AGMA 915-1-A02 Gears Inspect

8/16/2019 AGMA 915-1-A02 Gears Inspect

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AGMA INFORMATION SHEET(This Information Sheet is NOT an AGMA Standard)

A G M A 9 1 5 - 1 - A 0 2

AGMA 915- 1- A02

AMERICAN GEAR MANUFACTURERS ASSOCIATION

Inspection Practices - Part 1:

Cylindrical Gears -

Tangential Measurements


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Inspection Practices -- Part 1: Cylindrical Gears -- TangentialMeasurements

AGMA 915--1--A02

CAUTION NOTICE: AGMA technical publications are subject to constant improvement,

revision or withdrawal as dictated by experience. Any person who refers to any AGMA

technical publication should be sure that the publication is the latest available from the As-

sociation on the subject matter.

[Tables or other self--supporting sections may be quoted or extracted. Credit lines should

read: Extracted from AGMA 915--1--A02, Inspection Practices -- Part 1: Cylindrical Gears

-- Tangential Measurements, with the permission of the publisher, the American Gear

Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia 22314.]

Approved April 16, 2002

ABSTRACT

This information sheet provides a code of practice dealing with inspection relevant to tangential element and

composite deviations of cylindrical involute gears (measurements referred to single flank contact) and serves

as a supplement to ANSI/AGMA 2015--1--A01, Accuracy Classification System -- Tangential Measurements for

Cylindrical Gears.

Published by

American Gear Manufacturers Association1500 King Street, Suite 201, Alexandria, Virginia 22314

Copyright ! 2002 by American Gear Manufacturers Association

All rights reserved.

No part of this publication may be reproduced in any form, in an electronic

retrieval system or otherwise, without prior written permission of the publisher.

Printed in the United States of America

ISBN: 1--55589--798--3

American

GearManufacturers Association


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AGMA 915--1 --A02AMERICAN GEAR MANUFACTURERS ASSOCIATION

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Contents

Page

Foreword v. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Scope 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 References 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Symbols and corresponding terms 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Extent of gear inspection 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Identification of deviation position 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Measurement of pitch deviations 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Measurement of profile deviations 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8 Measurement of helix deviations 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 Measurement of single flank composite deviations 26. . . . . . . . . . . . . . . . . . . . . .

10 Contact pattern checking 37. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figures

1 Notation and numbering for external gear 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Notation and numbering for internal gear 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Schematic of single probe measuring device 6. . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Single pitch deviation, single probe device 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Pitch measurement with a pitch comparator 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Circular pitch measurement, two probe device 8. . . . . . . . . . . . . . . . . . . . . . . . . .

7 Single pitch deviation, two probe device 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8 Sample table with hypothetical deviation values obtained by pitchcomparator (two probe) device 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 Sample table with hypothetical deviation values obtained by indexing(single probe) device 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Sample graphic representation of single pitch deviations, f pt 10. . . . . . . . . . . . . .

11 Sample graphic representation of index deviations 10. . . . . . . . . . . . . . . . . . . . . .

12 Base pitch measurement, two probe device 11. . . . . . . . . . . . . . . . . . . . . . . . . . . .

13 Schematic of involute inspection device 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 Profile measuring method 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15 Profile inspection by coordinates 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Typical tooth profile measurement charts 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17 Tooth profile and profile diagram 15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18 Mean profile slope deviation, f H!m 16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19 Profile inspection by optical projection 18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20 Profile inspection by gear tooth caliper method 18. . . . . . . . . . . . . . . . . . . . . . . . .

21 Profile inspection by measurement over pins 18. . . . . . . . . . . . . . . . . . . . . . . . . . .

22 Helix deviation 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 Graphic charting of helix 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24 Helix diagram 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 Traces generated from four tooth flanks 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26 Helix of right hand helical gear with short lead (+ helix angle) 23. . . . . . . . . . . . .

27 Helix of right hand helical gear with long lead (-- helix angle) 23. . . . . . . . . . . . .28 Helix of left hand helical gear with long lead (-- helix angle) 24. . . . . . . . . . . . . . .

29 Helix of left hand helical gear with short lead (+ helix angle) 24. . . . . . . . . . . . . .

30 Principle of undulation inspection 25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31 Composite gear testing, double and single flank 26. . . . . . . . . . . . . . . . . . . . . . . .

32 Schematic of a single flank measuring device 27. . . . . . . . . . . . . . . . . . . . . . . . . .

33 Individual tooth deviations revealed by single flank testing 27. . . . . . . . . . . . . . .

34 Filtered signal from figure 33 (eccentricity removed) 28. . . . . . . . . . . . . . . . . . . .

35 Angular motion curves from tooth modification 29. . . . . . . . . . . . . . . . . . . . . . . . .


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36 Effect of contact transfer on the profile component in a tangentialcomposite deviation diagram (spur gears) 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37 Influence of overlap ratio 31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38 Single flank composite strip chart 32. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39 Single flank composite test, low number of teeth 33. . . . . . . . . . . . . . . . . . . . . . . .

40 Single flank composite test, high number of teeth 33. . . . . . . . . . . . . . . . . . . . . . .

41a Total composite deviation 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41b Long term component 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41c Short term component 35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42 Manual interpretation of composite test 36. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43 Part of tangential composite deviation diagram -- Interpretation example 36. . .

44 Tangential composite deviation diagrams showing influence of meshrelocation 37. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 Matching profiles, with tooth alignment mismatch and end relief 38. . . . . . . . . . .

46 Matching helix, with profile mismatch and end relief 38. . . . . . . . . . . . . . . . . . . . .

47 Waviness 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48 Typical specification: approximately 75% contact, excluding extremes of tooth, which are intentionally relieved 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Tables

1 Symbols and definitions 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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v

Foreword

This Information Sheet, AGMA 915--1--A02, Inspection Practices -- Part 1: Cylindrical

Gears -- Tangential Measurements is provided for informational purposes and is intended

for use with the Standard ANSI/AGMA 2015--1--A01, Accuracy Classification System --

Tangential Measurements for Cylindrical Gears.

AGMA 915--1--A02 replaces AGMA ISO 10064--1, Cylindrical Gears -- Code of Inspection

Practice -- Part 1: Inspection of Corresponding Flanks of Gear Teeth. and the information onsimilar subjects as covered in ANSI/AGMA 2000--A88, Gear Classification and Inspection

Handbook -- Tolerances and Measuring Methods for UnassembledSpur and Helical Gears.

The user of this Information Sheet is alerted that differences exist between it and

ANSI/AGMA 2000--A88 and AGMA ISO 10064--1. These include, but are not limited to:

-- Measuring methods refer to an accuracy grade numbering system that is reversed,

such that the smallest number represents the smallest tolerance;

-- Probe direction and measurement requirements for elemental and composite

tolerances may differ from ANSI/AGMA 2000--A88 or AGMA ISO 10064--1;

-- The measurement “profile evaluation range” and “helix evaluation range”, where

the tolerances are applied, are defined for differentarea than in ANSI/AGMA 2000--A88or AGMA ISO 10064--1;

-- The measurement of undulations is included;

-- Concepts of “mean measurement trace”, “design trace”, “slope deviation”, “form

deviation”, “gear form filter cutoff”, “tolerance diameter” and “data density” are defined.

Therefore, the user of this information sheet must be very careful when comparing

measurement methods formerly specified using ANSI/AGMA 2000--A88 or AGMA ISO

10064--1.

The first draft of AGMA 915--1--A02 was made in May, 1998. This document was approved

by the Inspection Handbook Committee on January 31, 2002. It was approved by the

Technical Division Executive Committee as an AGMA Information Sheet on April 16, 2002.

Suggestions for improvement of this document will be welcome. They should be sent to the

American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria,

Virginia 22314.


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PERSONNEL of the AGMA Inspection and Handbook Committee

Chairman: Edward Lawson M&M Precision Systems. . . . . . . . . . . . . . . . . . . . . .

ACTIVE MEMBERS

W.A. Bradley Consultant. . . .

D.R. Choiniere Profile Engineering, Inc.. .

J. Clatworthy Gear Metrology, Inc.. . . .B.L. Cox BWXT Y12 LLC. . . . . . .

T.C. Glasener Xtek, Incorporated. . .

G.G. Grana The Gleason Works. . . . .

B. Hofrichter Arrow Gear Company. . . .

T. Klaves Milwaukee Gear. . . . . . .

I. Laskin Consultant. . . . . . . .

S. Lindley The Falk Corporation. . . . . .

M. May The Gleason Works. . . . . . . . .

D.A. McCarroll ZF Industries. .D.R. McVittie Gear Engineers, Inc.. . . .

S. Moore Martin Sprocket & Gear, Inc.. . . . . . .

R.W. Ott Caterpillar, Inc.. . . . . . . .

J.M. Rinaldo Atlas Copco Comptec, Inc.. . . .

L.J. Smith Consultant. . . . . .

R.E. Smith R.E. Smith & Company, Inc.. . . . . .

ASSOCIATE MEMBERS

M. Antosiewicz The Falk Corporation. .

M.J. Barron Gear Motions, Inc.. . . . .

D. Behling Hamilton Sundstrand Aero.. . . . . .

M.K. Considine Considine Associates. .

R. Considine Considine Associates. . . .

J.S. Cowan Eaton Corporation. . . . .

M.E. Cowan Process Equipment Company. . . .

B. Cowley Mahr Corporation. . . . . .

C. Dick The Horsburgh & Scott Co.. . . . . . . . .

H.D. Dodd Caterpillar, Inc.. . . . . .

R. Green R7 Group, Gear Consultants. . . . . . .

D. Gregory Gear Products, Inc.. . . . .

B. Gudates Fairfield Manufacturing Co., Inc.. . . . .

J.S. Hamilton Regal--Beloit Corporation. . .

H. Harary NIST. . . . . . .

D. Heinrich Xtek, Incorporated. . . . .G. Henriot Consultant. . . . . .

J. Horwell Brown & Sharpe. . . . . .

S. Johnson The Gear Works -- Seattle, Inc.. . . . .

T. Klemm Liebherr. . . . . . .

D.E. Kosal National Broach & Machine Co.. . . . . .

J. Koshiol Columbia Gear Corporation. . . . . .

W.E. Lake Mitsubishi Gear Technology Ctr.. . . . . .

A.J. Lemanski Penn State University. . .

G.A. Luetkemeier Rockwell Automation/DodgeD. Matzo Northwest Gears, Inc.. . . . . . .

P.A. McNamara Caterpillar, Inc..

W.J. Michaels Sundstrand Corporation. . .

M. Milam Amarillo Gear Company. . . . . . .

T. Miller The Cincinnati Gear Company. . . . . . . .

M. Nanlawala IIT Research Institute/INFAC. . .

M. Octrue Centre Technique Des Ind. Mec.. . . . . .

T. Okamoto Nippon Gear Company, Ltd.. . . . .

J.A. Pennell Univ. of Newcastle--Upon--Tyne. . . . .

K.R. Price Eastman Kodak Company. . . . . .

R.S. Ramberg The Gear Works -- Seattle, Inc.. . .

V.Z. Rychlinski Brad Foote Gear Works, Inc.. .D.H. Senkfor Precision Gear Company. . . .

S. Shariff PMI Food Equipment Group. . . . . . .

E. Storm Consultant. . . . . . .

R.F. Wasilewski Arrow Gear Company.

F.M. Young Forest City Gear Company. . . . .

P. Zwart Caterpillar, Inc.. . . . . . . .


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1

AGMA 915 --1 --A02AMERICAN GEAR MANUFACTURERS ASSOCIATION

American Gear Manufacturers Association --

Inspection Practices --Part 1: Cylindrical

Gears -- Tangential

Measurements

1 Scope

This information sheet constitutes a code of practice

dealing with tangential measurements on flanks of

individual cylindrical involute gears., i.e., with the

measurement of pitch, profile, helix and tangential

composite characteristics.

In providing advice on gear measuring methods and

the analysis of measurement results, it supplements

the standard ANSI/AGMA 2015--1--A01, Accuracy

Classification System -- Tangential Measurements

for Cylindrical Gears.

2 References

The following standards contain provisions which

are referenced in the text of this information sheet.

At the time of publication, the editions indicated were

valid. All standards are subject to revision, and

parties to agreements based on this document are

encouraged to investigate the possibility of applying

the most recent editions of the standards indicated.

AGMA 915--3--A99, Inspection Practices -- Gear

Blanks, Shaft Center Distance and Parallelism

ANSI/AGMA 2015--1--A01, Accuracy Classification

System -- Tangential Measurements for Cylindrical

Gears

ISO 53:1998, Cylindrical gears for general and

heavy engineering -- Standard basic rack tooth

profile

ISO 54:1996, Cylindrical gears for general

engineering and for heavy engineering -- Modules

ISO 701:1998, International gear notation --

Symbols for geometrical data

ISO 1122--1:1998, Vocabulary of gear terms -- Part

1: Definitions related to geometry

3 Symbols and corresponding terms

The symbols and terms used throughout this manual

are in basic agreement with the symbols and terms

given in ISO 701:1998, International gear notation --Symbols for geometrical data. In all cases, the first

time that each symbol is introduced, it is defined and

discussed in detail. See table 1.

NOTE: The symbols and definitions used in this infor-

mation sheet may differ from other AGMA standards.

The user should not assume that familiar symbols can

be used without a careful study of their definitions.

Table 1 -- Symbols and definitions

Symbols Definition1) UnitsWhere

first used

b Facewidth mm Figure 24

D Design pitch diameter mm Eq 4

Db Design base diameter mm Eq 3

d Reference diameter mm Eq 24

d b eff Effective base diameter mm 6.5.3

d T Tolerance diameter mm 6.2

F " Total helix deviation mm Figure 22

(continued)


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2

Table 1 (continued)


first used

F is Total single flank composite deviation mm 9.1

F p Total cumulative pitch deviation mm 6.1

F ps/8 Sector pitch deviation2) mm 6.2

F r Radial runout mm 9.3.6

F ! Total profile deviation mm Figure 17 f dbm Mean base diameter difference

2) mm 6.5.3

f e Eccentricity between gear axis and axis of gear teeth mm Figure 18

f f ! Profile form deviation mm Figure 17

f f " Helix form deviation mm Figure 24

f H! Profile slope deviation2) mm Figure 17

f H!m Mean profile slope deviation2) mm 7.6

f H" Helix slope deviation2) mm Figure 24

f H"m Mean helix slope deviation2) mm 8.6

f H"mt Mean helix slope deviation, in the transverse plane and tangent to thetolerance diameter2)

mm Eq 18

f id Tooth--to--tooth double flank composite deviation mm 9.3.6 f is Tooth--to--tooth single flank composite deviation mm 9.1

f Lm Mean lead difference2) mm 8.7

f pbm Mean normal base pitch deviation2) mm 6.5.3

f pbn Normal base pitch deviation2) mm 6.5

f pt Single pitch deviation2) mm 6.1

f w" Undulation height (along helix) mm Figure 24

f 1, f 2 Reading head frequency pulses/sec Figure 32

f ! Pressure angle deviation2) degrees 7.5

f !mn Mean normal pressure angle deviation2) degrees 6.5.3

f !mt Mean transverse pressure angle deviation2) degrees 6.5.3

f " Helix angle deviation2) degrees 8.5 f "m Mean helix angle deviation

2) degrees 8.7

g! Length of path of contact mm Figure 36

k Number of pitches in a sector -- -- 5.6

L Left flank -- -- 5.2

L Lead of the design helix mm Eq 17

Leff Effective lead mm 8.7

L! Profile evaluation range mm Figure 17

L!c Functional profile length mm Eq 9

L" Helix evaluation range mm Figure 24

L# Base tangent length to start of active profile mm Figure 17

l Left hand helix -- -- 5.3mn Normal module mm Eq 1

N Pitch number -- -- 5.5

n Number of deviation values included in the mean -- -- Eq 8

pb Base pitch mm Figure 36

pbn Theoretical normal base pitch mm 6.5

pm True position pitch2) mm 6.3.2

(continued)


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Table 1 (concluded)


first used

R Right flank -- -- 5.2

r Right hand helix -- -- 5.3

s Undulation measurement bar length mm Figure 30

z Number of teeth -- -- Eq 2

z M Number of teeth in master indexing worm wheel -- -- Eq 24 z 1 Driving gear -- -- Figure 32

z 2 Driven gear -- -- Figure 32

!Tt Transverse pressure angle at the tolerance diameter degrees 6.5.2

!n Normal pressure angle degrees Eq 1

!n eff Effective normal pressure angle degrees 6.5.3

!t Design transverse pressure angle degrees Eq 6

!t eff Effective transverse pressure angle degrees 6.5.3

" Helix angle degrees Eq 5

"b Design base helix angle degrees Eq 2

"eff Effective helix angle at the standard pitch diameter degrees 8.7

"T eff Effective helix angle at the tolerance diameter degrees 8.7#$ Total contact ratio -- -- 9.3.5

%" Undulation wave length mm Eq 24

%"x Axial wavelength of undulation mm Figure 24

& Involute roll angle degrees Figure 17

I Reference face -- -- 5.2

II Non--reference face -- -- 5.2

NOTE:1) Symbols used for deviations of individual element measurements from specified values are composed of lower caseletters “ f ” with subscripts (exceptions include f e, f 1 and f 2) whereas symbols used for “cumulative” or “total” deviations,which represent combinations of several individual element deviations,are composed of capital letters “ F ” also with sub-scripts. It is necessary to qualify some deviations with an algebraic sign. A deviation is positive when e.g., a dimension

is larger than optimum and negative when smaller than optimum.2) These deviations can be + (plus) or -- (minus).

4 Extent of gear inspection

It is rarely necessary or economical to measure all

possible deviations on all gears manufactured.

Certain elements may not significantly influence the

function of the gear under consideration. Some

measurements can be substituted for others. Stable

manufacturing processes allow a relatively small

number of samples to be measured and still ensure

that the required quality level is maintained. It isrecommended that specific measuring plans be

negotiated between purchaser and supplier.

4.1 Required inspection information

Certain necessary information should be provided to

the operator(s) of the measuring equipment. The

information required will vary depending on the type

of measurement(s) required. Most measurement

processes require basic gear and blank data,

number of teeth, pitch, pressure angle, helix angle,

tooth size, outside diameter, root diameter, face

width, design profile, design helix, etc. Certain

measuring tasks require additional information. For

example, to measure profile, the profile control

diameter and start of tip break must be provided.

With mechanical measuring equipment, additional

information may be required: base circle diameter

(radius), base helix angle, sine bar setting, etc.

The design engineer or engineering department

should be responsible for supplying this minimum

required inspection information to those performing

the measurements.

4.2 Measurement selection

Inspection may be carried out using a number of

alternate methods. Some measurements may be


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substituted for others. For example single flank

composite measurement may be substituted for

pitch measurement, or radial composite measure-

ment may replace runout measurement.

A number of factors should be considered when

selecting the measurements, including the quality

level required, size of the gear, manufacturing cost

and most important the application of the productgear.

4.2.1 Sampling

Gears, like other parts,are manufactured to a certain

level of accuracy dependant on the production

process used. When the process used is proven

capable of producing the required accuracy level

using statistical methods, sampling inspection may

be utilized. Many factors may influence the sample

size and frequency, foremost among these should

be the assurance that the required accuracy level of

the parts is met.

4.2.2 First piece inspection

It may be possible to inspect only the first piece of a

batch to verify that the setup is correct, allowing the

inherent accuracy of the process to assure the

quality of subsequent parts.

5 Identification of deviation position

It is convenient to identify deviations associated with

measurements of gear teeth by specific reference to

individual right flanks, left flanks, pitches or groups of

these.

In the following, conventions are described which

enable positive determination of the location of

deviations.

5.1 Datum axis

Specification of the design profile, design helix, and

design pitch requires definition of an appropriate

reference axis of rotation, called the datum axis. It is

defined by specification of datum surfaces. See

AGMA 915--3--A99.

The datum axis determines tooth geometry, thereby

being the reference for measurements and associat-

ed tolerances. The location and orientation of the

tolerance diameter circle are determined by the

datum axis.

Ideally the surfaces used to construct the datum

axis, the surfaces used to locate the gear for

manufacturing, and the functional surfaces that

define the gear axis of rotation in its final assembly

would all be the same. In practice this is often not the

case. For example, shaft type parts are often

manufactured and inspected using female centers to

define the datum axis. In cases where the inspec-

tion, manufacturing, and/or functional datum sur-faces are different, these surfaces must be

coincident with each other to a level of accuracy

sufficient to assure the final quality of the gear is

adequately represented during measurement.

The gear being measured should be oriented so that

its datum axis is coincident with the axis of rotation of

the measuring instrument. In the case of mounting

the gear between centers, care must be taken to

assure that the mounting arbor, if used, is in good

condition, and the female centers are clean and

concentric with thedatumsurfaces of thegear. In thecase of computer controlled measuring instruments,

it may be possible to mount the gear with significant

deviation to the instrument’s axis of rotation. In that

case, the measuring program must be capable of

mathematically correcting the errors resulting from

this off axis mounting condition.

5.2 Right or left flank

It is convenient to choose one face of the gear as the

reference face and to mark it with the letter “I”. The

other non--reference face might be termed face “II”.

For an observer looking at the reference face, so that

the tooth is seen with its tip uppermost, the right flank

is on the right and the left flank is on the left.

Right and left flanks are denoted by the letters “R”

and “L” respectively.

5.3 Right hand or left hand helical gears

The helix of an external or internal helical gear is

referred to as being right hand or left hand. The hand

of helix is denoted by the letters “r” and “l”

respectively.

The helix is right hand (left hand) if, when lookingfrom one face, the transverse profiles show succes-

sive clockwise (counter--clockwise) displacement

with increasing distance from an observer.

5.4 Numbering of teeth and flanks

Looking at the reference face of a gear, the teeth are

numbered sequentially in the clockwise direction.

The tooth number is followed by the letter R or L,


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5

indicating whether it is a right or a left flank. Example:

“Flank 29 L”.

5.5 Numbering of pitches

The numbering of individual pitches is related to

tooth numbering as follows: pitch number “ N ” lies

between the corresponding flanks of teeth numbers

“ N --1” and “ N ”; with a letter R or L it is indicatedwhether the pitch lies between right or left flanks. For

example “Pitch 2 L”, (see figures 1 and 2).

5.6 Number of pitches “k ”

The subscript “k ” of a deviation symbol denotes the

number of consecutive pitches to which thedeviation

applies.

In practice, a number is substituted for “k ”, for

example F p3 indicates that a given cumulative pitch

deviation refers to three pitches.

6 Measurement of pitch deviations

6.1 Pitch deviation

Index, single pitch ( f pt), and total cumulative pitch

( F p) are elemental parameters relating to theaccura-

cy of tooth locations arounda gear. The following is a

description of the measuring methods and a guide to

the interpretation of data generated by the measur-ing devices.

6.2 Pitch deviation measurement

Measurements for determining index, single pitch

( f pt), and total cumulative pitch ( F p) are made:

-- relative to the datum axis of the gear;

-- at the tolerance diameter, d T ;

-- In the specified tolerancing direction (within

thetransverse plane along the arc of thetolerance

diameter).

leftflank

30R 2L

tip

rightflank

29

30 1

2

30 R = pitch No. 30, right flank

2 L = pitch No. 2, left flank

Figure 1 -- Notation and numbering for external gear

tip

left flank

2

1 30

29

right

flank

30R1L

1 L = pitch No. 1, left flank30 R = pitch No. 30, right flank

Figure 2 -- Notation and numbering for internal gear


12/46


6

Measurements made at different diameters or in

other directions must be adjusted so that they are

equivalent to measurements at the tolerance diame-

ter and in the tolerance direction. This adjustment

must be made before comparison of test results to

tolerances.

Sector pitch deviation ( F ps/8) is an optional parame-

ter described in Annex E of ANSI/AGMA2015--1--A01. Measurements of sector pitch devi-

ation are also expected to conform to the above

specified requirements.

Pitch should be measured on both left and right

flanks. However, if the specific operating direction of

the gear is known, only the loaded flanks need to be

measured.

6.3 Pitch deviation measurement methods

Pitch parameters can be measured by either of two

types of device. The indexing (single probe) devicedetermines the location of each tooth around a gear,

relative to a datum tooth (the index). The pitch

comparator (two probe) device compares the dis-

tances between adjacent tooth flanks to the distance

between an initial reference pair of adjacent tooth

flanks.

The various pitch parameters can all be determined

by either measuring device with the application of

suitable calculations. The indexing method is

usually preferred because of its accuracy and

simplicity. However, for large diameter gears, use of

the pitch comparator method may be preferable.

Coordinate measuring machines without a rotating

table can also be used for measurements of pitch

parameters by probe movements that correspond to

the principle of the indexing method.

6.3.1 Indexing pitch measurement method

The indexing (single probe) device uses an angular

indexing apparatus such as an index plate, circle

divider, optical or electronic encoder, or polygon and

auto collimator to precisely rotate the gear by anangular increment equal to its pitch, or 360" / z (see

figure 3). The degree of its precision must be

consistent with the quality grade and diameter of the

gear.

Index mechanism

Tolerancediameter, d T

Index readings+ Indexdeviation

-- Indexdeviation

Dash lines representtheoretical location

5

4

3

2

1

Figure 3 -- Schematic of single probe measuring device


13/46


7

The single probe should be oriented to contact the

tooth flanks at the tolerance diameter, d T, and to

gather measurements in the specified measurement

direction. The single probe is adjusted to indicate

zero while the device is contacting the randomly

selected initial test tooth flank. As the gear is

incrementally rotated around its datum axis, the

single probe moves in and out on a precision slide

and stop, measuring each successive tooth flankposition, relative to the indexing mechanism. This

process is repeated until every tooth has been

measured.

It is common practice to complete this series of

measurements by taking a final measurement on the

initial reference tooth, thereby closing the circle.

Ideally, this would produce a second measurement

value of zero for the first tooth, as was set at the

beginning of the process. Excessive deviation of this

second measurement value from zero indicates a

problem with the measurement.

6.3.1.1 Calculation of index

If the indicator always reads plus material as a plus

reading and the gear is indexed counterclockwise

(teeth are numbered clockwise), then the right flank

measurement values provided by the indexing

(single probe) pitch measurement device can be

used directly as the plus and minus values of index

for each tooth of the gear (see figure 3). Left flank

single probe measurement values must be multi-

plied by –1 to produce plus and minus index values.

Other pitch parameters may then be calculated fromthat data.

If a graphical recorder is used, data gathered by the

single probe measurement device will appear in the

form shown in figure 4. This figure shows the

measurement value of the initial measured tooth set

to zero, thereby establishing it as the reference. The

measured values shown for all other teeth then

represent the positional deviations of those teeth

from the initial reference tooth.

6.3.1.2 Calculation of single pitch, f pt

Subtraction of each successive pair of index values

produces the plus and minus values of single pitch

deviation for each adjacent pair of tooth flanks of the

gear. See Clause 5 for specified tooth numbering,

pitch numbering, and flank naming conventions.

The number 1 single pitch deviation value is equal to

the index value of the last tooth subtracted from the

index value of the first tooth. The number 2 single

pitch deviation value is equal to the index value of the

first tooth subtracted from the index value of the

second tooth. Since the index value of the first tooth

is set to zero, the number 2 single pitch deviation

value is equal to the index value of the second tooth.

The number 3 single pitch deviation value is equal to

the index value of the second tooth subtracted from

the index value of the third tooth, and so on.

1 2 3 4 5 6 7 8 9 10

+ f pt

--f pt

Tooth number

0

--

+

I n d e x d e v i a t i o n

Figure 4 -- Single pitch deviation, single probe

device


single probe measurement device will appear in the

form shown in figure 4. Single pitch deviation values,

f pt, are shown as the differences between adjacent

index values.

6.3.1.3 Calculation of total cumulative pitch

deviation, F p

The total cumulative pitch deviation, F p, is equal tothe difference between the most positive and the

most negative index value for the complete gear.

6.3.1.4 Calculation of sector pitch deviation,

F ps/8

Calculation of the sector pitch deviation, F ps/8, is

presented in Annex E of ANSI/AGMA 2015--1--A01.

6.3.2 Comparator pitch measurement method

The pitch comparator (two probe) device may be

mechanized or hand--held. Measurements made by

the mechanized version are preferred. In either

case, both probes should be oriented to contactadjacent tooth flanks at the tolerance diameter.

One probe serves to establish a reference position

upon a tooth flank. The second probe is fitted with

either a mechanical or an electronic indicator to

measure variations of its position from the first probe.

The device is adjusted to indicate zero while the

probes are contacting the randomly selected initial

pair of teeth (see figure 5).


14/46


8

Figure 5 -- Pitch measurement with a pitch

comparator

The mechanized pitch comparator is a device with a

rotational axis that positions the gear for measure-

ment. The gear must be mounted with its datum axis

coincident with the pitch comparator’s rotational

axis.

The two probes should be oriented to contact the

adjacent tooth flanks within the same transverse

plane, at the tolerance diameter, d T. As the gear is

rotated around its datum axis, the pitch comparator

moves in and out on a precision slide and stop,measuring each successive adjacent tooth pair.

This process is repeated until every adjacent pair of

teeth has been measured.

The hand--held pitch comparator is a portable device

that lacks a means of referencing the datum axis of

the gear. It is therefore fitted with a positioning stop

that contacts the outside diameter of the gear, which

thereby becomes the reference for pitch measure-

ments. This method requires that special consider-

ation be given to the concentricity of the outside

diameter of the gear with its datum axis.

The two probes must be oriented to contact the

adjacent tooth flanks within a normal plane. The

hand--held pitch comparator is applied successively

to each pair of teeth with each indicator measure-

ment observed and recorded. This process is

repeated until every adjacent pair of teeth has been

measured (see figure 6).

springloaded

Tolerancediameter,

d T

Figure 6 -- Circular pitch measurement, two

probe device

Since the hand--held pitch comparator measures in

the normal plane, the measurements must be

converted to transverse pitch deviations before

being summed to determine index as described in

6.3.2.3.

It is important to understand that the readingscollected from two probe pitch comparators are

relative to a randomly selected tooth pair of unknown

position. They must not be compared to the single

pitch tolerances, until they are adjusted by true

position pitch, pm.

6.3.2.1 Calculation of true position pitch, pm

The true position pitch, pm, is the measurement

value for any perfectly spaced tooth pair, with the

given setup of the pitch comparator. It is equal to the

average value found by summing all the adjacent

tooth pair measurements then dividing the result bythe number of tooth pairs (i.e., the number of teeth).


pitch comparator method will appear in the form

shown in figure 7. This figure shows the measure-

ment value of the initial pair of teeth (1--2) set to zero.

Also shown is the true position pitch, pm, as the

calculated mean of pitch comparator measurement

values.

6.3.2.2 Calculation of single pitch deviation, f pt

Subtraction of the true position pitch, pm

, from each

adjacent tooth pair measurement produces the plus

and minus values of single pitch deviation, f pt, for

each tooth pair of the gear. See Clause 5 for

specified tooth numbering, pitch numbering, and

flank naming conventions.


pitch comparator method will appear in the form

shown in figure 7. Single pitch deviation values, f pt,


15/46


9

are shown as the deviations of individual pitch

comparator measurement values to the true position

pitch, pm.

0

--

+

1--2 2--3 3--4 4--5 5--6 6--7 7--8 8--9 9--10 10--11

Pairs of adjacent teeth

+ f pt

-- f pt

pm pm

P i t c h c o m p a r a t o r r e a d i n g s

Figure 7 -- Single pitch deviation, two probe

device

6.3.2.3 Calculation of index

The plus and minus index values for each tooth ofthe

gear can be produced by successive summation of

the single pitch deviation values. See clause 5 for

specified tooth numbering, pitch numbering, and

flank naming conventions.

In all cases, the number one (first) tooth shall be the

datum tooth and its index value set to zero

accordingly.

The index value of the second tooth is equal to the

index value of the first tooth plus the number 2 single

pitch deviation value. Since the index value of the

first tooth is set to zero, the index value of the second

tooth is equal to number 2 single pitch deviation

value. The index value of the third tooth is equal to

the index value of the second tooth plus the number

3 single pitch deviation value, and so on.

At the end of this process, the index value of the first

tooth will be found by adding the number 1 single

pitch deviation value to the index value of the last

tooth. Ideally, this would produce a second index

value of zero for the first tooth. Excessive deviation

from zero, of this calculated index value, for the first

tooth indicates a problem with the measurement.

6.3.2.4 Calculation of total cumulative pitch

deviation, F p

The total cumulative pitch deviation, F p, is equal to

the difference between the most positive index value

and the most negative index value for the complete

gear.

6.3.2.5 Calculation of sector pitch deviation, F ps/8

Calculation of the sector pitch deviation, F ps/8, is

presented in Annex E of ANSI/AGMA 2015--1--A01.

6.4 Relationships of pitch parameters and

measuring methods

The relationships of pitch parameters using different

measuring methods is illustrated within figures 8

through 11.

6.5 Base pitch measurement

The normal base pitch measurement device is a two

probe instrument of similar construction to the

hand--held pitch comparator. However, its measur-

ing principles are substantially different from those

described under 6.3.2:

-- Rather than measuring the relative normal

pitch at a given measurement (tolerance) diame-

ter, it measures the normal base pitch, pbn, which

is the shortest distance between adjacent tooth

flanks (see figure 12).

-- This method cannot directly or indirectly

reference the datum axis of the gear. The tooth

flank features themselves become the reference.

Therefore, observations of index and total cumu-

lative pitch, F p, can not be properly made with this

device.

-- If the instrument is adjusted to the specified

normal base pitch of a gear prior to commencing

measurements, it can provide an observation of

normal base pitch deviation, f pbn.

The normal base pitch parameter provides a local-

ized composite observation of gear tooth flank

accuracy. It is localized, in that the observation is

made only at a single point on the tooth flank. It is

composite in that it combines the effects of involute

profile, helix, and pitch into a single observation that

directly relates to the gear’s ability to achieve

smooth, conjugate meshing action with its mate.


16/46


10

Tooth numbers of pitches 18:1 1:2 2:3 3: 4 4: 5 5:6 6:7 7:8 8:9 9:10 10:11 11:12 12: 13 13:14 14:15 15:16 16:17 17:18

Pitch number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

2--probe pitchcomparator readings

0 1 --1 1 --1 --3 --5 --4 --4 --5 --6 --4 --3 --3 --1 1 1 0

True position pitch pm(mean of readings)

--2

Singlepitch deviations f pt(readings -- pm)

2 3 1 3 1 --1 --3 --2 --2 --3 --4 --2 --1 --1 1 3 3 2

Tooth numbers for Indexvalues

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Index deviations (calcu-lated)

0 3 4 7 8 7 4 2 0 --3 --7 --9 --10 --11 --10 --7 --4 --2

Figure 8 -- Sample table with hypothetical deviation values obtained by pitch comparator

(two probe) device(In practice, integer values are seldom encountered. Maximum value of f pt and minimum and maximum

values for index deviations are shaded.)

1--probe readings,right flanks

0 3 4 7 8 7 4 2 0 --3 --7 --9 --10 --11 --10 --7 --4 --2

Index deviations 0 3 4 7 8 7 4 2 0 --3 --7 --9 --10 --11 --10 --7 --4 --2

Singlepitchdeviations f pt (calculated)

2 3 1 3 1 --1 --3 --2 --2 --3 --4 --2 --1 --1 1 3 3 2

Figure 9 -- Sample table with hypothetical deviation values obtained by indexing

(single probe) device

(In practice, integer values are seldom encountered. Maximum value of f pt and minimum and maximum

values for index deviations are shaded.)

--12--10

--8

--6

--4

--20

2468

1012

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Single pitch deviations, f pt

Pitch number

0 . 0

0 1 m

m

Figure 10 -- Sample graphic representation of single pitch deviations, f pt

--12--10

--8

--6

--4

--2024

68

1012

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Index deviations

0 . 0

0 1 m m

Flank number

Figure 11 -- Sample graphic representation of index deviations


17/46


11

Base circle

pbn

Figure 12 -- Base pitch measurement, two

probe device

The theoretical normal base pitch can be calculated

as follows:

bn ! m n ' cos!n (1)

where

pbn is the theoretical normal base pitch, mm;

mn is the normal module, mm;

!n is the normal pressure angle, degrees.

6.5.1 Normal base pitch measurement device

The normal base pitch measurement device is

usually a hand--held device, which can either be set

to measure directly the deviations from the theoreti-

cal normal base pitch, with the aid of a suitable gage,or set to reference a randomly selected initial pair of

adjacent teeth.

The two measurement probes of the device are

oriented to contact adjacent tooth flanks within a

base tangent plane. In practice, this involves rocking

the device through the possible range of contact of

the measuring probe with the tooth flank while

observing the measurement indicator. The ob-

served minimum deviation of the indicator will occur

at the point of contact corresponding with a base

tangent plane. It is important to ensure that the

points of contact of the probes do not lie in zones withprofile or helix modifications, especially when mea-

suring deviations from the theoretical normal base

pitch.

The normal base pitch measurement device is

applied successively to each pair of teeth with each

indicator measurement recorded. This process is

repeated until every adjacent pair of teeth has been

measured.

6.5.2 Calculation of single pitch deviation, f pt,

from normal base pitch measurements

Normal base pitch measurements are inherently

composite observations, combining the influences

of pitch, profile, and helix deviations. It is not

possible to decompose normal base pitch deviations

into observations of those individual constituent

deviations such as single pitch. However, sincenormal base pitch is a better indicator of gear quality

than single pitch, this document permits comparison

of normal base pitch deviations to single pitch

tolerances.

Before commencing to calculate single pitch devi-

ations, the direction in which normal base pitch devi-

ation values are reported must be converted from

normal to the tooth surface to along the arc of the

tolerance diameter, d T, circle within the transverse

plane, as required by ANSI/AGMA 2015--1--A01.

The first step is to convert the normal base pitch

values to the transverse plane, which requires divid-

ing each by the cosine ofthe base helix angle,cos"b.

Then, dividing the results by the cosine of the

transverse pressure angle at the tolerance diameter,

cos !Tt, converts the values to a direction along the

arc of the tolerance diameter circle.

As is the case with any pitch comparator (two probe)

measurements, these values must be compared

with the true position pitch, pm, to derive single pitch

values. This method can be applied to measure-

ments made by devices set relative to a randomly

selected tooth pair or relative to the theoreticalnormal base pitch.

The true position pitch, p m, is equal to the average

value found by summing all the adjacent tooth pair

measurements, then dividing the result by the

number of tooth pairs (i.e., the number of teeth).

Subtraction of the true position pitch, pm, from each

adjacent tooth pair measurement produces the plus

and minus values of single pitch deviation, f pt, for

each tooth pair of the gear.

6.5.3 Additional calculations for normal base

pitch measurements

When the normal base pitch measurement device is

initially set to the theoretical normal base pitch,

resulting measurements can be used to calculate a

variety of parameters that are useful for controlling

the quality of gear involute profiles.

It is important to understand that these calculations

are based upon the assumption that the helical lead

of the gear, which also affects normal base pitch


18/46


12

measurements, is correct. Included in these calcu-

lated parameters are:

-- normal base pitch deviation, f pbn;

-- mean normal base pitch deviation, f pbm;

-- mean base diameter difference, f dbm;

-- effective base diameter, d b eff ;

-- effective transverse pressure angle, !t eff ;

-- effective normal pressure angle, !n eff ;-- mean transverse pressure angle deviation,

f !mt;

-- mean normal pressure angle deviation, f !mn.

6.5.3.1 Calculation of normal base pitch

deviation, f pbn

Determination of normal base pitch deviation, f pbn,

requires setting of the normal base pitch measure-

ment device to the theoretical normal base pitch,

with theaid of a suitable gage, before measurements

are taken. Resulting measurement values can then

be used directly as the plus and minus values of

normal base pitch deviation, f pbn, for each adjacent

tooth pair of the gear.

6.5.3.2 Calculation of mean normal base pitch

deviation, f pbm

The mean normal base pitch deviation, f pbm, is equal

to the average value found by summing all the

adjacent tooth pair deviations of normal base pitch,

f pbn, then dividing the result by the number of tooth

pairs (i.e., the number of teeth).

6.5.3.3 Calculation of mean base diameterdifference, f dbm

Mean base diameter difference, f dbm, can be

calculated as follows:

dbm ! pbm z

' cos"b(2)

where

f dbm is the mean base diameter difference, mm;

f pbm is the mean normal base pitch deviation,

mm;

z is the number of teeth;

"b is the design base helix angle, degrees.

6.5.3.4 Calculation of effective base diameter,

d b eff

Effective base diameter, d b eff , can be calculated as

follows:

d b eff ! Db " # f dbm $ 10%3& (3)

where

d b eff is the effective base diameter, mm;

Db is the design base diameter, mm.

6.5.3.5 Calculation of effective transverse

pressure angle, !t eff

Effective transverse pressure angle, !t eff , can be


!t eff ! acos#d b eff D & (4)where

!t eff is the effective transverse pressure angle,

degrees;

D is the design pitch diameter, mm.

6.5.3.6 Calculation of effective normal

pressure angle, !n eff

Effective normal pressure angle, !n eff

, can be


!n eff ! atan#tan!t eff cos "& (5)where

!n eff is the effective normal pressure angle,

degrees;

" is the helix angle, degrees.

6.5.3.7 Calculation of mean transverse

pressure angle deviation, f !mt

Mean transverse pressure angle deviation, f !mt, can

be calculated as follows:

!mt ! ! t eff % ! t (6)

where

f !mt is the mean transverse pressure angle

deviation, degrees;

!t is the design transverse pressure angle, de-

grees.

6.5.3.8 Calculation of mean normal pressure

angle deviation, f !mn

Mean normal pressure angle deviation, f !mn, can becalculated as follows:

f !mn ! !n eff % !n (7)

where

f !mn is the mean normal pressure angle

deviation, degrees;

!n is the design normal pressure angle,

degrees.


19/46


13

7 Measurement of profile deviations

7.1 Profile

Profile is the shape of the tooth flank from its root toits tip. The functional profile is the operating portion,

which is in actual contact during tooth mesh, andcannot extend below the base cylinder.

Profile deviation is the difference between thespecified and the measured profile of the gear.

Unless modifications are specified, the shape of theprofile in the transverse plane is an involute curve.

ANSI/AGMA 2015--1--A01 specifies the direction of

tolerancing for profile deviation to be within the

transverse plane, tangent to the base circle.

7.2 Profile inspection methods

The standard methods of profile measurement arewith generative, coordinate, or portable involute

measurement instruments.

7.2.1 Generative involute measurementinstruments

Generative involute measuring instruments mea-

sure the deviation of the actual profile from a nominal

involute profile, which is generated by theinstrument. Generating the nominal involute re-

quires a tangential movement of a measurementprobe, within the plane tangent to the base cylinder

of the given gear, together with a rotational move-

ment of the gear mounted on the instrument spindle.

These movements must be synchronized such that

the linear movement of the probe is equal to the

distance along the circumference of the base circlediameter associated with the rotational movement

(see figure 13).

Spindle

Basecircle

Probe

Figure 13 -- Schematic of involute inspection

device

Generative involute measurement instruments may

employ a master base circle or master involute camto generate the nominal involute curve. Such

instruments may include a ratio mechanism, whichrelates the actual workpiece base circle to the

master base circle. Generative involute measuring

instruments may use a computer numerical control

electronic drive system to generate the nominal

involute curve.

Profile measurements must be made relative to the

datum axis of rotation of the gear. Refer to 5.1 formore information concerning the datum axis of

rotation.

The probe tip must be accurately positioned within

the plane tangent to the base cylinder, with its zero

roll position precalibrated (see figure 14). Probe tips

may be chisel point, disk, or spherical, provided that

accurate positioning of the point of contact betweenthe probe tip and the gear tooth surface is main-

tained within the base tangent plane. Measurement

of extreme profile modifications may be adversely

affected by shifting of the probe contact vector.

Root circle

Base circle Pitch circle

Outside circle

Base tangent plane Probe Axis

Figure 14 -- Profile measuring method

It is often desirable to orient the measurement probe

path of motion normal to the tooth surface.

ANSI/AGMA 2015--1--A01 specifies profile toler-ances in the transverse plane. If measurements are

made normal to the tooth surface, all values must becorrected by dividing by the cosine of the base helix

angle, cos "b, before comparison against the

tolerances.

7.2.2 Coordinate measurement inspection

instruments

Involute profile can be inspected by non--generative,

coordinate measurement instruments. Such instru-ments indicate the tooth profile by a series of points,

storing the coordinates of each point. The deviation

of the actual profile from the nominal is thendetermined by comparison of the stored test point

coordinates against calculated coordinates of the

theoretical nominal profile (see figure 15).

Coordinate measurement inspection instruments

may operate in two dimensions (X and Y coordi-nates) or three dimensions (X, Y, and Z coordinates).

Measurement of an involute profile with two--dimensional systems requires accurate mounting of


20/46


14

the gear with its datum axis perpendicular to the X--Y

plane. Three--dimensional systems require align-

ment of the gear datum axis parallel to one of the

three instrument axes. This may be accomplishedby accurate mounting of the part, or mathematically

adjusting the instrument axes to coincide with thegear axis. Coordinate measurement inspection

instruments may use spherical measurement probe

tips, which require correction for shifting of the probecontact vector.

Y2

Y1

X3

Y3

X2

X1

Figure 15 -- Profile inspection by coordinates

7.2.3 Portable involute measurement

instruments

Profile measuring instruments are generally fixed

type machines. Gears to be tested must be brought

to the instrument and accurately mounted, typically

on--axis, between centers or on a table. For verylarge gears it may be necessary to employ a portable

involute measuring instrument that can be taken tothe gear. Such instruments may operate on a variety

of generative or non--generative principles. The

portable instrument must be accurately mounted at a

known distance from, and in alignment with, the gear

axis. This requires care in design and manufacture

of the gear blank.

7.3 The profile diagram

Amplified traces of the profile inspection test results

should be presented on charts that are graduated for

rolling path length or degrees of roll. They should

also be labeled for magnification and evaluationpoints in conformance with the specification.

An unmodified involute profile with no deviations will

be charted as a straight line. Deviations of the curvefrom a straight line represent, in magnified form,

deviations of the actual profile from an unmodified

involute. Profile modifications introduced by the

designer also appear as departures from the straight

line, but they are not considered to be deviations

from the “design profile”.

Excess material on the profile is considered a plus

deviation, while insufficient material is considered a

minus deviation. In addition to identifying thelocation and magnitude of the highest point on theprofile or the maximum profile deviation, these

charts are valuable for determining profile character-

istics such as tip break, undercut, and tip or root relief

(see figure 16).

Any point along the profile diagram can be related to

a diameter (radius), a base tangent length and an

involute roll angle.

Figure 17 shows a sample tooth profile and the

relation to the corresponding profile trace, togetherwith the appropriate terms. Details of terms,

definitions and concepts concerning the profile

trace, are provided in ANSI/AGMA 2015--1--A01.

Trueinvolute profile

Plus profile(minus pressure angle)

Minus profile(plus pressure angle)

Undercut &tip chamfer

Undercut

Trueinvolute

Tip break

Tip break

UndercutProfile control

diameter

Figure 16 -- Typical tooth profile measurement charts


21/46


15

tip circle

root circle

base circle

12

C

L#

Q

&Creference circle

+

2

3

1

A

C

D

F !

f H!

f f !

L!c

B

E

FE

F

A

B

D

L!c

A

E

tip circle of mating gear

1 Design profile C--Q Base tangent length to point C

2 Measured profile &c Involute roll angle to point C

3 Mean profile line Q Start of roll (point of tangency of transversebase tangent)

A Tip circle point L!c Profile evaluation rangeB Start of tip break (chamfer) L# Base tangent length to start of active profile

D Start of active profile F ! Total profile deviation

E Profile control diameter f f ! Profile form deviation

F Origin of involute f H! Profile slope deviation

B--D Active profile

B--E Usable profile

Figure 17 -- Tooth profile and profile diagram


22/46


16

7.4 Evaluation of profile diagrams

Depending on accuracy class specified, it may only

be necessary to measure total profile deviation, F !.

See ANSI/AGMA 2015--1--A01, clause 4.

It may also be necessary to determine the profile

slope deviation, f H!, and the profile form deviation,

f f !. For this it is necessary to superpose the meanprofile line onto the diagram as shown in figure 17,

also in figure 2 of ANSI/AGMA 2015--1--A01. Allow-

able values of f H! and f f ! can be calculated in accor-

dance with ANSI/AGMA 2015--1--A01, clause 7.

7.5 Algebraic signs of f H! and f !

The profile slope deviation, f H!, is termed positive

and the corresponding pressure angle deviation, f !,

is termed negative when the mean profile line rises

towards thetooth--tip endA of thediagram,as shown

in figure 17. In figure 18, both positive and negativeslopes, caused by eccentricity of mounting on the

gear generating machine, are shown.

If the slopes seen in the profile diagrams of mating

gears are equal and have the same sign, the

deviations are mutually compensating. This applies

to both external and internal gears.

7.6 Mean profile slope deviation, f H!m

Slope deviations of individual profiles can be caused

by eccentricity due to inaccuracies of manufacturing

or inspection set--up. Such deviations will vary

around the gear. The use of mean profile slope

deviations cancels out the influence of eccentricity

on individual profile traces.

The effect of eccentricity on profile slope, and thedetermination of mean profile slope deviation, are

illustrated in figure 18.

Calculating the mean profile slope deviation is a step

towards the correction of manufacturing processes

or other suitable action.

For all practical purposes, it is usually sufficient to

calculate the arithmetic mean of the profile slope

deviations by calculating the average of the devi-

ations measured on three or more corresponding

flanks of equally spaced teeth around the gear

circumference according to the following equation:

H!m ! 1n # f H!1 " f H!2 "''' " f H!n& (8)

where:

f H!m is the mean profile slope deviation, mm;

f H!n is the individual profile slope deviations, mm;

n is the number of profile slope deviation

values included in the mean.

1

3

C M

I 2

1

2

3

A E+

--

+

+

--

--

f H#m ! 13

(% 11.1 % 6.6 " 5.7) ! % 4mm

f H !

5 . 7

- - 6 . 6

- - 1 1 . 1

L!c

f e

(

B

M = axis of rotation of the gear on the machine tool. I = axis of rotation of the gear on the inspection apparatus.C = position of tool or profile measuring probe1, 2, 3 = Positions of the profiles from which the traces were obtained (at 45", 165", 285") andrelevant profile traces

Figure 18 -- Mean profile slope deviation, f H!m


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17

7.7 Additional calculations for profile

measurements

The mean profile slope deviation, f H!m, can be used

to calculatea variety of parameters that areuseful for

controlling the quality of gear involute profiles.

Included in these calculated parameters are:

-- mean base diameter difference, f dbm;

-- effective base diameter, d b eff ;

-- effective transverse pressure angle, !t eff ;

-- effective normal pressure angle, !n eff ;

-- mean transverse pressure angle deviation,

f !mt;

-- mean normal pressure angle deviation, f !mn.

All of the following equations are based upon the

mean profile slope deviation, f H!m. Alternatively, the

same formulas could be applied to the case of

individual tooth data. The calculation sequencewould then commence with the entry of the individual

profile slope deviation, f H!.

7.7.1 Calculation of mean base diameter

difference, f dbm

Mean base diameter difference, f dbm, can be calcu-

lated as follows:

dbm ! b

L!c f H!m

(9)

where:

f dbm is the mean base diameter difference, mm;

Db is the base diameter, mm;

L!c is the functional profile length, mm;

f H!m is the mean profile slope deviation, mm.

A positive mean profile slope deviation (profile trace

rising towards its tooth tip end) implies that the

effective base diameter is too large, and visa versa.

when f H!m > 0, then f dbm > 0

7.7.2 Calculation of effective base diameter,d b eff

Effective base diameter, d b eff , can be calculated as

follows:

d b eff ! Db " # f dbm $ 10%3& (10)

where:

d b eff is the effective base diameter, mm.

7.7.3 Calculation of effective transverse

pressure angle, !t eff

Effective transverse pressure angle, !t eff , can be


!t eff ! acos #d b eff D & (11)where:

!t eff is the effective transverse pressure angle,

degrees;

D is the design pitch diameter, mm.

7.7.4 Calculation of effective normal pressure

angle, !n eff

Effective normal pressure angle, !n eff , can be


!n eff ! atan #tan !t eff cos "& (12)where:


degrees;

" is the helix angle, degrees.

7.7.5 Calculation of mean transverse pressure

angle deviation, f !mt

Mean transverse pressure angle deviation, f !mt, can

be calculated as follows:

!mt ! ! t eff % !t (13)

where:

f !mt is the mean transverse pressure angledeviation, degrees;

!t is the design transverse pressure angle,

degrees.

Alternatively, f !mt can be calculated (in degrees) by:

!mt ! % 1# f H!m L!c #tan !t& $ 103

´' & (14) A positive mean profile slope deviation (profile trace

rising towards its tooth tip end) implies that the

effective pressure angle is too small, and visa versa.

when f H!m > 0, then f !mt < 0

7.7.6 Calculation of mean normal pressure

angle deviation, f !mn

Mean normal pressure angle deviation, f !mn, can be


!mn ! !n eff % !n (15)

where:


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18

f !mn is the mean normal pressure angle

deviation, degrees;


degrees;

!n is the design normal pressure angle,

degrees.

A positive mean profile slope deviation (profile trace

rising towards its tooth tip end) implies that theeffective pressure angle is too small, and visa versa.

when f H!m > 0, then f !mn < 0

7.8 Other profile measuring methods

While not commonly used or recommended, the

following profile measuring methods may prove

valuable when more conventional methods are not

practical or available.

7.8.1 Projection

A shadow of the gear tooth under inspection may be

optically magnified and directly or reflex projected topermit comparison of the profile to a large scale

layout of a specified profile (see figure 19). This

method is normally applied only to fine pitch gears.

When gears are too large to be mounted in the

projector, a thin wafer (manufactured simultaneous-

ly with the gear), or a mold of a gear tooth form may

be used for projection. This method requires two

known reference surfaces to locate the image both

radially and angularly.

Scalelayout

Projection

Figure 19 -- Profile inspection by optical

projection

7.8.2 Indirect profile inspection methods

The following techniques may be employed forinspection of gear profiles. These methods do not

yield actual measurements of deviation of an in-

spected profile from a nominal.

-- Multiple thickness measurement. The chord-

al tooth thickness and associated addendum

depth for several positions on a tooth may be

computed for a gear tooth caliper. Comparison of

measurements with the computed values will give

an indication of profile accuracy (see figure 20).

However, readings give no indication as to which

profile may have an error, since two flanks of a

measured tooth are contacted at the same time.

This method will not reveal deviations that cancel

each other, such as those caused by a form cutter,

which has been offset from a true radial position.

Figure 20 -- Profile inspection by gear --tooth

caliper method

-- Auxiliary gaging elements. The theoretical

position of wires, rolls, pins, or balls of several

different diameters placed in a tooth space may

be computed and compared to actual measure-

ments (see figure 21). This method has limita-

tions similar to those of gear tooth caliper

measurements.

Figure 21 -- Profile inspection by measurement

over pins


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19

7.8.3 Profile measuring with master gear

Contact pattern checking with a master gear may be

used to check the profile deviation of gears in place

or when gears are too large to be accommodated by

a profile measuring instrument. The axis of the gear

and master must be parallel. Refer to clause 10 for

more information concerning this method.

8 Measurement of helix deviations

8.1 Helix

Helix is the lengthwise shape of the tooth flank

across the face from one end to the other. The

theoretical helix of a helical gear is contained on the

surface of a cylinder, which is concentric with the

datum axis of rotation of the gear, at the intersection

of that cylinder with the tooth flank. The theoreticalhelix of a spur gear is a straight line parallel to its

rotating axis. Helix is restricted to the operating

portion, which is intended to be in contact during

loaded operation, and does not include edge rounds

or chamfers.

Lead, as a term used for helical gears, is the axial

advance of a helix for one complete turn of the gear.

The lead of a spur gear, therefore, is infinite. The

lead of a helical gear is commonly defined by the

angle between the helix at the standard pitch

diameter and the axis of rotation.

Helix deviation is the difference between the speci-

fied and the measured helix of the gear (see figure

22). ANSI/AGMA 2015--1--A01 specifies the

direction of tolerancing for helix deviation to be within

the transverse plane, tangent to the base circle.

Measuredhelix

Design helix

Helical tooth

Total helixdeviation, F "

Figure 22 -- Helix deviation

8.2 Helix inspection methods

The standard methods of helix measurement are

with generative, coordinate, or portable helix

measuring instruments.

8.2.1 Generative helix measuring instruments

The most common instruments used for measure-

ment of helix are generative helix measurement

instruments. Such instruments measure the devi-

ation of the actual helix from a nominal helix, which is

generated by the instrument. Generation of the

nominal helix requires the axial movement of a

measurement probe together with a rotational move-

ment of the gear mounted on the instrument spindle.

These movements must be synchronized according

to the specified lead of the gear (see figure 23).

When measuring spur gears, the rotational move-

ment is eliminated.

Helix angle

Probe travel

Referencezero

0

Total helix deviation, F "

Figure 23 -- Graphic charting of helix

Generative helix measuring instruments may

employ a variety of mechanical configurations to

generate the nominal helix. For example, the gear

can be rotated by a master disk driven by a straight

edge, which in turn is driven by the axial movement

of the probe slide. The tangential movement of the


26/46


20

straight edge is translated into axial movement of the

probe by a ratio mechanism. Combination instru-

ments also capable of measuring involute profile

often utilize their master base circle mechanisms in

this manner.

Other configurations include master lead bar and

follower mechanisms, and master lead screw and

change gearing mechanisms. Newer generativehelix measuring instruments typically use a comput-

er numeric control drive system to generate the

nominal helix.

Helix measurements must be made relative to the

datum axis of rotation of the gear. Refer to 5.1 for

more information concerning the datum axis of

rotation.

Probe tips most commonly used are spherical or

disk--shaped. The probe tip must be positioned to

contact the tooth surface at the specified tolerance

diameter, d T.

It is often desirable to orient the measurement probe

path of motion normal to the tooth surface.

ANSI/AGMA 2015--1--A01 specifies helix tolerances

in the transverse plane. If measurements are made

normal to the tooth surface, all values must be

corrected by dividing by the cosine of the base helix

angle, cos "b, before comparison against the

tolerances.

8.2.2 Coordinate measurement inspection

instrumentsHelix can be inspected by non--generative, coordi-

nate measurement instruments. Such instruments

probe the tooth lengthwise at a series of points,

storing the coordinates of each point. The deviation

of the actual helix from the nominal is then deter-

mined by comparison of the stored test point

coordinates against calculated coordinates of the

theoretical nominal helix.


operate in three dimensions (X, Y, and Z coordi-

nates) to measure helix. The gear axis must bealigned parallel with one of the three instrument

axes. This may be accomplished by accurate

mounting of the part, or mathematically adjusting

instrument axes to coincide with the gear axis.


commonly use spherical measurement probe tips,

which require correction for shifting of the probe

contact vector.

8.2.3 Portable helix measuring instruments

Helix measuring instruments are generally fixed type

machines, which require that gears to be tested must

be brought to the instrument and accurately

mounted, typically on--axis between centers or on a

table. However, for very large gears it may be

preferable to employ a portable helix measuring

instrument, which can be taken to the gear. Theportable instrument must be accurately mounted at a

known distance from, and in alignment with, the gear

axis. This often requires extra care in design and

manufacture of the gear blank.

8.3 The helix diagram

Amplified traces of helix inspection test results

should be presented on charts that are calibrated for

axial probe travel as well as magnification of

measured deviation. Sometimes trace lengths are

magnified representations of small facewidths, orreduced representation of large facewidths.

An unmodified helix with no deviations will be

charted as a straight line. Deviations of the curve

from a straight line represent, in magnified form,

deviations of the actual helix from an unmodified

helix. Helix modifications introduced by the designer

also appear as departures from the straight line, but

they are not considered to be deviations from the

design helix.

Excess material on the helix is considered a plus

deviation while insufficient material is considered a

minus deviation. In addition to identifying the

location and magnitude of the helix deviation, these

charts are valuable for determining helix characteris-

tics such as edge rounds, crowning, and end relief.

Relevance to right hand and left hand helices can be

indicated by means of the letters “r” and “l”,

respectively, used either as symbols or as sub-

scripts.

In figure 24, a typical example of a helix diagram

shows the helix deviations of a tooth flank of whichthe design helix is an unmodified helix. Had the

design helix been crowned, end relieved or other-

wise modified, traces representing it would be

appropriately formed curves.

Details of terms, definitions and concepts concern-

ing the helix trace are provided in ANSI/AGMA

2015--1--A01.


27/46


21

1

2 3

L$

b

II

F $

f f $

f H $

%$x %$x

f w "

I

1 Design helix F " Total helixdeviation

2 Actual helix trace f f " Helix formdeviation

3 Mean helix line f H" Helix slopedeviation

b Facewidth ordistance betweenchamfers

%"x Axial wavelengthof undulation

L" Helix evaluationrange

f w" Undulation height

I Reference face II Non--referenceface

Figure 24 -- Helix diagram

The helix evaluation range, L", is equal to the length

of trace, reduced at each end by the smaller of two

values: 5% of the helix length of trace, or the lengthequal to one module. This reduction is made in order

to ensure that unintentional, slight end reliefs caused

by some machining conditions, are not normally

included in the assessment of the deviation magni-

tudes intended for comparison with stringent toler-

ances. For assessment of the total helix deviation,

F ", and the helix form deviation, f f ", excess material

within the end zones of 5%, which increases the

amount of deviation shall be taken into account.

8.4 Evaluation of helix diagrams

For purpose of gear quality classification, it may be

necessary to measure only “total helix deviation”, F ".

See ANSI/AGMA 2015--1--A01, clause 4.

It may also be necessary to determine the “helix

slope deviation”, f H", and the “helix form deviation”,

f f ". For this it is necessary to superpose the “mean

helix line” onto the diagram as shown in figure 24

(also in ANSI/AGMA 2015--1--A01, figure 1). Allow-

able values of f H" and f f " can be calculated in accor-

dance with ANSI/AGMA 2015--1--A01, clause 7.

8.5 Algebraic signs of f H" and F "

Helix slope deviation, f H", and the total helix devi-

ation, F ", are to be reported with an algebraic sign.

Deviations are deemed to be positive ( f H" > 0 and

F " > 0) when helix angles are larger, and negativewhen helix angles are smaller, than the design helix

angle.

The helix deviations of spur gears if other than zero

are indicated by the subscripts “r” and “l”, instead of

an algebraic sign, implying deviations in the sense of

right or left hand helices, respectively.

In figure 25, both positive and negative slopes,

caused by eccentricity or wobble of mounting on the

gear generating machine, are shown.

+ + + +-- -- -- --

0" (360") 90" 180" 270"

b L $

H$1 H$2 H$3 H$%

Figure 25 -- Traces generated from four tooth

flanks

If the helix slope deviation, f H", (assuming equal

evaluation ranges) of the corresponding flanks of

two mating gears are equal in magnitude and

algebraic sign, the deviations are mutually compen-

sating.

8.6 Mean helix slope deviation, f H"m

For correction of machine tool settings or adaptation

to a mating gear, determination of the mean helix

slope deviation, f H"m, of the gear is useful.

If the helix slope deviations are either random or arefairly consistent, then the mean helix slope deviation

may be used to correct the helix setting of the

machine used to manufacture the gear. In the case

of a matched set of mating gears where one has

been manufactured and inspected, then the mean

helix slope deviat

Documents

AGMA 915-1-A02 Gears Inspect