinke, Versch le iB - e i n e Systemeigenschaft ; Auswirkungen a u f d i e VerschleiBprufung, Z. Werks to f f t echn i k, 6 ( 1975) 164,

R.D. Brown, Tes t methods, i n : Boundary l u b r i c a t i o n , e d i t e d by F.F. L ing , E.E. Klaus and R.S. Fein, ASME, New York, 1969, p. 241.

K. Kutzbach, Reibung und Abnutzung von Zahnradern,

see Ref. 4.131, chapter 26.

R.B. Howarth, L u b r i c a n t p r o p e r t i e s and t e s t i n g , i n Ref. 1.8, p. 202.

C. Zerbe, M i n e r a l o l e und verwandte Produkte, Spr inger -Ver lag , B e r l i n , 1969.

H. Junemann, Mechanische Pru fve r fah ren fur Schmiers to f fe , Erdol und Kohle, 29(1976) 259.

see Ref. 4.131, p. 20-17.

V D I - Z . , 70(1926) 999.

379

7.34

7.35

7.36

7.37

7.38

7.39

7.40

7.41

7.42

7.43

7.44

7.45

7.46

7.47

7.48

7.49

7.50

7.51

7.52

7.53

7.54

S.C. Dodson and L.A. Godsave, L u b r i c a t i n g o i l s , i n Ref. 1.7, p. 501.

see Ref. 4.131, p. 27-8.

D. Sco t t , F a i l u r e d iagnos is and i n v e s t i g a t i o n , T r ibo logy , (1970) 22.

see Ref. 6.15.

F.K. O r c u t t , Das Au f f i nden von Storungen an mechanischen Komponenten, ve ru rsach t durch Reibung und Versch le iB , Technica, (1970) 883.

G.H. Go t tne r , Zur Funkt ionsdiagnose von Masch inenbaute i len und -anlagen gee ignete MeRgroBen, Schmiertechnik und T r i b o l o g i e , 24(1977) 3.

K. Z i e g l e r , Funktionsuberwachung von Maschinen und B a u t e i l e n r n i t H i l f e de r Schal lmeBtechnik, Schmier techn ik und T r i b o l o g i e , 24(1977) 5.

K.A. Bowen and T.S. Graham, Noise and a n a l y s i s : a maintenance i n d i c a t o r , Mech. Engng, (Oct. 1967) 31.

ALLIANZ, Handbuch de r Schadenverhutung, 2. erwei t e r t e und ubera r - b e i t e t e Auf lage, Munchen, 1976, p. 672.

see Ref. 7.36.

A. Beerbower, Spectrometry and o t h e r a n a l y s i s t o o l s f o r f a i l u r e p rognos is , Lubr . Engng, 32(1976) 285.

see Ref. 6.15, p. 258.

A. Gervb, E insa tz rnog l ichke i ten von Rad ionuk l iden z u r Untersuchung k o n s t r u k t i v e r und schmiers to f fabhang iger E i n f l u s s e a u f den Versch le iR von Masch inente i len , VDI -Ber ich te , N r . 196(1973) 43.

W . W . S e i f e r t and V . C . Westcott , A method f o r t he s tudy o f wear p a r t i c l e s i n l u b r i c a t i n g o i l , Wear, 21(1972) 27. A.W. Ruf f , C h a r a c t e r i z a t i o n o f d e b r i s p a r t i c l e s recovered f rom wear ing systems, Wear, 42( 1977) 49.

D. S c o t t , W . W . S e i f e r t and V . C . Westco t t , The p a r t i c l e s o f wear, S c i e n t i f i c American, 230( 1974) 88.

H. Czichos, MeRtechnische Methoden zu r Untersuchung t r i b o l o g i s c h beanspruchter Werks to f fober f lachen, Schmiertechnik und T r i b o l o g i e , 21(1974) 25.

G. Nomarski e t A.R. W e i l l , A p p l i c a t i o n d l a m6 ta l l og raph ie des msthodes i n t e r y e r e n t i e l l e s a’ deux oudes po la r i sbes , Revue de M e t a l l u r g i e , 52(1955) 121.

H . -U . Mi t tmann und H. Czichos, Reibungsmessungen und Oberf lachen- untersuchungen an K u n s t s t o f f Meta l l -G le i tpaarungen. Ma te r ia lp ru fung , 17(1975) 366.

S. Tolansky, Mu l t ip le -beam I n t e r f e r o m e t r y o f Surfaces and F i lms, C1 arendon Press, Oxford, 1948.

H. Trumpold, Die Anwendungsgrenzen de r L i c h t i n t e r f e r e n z e n b e i Rauheitsmessungen, Fe inge ra te techn ik , 18(1969) 247.

K.H. Habig, Der E insa tz des Raster-Elektronenmikroskops z u r Au fk la rung von VerschleiBmechanismen, Bei tr. Elektronenmi kroskop D i rek tabb . O b e r f l . 3(1970) 235.

380

7.55

7.56

7.57

7.58

7.59

7.60

7.61

7.62

7.63

7.64

7.65

7.66

7.67

L. Reimer und G. P f e f f e r k o r n , Rasterelektronenmikroskopie, Spr inger -Ver lag , B e r l i n , 1973.

R. S t i c k l e r , C.W. Hughes, G.R. Booker, A p p l i c a t i o n o f t he se lec ted area ECP method t o de format ion s tud ies , Proc. 4 Annual SEM Symp., JJTRJ, Chicago, A p r i l 1971, p . 473.

H. Czichos und D. K l a f f k e , Deforrnationsuntersuchungen an t r i b o l o g i s c h beanspruchten Me ta l l obe r f l achen m i t de r Methode de r e l e c t r o n chanel- l i n g pa t te rn , BAM, Berlin-Dahlem, (1977) u n v e r o f f e n t l i c h t .

J.B.P. Wi l l iamson, Microtopography o f sur faces , i n : P r o p e r t i e s and Met ro logy o f Surfaces, Proc. I n s t . Mech. Engrs, London, Vol . 182, 3K(1968) 21.

T.F.J. Quinn, The a p p l i c a t i o n o f modern phys i ca l techniques t o t r i b o l o g y , Newnes - Bu t te rwor th , London, 1971, p. 221.

A. Benninghoven, New developments i n t h e sur face a n a l y s i s o f s o l i d s , Appl. Phys. l ( 1 9 7 3 ) 3.

J. Fer ran te , D.H. Buckley, S . V . Pepper, W.A. B ra inard , Use o f LEED, Auger emiss ion spectroscopy and f i e l d i o n microscopy i n m ic ros t ruc - t u r a l s tud ies , i n : M i c r o s t r u c t u r a l Ana lys is -Too ls and Techniques, ( E d i t e d by J.L. Mc C a l l and W.M. M u e l l e r ) , Plenum Publ. Co, New York, 1973, 241 f f .

R. Holm und S. S torp , Monolagenanalyse an "schmutzigen" Oberf lachen?, Phys. B l a t t e r , 32( 1976) 342.

D.H. Buckley, The use o f a n a l y t i c a l su r face t o o l s i n t h e fundamental s tudy o f wear, Proc. I n t . Conf., Wear o f M a t e r i a l s , S t . Lou is , Apr. 1977, ASME, New York, 1977, p. 12.

0. R. Wheeler, X-ray pho toe lec t ron spec t roscop ic s tudy o f su r face chemis t ry o f d ibenzy l -d i su lph ide on s t e e l under m i l d and severe wear cond i t i ons , submi t ted t o Wear.

A. Benninghoven und S. S to rp , Untersuchung der Grenzf lachen und des Vol umens dunner Schi chten m i t H i 1 f e de r Sekundarionen - Massenspek- t roskop ie , 2 . angew. Phys ik , 31(1971) 31.

P.L. Stohr, Nachweis und Analyse von Reakt ionssch ich ten b e i metal- l i s c h e n Re ibpar tnern i m ReibverschleiB-Modellgerat und i m Verbren- nungsmotor, D i s s e r t a t i o n , Eberhard-Karls-Universitat, Fachbereich Physik, Tubingen, 1976.

E.W. Mu l l e r , F i e l d i o n microscopy, American E l s e v i e r , New York, 1969.

CHAPTER 8 8.1 A. Pieuchot, J . Blouet , R . Gras, M. A l f r e d and R. Cour te l ,

M'ethodologie e t classement des essa is de f r o t t e m e n t e t de l e u r s r ' esu l ta t s , Mbc. E l e c t r . Oct. 1969, p. 8.

8.2 H . Czichos, A systems a n a l y s i s da ta sheet f o r f r i c t i o n and wear t e s t s and an o u t l i n e f o r s i m u l a t i v e t e s t i n g , Wear, 41(1977) 45.

8 .3 M.N. Gardos, L a b y r i n t h s e a l i n g o f aerospace mechanisms - theo ry and p r a c t i c e , ASLE Trans., 17(1974) 237.

381

8.4

8.5

8.6

8.7

8.0

8.9

8.10

8.11

8.12

8.13

8.14

8.15

8 ,16

8.17

8.18

8.19

8.20

a. 21

8.22

G. Katzenmeier, Das Versch le iBverha l t e n und d i e T rag fah igke i t von G l e i t l a g e r n i m Obergangsbereich von de r Vo l l schmierung zu p a r t i e l l e m Tragen (Untersuchungen m i t H i1 f e von Rad io iso topen) , Kernforschungs- zentrum Kar ls ruhe, KFK, 1569, Febr. 1972.

D.H. Buckley and R.L. Johnson, Marked i n f l u e n c e o f c r y s t a l s t r u c t u r e on t h e f r i c t i o n and wear c h a r a c t e r i s t i c s o f c o b a l t and coba l t -base a l l o y s i n vacuum t o m i l l i m e t e r mercury, NASA TND-2523, Washington, 1964.

J.K. Appeldorn, J.B. Goldniann and F.F. Tao, Cor ros i ve wear by a t - mospheric oxygen and mois tu re , ASLE Trans, 12(1969) 140.

J . Mdlgaard, A s i m u l a t i v e wear s tudy c r i t i c a l l y reviewed, Wear, 41(1977) 57.

J.K. Lancas ter , Dry bear ings : a survey o f m a t e r i a l s and f a c t o r s a f - f e c t i n g t h e i r performance, T r i b o l o g y i n t e r n a t i o n a l , 6(1973) 219.

L.H. Lee ( E d i t o r ) , Advances i n Polymer F r i c t i o n and Wear, Polymer sc ience and technology, Vol . 5 , Par ts A and 6, Plenum Press, New York, 1974.

see Ref. 7.51.

B.J. Br iscoe, C.M. Pooley and D. Tabor, F r i c t i o n and t r a n s f e r o f some polymers i n u n l u b r i c a t e d s l i d i n g , see Ref. 8.9, P a r t 5A,

K.H. Habig, R. Chater jee-F ischer und F. Hoffmann, Zum t r i b o l o g i s c h e n Verhal t e n von Ober f lachensch ich ten , d i e durch E i n d i f f u s i o n von S t i c k s t o f f , Bor oder Vanadin i n E i senwerks to f fe g e b i l d e t werden, Har te re i techn . M i t t e i l u n g e n , i n p r i n t .

H. Hubner, Unterdruckung s t i c k - s l i p i n d u z i e r t e r Kurvengerausche b e i Eisenbahnschienen durch phys ika l i sch-chemische Oberf lachen- behandlung, D i s s e r t a t i o n , TU-Berl i n , 1973, D83.

H. Czichos und H. Hubner, Model luntersuchungen uber s t i c k - s l i p Vorgange, BAM, B e r l in-Dahlem, (1973), u n v e r o f f e n t l i c h t .

G.H.G. Vaessen and A.W.J. de Gee, I n f l u e n c e o f wa te r vapour on t h e wear of l i g h t l y loaded contac ts , Wear, 18(1971) 325.

M.E. Merchant, F r i c t i o n and Adhesion, i n : I n t e r d i s c i p l i n a r y approach t o f r i c t i o n and wear ( E d i t o r : P.M. Ku), NASA SP-181, Washington, 1968, p. 198.

J.A. Schey, Meta l Deformat ion Processes. F r i c t i o n and L u b r i c a t i o n , Marcel Dekker, New York, 1970.

G.W. Rowe, P r i n c i p l e s o f I n d u s t r i a l Meta lwork ing Processes, Arnold, London, 1977.

A. G i l e j i , Bi ldsame Formgebung der M e t a l l e , Akademie-Verlag, B e r l i n , 1967.

0. Pawelski , G. Graue und D. Lohr, Reibungsbeiwert und Temperatur- v e r t e i l u n g beim Warmformen von S tah l m i t verschiedenen Schmiermi t- t e l n , Schmier techn ik und T r i b o l o g i e , 17(1970) 120 und 170.

H. Krause und A.H. Demi rc i , Fac to rs i n f l u e n c i n g t h e r e a l t r e n d o f t he c o e f f i c i e n t o f f r i c t i o n o f two e l a s t i c bod ies r o l l i n g over each o t h e r i n t h e presence o f d r y f r i c t i o n , i n Ref. 4.1.

M. Gierzynska, Problem o f f r i c t i o n i n r o l l i n g and f o r g i n g processes, i n : T r i b o l o g y i n i r o n and s t e e l works, ISI P u b l i c a t i o n , The I r o n and Stee l I n s t i t u t e , London, 1970, p . 156.

p . 191.

List symbols

I Character is t ics o f a system (Chapter 2 )

set o f the elements o f a system

se t o f element's p roper t ies

s e t o f i n t e r r e l a t i o n s between elements

s t ruc tu re o f a system

inputs o f a system

use-outputs o f a system

loss-outputs o f a system

input-output r e l a t i o n ( t r a n s f e r func t ion )

I 1 General symbols

a c o e f f i c i e n t o f adhesion

a,, radius o f Her tz ian contact

A (see I )

Ac Arrhenius constant

A, geometric area o f contact

Am mantle surface o f a body

383

Ar

*W

b

B

1:

0 C

‘r

C

‘d

CS

d

E

AE

A E~

Ee

A ES

E: . W f:

f

F

FA

FF

FN

FS

FT

F ( t )

9

G

r e a l area o f c o n t a c t

wear - t rack area

Burgers v e c t o r

magnet ic f i e l d

s p e c i f i c heat

v e l o c i t y o f l i g h t

r a d i a l c learance

general cons tan t

damper cons tan t

s p r i n g cons tan t

d iameter

modulus o f e l a s t i c i t y

energy

mechanical energy o r work

energy o f edge d i s l o c a t i o n

errergy o f screw d i s l o c a t i o n

power

mechanical power

c o e f f i c i e n t o f f r i c t i o n

f o r c e

f o r c e o f adhesion

f r i c t i o n f o r c e

normal f o r c e

separa t i on f o r c e

t a n g e n t i a l f o r c e

f a i l u r e d i s t r i b u t i o n f u n c t i o n

a c c e l e r a t i o n due t o g r a v i t y

shear modulus

h f i l m t h i ckness

384

TI P lanck ' s cons tan t / 2 n

H hardness

AH en tha lpy

i e l e c t r i c c u r r e n t

i, j counter

J mechanical e q u i v a l e n t o f heat

k thermal c o n d u c t i v i t y

5' k 2

k P

KC

K, K '

I

rn

M

MF

n

"1' n2

N

Hamaker cons tan ts

p a r a b o l i c o x i d a t i o n r a t e cons tan t

wear c o e f f i c i e n t s

c rack parameter

l e n g t h o r d i s tance

mass

to rque

f r i c t i o n to rque

a s p e r i t y d e n s i t y pe r u n i t area

e l e c t r o n number d e n s i t y

gear r a t i o

hea t e m i t t i n g area e a t absorb ing volume 0 r a t i o :

P p ressure

P l oad /bear ing p r o j e c t e d area

pH maximum Her tz p ressure

pH mean Her tz p ressure

-

-

pump pressure

y i e l d p ressure pP

PY

P (see I )

qe e l e c t r i c charge

9 f l o w r a t e

qm f low r a t e o f mass

385

91

Q

r

R

1?

AS

S

so

t

T

T

U

A u

V

V

"W

W

W

'i

X

Y

Y

Z

f l o w r a t e o f l u b r i c a n t

amount o f hea t

r a d i u s

(see I )

mean roughness

cen te r - l i ne -ave rage roughness

peak-to-Val 1 ey-hei g h t roughness

gas cons tan t

r e l i a b i l i t y f u n c t i o n

s tandard d e v i a t i o n

(see I )

en t ropy

en tha lpy f l o w genera t i on r a t e

Sommerfeld number

t ime

(see I )

tempera ture

vo l tage

p o t e n t i a l energy

ve l oc i ty

vo l ume

wear volume

wear r a t e

work

coord ina tes ( i = 1, 2, 3 )

(see I )

su r face p r o f i l e h e i g h t

(see I )

d i s t a n c e o f approach o r separa t i on

2 (see I )

Z (A) a u t o - c o r r e l a t i o n f u n c t i o n o f p r o f i l e

p ressure-v i scos i ty c o e f f i c i e n t

rad ius o f a s p e r i t y c u r v a t u r e

su r face f r e e energy

cons tan t (zero-wear model )

gamma f u n c t i o n

f r i c t i o n ang le

d i f f e r e n c e o f q u a n t i t i e s

ratio: c o n t a c t area

wear r e s i s t a n c e

no-contac t t ime f r a c t i o n

v i s c o s i t y

e f f i c i e n c y

convec t ion h e a t - t r a n s f e r c o e f f i c i e n t

adhesion parameter

thermal d i f f u s i v i ty

f i l m thickmess t o roughness r a t i o

f a i l u r e r a t e

mean o f normal d i s t r i b u t i o n

Poisson number

c r i t i c a l ox ide f i l m th i ckness

d e n s i t y

s t r e s s o r s t r e n g t h (genera l )

adhesion bond s t r e n g t h

y i e l d s t r e n g t h

mean d e v i a t i o n o f a s p e r i t y h e i g h t

shear s t r e s s

wear t r a c k area

387

tS shear strength

Ip angle (general)

@ potential

cc1 plas t ic i ty index ratio: radial clearance

shaft radius Jlr

w angular velocity

Nabla operator

Laplace operator V = - + - + L 2 a* a2

a x 2 ay2 a22

Author index

The numbers are reference numbers, composed o f the number o f the chapter

i n which an author 's work i s r e f e r r e d t o and the running number. The com-

p l e t e references are l i s t e d on pages 360 t o 381.

Abrahamson, E.P. , 5.43 Al f red, M., 8.1 Al len, C.M., 4.134 ALLIANZ, 6.16 Amontons, G., 1.9 Andarel li , G., 4.77 Anderson, W. J. , 6.39 Ant ler , M., 4.113 Anwar, M.I., 5.36 Appeldorn, J . K . , 8.6 Archard, J . F . , 1.25, 4.5, 4.12,

4.13, 4.19, 4.86, 4.89, 4,144 Arnel l , R.D., 5.23 Ausherman, V . K. , 4.147 Avallone, E.A., 4.131

Ba i l e , G.H., 5.31 Bailey, J.A., 6.4 Bakashvil i , D. L. , 4.138 Baldwin, B.A. , 5.17 Bartz, W.J., 6.33 Barwell, F.T., 5.6 Bayer, R.G., 6.43, 7.17 Beerbower, A., 7.44 Begelinger, A., 4.179, 4.186 Be l l , J.C., 4.134 Bel l , G.R., 5.42 Benninghoven, A., 7.60, 7.65 Benzing, R., 7.6 Bergl ing, G., 6.30 Ber ta lanf fy , L. von, 2.1

Berthe. D. , 4.151 B i e l , C., 1.31 Bi rd, R.J., 5.18 Bisson, E.E., 6.39 Blok, H., 4.85 Blouet, J . , 7.1, 8.1 Bones, R.A., 6.23 Booker, G.R., 7.56 Booser, E.R., 6.38 Bo l l i nge r , J.G.. 4.78 Bouchk, Ch., 6.8 Boulding, K.E., 2.2 Bourne, A.J., 6.42 Bowden, F.P . , 1.4, 1.17, 1.18,

4.31, 4.160 Bowen, E.R., 5.30, 5.31 Bowen, K.A., 7.41 Boyd, J . , 4.131 Brainard, W.A., 7.61 Braun, E.D., 7.9, 7.23 Bremble, G.R., 4.59 Briscoe, B.J., 4.25, 8.11 Brdnsted, J.N., 3.9 Broszeit, E . , 4.93, 7.4, 7.13 Brothers, B.G., 4.59 Brown, R.D., 7.27 Buckley, D.H., 4.30, 4.33, 4.34,

4.36, 4.37, 4.39, 4.50, 4.111, 4.115, 5.11, 7.61, 7.63, 8.5

Bueche, A.M., 4.61 Burton, R.A., 4.97 Burwell , J .T. , 1.23, 1.26, 5.22

389

Cameron, A., 1.7, 4.139 Campbell, J.C., 5.5 Campbell, W.E. , 4.161 Cannon, R.H., 1.1 Carslaw, H.S., 4.83 Car ter , F.W., 4.55 Casimir, H.B.G., 4.24 Chater jee-Fischer, R., 8.12 Charron, F., 4.88 Chaudhari, P., 4.74 Cheng, H.S., 4.137, 6.40 Chiu, Y . P . , 4.96, 4.172 Christensen, H . , 4.150, 5.7 c iz inadze, A.V., 7.23 Clu ley, J.C., 6.22 Cocks, M . , 4.112 C o l l a c o t t , R.A., 6.15 Constantinescu, V.N., 4.170 Coulomb, E., 1.10 Cour te l , R., 4.48, 4.77, 8.1 Courtney-Prat t , J.S., 4.45, 4.158 Coy, R . C . , 5.19 Cramer, B . , 6.37 Creamer, R.H., 6.9 Crook, A .W. , 4.66 Cros, G., 5.46 Czaika, N., 7.12 Czichos, H., 1.34, 3.3, 3.4, 3.5,

4.29, 4.46, 4.52, 4.69, 4.90, 4.121, 4.173, 4.174, 4.180, 4.182, 4.187, 6.6, 7.3, 7.5, 7.12, 7.14, 7.20, 7.49, 7.51, 7.57, 8.2, 8.14

Dala l , H., 5.31 Davies, P.B., 5.34 de Gee, A.W.J., 4.179, 4.186,

Demirci , A.H., 8.21 de Pater, A.D., 4 .1 Depeyrot, M., 2.7 Der jaguin, B .V . , 4.71 Desagul ier , J.T., 1.11 Dies, K., 1.21, 5.13 Dimarogonas, A.D., 4.87 d i Prima, R.C., 4.169 Dismant, J.H., 4.72 Dombrowski, E., 6.21 Dodson, S.C., 7.34 Dixhoorn, J.J. van, 2.6 Dowd, J.R., 5.6 Doubleday, J., 1.33 Donovan, M., 5.42 Dowson, D., 4.136, 4.142 Dumbleton, J.H. , 6.44 D,yer, L.D., 4.64 Dyson, A., 4.143, 4.166

7.25, 8.15

Eaton, L. , 6.5 Eisner, E., 4.45 Eiss, N.S., Jr., 7.10 E lde r , J.A., J r . , 7.10 Eldredge, K.R., 4.63 Engel, P.A., 4.91 E rns t , H., 1.16 Eschmann, P., 6.31 Evans, F.J., 2.6 Eyre, T .S. , 4.103, 5.14

Faurre, P., 2.7 Feder, R . , 4.74 Fein, R.S., 4.161, 4.163, 4.175,

4.176, 7.27 Fe r ran te , J., 4.27, 4.28, 4.81,

7.61 Feynman, R . P . , 1.27 F ink, M. , 1.20, 5.12 F le i sche r , G. , 3.1, 6.29, 6.34 Flom, D.G., 4.61 Fohl , J., 4.110, 5.28

Forbes, E . S . , 4.154 Fr iedst rom, S., 5.15 Fuchsel, M., 1.19 F u l l e r , K.N.G., 4.42

Galv in , G.D., 5.18 Gane, N . , 4.40, 4.76 Gardos, M.N., 8.3 Gatos, H.C., 4.22 Gerisch, Id., 6.24 Gerv6, A , , 7.46 Gierzynska, M. , 8.22 G i l e j i , A., 8.19 Godet, M . , 4.47, 4.151, 7.24 Godfrey, D., 4.156, 4.157 Godsave, L.A., 7.34 G o l d b l a t t , I . , 7.6 Goldmann, J.B., 8.6 Got tner , G.H., 1.36, 7.8, 7.39 Graham, T.S., 7.41 Gras, R., 8.1 Graue, G . , 8.20 Green, A . E . , 6.42 Greenwood, J.A., 4.14, 4.18, 4.152 Gr imald i , J. V . , 6.14 Grimmer, W. , 7.20 Gumbel , L., 4.148 Gur ley i k , M . , 4.105 Gustafsson, O.G., 5.31

Haasen, P., 4.98 Habig, K.-H., 1.34, 4.35, 4.38,

4.90, 5.24, 5.25, 7.16, 7.18, 7.54, 8.12

FOppl, L., 4.57

390

Haddon, W . J r . , 6.13 Halaunbrenner, 3.6. , 4.62 H a l l , A.D., 2.13 H a l l i n g , J . , 1.8 Hamil ton, G.M., 4.67 Hardy, J.K., 1.13 Hardy, W.B., 1.13 Hazzard, R., 5.42 Heathcote, H.L. 4.54 He in ike , G., 4.116 Heinke, G., 7.26 He in r i ch , H.W., 6.12 Herod, A.P. , 5.23 Hersey, M.D., 4.126 Her tz , H., 4.3 Hess, F.J. , 7.13 Higginson, G.R . , 4.136 H i ldebrand, S., 5.40 Hironaka,S,, 4.184, 4.185, 5.15 H i r s t , W., 1.25 H i r t h , J.P., 4.102 Hofmann, U., 1.20, 5.12 Hogmark, S., 5.15 Hol land, J . , 4.128 Holm, Ragnar, 1.15, 4.84, 4.159,

Holm, R . , 7.62 Hopkins, V . , 7.6 Hornbogen, E., 4.100 Howarth, R.B., 5.34, 7.30 Howel ls, R.I.L., 4.4 Hubner, H., 8.13, 8.14 Hughes, C.W., 7.56 Hunt, J.B., 6.3 Hunt, R.T., 5.1 Hur r i cks , P.L., 4.109, 4.118 Hut ten locher , D.F., 4.172

I-Meng, Feng, 1.23

Jackson, A. , 4.140 Jaeger, J.C., 4.83 Jahanmir, S., 5.43 Jamison, W., 7.6 Johnson, K.L., 4.41, 4.65, 4.68,

4.141, 4.152 Johnson, R.L., 4.34, 8.5 Jones, A.M. , 4.10 Jones, M.H., 4.4 Jos t , P., 1.37 Junemann, H., 7.32

Kaffanke, K., 7.14 Ka lker , J.J., 4 .1 Kamenshine, J.A., 4.172 Kannel, J.W., 4.134 Kirmkn, T. von, 4.167

7.19

Karnopp, D., 2.11 K a t t e r l o h e r , R., 5.37 Katzenmeier, G., 8 .4 Kendal l , K., 4.41, 4.70 Kennedy, F.E., 6.40 Ker r idge, M., 1.24 Khrushov, M.M., 4.106, 4.107 King, T.G., 5.3 Kirschke, K., 1.34, 4.177, 5.24,

K l a f f k e , D. , 7.57 Klaus, E . E . , 4.142, 7.27 K l i r , G.J., 2 .5 Kloos, K.H. , 4.93, 7.13 Kodnir , D .S . , 4.138 K o s t e t s k i i , B.J., 4.73 Kounas, P.S., 4.87 K r a g e l s k i i , I . V . , 1.6 Krause, H., 8.21 Kreuz, K.L., 4.175 Ku, P.M., 4.89, 4.97, 4.157, 6.17 Ku, T.C., 6.43 Kuhlmann-Wilsdorf, D . , 4.99 Kutzbach, K., 7.28

La i rd , C . , 4.99 Lancaster, J.K., 8.8 Landheer, D., 4.114 Lang, O.R., 4.92 Lee, L.H., 8.9 Le igh ton , R.B., 1.27 L e i t n e r , A , , 6.8 Levy, G., 5.20 L i n f o r d , R.G. , 5.20 Ling, F.F., 4.2, 4.142, 4.161, 7.27 L i t tmann, W.E., 4.95 Lohr, D., 8.20 Ludema, K.C. , 4.16

Maennig, W.-W. , 5.24, 5.25 Mansford, R .E . , 5.42 Mathhai, G., 6.26 Maugis, D., 4.77 Maynard, D., 5.14 Mc Cool, J . I . , 4.96 Mc Far lane, J.S., 4.44 Mecklenburg, K., 7.6, 7.7 Merchant, M.E., 1.16, 8.16 Merwin, J.W., 4.68 Mesarovic, M.D., 2.4 Messerschmitt-Bo1 kow-Blohm, 6.25 Meyer, K . , 4.116 M i n d l i n , R.D., 4.43 M i r a f e r i , A . , 6.10 M i t c h e l l , L.A., 4.49, 5.20 Mittmann, H.-U. , 6.6, 7.12, 7.20,

5.25

7.51

391

8.7 Ropohl, G., 2.3 Rosenberg, R., 2.11 Rounds, F.G., 4.162 Rowe, C.N., 4.164, 4.165, 4.175 Rowe, G.W., 4.31, 5.8, 8.18 R u f f , A.W., 7.47

Saibel , 4.171, 5.9 Sakurai , T., 4.183, 4.184, 4.185,

Salomon, G., 3.2, 4.181, 7.2, 7.11 Salukvadze, R.G., 4.138 Sanborn, D., 4.147 Sanders, J .L . , 5.42 Sandor, G.N., 4.87 Sands, M., 1.27 Sass, F., 6.8 Schey, J.A., 8.17 Schlosser, W.M.J., 3.7, 6 . 1 Schmaltz, G. , 4.23 Schouten, M.J.W., 4.94 Schul tze, G.E.R., 4.75 Schwarzman, V.Sh., 4.138 Sco t t , D., 6.20, 7.36, 7.48 Seely, S . , 2.8 S e i f e r t , W . W . , 7.47, 7.48 Seireg, A., 4.15 Seth, B.B., 7.21 Sethuramiah, A. , 4.183 Shooman, M.L., 6.35 S ib ley , L.B., 4.172 S iebe l , E., 1.22 S i k o r s k i , M.E., 4.32 Simpson, F.F., 6.19 S ind l i nge r , N.E., 4.172 Skinner, J. , 4.76 Smilga, V.P., 4.71 Smith, A . , 6.20 Smith, J.R., 4.27, 4.28 Sommerfeld, A . , 1.30 Stanton, G.B., 6.11 Stewart , D.G., 6.3 S t i c k l e r , R . , 7.56 Stohr, P.L., 7.66 Storp, S., 7.62, 7.65 Stout , K.J., 5.3 Strang, C.D. , 1.23, 5.22 S t r i beck , R., 1.29, 4.17 S tud t , P., 1.34, 4.155 Suh, N .P . , 4.101, 5.43 Summers-Smith, D., 1.38 Suratkar , P.T., 4.11

Tabor, D., 1.4, 1.17, 1.18, 4.16, 4.20, 4.25, 4.40, 4.42, 4.44, 4.51, 4.58, 4.60, 4.63, 4.160, 8.11

4.187

Mblgaard, J., 3.5, 3.6, 4.122, Moore, D.F., 4.130 Mu l le r , E.W., 7.67 Munnich, H., 4.146

Nagaraj, H.S., 4.147 Nazarenko, P .V . , 4.73 Neale, M.J., 5.2 Neumann, J. von, 6.46 Nicholas, J.F., 4.21 Niemann, G., 6.7 Nomarski, G . , 7.50

O'Cal laghan, P.W., 4.10 O'Connor, J.J., 4.131 Orcu t t , F.K., 4.137, 7.38 Osgood, C. , 4.49 b s t v i k , R. , 5.7

Pandi t , S.M., 4.11 Pawelski, O., 8.20 Paynter, H.M., 2.10 Peeken, H., 6.41 Peklen ik , J., 4.9 Pepper, S . V . , 7.61 Peterson, M.B., 7.6 Petrousevi tch, A.J., 4.138 P fae lze r , P.F., 4.40 P f e f f e r k o r n , G., 7.55 Pieuchot, A . , 8.1 Pinegin, S .V . , 7.23 P i t t r o f f , H . , 6.32 Pogosi an, A . K. , 7.22 P o l t i , J.-L., 5.46 Pooley, C.M., 8.11 Poon, S.Y. , 4.152 Por i t sky , H., 4.56 Po t te r , J .L . , 5.38 Prober t , S.D., 4.4, 4.10 Pul len, J., 5 . 1

Quinn, T.F.J., 5.16, 5.19, 7.59

Rabinowicz, E., 1 .5 Radzimovsky, E., 6.10 Rafique, S.O., 6.18 Reda, A.A. , 5.30 Reimer, L., 7.55 Re t i , L . , 1.12 Reynolds, O., 1.28, 4.53 Rhee, S.R., 6.44 Richardson, R .C .D . , 4.108 Rigney, D.A., 4.102 Rippel , H.C., 4.127, 5.33 Roberts, A.D., 4.41 Rodkiewicz, C.M., 5.36 Raemer, E . , 5.47

392

T a i t , J., 6.20 T a l l i a n , T.E., 4.96, 4.153, 4.172,

Tao, F.F., 8.6 Tay lor , C.M., 5.35 Taylor , G . I . , 4.168 Teer, D . G . , 5.23 Tevaarwerk, J . , 4.141 Theyse, F.H., 4.133 Thiessen, P.A., 4.116 Thorna, J.U., 2.9, 3.8 Thomas, T.R., 4.7 Thum, H . , 6.27 Tischer, H., 5.24, 5.25 Tolansky, S., 7.52 T o l s t o i , D.M., 4.79 Tomlinson, G . A . , 1.14 Tremain, G . R . , 6.20 Tr ipp, J.H., 4.14 Trumpold, H., 7.53 Ty ler , J .C . , 4.97

5.31

Uetz, H., 4.104, 4.105, 4.110, 5.28

Vaessen, G.H., 8.15 Vingsbo, O., 5.15 Vogelpohl, G., 1.32, 4.129, 4.149 Volz, J., 5.10

Wagner, E., 7.13 Walters, C.T., 6.2 Wedeven, L.D., 4.132. 4.145 W e i l l , A.R., 7.50 Weingraber, H. von, 4.8 Weiter, E.J., 4.15 Wel l inger , K., 4.104, 4.105 Welsh, N.C., 5.26 Westcott, V.C., 5.30, 5.31, 7.47,

Westlake, F.J., 4.139 Wheeler, D.R., 7.64 Whitehouse, D.J., 4.6, 4.19, 5.3 Wiegand, H., 7.4 Wiener, N., 2.12 Wilcock, D.F., 6.38 Wil l iamson, J.B.P., 4.18, 5.1, 7.58 W i l l i s , T., 7.21 Wi l l n , J.E., 5.4 Winer, W.O., 4.147 Wooley, J.L., 5.16 Wortmann , J., 4.82 Wu, S.M., 4.11

Yoshikawa, H . , 6.28

Zaat, J.H., 4.114 Zerbe, C . , 7.31 Z i e g l e r , K., 7.40 Ziman, J.M., 4.26 Zudans, Z . , 4.127

7 - 4 8

393

Subject index

Abrasion, .- t h r e e body, 113 - two body, 113 Abras ive c u t t i n g , 353 Abras ive wear mechanisms, 112 Abras ive wear r e s i s t a n c e o f

su r face coat ings , 323 Acous t i c waves, emiss ion o f , 91 Across v a r i a b l e s , 19 Ac tua tors , 351 Adhesion, - bonding mechanisms, 58 -. c o e f f i c i e n t , 63 - hypothes is o f f r i c t i o n , 5 - i n r o l l i n g f r i c t i o n , 86 -. i n s l i d i n g f r i c t i o n , 78 -. o f s o l i d s , 59 - parameter, 68 Adhesive wear mechanisms, 119 Adhesive wear r e s i s t a n c e o f

su r face coat ings , 323 A l l o y i n g elements, i n f l u e n c e on

adhesive wear, 121 Almen t e s t , 276 A l t e r n a t i v e s o l u t i o n s t o mechanical

systems, 240 Amontons-Coulomb laws, 73, 79 Amsler t e s t , 276 Ana log ies between systems, 19 Analogue computer, use i n

s t i c k - s l i p s t u d i e s , 218 Analogue system elements, 217 Ana lys i s o f t r i b o - t e c h n i c a l

systems, 302 Anchor-buoy bear ing , 326 Ant i -wear (AW) a d d i t i v e s , 159, 165

Archard, - wear c o e f f i c i e n t , 262 - wear law, 100 Area o f con tac t , 53 Aromat ic hydrocarbons, 158 A t t r i t i o n , 41 Audio pick-ups, 352 Auger e l e c t r o n spectroscopy

- a p p l i c a t i o n example, 188 A u t o - c o r r e l a t i o n f u n c t i o n o f

(AES), 293

su r face p r o f i l e , 52

B a l l and r o l l e r bear ings , 351 B a l l -and-screw mechanisms, 351 Band brakes, 351 Band c lu t ches , 351 Bath- tub f a i l u r e r a t e curve, 240 Bear ing area curve, 51 Bear ing bushing design, 210 Bear ing m a t e r i a l s , s i m u l a t i ve

Bear ings, comp i la t i on o f , 351 B e l t d r i v e s , 351 Bevel gears, 351 B i b l i o g r a p h i c work i n t r i b o l o g y , 356 B ind ing energ ies i n adhesion, 66 Black-box d e s c r i p t i o n , 25, 29 B l a s t i n g , 353 B lock brakes, 351 B lok temperature theory , 94 B o l t se ts , 351 Bond graph methods, 20 B o r i d i n g , 208, 322 Bor ing , 353 Boundary l u b r i c a t i o n , 156

t e s t i n g o f , 268

394

Bour re l e t f r o n t a l , 78 Boussinesq problem, 48, 147 Bowden-Tabor theory o f f r i c t i o n , 76 B r i t t l e s o l i d s , f r i c t i o n o f , 8 1 Brushing, 353

Cam-and-fol 1 owers , 352 Cam d r i v e s , 351 Cam-tappet wear reduc t i on , 335 Carbur iz ing , 208, 322 Car te r -Por i tsky-Fopp l s l i p i n

r o l l i n g f r i c t i o n , 83 Case s tud ies o f t r i b o l o g i c a l

s o l u t i o n s , 315 Cast ing, 352 C a v i t a t i o n wear, 103 Chain d r i ves, 351 C h e c k - l i s t f o r t r ibo-mechan ica l

systems, 303, 309 Chemical conversion coat ings , 208 Chemical reac t i ons i n boundary

l u b r i c a t i o n , 162 Chemical vapour d e p o s i t i o n

(CVD), 206 Chemisorption, 161 Ch ip less c u t t i n g , 353 C 1 ass i f i ca t i on , - o f mechanical systems, 35 - o f systems, 21 - o f t r i b o - e n g i n e e r i n g systems, 350 - o f wear, 102 C lean ing o f t e s t specimens, 252 Clock-works, 352 C o e f f i c i e n t , - o f adhesion, 63 - o f f r i c t i o n , 4, 73, 308, 317 - o f wear, 262 Cohesion o f s o l i d s , 59 Cold-welded j u n c t i o n s , 119 Comminution, 352 Components t e s t i n g , 272 Cond i t i on m o n i t o r i n g techniques, 277 Cone c lu t ches , 351 Con t a c t , - area, 53 - area i n t r i b o - t e s t i n g , 253 - area t o wear - t rack area r a t i o , 267 - f a t i g u e , 108 - mechanics, 47 - phys ics and chemis t ry , 56 - pressure , Her t z ian , 49 - pressure i n t r i b o - t e s t i n g , 253 - processes, 47 Contaminants, 57 - d i s p e r s a l o f , 72 - i n f l u e n c e on f r i c t i o n , 8 1

Cont ro l , - methods, 248 - o f o p e r a t i n g v a r i a b l e s i n

Conveyors, 352 Cou 1 omb-f r i c t i o n , - laws o f , 73 - v a l i d i t y o f , 316 Cova len t adhesion bonding, 58 Cor ros ion , f a i l u r e d i s t r i b u t i o n

o f , 239 Crack i n i t i a t i o n and

propagat ion , 109 Crank d r i v e s , 351 Creep, f a i l u r e d i s t r i b u t i o n o f , 239 Crys ta l s t r u c t u r e , - in f l uence on adhesion, 63 - i n f l u e n c e on adhesive wear, 120 Cu t t i ng , 353 Cybernet ics , 21

Data banks, 315 Data sheet f o r t r i b o l o g i c a l

systems, 309 Deep drawing, 352 De laminat ion theory o f wear, 111 D e s c r i p t i o n o f t r i b o - e n g i n e e r i n g

systems, 310 Oesi gn, - o f t r ibo-mechan ica l systems, 242 - p r i n c i p l e s o f redundancy, 243 D e t e r i o r a t i o n modes, 239 D i benzy ld i su l f i d e , 159 Die, 347 D i f f u s i o n , - coat ings , 208, 321 - f a i l u r e d i s t r i b u t i o n o f , 239 D isc brakes, 351 D isc c lu tches , 351 D i s l o c a t i o n processes, - i n f r i c t i o n , 89 - i n wear, 110 D i s s i p a t i v e systems, 16 D i s s i p a t i v e processes, - i n c o n t a c t mechanics, 54 - i n f r i c t i o n , 87 DOCUMENTATION TRIBOLOGY, 356 Donor-acceptor hypothes is o f meta l -

l i c adhesion bonding, 6 1 Dowson-Higginson formula, 151 Drawing, 346, 352 Dredging, 352 D r i l l i n g , 353 Dura t i on o f t e s t i n g , 256 Dynamics , - o f phys i ca l systems, 1 - o f tri bo-mechanical systems , 215

t r i b o - t e s t i n g , 254

396

E a r t h moving u n i t s , 352 E f f i c i e n c y , 222 - i n f l u e n c e o f f r i c t i o n and

- o f t r a n s l a t i o n screw, 225 - o f wedge d r i v e system, E f f o r t v a r i a b l e s , 19 E l a s t i c con tac t , - de format ion , 48 - displacement, 70 E l a s t i c h y s t e r e s i s , 55 - i n r o l l i n g f r i c t i o n , 84 E l a s t i c waves genera t ion , 54 Elastohydrodynamic (EHD)

E las tomer ic bea r ing , 204 E l a s t o s t a t i cs, 48 E l e c t r i c a l con tac ts , 352 - r e s i s t a n c e measur ing techn iques ,

- f a i l u r e i n v e s t i g a t i o n o f , 341 E l e c t r o n c h a n e l l i n g p a t t e r n (ECP)

technique, 289 E l e c t r o n gas, 60 E l e c t r o n i c s t r u c t u r e o f meta ls , 61

l u b r i c a t i o n , 226

225

l u b r i c a t i o n , 146

262

E l e c t r o n probe m ic roana lyze r IEPMA), 291

E l ec t ron sca t t e r i ng f o r c hemi ca 1 a n a l y s i s (ESCA), 293, 296

- a p p l i c a t i o n examples, 190 E l e c t r o p l a t i n g , 208 E l e c t r o s t a t i c adhesion, 58 Elements o f t r ibo-mechan ica l

Emission o f f r i c t i o n a l energy, 9 1 Energy, - balance, 18 - d i s s i p a t i o n , 56, 87 - t ransac t i ons , 36 ENPORT computer program, 20 Ent ropy genera t i on due t o f r i c t i o n ,

Equidensi t i e s o f i n te r fe rog rams , 288 Eros ion , 103 - abras ion , 114 - f a i l u r e d i s t r i b u t i o n o f , 239 Exo-el e c t r o n emiss ion (EEE) , 92 Exponent ia l d i s t r i b u t i o n , 236 E x t e r n a l l y p ressu r i zed bear ings , 200 Extreme pressure (EP) a d d i t i v e s ,

Fa i 1 u re , - causes, 229 - c o n d i t i o n i n l u b r i c a t i o n , 169, 175 - d i s t r i b u t i o n s , 236

systems, 305, 354

38

159, 165

- i n v e s t i g a t i o n s o f e l e c t r i c a l

- modes, 239 - modes o f gears, 230 - o f b a l l bear ings , 237 - o f D iese l engine u n i t s , 237 - o f eng inee r ing systems, 228 - r a t e , 235 - sur face , 172 Fa lex t e s t , 276 Fas tener se ts , 351 Fat igue, 105 - f a i l u r e d i s t r i b u t i o n , 239 - f a i l u r e i n r o l l i n g con tac t , 108 Ferrography, 284 F i e l d i o n microscopy (FIM), F i l i n g , 353 F i lm- th ickness- to - roughness

r a t i o , 153 Flanges, 351 F1 ash tempera ture , 94 F l e x u r a l bear ings , 205 Flow v a r i a b l e s , 19 F l u i d f i l m s , 200 Forg ing , 346, 352 Force t ransducer , 258 Four b a l l t e s t , 276 F rac tu re , - f a i l u r e d i s t r i b u t i o n , 239 - processes i n adhesive wear, 121 - processes i n su r face f a t i g u e

wear, 109 F r e t t i n g wear, 127 F r i c t i o n , 1 - adhesion hypothes is o f , 5 - c o e f f i c i e n t , 4, 73, 317 - c o e f f i c i e n t , fo rmal representa-

t i o n , 308 - dampers, 351 - d r i v e s , 351 - energy emiss ion processes, 9 1 - i n boundary l u b r i c a t i o n , 163 - i n s t a b i l i t i e s , 215 - measuring techn iques , 257 - processes, 69 - r o l l i n g , 81 - roughness hypothes is o f , 4 - s l i d i n g , 73 - s tud ies , h i s t o r i c s o f , 3 - t e s t methods, 250 - t e s t r i g s , 252 F r i c t i o n a l heat , 94 F u l l - s c a l e t e s t s , 277 Func t ion , - o f a system, 17 - o f t r ibo-mechan ica l systems, 27, 211 Func t iona l f a i l u r e s , 227

con tac ts , 341

293, 299

396

Gamma d i s t r i b u t i o n , 238 Gear, - coup l ings , 351 - f a i l u r e modes, 230 - t e s t r i g s , 273 Gear t r a i n , - i d e a l f u n c t i o n a l behaviour, 212 - network rep resen ta t i on , 213 Geometry o f t e s t systems, 252, 265 Gouging abrasion, 114 G r i f f i t h theory, 111 Gr ind ing abrasion, 114 Guides, 351 Gyroscopic bear ings, 351

Hamaker constants, 60 Hardness, i n f l u e n c e on wear,

115, 192 Heat genera t ion i n f r i c t i o n ,

38, 267 Heathcote-sl i p i n r o l l i n g

f r i c t i o n , 83 Her tz theory , 49 H ie ra rchy o f systems, 15 Hinges, 351 Human, - j o i n t s , 351 - tee th , 352 - ve ins , 352 Hydrocarbons, 157 Hydraul i c d r i v e s , Hydrodynamic 1 u b r i c a t i o n , 132 H y d r o s t a t i c bear ings , 200 Hypoid gears, 351

Impact wear, 103 Impu ls i ve contac t , 54 I n e r t i a , p r i n c i p l e o f , 4 In fo rma t ion , - genera t ion systems, 350 - rep roduc t i on systems, 350 - t ransmiss ion o f , 27 I n f r a r e d pyrometer, 259 I n j e c t i o n moulding, 352 I n n e r sur face l aye rs , 57 I n t e r f a c i a l , - bonding, 57 - s l i p , 54 In te r fe rence microscopy, 286 I n t e r r e l a t i o n s between the elements

o f t r i b o - t e c h n i c a l systems, 306

J e l l i u m model o f m e t a l l i c adhesion, 60

J o s t r e p o r t , 10 Journal bear ing , 143 - data sheet o f , 311

351

Junc t ion , - growth, 71 - i n t e r f a c i a l , 57

Kirm’an vo r tex s t r e e t , 167 Khrushov diagram o f ab ras i ve wear

K i r c h h o f f ’ s laws, 19, 212, 217 Kramer e f f e c t o f exo-e lec t rons , 92

Lamel la r s o l i d s , f r i c t i o n o f , 81 Laminar f l u i d f low, 167 Lap1 ace equat ion , 201 Lapping, 353 L i m i t s o f l u b r i c a t i o n , 166 Load a p p l i c a t i o n methods i n t r i b o -

Load-car ry ing capac i t y , 165, 170 Long range fo rces , 59 Low energy e l e c t r o n d i f f r a c t i o n

Lubr i can t , - f i l m th ickness , measuring

- s e l e c t i o n procedure, example, 332 - supply, m o n i t o r i n g o f , 281 - t e s t methods, 274 - types, 157 Lubr i c a t i o n , - modes, 130 - o f mechanical systems, 33 - s tud ies , h i s t o r i c s o f , 8

res i s tance , 116

t e s t i n g , 254

(LEED), 293, 295

methods, 264

Machinery c o n d i t i o n mon i to r i ng , 246, 277

Magnetic, - c h i p de tec to rs , 283 - f i e l d s , 202 - suspension bear ings , 202 Magnetohydrodynami c (MHD)

Ma l func t i ons , - o f eng inee r ing systems, 246 - o f l i v i n g systems, 246 Manufac tur ing processes, 345 M a r t e n s i t i c t rans fo rma t ion , 194 Mass balance, 41 M a t e r i a l , - fo rming systems, 350 - losses due t o wear, - q u a n t i t i e s i n t r i b o - t e s t i n g , 257 - s e l e c t i o n procedure, example, 326 - t ransac t i ons , 40 - t r a n s p o r t a t i o n systems, 350 Maxwell model o f v i s c o e l a s t i c i t y ,

Mean t ime t o f a i l u r e , 235

bear ings , 202

195

55

397

Mechanical, - c a l c u l a t i n g machine, 241 - c lock , 241 - e f f i c i e n c y , 221 - equipment r e l i a b i l i t y , 234 .- f a u l t s , 229 - q u a n t i t i e s i n t r i b o - t e s t i n g , 257 - systems, c l a s s i f i c a t i o n o f , 35, 350 M e t a l l i c adhesion bonding, 58 Metal-working, 345, 348 Methodology f o r t h e s o l u t i o n o f

M ic ro -con tac t areas, 53 M i c r o - c u t t i n g processes, 112 Microdisplacements, 73 Mic roprocessors , 241, 278 M i c r o - s l i p , 54 - i n r o l l i n g f r i c t i o n , 82 M i l d wear, 99 Min ing , 352 Mixed l u b r i c a t i o n , 154 Monolayer a n a l y s i s techniques, 293 Mot ion, 1, 4 - i n f l u e n c e o f f r i c t i o n on, 215 - t ransmiss ion systems, 350 - types, 304 M u l t i p o r t system, 214

Naphthenic hydrocarbons, 158 Navier-Stokes equat ions , 135, 138 Needle bear ings , 351 Network, - theory , 18 - r e p r e s e n t a t i o n o f gear t r a i n

- r e p r e s e n t a t i o n o f n -po r t

Newtonian f l u i d s , 134 N i t r i d i n g , 208, 322 No-contact t ime f r a c t i o n , 167 Noise, - measuring techn iques , 258, 279 - reduc t i on , example o f , 338 - spectrum o f w h e e l - r a i l system, 338 Nomarski o p t i c a l microscopy, 286 Non r e t a r d e d van de r Waals fo rces ,

Normal d i s t r i b u t i o n , 236 No-wear c o n d i t i o n s , s o l u t i o n s f o r ,

Of f -shore bear ing a p p l i c a t i o n , 326 O i l i n e s s aqents, 158

f r i c t i o n and wear problems, 315

system, 213

system, 214

59

199

O l e f i n i c hydrocarbons, 158 O l e i c ac id . 159

Opera t ing v a r i a b l e s , 30 - c o n d i t i o n s f o r p roper cho ice o f ,

- i n t r i b o t e s t i n g , 251 - o f t r i b o - t e c h n i c a l systems, 304 O p t i c a l microscopy, 286 Op t im iza t i on o f dynamic behav iour o f

t r ibo-mechan ica l systems, 221 Outer su r face l a y e r s , 57 Oxygen, i n f l u e n c e on boundary

l u b r i c a t i o n , 190, 314

Packings, 352 P a r a f f i n i c hydrocarbons, 157 P a r t i a l e lastohydrodynamic (EHD)

l u b r i c a t i o n , 155 P e t r o f f ' s fo rmula , 8 Phonons, emiss ion o f , 91 Photons, emiss ion o f , 92 Phys i so rp t i on , 160 P in-on-d isc t r i b o m e t e r , 265, 313 P i p e l i n e s , 352 P i s t o n - c y l i n d e r assembl ies, 352 - c o n d i t i o n moni t o r i n g , 282 - f a i l u r e d i s t r i b u t i o n , 237 P i t t i n g o f gears, 232 P i v o t bear ings , 351 - l u b r i c a t i o n o f , 332 P lane ta ry gears, 351 P lan ing , 353 P l a s t i c c o n t a c t processes, 55 P l a s t i c de format ion i n r o l l i n g

P l a s t i c i t y index , 55, 101, 179 P lough ing component o f s l i d i n g

f r i c t i o n , 77 Poisson s t a t i s t i c a l process, 238 P o l i s h i n g , 353 Po lye thy lene (HDPE), f r i c t i o n a l

Po lymer -s tee l s l i d i n g p a i r s ,

P o l y t e t r a f l u o r e t h y l e n e (PTFE) ,

Power, - balance, 37 - c i r c u l a t i n g p r i n c i p l e , 274 - screws, 351 - t ransmiss ion systems, 350 P r e l i m i n a r y displacements, 73 P resen ta t i on o f research data, 312 Press ing , 346, 352 P r i n t i n g u n i t s , 352 P r o f i 1 ometer techn ique, 289

244

f r i c t i o n , 85

behav iour o f , 317

f r i c t i o n o f , 316

f r i c t i o n a l behav iour o f , 317

P r o p e r t i e s o f t h e elements o f On- l ine m o n i t o r i n g techniques, 277 t r ibo-mechan ica l systems, 306

398

Prow fo rmat ion , 121 Punching , 353

Q u a r r y i ng , 352 Q u i n n ' s theory o f t r i b o o x i d a t i v e

wear, 124

Rack-and-pinions, 351 Rad ioac t ive t r a c e r methods, 283 Ray le igh d i s t r i b u t i o n , 236 Real a rea o f con tac t , 53 Reduction, - o f f r i c t i o n - i n d u c e d noise,

example, 338 - o f severe wear, example, Redundancy, 242 - o f mechanical systems, 243 Relays, 352 Re1 i ab i 1 i ty, 234 - f u n c t i o n , 235 - o f mechanical equipment, 234 Rep1 acement o f mechanical systems,

Requirements f o r p roper f u n c t i o n a l

Research da ta p resen ta t i on , 312 Retarded van der Waals fo rces , 60 Reynolds, - c o n d i t i o n , 141 - equat ion , 139, 147, 155 * - number, 167 - s l i p i n r o l l i n g f r i c t i o n , R o l l i ng , - con tac t f a i l u r e , 108 - f r i c t i o n , 81 - i n metalworking, 346, 352 Rope d r i v e s , 351 Roughness, - hypothes is o f f r i c t i o n , 4 - o f sur faces , 51 Runni ng- i n , - o f bea r ing sur faces , 182 - schedules, 185 Rust ing, f a i l u r e d i s t r i b u t i o n o f ,

335

241

behaviour, 240

82

239

SAE t e s t , 276 Sa fe ty o f eng ineer ing systems, 228 Sawing, 353 Scale f a c t o r s i n s i m u l a t i v e t r i b o -

Scanning e l e c t r o n microscopy (SEM) , Scu f f i ng , 119, 167 - i n c i p i e n t , 171 - o f gears, 233 Seals, 352

t e s t i n g , 267

289

Secondary i o n mass spectroscopy

Seizure, 119, 167 Severe wear, 99 Shakedown l i m i t i n r o l l i n g , 85 Shaping, 353 Shoe-on-ground, 351 Shor t range fo rces , 59 S i mu1 a t i on, - methods, 248 - o f s t i c k - s l i p behaviour, 218 S imu la t i ve t e s t i n g , 264 - o f bea r ing m a t e r i a l s , 268 - schematic o u t l i n e o f , 270 S1 i deways , 351 S l i d i n g bear ings , 351 S l i d i n g f r i c t i o n , 73 S1 i p - r i ng assembl i e s , S l i p systems i n c r y s t a l s , 66 S o l u b i l i t y o f meta ls and t r i b o l o g i -

So lu t i ons o f t r i b o l o g i c a l problems,

Sommerfel d, - c o n d i t i o n , 141 - number, 143 Sound, emission o f , 91, 338 S p a l l i n g f a t i g u e f a i l u r e i n

r o l l i ng contac t , 108 Spect rograph ic o i 1 a n a l y s i s procedure

(SOAP), 282 Sp ind les , 351 Spinning, 352 Sp l ines , 351 Spur gears, 351 Squeeze te rm o f Reynolds equat ion ,

S ta in ing , f a i l u r e d i s t r i b u t i o n o f ,

S t a r v a t i o n o f l u b r i c a n t , 152 S t e a r i c ac id , 159 S t i c k - s l i p e f f e c t s , 215 - analogue computer s imu la t i on , 218 - i n w h e e l - r a i l system, 338 Storage o f f r i c t i o n a l energy, 89 S t r a i n gauges, 258 S t r a i n harden ing due t o f r i c t i o n

and wear, 192 S t r e t c h te rm o f Reynolds equat ion ,

139 S t r i b e c k curve, 130, 219 S t ruc tu re , - o f a system, 16 - o f t r ibo-mechan ica l systems, 30,

Subsurface con tac t shear s t resses ,

( S I M S ) , 293, 296

352

c a l behaviour, 63, 120

315

139

239

176, 305

107

399

Superpos i t i on o f wear mechanisms, 127

Surface, - coat ings , 208 - compos i t ion , 57, 186, 190 - compos i t ion i n v e s t i g a t i o n t e c h n i -

ques, 291 - contour maps, 291 - energy, 67 - energy c r i t e r i o n , 196 - f a t i g u e wear mechanisms, 105 - i n v e s t i g a t i o n techn iques , 286 - p r e p a r a t i o n i n t r i b o - t e s t i n g , 252 - roughness, 51 - roughness i n EHD l u b r i c a t i o n , 170

~ s t r e n g t h p r o p e r t i e s , 191 '- topography, 51, 180, 181 - topography measuring techniques,

S w i tches , 352 Sys tem, I concept, 14 - d e f i n i t i o n , 16 I dependent c h a r a c t e r i s t i c s , 65, 265 .- f unc t i on , 16, 27, 211, 303 .- h ie ra rchy , 15 - independent c h a r a c t e r i s t i c s , 65, 274 - methodology, 300, 315 - m o d e l l i n g techniques, 18 - s t r u c t u r e , 16, 30, 176, 242, 305 - t e a r i n g , 25

Tangent ia l f o rces i n c o n t a c t p ro- cesses, 69

Tape reco rde r heads, 352 Tay lo r vo r tex f l ow , 167 Technical f u n c t i o n s o f t r ibo-mechan i -

c a l systems, 27, 211, 303, 350 Temperature, - c o n t r o l l e v e l s f o r bear ings , 280 - e f f e c t s i n EHD l u b r i c a t i o n ,

- measuring techniques, 255, 259 .- r i s e s due t o f r i c t i o n , 94 Test, - du ra t i on , 256 - methods, 248 Tes t ing , 248 - f u l l - s c a l e , 277 - o f l u b r i c a n t s , 274 - o f machine elements, 272 Thermal, - e f f e c t s due t o f r i c t i o n , 94 -. q u a n t i t i e s i n t r i b o - t e s t i n g , 257 -. t ransac t i ons , 38 Thermocouples , 259 Through v a r i a b l e s , 19

286

153, 170

T i l t i n g pad bear ing , 134 Timken t e s t , 276 Topography o f sur faces , 51 Transac t ions o f q u a n t i t i e s i n

T r a n s i t i o n s i n l u b r i c a t i o n modes,

Transmission o f mot ion , i n f l u e n c e

Tr ibo-chemica l wear mechanisms, 123 T r i bo-engi n e e r i ng systems,

T r i b o l o g y , - d e f i n i t i o n , 11 - genera l theory , 24 - h i s t o r i c a l development, 3 - meaning o f , 11 T r i bo l o g i c a l processes, 33, 45 ,

- i n f l u e n c e on t h e f u n c t i o n o f

- i n f l u e n c e on t h e s t r u c t u r e o f

T r i b o l o g i c a l systems da ta sheet,

T r i b o l umi nescence , Tribo-mechanical system, d e f i n i t i o n ,

Tr ibometer , 4, 248 T r i b o m e t r i c c h a r a c t e r i s t i c s , 251 T r i bometry, 248 Tr ibo-process diagram, 32 T r i bo- t e s t i n g , 248 Turbulences, 167 Turn ing , 353 Two-port system, 214 Typewr i te r u n i t s , 352 Tyre and road, 352

Un i t event, - i n f r i c t i o n , 75 - i n wear, 100

Valency fo rces , 59 Valves, 352 Vanadi z i ng , 322 Van de r Waals adhesion, 58 V e l o c i t y c o n t r o l methods i n t r i b o -

t e s t i n g , 255

systems, 21, 30

168, 171

o f f r i c t i o n , 215

c o m p i l a t i o n o f , 350

307

mechanical systems, 211

mechanical systems, 176

301, 309 92

27

V i b r a t i o n measuring techn iques , 258. 279

Video p ick -ups , 352 V i scoel a s t i c i ty, 55 V i s c o s i t y , 134 - pressure c o e f f i c i e n t , 148 - temperature dependence, 153 Vogelpohl ' s method, 245

400

Vo ig t model o f v i s c o e l a s t i c i t y , 55 Vortex f low, 167

Washers, 352 Wear, 2 - c o e f f i c i e n t , 262 - c l a s s i f i c a t i o n , 7, 102 - debr i s , 189 - i n boundary l u b r i c a t i o n , 164 - mon i to r i ng techniques, 281 - p a r t i c l e s , 122, 197, 198 - processes, 97 - processes, superpos i t i on o f , 127 - q u a n t i t i e s , 261 - q u a n t i t i e s , fo rmal rep resen ta t i on ,

- reduc t i on , example, 335 - res i s tance , d e f i n i t i o n , 114 - r e s i s t a n t coa t ings , 207, 321 - s tud ies , h i s t o r i c s o f , 6 - t e s t methods, 250, 262, 281 - t e s t r i g s , 252 - t ime behaviour, 195, 235

308

Weaving, 352 Wedge d r i v e , 222 Wedge te rm o f Reynolds equat ion,

Weibu l l d i s t r i b u t i o n , 238 Well d r i l l i n g , 352 Wheel and r a i l , 338, 352 Workpiece - d i e i n t e r f a c e , 347 Work, - t ransac t i ons , 36 - t ransmiss ion systems, 350 Worm gears, 351 W r i t i n g u n i t s , 352

Y ie ld ing , f a i l u r e d i s t r i b u t i o n o f ,

Z inc d ioc ty l -d i th io -phospha te , 159 Zero-wear model, 244

139

2 39