Vibration Isolation of Precision Machines

7/21/2019 Vibration Isolation of Precision Machines

1/16

U E T T E R W O R T H

I N E M A N N

ibra t ion iso la t ion of

p r ec is ion equ ipment

Eugen e I R iv in

Depar tment o f Mechanica l Eng ineer ing, Wayne S ta te Univers i ty ,

Detroi t , MI, USA

I s o la t ion o f p rec i s ion equ i pm en t f r om env i r onm en ta l v i b r a t ions f r equen t l y is

c r i t i ca l fo r assur ing the i r adequate per formance. In many cases , v ib ra t i on

i so la t i on is obta ined b y us ing expens ive an d not very re l iab le ac t ive i so la t ion

sys tems. The pa pe r prov ides a sys temat i c ana lys is o f v ib ra tory env i ron-

me nts as wel l as pr inc ip les a nd c r i te r i a o f v ib ra t i on i so la t ion . The resu l ts o f

th is ana lys is are app l i ed to determ ine requ i rem ents fo r v ib ra t i on i so la t ion o f

f ou r h i gh - p r ec is i on p i ec es o f appar a tus f o r e l ec tr on ic p r oduc t i on and nu m er -

ous prec i s ion ma ch ine too ls . I t is de mo ns t ra ted that i n mos t o f the cases , the

i so la ti on requ i reme nts can be sat is f i ed by prope r l y se lec ted pass ive i so la tors

hav ing h igh dam ping. I t was fou nd tha t on l y in except iona l cases, the act ive

i so la ti on sys tem s a re requ i red. Issues o f the i n f luence o f i so la tors on the

r ig id i ty o f iso la ted ob jec ts as wel l as on the i r s tab i l i t y rock ing) are ad-

dressed.

Keywords :

v i b r a t ion ; i s o la t i on ; p r ec i si on ; dam p i ng

I n t r o d u c t i o n

Cont inuous t i gh ten ing o f mach in ing and measur -

ing to lerances for par ts of machines and instru-

ments l eads to dev e lopm ent o f ever more accura te

m ac h i ne t oo l s and m eas ur em en t appar a tus . M ag-

ni tudes o f the to lerance s are expressed in f ract ions

o f m i c r om ete r s o r i n nanom ete r s . I t has been

wid e ly accepted f rom the t ime o f Wo r ld W ar II tha t

prec i s ion mach inery and ins t ruments mus t be i so-

la ted f rom ex terna l v ib ra t i ons whose ampl i tudes

may s ign i f i cant l y exceed the magni tudes o f a l l ow-

ab le mach in ing/measurement dev ia t i ons . To sat -

is fy th is obv ious need, a w ide inve nto ry of pass ive

v ibra t i on i so la t i on mounts was deve loped and i s

com me rc ial ly available. ~ 2 Recent ly , th is inven tory

was complemented by ac t i ve l y cont ro l l ed i so la tors

that can prov ide even bet ter v ib ra t i on pro tec t ion

and /o r m a i n ta i n a c ons tan t l ev e l o f t he dev i c e

mounted on sof t i so la t i ng mounts , regard less o f

changes o f mass d i s t r ibu t i on w i th in the m ach ine. 2 3

Improvements i n the v ibra t i on i so la t i on e f f i -

c iency can be achieved by us ing sof ter isolat ing

mounts , but the sof t mount ing causes s ta t i c and

dyn am ic instab i l ity . Stat ic ins tab i l ity is a chan ge of

Address rep r int requests to Eugene L Riv in Mac hine Tools Re-

search Labora to ry Wayne S ta te Un ive rs i t y 5050 An th ony

Wayne Drive Detroit M I 48202 U SA.

l eve li ng wh en mass d i s tr i bu t i on w i th in the i so la ted

sys tem change s because o f add i t ion /sub t rac t ion o f

components to the sys tem or i s caused by move-

ments of mass ive par ts in the system. Dynamic in-

s tabi l i ty is rock ing of the isolated system at t r ibut-

able to both externa l exc i tat ions ( touch ing o f the

isolated body, a i r draf ts , etc . ) and internal exc i ta-

t ions ( forces caused by accelerat ion/d ecelerat ion of

the mov ing components ) . These rock ing mot ions

are undesi rable because they may induce displace-

ments i n the work ing zone o f the sys tem (e .g . ,

cut t ing area or measurement area) , poss ibly even

exceeding the external v ibrat ion-caused displace-

ments f rom which the sys tem i s be ing i so la ted.

Both s tat ic and dynamic instabi l i t ies can be al lev i -

ated by the appro pr iate act ive (servo-co ntrol led)

sys tems, b ut such sys tems add s ign i f i cant l y to the

cost and dimen sions of the isolated o bject . In ad-

d i t i on , the add i t i on o f complex e lec t ron ic and/or

pneumat ic control systems can resul t in a reduc-

t ion of i ts rel iabi l i ty.

Th is paper demons t ra tes that , i n many cases ,

v ibrat ion isolat ion spec i f icat ions for h igh-prec is ion

ob jec ts may not be as s t r i ngent as usua l l y as -

sumed. The main reason for th is is that sens i t iv i ty

to external v ibrat ions does not necessar i ly increase

wi th i nc reas ing accuracy requ i rements , because

improvements i n accuracy o f prec i s ion mach ines

and apparatus i s usua ll y accompa nied by be t ter de-

P r e c i s io n E n g i n e e r i n g 1 7 : 4 1 - 5 6 , 1 9 9 5

1995 by E l s ev i e r S c i enc e I nc .

6 5 5 A v e n u e o f t h e A m e r i c a s , N e w Y o r k , N Y 1 0 0 1 0

0141 - 6359 / 95 / 10 . 00

S S D I 0141 - 6359 ( 94 ) 00006 - L


2/16

Rivin Vibration isolat ion of precision equ ipme nt

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FRCQUENCY~ HZ

F i g u r e 6 V i b r a t i o n s e n s i t i v it y c u r v e s f o r P h i l ip s

E l e c t ro n B e a m P a t te r n G e n e r a t o r B e a m w r i t e r

EBPG-47

4 4 J A N U A R Y 1 9 95 V O L 1 7 N O 1


5/16

Rivin: Vibration isolation o f precision equ ipm ent

F i g u r e 7

line 12

100 .1100 . 000

/

F o r e l A f - t ..~ 5 0 . 0 0 0

V u-~JcH

/

9 n e , d , 1 5 i d e / 1 ~ - - } 0 . 0 0 0

~0, aO0

It

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o o

/

5 V- IZSm~c~1/ le~: ' - - ~

I I I I I ] ] I l } I 1 ~ I

3 5 7 10 20 39 50 70 :~$

Frequency. Hz

V ib ra t i o n

s e n s i t i v it y c u r v e s f o r 1 0 0 0 x O p t ic a l M i c r o s c o p e f o r d e t e c t a b l e m o t i o n o n 1 1 xm t e s t

F i g u r e 8 T w o m a s s d y n a m i c m o d e l s im u l a ti n g v i

b r a t i o n s e n s i t i v i ty o f a p r e c i s i o n m a c h i n e in o n e

p r i n c i p a l d i r e c t i o n

f ace , b lu r the measurement resu l t s and e f fec t ive ly

reduce reso lu t ion o f the measur ing ins t rument .

M o d e l o f v i b r a t i o n t r a n s m i s s i o n

Floor v ib ra t ion s a re de t r ime nta l to the per fo rm ance

o f p rec is ion equ ip m ent because they exc i te re la ti ve

v ib ra t i o n s i n t h e w o rk in g cu t t i n g ) / m e a su re m e n t

zo n e o r i n t h e j o i n t s co m p r i s i n g t h e d im e n s io n a l

se t -up cha in . Tes ts have shown tha t the e f fec ts o f

f loo r v ib ra t ions on a mach ine too l usua l ly a re s ig -

n i f ican t on ly a t the lowe st se ldom a lso at the sec-

B 1

B

\ \ \ \ \ \ \

- - l -

I

\

/

r

\ \ \ \ \ \ , , \ , ] : , , \ \ \ \ \ \ \ \

Y X l z

L ~ d - - ~ X ( e l z

____0 x

Figure 9 Dyna mic mode l i l lus t ra t ing in fluence o f

des ign paramete rs on re la t ive v ib ra t ions be tween

upper un i t and bed o f a mach ine

o n d ) n a t u ra l f r e q u e n cy o f t h e d yn a m ic sys t e m ,

la rge ly because the h igh er n a tu ra l f requenc ies l ie

co n s id e ra b l y a b o ve t h e f re q u e n cy ra n g e o f s i g n i fi -

can t exc i ta t ion amp l i tudes . For example , the f i rs t

na tu ra l f requency fo r g r inders t yp ica l l y occurs be-

tween 30 and 70 Hz, whereas the second na tu ra l

f requency l ies between 100 and 150 Hz.

Figures 4-7

t aken f rom Refe rences 7 and 8 ,

s h o w v i b r a t io n s e n s i t i v it y c u r v e s f o r p r e c i s i o n

equ ipment used in the p roduct ion o f e lec t ron ic m i -

c roc i rcu i t ry . The m in ima on these p lo ts represen t

s t ruc tu ra l na tu ra l f requenc ies o f the dev ices . I t can

be seen tha t the low est na tu ra l f reque nc ies a re be-

twee n 4 and 20 Hz, and m any o f the h ighe r na tu ra l

f requencies l ie between 30 and 70 Hz; that is , in the

PRECISION ENGINEER ING 45


6/16

Rivin Vibration isolation o f precision equipm ent

T a b l e 1 P a r a m e t e r s f o r t h e d e s ig n o f v i b r a t io n i s o la t io n s y s t e m s f o r s e le c t e d m a c h i n e t o o l s

7 xy 7 zz 7 yy yz Y y

,x fm (Hz)

I n t e r n a l G r i n d e r s

J o t e s S O C - 1 0 0 ( M = 1 7 5 0 k g ,

Oma x

1 0 0 m m ) 0 . 0 2 5 0 . 0 4 3 0 . 8 5 0 . 2 5 0 . 3 2 - - 7 0

J u n g ( M = 2 5 0 0 k g , D m . x = 1 7 5

m m )

- -

0 . 4 8 0 . 6 5 0 . 2 8 - - - - 7 0

H e a l d 7 2 A ( M = 2 4 0 0 kg ,

D r , a x = 1 1 5 m m ) - - - - 0 . 4 8 0 . 4 0 . 1 8 0 . 4 5 6 0

k g ,

= 2 000 k g ,

2 0 0 0 k g ,

L a n d i s ( M = 5 1 0 0 kg ,

O m a x = 4 1 0 m m

J o t e s S W A - 2 5 ( M = 3 5 0 0 k g ,

Omax = 2 5 0 m m

F o r t u n a ( M = 3 8 0 0

D m . = 2 2 5 m m

M i p s a R U S - 4 5 0 ( M

O m a x = 2 4 0 m m

M i p s a ( 1 9 4 8 ) ( M

=

D m ax = 2 4 0 m m

H a r t e x K H 6 2 0 ( M = 2 1 0 0 kg ,

D m a x = 3 1 0 m m

3 A 1 5 1 ( M = 3 8 0 0 kg ,

D m a x = 2 0 0 m m

3151

3 4 5 1 G ( M = 6 5 0 0 k g ,

D max = 125 m m )

3 7 1 M 1 ( M = 1 9 0 0 k g , T a b l e

2 0 0 x 6 0 0 m m )

J u n g

3 B 7 1 ( M = 2 0 0 k g , T a b l e 2 0 0 x

6 0 0 m m )

3 B 7 2 2 ( M = 6 8 0 0 k g , T a b l e

3 2 0 x 1 0 0 0 m m )

M a a g H S S - 3 0

5 8 3 1 ( M = 4 5 0 0 k g , m m a x = 6

m m )

5 8 4 M ( M = 6 0 0 0 k g , m m . x = 6

m m )

2 B 4 4 0

= 200

2 A 7 1 5 ( M = 2 6 0 0 kg ,

D m ax = 2 0 0 m m )

2 7 0 6 ( M = 2 6 0 0 k g , D ma x

m m )

C i r c u l a r G r i n d e r s

- - - - 0 . 2 5

- - - - 0 . 3 2

- - - - 0.2

0 .26 - - 1 .5

- - - - 0 . 0 2 1

0 . 1 2 - - 0 . 3 5

0 .1 - - 0 . 6

0 . 0 4 - - 0 . 1 2

S p l i n e G r i n d e r s

- - 0 . 4 3

- -

S u r f a c e G r i n d e r s

0 .52

0 . 0 2 4

0 .28

G e a r G r i n d e r s

0 , 1 2 - - 0 . 4 5

- - 0 . 6 4

0 . 0 8 3 - - 0 . 6 6

J i g B o r e r s

0 , 1 3 0 , 3 9 0 , 2 9

D i a m o n d B o r i n g M a c h i n e s

0 .044 0 .044 1 .7

0 .23 0 .23 0 .95

U n i v e r s a l G r i n d e r s

0 . 1 5 0 . 1 4

U n i o n

M =

3 6 0 0 k g ,

D s p i n d l e = 6 m m )

0 . 2 5

0 .95

0 .45

3 .5

0 .52

1.7

0 . 9 5

0 . 2 5

0.1

0 . 0 0 2

0 .45

0 . 0 0 9

0 .08

0 .17

0 . 1 8

0 .55

0 .6

0 .39

5 0

45

4O

100

6O

8 0

4 0

5 0

0.11 57

- -

6 0

0 .65 50

0.11 28

0.21 70

- - 3 2

- - 4 5

- -

3 5

1 .55 45

9 0

100

0 . 0 4 5 - - 4 0

4 6 J A N U A R Y 1 9 95 V O L 1 7 N O 1


7/16

R i v i n V i b r a ti o n i s o l a ti o n o f p r e c i s i o n e q u i p m e n t

~o ~m ) ~z Hz ) ~ y Hz ) t)x Hz)

fw Hz) ~ fv~ fvp Hz)

0 .16 45 .5 11 .5 18 .3

0 .5 2 5 2 3 .8 - -

0 .1 6 - - 1 2 .9 1 2 .5

0 .1 6 - - 1 4 .8 4 7 .3

0 .1 6 - - 1 2 .0 2 1 .3

0 ,1 6 - - 1 3 .4 1 3 .4

0 .16 26 .5 11 .2 21 .3

0 .1 6 - - 4 1 .3 6 2 .6

0 ,16 31 .5 19 .4 41

0 ,32 24 .2 10 .4 19 .5

0 ,32 48 28 .9 23 .6

0 ,64 23 .6 33 49 .7

0 .64 22 .6

0 .32

0 .32 34 .6

0 .32 25 .4

0 .5 22 .7

0.5

0 .64 33

0 .5 17 .3

32 .3 0 .4 0 .25 32 .3

1 7 .6 - - 0 .9 5 1 5

18.7 0.8 0.42 16.3

22.3 1.3 0.61 18.5

17 .2 0 .8 0 .43 12 .8

34 .0 0 .49 0 .6 32 .4

16.6 2.1 1.4 14.4

1 6 . 0 14.1

11 13 .3 . . . .

8 .4 17 24 .5 0 .49 0 .24 17 .9

7.7 30.7 18.0 1.2 0.3 15.5

12.3 11.1 16.0 0.49 0.5 4 11

16 .5 . . . . .

12.1 12.9 23.2 0.39 0.37 16.7

4 .9 9 .3 12 .3 0 .53 0 .28 10 .4

0 .0 8 4 3 7 .4

0 .16 28 .4 14 .4

0 .64 28 30 .7 52 .3

30 .3 - - 0 .17 30 .1

20 - - 0 .51 17 .1

19.7 1.9 1.1 21

P R E C I S IO N E N G I N E E R I N G 4 7


8/16

R i v in : V i b r a t io n i s o l a t io n o f p r e c i s i o n e q u i p m e n t

Tab l e

1 C o n t i n u e d )

~xy ~ /yy /y~ Yxy Y~ fm (Hz )

athes

1 K6 2 ( M = 2 3 0 0 kg , Dma x = 4 0 0

m m ) 0 .2 7 - - 0 .2 9 - - - - - - 7 5

G u s t l o f f A 5 ( D m a x = 4 0 0 m m ) 0 .1 8 - - 0 .6 - - - - - - 7 0

T C - 1 3 5 M ( M = 1 1 0 0 k g ,

D m ax = 2 7 0 m m ) 0 .2 - - 0 .1 3 - - - - - - 8 0

KEY:

~ / i /

X r e l / X r e l g

x r e r - -a c t u a l r e l a t i v e d i s p l a c e m e n t i n w o r k a r e a

Xre~ Q--ge neralized relativ e disp lacem ent

--displacemen t of upper m ass Mu relative to base mass M 8 in equivalen 2 - mass system Figure 8)

i, j--x , y, z

/--coordinate direction of motion of bed

j--coordinate direction of m otion of upper structure

f,,--resonance frequency of upper system M u - K m - Mb, F igu re 7 )

Ao--maximum relative displacement al lowed in work area

,---maxim um acceptable value of fv~~v,. (vibration isolation criterion)

fv,---resonance frequen cy of m ounted (isolated) system for mo tion in i direction

5v,---logarithmic decrem ent associated with above

fvp--m axim um resonance frequenc y of vertical (z-direction) mo tion of isolated system for adequate vertical isolation of pulse (shock)

motions (value of fvp show n in lowes t of the two calculated for pu lses with ar - 50 t~m, r - 0.05 s and at - 30 t~m, r = 0.025 s)

M-- total mass of machine

Dmax--greatest overa ll dime nsion

mmax--maximum m odule of machined gear (m - 25.40/DP mm where D P--dimetr ical pitch of gear)

f r e q u e n c y r a n g e o f t h e r e d u c e d f l o o r a m p l i tu d e s

( se e

F i g u r e

1 ). F o r th e c a s e s s h o w n i n

F i g u r e s

5 a n d

6 , t h e i n c r e a s e i n t h e s e n s i t i v i t y to f l o o r v i b r a t i o n a t

t h e s e c o n d n a t u r a l f r e q u e n c y is m u c h l es s s t e e p

t h a n th e r e d u c t i o n in a m p l i t u d e s o f f l o o r v i b r a t i o n s

a s s h o w n in F i g u r e 1 . F o r t h e c a s e s s h o w n in F i g -

u r e s 4 a n d 7, t h e i n c r e a s e s i n v i b r a t i o n s e n s i t i v i t y

a r e a b o u t t h e s a m e a s t h e r e d u c t i o n in f lo o r v i b r a -

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

o r h i g h e r. H o w e v e r , f l o o r v i b r a t i o n s a t t h e h i g h e r

f r e q u e n c i e s u s u a l l y u n d e r g o m u c h h i g h e r a tt e n u a -

t i o n b y v i b r a t i o n i s o l a t io n s y s t e m s .

A p p r o x i m a t e d y n a m i c s o f v i b r a t io n t r a n s m i s -

s i o n f r o m t h e f lo o r i n t o th e w o r k i n g z o n e o f a p r e -

In F i g u r e 8 , M b r e p r e s e n t s m a s s o f th e b e d o f

t h e m a c h i n e ; M u i s t h e m a s s o f i ts u p p e r s t r u c t u r e

( e .g ., t o o l h e a d o r m e a su r i n g h e a d ) ; k r ,, a n d Cr, , r e p -

r e s e n t e q u i v a l e n t s t i f f n e s s a n d d a m p i n g o f t h e

s t r u c t u r a l c o m p o n e n t s a n d j o i n t s ; a n d k~, Cv a r e t h e

s t if f n es s a n d d a m p i n g o f t h e m o u n t i n g d e v i ce s

( e .g . , j a cks o r i so l a to r s ) .

T h e e ff e c t o f v i b r a t i o n s o n a n e q u i p m e n t u n i t

r e p r e s e n t e d b y s uc h a t w o - m a s s m o d e l m a y b e in -

v e s t i g a t e d i n t e r m s o f th e r a t i o o f t h e g e n e r a l i z e d

r e la t iv e d i s p l a c e m e n t a m p l i t u d e X r e I g b e t w e e n

m a s s e s M u a n d M b t o th e d i s p l a c e m e n t a m p l i t u d e

X b o f t h e b e d M b. T h i s r a t i o i s g i v e n b y t h e f o l l o w -

i n g :

X r e l g f21f2m

Xb - % / [ 1 - ( f2 /f2n,) ]2 + [ M b / M u + M b) ] (8~f2Hr2f2n,) - I~(f)

1 )

c i s io n e q u i p m e n t u n i t c a n b e r e p r e s e n t e d b y t h r e e

u n c o u p l e d t w o - m a s s s y s t e m s ( w i th g e n e r a li z e d p a -

r a m e t e r s ) , s u c h a s th e o n e i n F i g u r e 8 , o n e f o r e a c h

c o o r d i n a t e d i r e c t i o n o f t h e fl o o r v i b r a t io n s . M a s s e s

a n d s p r i n g s i n t h e m o d e l i n F i g u r e 8 r e p r e s e n t g e n -

e r a l i z e d i n e r t i a s a n d s t i f f n e s s e s o f t h e u n i t , a n d

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

n a t e d i r e c t i o n .

w h e r e f r e p r e s e n t s f r e q u e n c y o f i n t e r e s t , f r , , = 1 / 2 ~

V k m / M u i s t h e ( p a r t ia l ) r e s o n a n c e f r e q u e n c y o f t h e

u p p e r s t r u c t u r e a n d 8n~ i s t h e l o g - d e c r e m e n t o f t h a t

s y s t e m .

T h e a c tu a l r e l a ti v e d i s p l a c e m e n t in th e w o r k i n g

a re a o f t h e e q u i p m e n t u n i t i s p r o p o r t i o n a l t o X re ~g

X r e I = ~ / X r e I g (2)

4 8 J A N U A R Y 1 99 5 V O L 1 7 N O 1


9/16

R i v i n : V i b r a t io n i s o l a t io n o f p r e c i s i o n e q u i p m e n t

A o (~m ) ~z (Hz) ( t) y (Hz) ~x (Hz)

f w (Hz) f -~ fvz fvp (Hz)

0 .6 4 3 9 3 9

0 .6 4 4 4 .5 2 5 .8

0 .3 2 3 4 .2 4 4 .5

2 2 .5 - - 1 .0 2 9 .5

3 1 . 4 - - 0 . 5 8 3 1 . 3

24 .1 - - 1 .3 26 .4

a n d th e p r o p o r t i o n a l i t y c o n s t a n t ~ / ( d e s i g n c o n -

s t a n t) d e p e n d s o n th e g e o m e t r y o f t h e m a c h i n e .

F o r e x a m p l e , f o r a n u p p e r s t r u c t u r e t h a t c a n b e

r e p re s e n t e d b y th e m o d e l s h o w n i n F i g u r e 9

y zx = M u b l c / I o l = b l c / ( p y 2 + b 2 + c 2)

~ z z = M u C d / I o l = c d / ( p y 2 + b 2 + c 2) (3)

w h e r e t h e f i r s t s u b s c r i p t o n -y r e f e r s t o d i r e c t i o n o f

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

t o d i re c t i o n o f m o t i o n o f t h e u p p e r s t r u c t u r e r e la -

t i v e t o t h e b e d . H e r e M u d e n o t e s t h e m a s s o f t h e

u p p e r s t r u c t u r e ; /01 i ts m a s s m o m e n t o f i n e rt ia

a b o u t t h e a c t u a l a x i s o f r o t a t i o n , a n d p y i s t h e r a d i u s

o f g y r a t i o n a b o u t t h e p r in c i p a l y - a xi s. T h e d i m e n -

s i o n s b , b l , c , a n d d , a s i n d i c a t e d i n F i g u r e 9 , a r e

m e a s u r e d f r o m t h e c e n t e r o f g r a v i t y 0 1 o f t h e s y s -

t e m . O b v i o u s ly , ~ / d e p e n d s u p o n h o w t h e m a c h i n e

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

u p p e r s t r u c t u r e w i t h r e s p e c t to t h e b e d . I n t h e c a s e

o f

F i g u r e 9 ,

t h e u p p e r s t r u c t u r e is c o n n e c t e d t o th e

b e d b y a s p r i n g a l l o w i n g o n l y a n g u l a r d e f o r m a t i o n

a n d h a v i n g i n f i n i t e v e r t i c a l s t i f f n e s s . T h i s i s a g o o d

a p p r o x i m a t i o n f o r s t r u c tu r a l d e s i g n s of n u m e r o u s

m a c h i n e t o o l s a n d m e a s u r i n g s y s t e m s , b e c a u s e

g u i d e w a y s u s u a l l y h a v e v e r y h i g h t ra n s l a t i o n a l

s t i ff n e s s p e r p e n d i c u l a r t o t h e m o t i o n d i r e c t io n , b u t

t h e i r a n g u l a r d e f o r m a t i o n s m a y h a v e s ig n i fi c a n t

m a g n i t u d e . S e n s i t i v i ty o f h o r i z o n t a l d i s p l a c e m e n t s

i n t h e w o r k z o n e o f s u c h a m o d e l t o v e r t ic a l v i b r a -

t i o n s o f t h e b e d (~ /z x) c a n b e r e d u c e d b y r e d u c i n g

s t r u c t u r a l ( d e s i g n ) d i m e n s i o n s c a n d b l b y r e d u c -

i ng o v e r h a n g o r b y a d d i n g c o u n t e r w e i g h t s t o th e

b a c k s i d e o f t h e m a c h i n e . S e n s i t i v i t y o f v e r ti c a l d i s -

p l a c e m e n t s in th e w o r k z o n e t o v e rt ic a l v i b r a t i o n s

o f t h e b e d (~ /zz) c a n b e r e d u c e d b y r e d u c i n g s t r u c -

t u r a l ( d e s ig n ) d i m e n s i o n s c a n d d .

E x p e r i m e n t a l l y o b t a i n e d d a t a f o r se v e r a l m a -

c h i n e t o o l s ( e x c e r p t e d f r o m R e f. 4 ) a r e g i v e n i n T a -

b l e 1 , f r o m w h i c h w e m a y c o n c l u d e t h a t t h e vi b ra -

t i o n s e n s i t i v it y o f s u c h m a c h i n e s c a n b e r e d u c e d b y

p r o p e r s e l e c t io n o f d e s ig n p a r a m e t e r s , b e c a u s e

s i m i l a r m a c h i n e s h a v e v e r y d i f f e r e n t s e n s i t i v it i e s t o

v i b r a t i o n s o f t h e i r b e d s . I t c a n b e s e e n , f o r e x a m p l e ,

t h a t in th e g r o u p o f c y l in d r i c a l g r i n d e r s ~ w v a r i e s

f r o m 0 . 02 1 ( n e g l i g i b l e ) t o 0 . 6 ( v e r y s i g n i f ic a n t ) .

T h e g e n e r a l i z e d a m p l i t u d e r a t io

X r e

g / X b = ~ f )

( E q u a t i o n 1 ), w h i c h is a m e a s u r e o f t h e v i b r a t io n

s e n s i t i v i ty o f t h e m a c h i n e a s a f u n c t i o n o f f r e -

q u e n c y f , d o e s n o t d e p e n d u p o n t h e m a c h i n e s

m o u n t i n g , b u t o n l y o n it s d e s i g n ( s t ru c t u r a l n a t u r a l

f r e q u e n c y fm a n d m a s s e s M b , M u ) . T o o b t a i n a r a ti o

b e t w e e n a m p l i t u d e s o f t h e r e la t iv e v i b r a t i o n s

w i t h i n t h e w o r k z o n e o f t h e m a c h i n e a n d a m p l i -

t u d e s o f t h e f l o o r v i b r a t i o n s , X r e ~ / X b s h o u l d b e m u l -

t i p li e d b y th e r a t io o f t h e b e d v i b r a t io n a m p l i t u d e s

t o t h e f l o o r v ib r a t i o n a m p l i t u d e s , a s s u m i n g t h a t t h e

d y n a m i c c o u p l i n g b e t w e e n th e m a c h i n e s t r u c t u r e

a n d th e v i b r a t io n i s o l a t io n s y s t e m i s w e a k , a n d

t h e s e s y s t e m s c a n b e c o n s i d e re d a s in d e p e n d e n t

o n e s . 9 A j u s t i f ic a t i o n o f t h i s a s s u m p t i o n i s t h a t i n

m o s t p r a c t i c a l c a s e s , n a t u r a l f r e q u e n c i e s o f th e i s o -

l a t e d b e d i n t h e t h r e e c o o r d i n a t e d i r e c t i o n s fvx, fvy,

a n d fvz a r e c o n s i d e r a b l y l o w e r t h a n t h e s t r u c t u r a l

n a t u r a l f r e q u e n c i e s f m ( s e e T a b l e I ) , a n d t h e m a s s

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

o f t h e u p p e r s t r u c t u r e M u.

rinciples and cri teria of vibrat ion isolat ion

P r i n c i p l e s a n d c ri t e ri a o f v i b r a t i o n i s o l a t i o n o f h i g h -

p r e c i s i o n e q u i p m e n t c a n b e c o n s i d e r e d f o r t h r e e

t y p i c a l c a s e s . T h e f i rs t c a s e d e a l s w i t h p r o t e c t i o n o f

a s p e c i fi c u n i t o f e q u i p m e n t f r o m s p e c i f ic s t e a d y -

s t a te v i b r a t i o n s o f t h e fl o o r . B e c a u s e t h e s t e a d y -

s t a te v i b r a t i o n s c a n b e r e p r e s e n t e d b y a d i s c r e t e

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

o f t h e u n i t o f e q u i p m e n t f r o m s i n u s o i d a l v i b r a t io n s

o f t h e f lo o r . T h e s e c o n d c a s e r e p r e s e n t s p r o t e c t i o n

o f a s p e c i f ic u n i t o f e q u i p m e n t f r o m a n y c o m b i n a -

t i o n o f t y p i c a l q u a s i s t e a d y - s t a t e f l o o r v i b r a t i o n s

w i t h i n t h e e n v e l o p e r e p r e s e n t e d i n F i g u r e I . Al -

t h o u g h t h e p l o t s i n

F i g u r e 1

p r e s e n t a f re q u e n c y

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

s p e c tr a l c o m p o n e n t s m a y h a v e a m p l i tu d e s a s h i g h

a s t h e p l o t i n d i c a t e s . I f a v i b r a t i o n i s o l a t i o n s y s t e m

p r o t e c t i n g t h e u n i t o f e q u i p m e n t f r o m a n y r e a li za -

t i o n o f t h e f lo o r v i b r a t i o n s p e c t r a r e p r e s e n t e d b y

p lo t s i n F i g u r e s 1 A a n d B i s t o b e d e v e l o p e d , t h e n

t h e u n i t c a n b e e q u i p p e d w i t h i s o l a t i n g m o u n t s t h a t

w o u l d e n s u r e it s s p e c i f ie d p e r f o r m a n c e f o r t h e m a -

j o r i t y o f i n s t a l l a t i o n s i te s . T h e t h i r d c a s e d e a l s w i t h

p r o t e c ti o n o f e q u i p m e n t f r o m t r a n s ie n t m o t i o n s o f

t h e f lo o r c a u s e d b y r e g u l a r o r a c c id e n t a l s h o c k e x -

c i t a t i o n s .

I n t h e f i r s t c a s e , il l u s t r a t e d b y F i g u r e 1 0 , t h e

d e g r e e o f a t t e n u a t i o n i ~ v o f o n e f r e q u e n c y c o m p o -



10/16

R i v i n : V i b r a ti o n is o l a t i o n o f p r e c i s i o n e q u i p m e n t

3 . 0

E

o

> . x 2 . 0

. -~ 0

E -

t o - -

~ l . o

c

c3

J

.

i o ~ 2 . 0 . 3 . 0 4 0

I / I v

| I f2

Figure 10 Pr inc ip les o f v ib ra t i on i so la t ion f rom

s ing le- f requency f l oor exc i ta t i on

nent f o f f l oor v ib ra t i ons by the v ibra t i on i so la t ion

s y s tem (s y s tem : bed - i s o l a t ing m ou n ts ) i s de te r -

m ined by the f requency ra t i o f / fv w h e r e

1

~ M k V

f v - 2 ~r b + M u

i s the natura l f requency o f the v ibra t i on i so la t i on

system in the cons idered di rect ion. I t i s expressed

as fo l l ow s :

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

e . g . , i s o l a t o r s w i t h o i l d a m p e r s ) , o r a s f o l l o w s :

1 -

f o r is o l a t o r s h a v i n g n o t v e r y h i g h s t r u c t u r a l o r h y s -

t e r e t i c d a m p i n g t y p ic a l f o r e l a s t o m e r i c is o la -

to r s ) .

1 Here gv is log-de crem ent of the isolators .

Thus , f rom the two s ine waves a t f requenc ies

f l and f2 hav ing the same magni tudes, the s ine

wave hav ing f requency f l is a t tenuated less than

the s ine wave hav ing h igher f requency f2 (and,

thus, h igher rat io f2/fv , see Figure 10. Wh en there i s

v iscous damping in the isolators , increas ing the

damping (which reduces the resonance peak; i .e. ,

s ens it iv i ty t o l ow- am p l i tude bac k g r ound no i s e

and improves s tabi l i ty of the uni t f rom acc idental

impacts and dur ing s tar t /s top regimes) leads to de-

ter iorat ion of isolat ion at h igher f requencies in ac-

cordance w i th Equat ion (4) . In ca se o f s t ruc tura l

damping, i nc reas ing damping would l ead to on ly

marg ina l deter io ra t i on o f i so la t i on whi l e p lay ing

the aforement ioned pos i t ive roles, in accordance

wi th Equat ion (5) .

For the second c ase the p r inc iples invo lved in

isolat ion of a prec is ion machine against f loor v ibra-

t ions are i l lus t rated in F igu re 11 . The bo t t om - m os t

graph here shows the spec t rum of f l oor d i sp lace-

men t am pl i tudes X f in a g iven d i rec t ion . Th is graph

is a s t reaml ined envelope of the plots in F i g u r e 1

fo r the cons idered d i rec t i on . The top-mos t graph

show s the cor responding re la t ive mo t ion i n the

machine ' s w ork area, w i th &o represent ing the l im i t

of acceptabi l i ty of such mot ions. For prec is ion ma-

chine tools and, to a lesser degree, for prec is ion

m eas ur i ng equ i pm en t and p r ec i s i on p r oc es s i ng

equipment fo r e lec t ron ics produc t ion, the dynamic

coup l i ng between the mach ine s t ruc ture and the

v ibrat ion isolat ion system is relat ively weak (see

abov e) . Cons equen t l y , t he app r ox i m a te r e l a t i v e

I s o la l o r s w i l h V i s c o u s D a m p i n g I s o l a to r s w i l h M a t e r i a l D a m p i n g

E i l n t e r n a l F r i c t i o n )

I

~5

t

f v 2 f v l f m f v 2 f v l f m

x

- - f _ f

fm fm

E

o x

: / i

~ v f v 1 f v 2 f v 1

x

o ~ .

o ~ . , f

u - o

F igure

Pr inc iples of v ibrat ion isolat ion f rom

broad spec t rum quas is teady-s ta te f l oor exc i ta t i on

50 J A NU A RY 1995 V OL 17 NO 1


11/16

m o t i o n g r a p h c a n b e o b t a i n e d s i m p l y b y m u l t ip l y -

i n g t h e X r ~ / X ~ X ~ / X ~ a n d X f g r a p h s , a n d t h e v i b r a -

t i o n i s o l a t io n c r i t e r io n c a n b e e x p r e s s e d a s f o l l o w s

X b

X r e l

X b

ao

X - -~ X - - b - < ~ o ,

o r a o

~ I ~ ( f) < A o ( 6 )

T h e s o l i d l i n e s in F i g u r e 1 1 c o r r e s p o n d t o a s t if f

m o u n t i n g s y s t e m u n d e r th e m a c h i n e , t h e d a s h e d

l in e s t o a s o f t e r i s o l a t io n s y s t e m w i t h t h e s a m e

d a m p i n g a s t h e s t i ff e r s y s t e m , a n d t h e d o t t e d l i n e s

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

i n g . T h e s e t o f g r a p h s i n t h e l e ft h a l f o f F i g u r e 1 1

p e r t a i n s t o v i s c o u s d a m p i n g i n t h e i s o l a to r s , f o r

w h i c h g r e a t e r d a m p i n g r e s u l ts in g r e a t e r v i b r a t i o n

t r a n s m i s s i o n a t f r e q u e n c ie s a b o v e V 2 f v ; t h e g r a p h s

o n th e r i g h t s i d e p e r t a in t o h y s t e r e t i c d a m p i n g i n

t h e i s o l a t o r s , w h i c h a f f e c t s t h e r e s p o n s e a t h i g h

f r e q u e n c i e s o n l y i n s i g n i f i c a n t l y . 1 I t i s c l e a r t h a t r e l -

a t iv e v i b r a t i o n s i n t h e w o r k a r e a a r e r e d u c e d b y u s e

o f a s o f t e r m o u n t i n g w i t h g r e a t e r d a m p i n g . It is

i m p o r t a n t t o n o t e , t h a t

a r e s o n a n c e o n v i b r a t i o n

i s o l a t o rs i s a l l o w a b l e , a n d t h e i s o l a t o r s m u s t b e se -

l e c te d i n s u c h a m a n n e r t h a t a m p l i t u d e o f r e la t iv e

v i b r a t i o n s X r e a t t h e r e s o n a n c e o f th e v i b r a t i o n i s o -

l a t io n s y s t e m d o e s n o t e x c e e d th e s p e c i f ie d a l l o w -

a b l e le v e l A o. A c c o r d i n g l y , i m p r o v e m e n t s i n i s o l a -

t i o n c a n b e a c h i e v e d b y r e d u c i n g f v o r b y

i n c r e a s i n g d a m p i n g 5v. W h i l e r e l a t iv e d i s p l a c e -

m e n t s

X r e

a t t h e s t r u c t u r a l n a t u r a l f r e q u e n c y fm a r e

i n c r e a s in g w i t h t h e i n c r e a s i n g d a m p i n g i n i s o la -

t o rs , d i m i n i s h i n g a m p l i t u d e s o f f l o o r v i b r a t i o n s a t

h i g h e r fr e q u e n c i e s t o g e t h e r w i t h n o t e d a b o v e f ea -

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

s y s t e m w i t h h y s t e r e ti c d a m p i n g m a k e t h e r e so -

n a n c e a t f m a l e s s d a n g e r o u s o n e t h a n a t f ~ .

U s e o f g e n e r a l i z e d s p e c t r u m o f f l o o r v i b r a -

t i o n s , a s i n F i g u r e 1 1 , i s a m o r e c o n s e r v a t i v e a p -

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

a t t h e i n s t a l l a t i o n s i te . T h e l a t t e r c a n c h a n g e a f t e r

r e l o c a t i o n o f o l d a n d in s t a l l a t i o n o f n e w e q u i p -

m e n t , w h e r e a s t h e s p e c t r u m a s s u m e d i n F i g u r e 1 1

r e p r e s e n t s th e w o r s t c a s e b a s e d o n m u l t i p l e m e a -

s u r e m e n t s g i v e n i n F i g u r e I .

T h e c o n c e p t o f is o l a t i o n p r e s e n t e d i n F i g u r e 1 1

c a n b e e x p r e s s e d a n a l y t i c a ll y . 12 I f d y n a m i c c o u -

p l i n g b e t w e e n th e v ib r a t i o n i s o l a t io n s y s t e m a n d

t h e m a c h i n e s t r u c t u r e i s n e g l e c t e d , t h e n t h e r e la -

t iv e v i b r a t i o n s i n t h e w o r k i n g z o n e a r e a s f o l l o w -

i n g :

X r e l ( f )

= X f ~ X b ( ~ X , = co n s tX r e l( ~ X b -

c o n s t

(7)

S u b s t i t u t i n g E q u a t i o n (5 ) f o r X b ( f ) x , _ coast in

E q u a t i o n ( 7 ) y i e l d s t h e f o l l o w i n g :

Xb(f~x ,= c o n s t ~ --- ~ v =

2

[ 1 - - ( ~ v 1 2 1 2 4 - ( - -~ 1 2

8 )

R i v i n : V i b ra t io n i s o l a t io n o f p r e c i s io n e q u i p m e n t

S u b s t i t u t i n g i n t o E q u a t i o n ( 7 ) E q u a t i o n s ( 1 ) a n d ( 2 )

f o r

X r e l f ) X b = c o n s t g i v e s t h e f o l l o w i n g :

X r e l ( f ) f 2 / f 2

X b = 3 / ( f 2 ~ 2 M b , 2 f 2

1 - - ~ + M u + M b ~ r2 12

(9)

- 3 f

R e l a ti v e v i b r a t io n s i n t h e w o r k z o n e c a n b e c o m -

p u t e d a n d c o m p a r e d w i t h t h e a l l o w a b l e a m p l i t u d e

A o i f a ll t h e p a r a m e t e r s i n E q u a t i o n (7 ) a re k n o w n .

In E q u a t i o n (9 ) 3 f i s t h e t r a n s m i s s i b i l i t y f r o m t h e

b e d i n t o t h e w o r k z o n e a t f r e q u e n c y f. I t i s o b v i o u s

th a t i f f ~ fm a n d f l


12/16

R i v i n : V i b r a ti o n i s o l a t io n o f p r e c i s i o n e q u i p m e n t

T a b l e 2 M a t e r i a l s e l e c t i o n c r i t e ri o n v e r s u s in t e n -

s i t y o f f l o o r v i b r a t i o n s

Kdyn/5 @

v i b r a t i o n

a m p l i t u d e , i ~ m

R u b b e r

R u b b e r t y p e d u r o m e t e r 6 2 5 1 00

N a tu r a l 4 1 4 .6 4 .3 2 .6

5 6 5 .4 4 .2 3 .0

61 5 .9 4 .4 3 .0

7 5 5 .0 3 .8 2 .2

N e o p r e n e 4 2 4 . 6 3 . 8 5 3 . 0

5 8 3 .7 5 3 .3 2 .5

74 3 .1 2 .0 1 .6

7 8 5 .8 2 .6 5 1 .8 5

2 6 % n i t r i l e 4 2 4 .0 3 .6 3 .3

56 3 .1 2 .9 2 .5

69 2 .9 2 .2 1 .95

4 0 % n i t r i l e 5 0 3 .1 3 .0 2 .0 5

8 0 2 .6 2 .3 1 .8 5

F e l t u n i s o r b 1 5 .0 7 . 0 4 . 0

W i r e m e s h i s o la t o r s V i b r a c h o k

I s o l a t o r t y p e L o a d , N

V4 3 9 - 0 4 0 0 3 0 9 .5 1 .5

1 ,1 5 0 4 5 4 .8

W 2 4 6 - 0 8 7 0 1 3 4 .5 1 .5

1 ,1 5 0 2 3 1 1 .2 2 .9

W 2 4 6 - 5 2 ,3 0 0 2 7 4 .1 1 .5 5

t i o n o f E q u a t i o n ( 1 5) i n t o E q u a t i o n ( 14 ) y i e l d s t h e

f o l l o w i n g :

dp = ~ M b k s .K~yn(a,f)

+ Mo 116

I t i s c l e a r f r o m E q u a t i o n ( 1 6) t h a t t h e s t a t i c s t i ff -

n e s s k = o f i s o l a t o r s f o r a g i v e n c a n b e i n c r e a s e d

( t h u s im p r o v i n g t h e s t a b i l it y o f t h e i s o la t e d m a -

c h i n e ) b y r e d u c i n g

K d y n / 6 v

B e c a u s e b o t h

d y n

a n d

5 v d e p e n d u p o n f r e q u e n c y a n d , e s p e c ia l ly , a m p l i -

t u d e o f v i b r a t i o n s , t h e i r r a t i o i s d i f f e r e n t f o r d i f fe r -

e n t m a t e r i a ls a n d f o r d i ff e r e n t v i b r a t i o n p a r a m e -

te r s . T a b l e 2 g i v e s m e a s u r e d v a l u e s o f t h i s r a t io f o r

s o m e m a t e r i a ls d e p e n d i n g o n v ib r a t io n a m p l i -

t u d e s . ~1 I t c a n b e s e e n t h a t f o r l o w v i b r a t i o n a m p l i -

t u d e s ( 6 i~ m ) s o m e b l e n d s o f n i t r il e r u b b e r a r e t h e

b e s t, w h e r e a s f o r h i g h a m p l i t u d e s ( 10 0 I~ m ) w i r e

m e s h - b a s e d i s o l a t o r s h a v e s u p e r i o r p r o p e r t i e s .

T a b l e 1 l is t s a c c e p t a b l e v a l u e s o f f o r th e

t h r e e c o o r d i n a t e d i r e c t io n s f o r s e v e ra l m a c h i n e

t o o ls , t o g e t h e r w i t h t h e c o r r e s p o n d i n g p e r m i s s i b le

r e la t iv e a m p l i t u d e s & o, t h e v a l u e s o f w h i c h w e r e

c h o s e n t o c o r r e s p o n d t o o n e - h a l f o f th e s p e c i f ie d

p r e c i s io n o f t h e p a r t b e i n g m a c h i n e d . F l o o r v i b r a -

t i o n l e v e ls a s p r e s e n t e d i n F i g u r e 1 ( l i m i t i n g l i n e s )

w e r e u s e d i n c o m p u t i n g dp. V a l u e s o f t h e n a t u r a l

f r e q u e n c y r a t i o s fvx/fv~ fvy/fvz c a n b e u s e d t o d e t e r -

m i n e t h e r e q u i r e d s t i f f n e s s r a t i o s o f i s o l a t o r s i n d i -

r e c t i o n s x y z a s it i s d e s c r i b e d i n R e f e r e n c e 9 . D a t a

in Tab le I w e r e v a l i d a te d b y s u c c e s s f u l i n s t a l la t i o n

o f m a n y t h o u s a n d s o f m a c h i n e t o o l s o f t h o s e l i s te d

a n d o t h e r s i m i l a r m o d e l s i n a c c o r d a n c e w i t h t h e

r e c o m m e n d a t i o n s f r o m Table 1.

I f v i b r a t i o n s e n s i t i v i t y ~ ( f ) o f a p r e c i s i o n o b j e c t

is k n o w n ( f or e x a m p l e f r o m t h e p l o t s s h o w n in F i g -

u r e s 4 - 7 ) , t h e n E q u a t i o n ( 1 3 ) c a n b e u s e d f o r s p e c -

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

o f F i g u r e 4 A o = 0 .1 i ~m i s s p e c i f i e d . A s s u m i n g & o

= 0 .1 t~m a l so fo r t h e ca se s i n F i g u r e s 5 6 a n d 7

E q u a t i o n ( 13 ) c a n b e u s e d t o f i n d t h e r e q u i r e d p a -

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

u n i t s .

T a b l e 3 g i v e s t h e v a l u e s o f ~ /( f) c a l c u l a t e d f o r

c r i ti c a l p o i n t s f r o m t h e p l o t s i n F i g u r e 4 f o r v e r t i c a l

a n d h o r i z o n t a l d i r e c t i o n s , r e s p e c t i v e l y . T h e ta b l e

a l s o c o n t a i n s v a l u e s o f ~ 1 c a l c u l a t e d f o r t h e s e

p o i n t s u s i n g E q u a t i o n ( 1 3 ) a n d a s s u m i n g t h a t f o r

ve r t i ca l d i r e c t i o n X~(f ) = co n s t = 3 .0 i~m fo r f r e -

q u e n c i e s 3 - 3 0 H z a n d X t( f) = 3 . 0 3 0 / f i ~m fo r f r e -

q u e n c i e s f > 3 0 H z ; f o r th e h o r i z o n t a l d i r e c t i o n X ~ ( f)

= c o n s t = 2 . 5 i~ m f o r f r e q u e n c i e s 2 - 2 0 H z , a n d X ~ (f)

= 2 .5 2 0 / f # m f o r f r e q u e n c i e s f > 2 0 Hz . I t a l s o

c o n t a i n s v a l u e s o f ~ 2 c a l c u l a te d u s i n g f l o o r v i b r a -

t i o n l e v e l s c o r r e s p o n d i n g t o l i n e VC-B in F i g u r e 3

( b o t h f o r v e r t i c a l a n d h o r i z o n t a l d i r e c t i o n s ) .

I t c a n b e s e e n f r o m T a b l e 3 A t h a t t h e l o w e s t

va lu e o f ~1 fo r ve r t i ca l v i b r a t i o n s i s 4 .5 1 H z . I f v i -

b r a t i o n is o l a t o r s w i t h m e d i u m d a m p i n g Sv = 0 .6

a r e u s e d , t h e n f r o m E q u a t i o n ( 1 4) , t h e _r re q u ir e d v e r -

t i c a l n a t u r a l f r e q u e n c y fv = 4 .51 V0 .6 = 3 .0 4 H z .

H o w e v e r , i f i s o l a to r s m a d e o f r u b b e r w i t h h i g h

d a m p in g 5 v = 1 .2 a r e u se d ( e .g . , se e R e f. 9 ) , t h e n fv

= 5 . 0 H z , w h i c h c a n b e r e a l iz e d b y p a s s i v e i s o l a -

t o rs . M u c h s t i ff e r i s o l a t o r s c a n b e u s e d to c o m p l y

w i t h v a l u e s o f ~ 2, w h i c h r e p r e s e n t f lo o r c o n d i t i o n s

a t t h e m i c r o e l e c t r o n i c s i n d u s t r y i n s t a ll a t io n s .

A s i m i l a r s i t u a t i o n i s s e e n i n T a b l e 3 B ; h o w -

e v e r, r e a l iz a t io n o f n a t u ra l f r e q u e n c i e s c o r r e s p o n d -

ing to ~Pl (4 .7 Hz fo r 5 v = 0 .6 , 6 .63 Hz fo r ~v = 1 .2 )

i n h o r i z o n t a l d i r e c t i o n s w i t h p a s s i v e i s o l a t o r s d o e s

n o t p r e s e n t a n y p r o b l e m 9 ; e v e n m u c h l o w e r v a l u e s

c a n b e e a s i l y r e a l iz e d . U s e o f ~ 2 g i v e s e v e n m o r e

l a t t i tu d e i n s e l e c t i n g i s o l a t o r p a r a m e t e r s .

T a b l e 4 l is t s s i m i l a r d a t a f o r t h e c a s e g i v e n i n

F igure 5 . In th i s c a se , t h e s a m e a s s u m p t i o n s a r e

m a d e a b o u t X ~ ( f) f o r c o m p u t i n g b o t h dP1 a n d ~ 2 .

T h e m i n i m u m r e q u i r e d ~ f o r t h e v e r ti c a l d ir e c t i o n

i s 4 . 9 H z , w h i c h c o r r e s p o n d s t o f v = 3 . 8 H z f o r m e -

d i u m - d a m p e d i s o l a t o rs (5 v = 0 .6 ) a n d fv = 5 .4 Hz

f o r h i g h l y d a m p e d i s o l a t o r s ( ~v = 1 .2 ). T h e l a t t e r

v a l u e o f fv i n t h e v e r t ic a l d i r e c t i o n c a n b e r e a l i z e d

b y u s i n g p a s s i v e i s o l a t o rs ; i t c a n b e 3 0 % h i g h e r f o r

r e a l i za t i o n o f ~2 .

T h e c o r re s p o n d i n g n u m b e r s f o r th e h o r i z o n ta l

5 2 J A N U A R Y 1 9 95 V O L 1 7 N O 1


13/16

R i v i n : V i b r a ti o n is o l a t i o n o f p r e c i s i o n e q u i p m e n t

T a b l e 3 V i b r a t i o n i s o l a t i o n c r i t e r i o n f o r c a se o f F i g u r e 4

A

V e ~ i c a l d i r e c t i o n

Y - a x i s )

Hz 11 12 20 25 30 32 41 70 80

~ ~ 0 .0 0 8 3 0 .0 1 0 0 .0 8 7 0 .0 0 91 0 .0 5 6 0 .3 0 3 0 .0 5 0 .0 0 7 7 0 .0 1 0

~, Hz 4.51 12.3 7.0 26.9 13.0 6.3 22.5 128 137

~2, Hz 12 .9 36 .6 26 .9 116 61 29 .7 106 601 644

Hz 95 100 110 140 150 160 220 250

~ ~ 0 .5 8 8 0 .2 9 4 0 .0 5 7 0 .4 5 5 0 .2 2 2 0 .2 1 .2 8 0 .7 7

~1, Hz 19 .7 30 .0 78 .7 40 .0 63 .6 73 .4 46 .8 73 .3

B H o r i z o n t a l d i r e c t i o n X - a x i s )

Hz 7 12 22 65 70 100 140 210

~ ~ 0 .003 3 0 .05 0 .0125 0 .071 0 .090 0 .090 0 .056 1 .25

1, Hz 13 .7 6 .05 22 .3 49 .6 49 .2 84 176 68 .6

~2 , Hz 23 .1 37 .5 78 174 172 294 616 240

V a l u e s ~ a r e c a l c u l a t e d u s i n g f l o o r v i b r a t i o n l e v e ls fr o m F i g u r e 1

V a l u e s ~ 2 a r e c a l c u la t e d u s i n g f l o o r v i b r a t i o n l e v e ls f r o m F i g u r e 3 VC-B).

T a b l e 4 V i b r a t i o n i s o l a t i o n c r i t e r io n fo r c as e o f

F i g u r e 5

T a b l e 5 V i b r a t i o n i s o l a t i o n c r i t e r i o n f o r c a s e o f

F i g u r e 6

A V e r t i c a l d i r e c t i o n ~ a x i s ) A

V e r t i c a l d i r e c t i o n ~ a x i s )

Hz 5 7 .5 35 45 100 ~ Hz 6 8 30 80

-y f ) 0 .011 0.00 43 0.01 5 0.25 0.56 ~ f ) 0 .48 0.83 1.0 5.0

t ) l, Hz 4 .9 11 .8 32 .4 11 .6 25 .6 ~1 , Hz 0 .8 0 .9 3 .08 6 .13

t)2, Hz 6.7 24.6 152 55 120 ~2 , Hz 1.2 2.2 14.5 28.8

B H o r i zo n ta l d i re c t io n X-a x is ) ~3 , H z 3 .4 6 .2 4 1 8 1 .5

B H o r i z o n t a l d i r e c t i o n X - a x i s )

Hz 4 6.5 10 45 100

~ ~ 0 .05 0 .033 0 .0043 0 .1 0 .5

~1 , Hz 2 .02 4 .03 17 .2 24 .1 35 .6

~2 , Hz 2 .3 6 .2 43 84 125

V a lu e s ~1 a r e ca l cu la te d u s in g f l o o r v i b r a t i o n l e ve l s fr o m

F ig u r e 1

V a l u e s ~ 2 a r e c a l c u la t e d u s i n g f l o o r v i b r a t i o n l e v e ls f r o m F i g u r e

3 VC-B).

d i re c t io n ~1 = 2 .0 2 H z , fv = 1.6 Hz fo r 5v = 0.6, fv

= 2 .2 Hz fo r 5v = 1 .2 ; ~2 = 2 .3 Hz) a re a lso rea l iz -

a b le .

F o r t h e c a s e s r e p r e s e n t e d i n F i g u r e s 6 a n d 7

c a l c u l a t i o n s o f ~ f ) f o r c r i t ic a l p o i n t s r e q u i r e s u s i n g

v i b r a t o r y v e l o c i t y o f r e l a t i v e m o t i o n i n t h e w o r k -

z o n e i n s t e a d o f A o. C a l c u l a t i o n s f o r F i g u r e 6 w e r e

p e r f o r m e d f o r th e l o w e s t l i n es b o u n d a r y o f t h e

s a fe r e g i o n ) . T h e r e s u l t s , s h o w n i n T a b l e 5 i n d i c a t e

t h a t f o r f r e q u e n c i e s a b o v e 5 H z , t h e r e q u i r e d ~ 1 i s

a s l o w a s 0 . 8 H z f o r t h e v e r t i c a l d i r e c t i o n w h i c h

f Hz 5 8 30 80

~ f ) 0 .31 0.83 1.0 5.0

~1 , Hz 1 .01 0 .99 3 .38 6 .6

[ { ) 2 ,

Hz 1.4 2.2 14.5 28.2

~3 , Hz 4 .0 6 .2 41 79 .8

V a lu e s ~1 a re ca l cu la t e d u s in g f l o o r v i b r a t i o n l e ve l s f r o m F i g u r e I

Values I )2 a r e c a l c u la t e d u s i n g f l o o r v i b r a t i o n l e v e ls f r o m F i g u r e

2 VC-B).

Va lues t )3 a r e c a l c u la t e d u s i n g f l o o r v i b r a t i o n l e v e ls f r o m F i g u r e

3 VC-E).

c o r r e s p o n d s t o fv = 0 .6 2 Hz f o r 5 v = 0 .6 a n d fv =

0 . 8 8 f o r 5 v = 1 .2 ). T h e s e v a l u e s c a n n o t b e e c o n o m -

i c a l ly r e a l iz e d b y a p a s s i v e v i b r a t i o n i s o l a t i o n s y s -

t e m b e c a u s e it w o u l d r e q u i r e a n e x c e s s i v e l y m a s -

s i v e i n e r t i a b l o c k , a n d a n a c t i v e p n e u m a t i c o r

e l e c t r o n i c s y s t e m w i t h a l e v e l l i n g fe a t u r e i s c a l l e d

f o r. B e c a u s e u n i t s o f s u c h p r e c i s i o n a r e u s u a l l y i n-



14/16

R i v i n : V i b r a t io n i s o l a t i o n o f p r e c i s i o n e q u i p m e n t

T a b l e 6 V i b r a t i o n i s o l a t i o n c r i t e r i o n f o r c a s e o f

F i g u r e 7

A V e r t i c a l d i r e c t i o n

f , Hz 18 22 .5 3 0 43 .5 5 2

- /(f ) 0 .1 4 0.1 8 0.71 0.61 2.7

~ , Hz 5 .0 5 .6 3 .7 7 .0 4 .4

~2 , H z 1 8 .4 2 2 .7 1 7 .6 3 3 2 0 .5

B F o r e / a f t d i r e c t i o n

f , H z 2 0 3 0 4 1 .5 5 4 6 6

y(f ) 0 .5 0 .31 0 .35 0 .54 0 .87

( I)1, Hz 3.2 7.4 11.4 13.6 14.5

~2 , H z 1 1 .2 2 6 4 0 4 8 5 1

C S i d e / s i d e d i r e c t i o n

f , Hz 12 .5 22 27 .5 35 39

f(f) O. 16 0 .93 1.4 0.49 4.0

~1 , Hz 3 .5 2 .6 3 .1 7 .4 3 .1

~2 , Hz 9 .8 9 .0 10 .7 26 .1 10 .7

V a l u e s ( t) l a r e c a l c u l a t e d u s i n g f l o o r v i b r a t i o n l e v e l s f r o m

F i g u r e I .

V a l u e s O 2 a r e c a l c u l a t e d u s i n g f l o o r v i b r a t i o n l e v e l s f r o m

F i g u r e

3 (VC-B).

s t a l l e d i n s p e c i a l f a c i li t ie s , i s o l a t i o n c r i t e ri a i n t h i s

c a s e w e r e a l s o c a l c u l a te d f o r t w o c l a s s e s o f p re c i -

s i o n f a c i li t ie s s p e c i f i e d i n

F i g u r e 3 :

VC-B ( ( I)2 ) and

t h e m o s t s t r i n g e n t V C - E ( (I )3 ). I t c a n b e s e e n t h a t i n

t h e l a s t c as e t h e u s e o f p a s s i v e i s o l a t o r s

( fv

= 3 .7 5

H z a t 6 v = 1 .2 ) i s m a r g in a l l y f e a s ib l e .

T a b l e 6 l is t s v i b r a t i o n i s o l a t i o n d a t a f o r th e

c a s e o f

F i g u r e 7

a s s u m i n g r e l a t i v e d i s p l a c e m e n t i n

t h e w o r k z o n e o f 0.1 ~ m . T h e m i n i m u m r e q u i r e d (I) 1

f o r v e rt ic a l d i r e c t i o n i s 3 . 7 Hz , w h i c h c o r r e s p o n d s t o

fv

-- 2 .9 H z f o r m e d i u m - d a m p e d i s o l a t o r s ; 6v = 0 . 6 ,

a n d fv = 4 .1 H z fo r 6 v = 1 .2 . Fo r h o r i zo n ta l d i r e c -

t i o n s ] l m i n . = 2 . 5 7 , a n d fv = 2 Hz fo r 6v = 0 .6 , fv =

2 . 8 f o r 6 v = 1 .2 . T h e n a t u r a l f r e q u e n c i e s f o r h i g h

d a m p i n g a r e r e a li z a b le w i t h p a s s i v e i s o la t o r s . T h e

m i n i m u m v a l u e o f ~ 2 fo r t h e v e r t ic a l d i r e c t i o n i s

1 8 .4 , w h i c h a l l o w s u s t o u s e c o m m e r c i a l l y a v a i la b l e

i s o l a t o r s f o r i n d u s t r i a l m a c h i n e r y .

T h u s , o n l y o n e o f t h e a n a l y z e d h i g h - p r e c i s i o n

i n s t r u m e n t s a c t u a l l y r e q u i r e s a n a c t iv e v i b r a t io n

i s o la t i o n s y s t e m f o r p r o t e c t i o n f r o m t h e t y p i c a l

s p e c t r u m o f i n d u s t r i a l s t e a d y f l o o r v i b r a ti o n s . H o w -

e v e r , s u c h u l t r a p r e c i s i o n u n i t s a r e n e v e r u s e d i n t h e

g e n e r a l i n d u s t r i a l b u i ld i n g s . A c c o r d i n g l y , m u c h

s t i f f e r p a s s i v e i s o l a t o r s c o u l d b e u s e d i n a l l c o n s i d -

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

t h e c a s e g i v e n i n F i g u r e 6 a n d T a b l e 5 i f t h e e q u i p -

m e n t w e r e l o c a t e d in t h e b u i ld i n g c o m p l y i n g w i t h a

v i b r a t i o n c r i t e r i o n V C - E . R e a l i z a t i o n o f t h i s c r i t e r io n

b y c i v il e n g i n e e r i n g m e a n s i s f e a s i b l e a s w a s

s h o w n i n R e f e r e n c e 7 .

T h e t h i r d c a s e o f v ib r a t i o n i s o l a ti o n i n v o l v e s

i s o la t i o n f r o m s h o r t d u r a t i o n ( i m p u l s i v e o r s h o c k )

m o t i o n s o f t h e f l o o r. S u c h e x c i t a t i o n s t e n d t o b e

l es s t r o u b l e s o m e , b e c a u s e o f t h e i r s h o r t d u r a t i o n s .

A c c o r d i n g l y , w e m a y t a k e t h e p e r m i s s i b l e p e a k re l-

a t iv e d i s p l a c e m e n t b op in r e s p o n s e t o fl o o r s h o c k s

a s 3 t i m e s t h e v a l u e o f 4 o p e r m i s s i b l e f o r s t e a d y

v i b r a t i o n s . W e m a y a n a l y z e a n i s o l a t i o n s y s t e m f o r

a m a c h i n e s u b j e c t to s h o c k e x c i t a t io n u s i n g t h e

m o d i f i e d s h o c k s p e c t r u m a p p r o a c h t h a t h a s be e n

d e s c r i b e d i n t h e c o n t e x t o f f o r g i n g h a m m e r i s o la -

t i o n 13 t o o b t a i n t h e f o l l o w i n g :

A p = A r e la b ~ / = A i A r e l Y a f (17)

w h e r e a b d e n o t e s t h e p e a k d i s p la c e m e n t o f th e b e d

c a u s e d b y s h o c k m o t i o n o f t h e f lo o r w i t h d i s p la c e -

m e n t m a g n i t u d e a A 1 r e p r e s e n t s t h e s h o c k s p e c -

t r u m c o r r e s p o n d i n g t o a v e r s e d s i n e p u l s e a c ti n g

o n t h e v i b r a t i o n i s o l a ti o n s y s t e m ; a n d

A r e I

r e p r e -

s e n t s t h e s h o c k s p e c t r u m f o r r e l a ti v e d i s p l a c e m e n t

in t h e w o r k a r e a c o r r e s p o n d i n g t o a v e r s e d - s i n e

m o t i o n o f t h e b e d ( F i g u r e 1 2 ) .

I f ~/ a n d A o a re k n o w n , a s w e l l a s t h e p u l s e

m a g n i t u d e

a f

a n d d u r a t i o n ~-f ( e .g . , f r o m

F i g u r e

2) ,

t h e n t h e v a l u e s o f t h e n a t u r a l f r e q u e n c y

fvp

o f t h e

i s o l a ti o n s y s t e m t h a t a re n e c e s s a r y fo r a d e q u a t e

i s o l a ti o n m a y b e d e t e r m i n e d f r o m t h e f o r e g o i n g

e x p r e s s i o n b y t r ia l a n d e r r o r . V a l u e s o f

fvp

f o r t h e

z - d i r e c ti o n t h a t h a v e b e e n d e t e r m i n e d i n t h i s m a n -

n e r a r e g i v e n i n

T a b l e I f o r

a n u m b e r o f m a c h i n e s .

W e m a y n o t e t h a t t h e s e v a l u e s a r e a p p r o x i m a t e l y

e q u a l t o t h e n a t u r a l f r e q u e n c y v a l u e s fv t h a t a r e

n e c e s s a r y w i t h 6 v = 0 . 5 t o p r o v i d e s u f f i c i e n t i s o l a -

t i o n o f s t e a d y v e r ti c a l v i b r a t i o n a c c o r d i n g t o t h e (/#z

c r i t e r i o n .

B e c a u s e t h i s c o r r e l a t i o n h o l d s f o r p r a c t i c a l l y a l l

m a c h i n e t o o l s i n Tab le 1 , w h i c h h a v e v e r y d i f fe r e n t

a n d d i v e r s e d e s i g n s t r u c t u r e s , i t c a n b e e x t r a p o -

l a te d to o t h e r p r e c i s i o n e q u i p m e n t , s u c h a s t h o s e

w h o s e s e n s i t i v i ti e s t o f l o o r v i b r a t i o n s a r e p r e -

2.0

1.0

0.5

0.2

0 . 0 5

Figure 13

i \

~0 15 20 25 30 35

F r e q u e n cy H z

R e l a t iv e m o t i o n i n w o r k i n g a r e a o f

3 B 7 1 s u r f a c e g r i n d e r e x c i t e d b y 5 t~m f l o o r v i b r a -

t i o n , f o r s e v e r a l t y p e s o f m o u n t s , a l l e m p l o y e d a s

r e c o m m e n d e d b y m a n u f a c t u r e r : 1 - - r u b b e r / m e t a l

C N F ,

fvz -

2 0 H z ; 2 - - s t e e l w e d g e s ,

fvz -

27 Hz;

3 - - w i r e - m e s h i s o l a t o r s , fvz - 2 5 H z ; 4 - - p l a s t i c

p a d s , fw - 3 0 H z ; 5 - - - r u b b e r /m e ta l i so l a to r s , fvz -

15 Hz

p r o v i d i n g a n a t u r a l f r e q u e n c y i n t h e v e rt i c a l z ) d i -

r e c t i o n o f 2 0 H z r e s u l t e d i n m u c h b e t t e r i s o l a t i o n

t h a n e v e n t h e b e s t c o n s t a n t - s t i f f n e s s i s o l a t o r s w i t h

t h e s u b s t a n t i a l l y l o w e r 1 5 H z r e s o n a n c e fr e q u e n c y

in t h e z - d i r e c t i o n . T h e d i f f e r e n c e b e t w e e n n a t u r a l

f r e q u e n c i e s o f 1 5 a n d 2 0 H z is e q u i v a l e n t t o a p p r o x -

i m a t e l y t w i c e t h e d i f fe r e n c e i n t h e i s o l a t o r s t i f f n e s s .

P r o d u c t i o n m o d e l s o f C N F is o l a t o r s f o r v e rt ic a l

n a t u r a l f r e q u e n c i e s o f 1 0 , 1 5 , 2 0 , 3 0 H z h a v e b e e n

d e v e l o p e d . = R e c e n t r e s e a r c h r e s u l t s o b t a i n e d i n th e

M a c h i n e T o o l R e s e a rc h L a b o r a t o r y o f W a y n e S t a t e

U n i v e r s i t y h a v e p r o v i d e d a b a s i s f o r d e s i g n i n g C N F

i s o l a t o r s f o r v e r y - l o w - v e r t i c a l n a t u r a l f r e q u e n c y ,

f r o m a s l o w a s 1 - 2 H z .

S i d e is s u e s f o r v i b r a t i o n i s o l a te d e q u i p m e n t

V i b r a t i o n i s o l a t i o n u s i n g p a s s i v e i s o l a t o r s r e s u l t s i n

a r e d u c e d s t i ff n e s s o f t h e c o n n e c t i o n b e t w e e n t h e

i s o la t e d e q u i p m e n t a n d t h e ri g id f l o o r f o u n d a t i o n ) .

T h i s c an le a d t o r o c k in g m o t i o n s o f t h e e q u i p m e n t

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

t a b l e s ) , a n d to r e d u c t i o n o f t h e e f f e c t iv e r i g i d i t y o f

t h e e q u i p m e n t s t r u c t u r e n o t t i e d to t h e r ig i d f o u n -

d a t i o n .

T h e r o c k in g m o t i o n o f is o l a t e d p r e c i s i o n m a -

c h i n e s is s o m e t i m e s o b j e c t i o n a b l e . T h i s r o c k i n g

m a y b e r e d u c e d b y i n s t a ll in g t h e m a c h i n e r i g i d ly

o n m a s s i v e f o u n d a t i o n b l o c k s a n d p l a c i n g i s o l a ti o n

u n d e r t h e s e b l o c k s . T h is a p p r o a c h t e n d s t o b e e x-

p e n s i v e , h o w e v e r , a n d m a k e s r e l o c a t i o n o f t h e m a -

c h i n e v e r y d i ff ic u l t. O n t h e o t h e r h a n d , w e o f t e n

m a y t a k e a d v a n t a g e o f t h e f a c t t h a t i n m o s t o f t h e

m a c h i n e s t h e d i re c t io n o f m a x i m u m v i b r a ti o n s e n -

s i t i v i t y i s a t r i g h t a n g l e s t o t h a t o f t h e i n t e r n a l e x -

c i t a t io n . I n s u c h c a s e s , th e u s e o f a n i s o t r o p i c i s o l a -

t o r s w i t h t h e r e q u i r e d s t i f fn e s s r a t io s c a n b e v e r y

b e n e f ic i a l. A n o t h e r a p p r o a c h i s t o u s e i n c re a s e d



16/16

Rivin: Vibration isolation of precision equ ipm ent

dis tances between isolators in the di rect ion of the

internal exc i tat ions. This decreases the rock ing mo-

t i on c om ponen t and i nc r eas es t he t r ans l a t i ona l

component , thus s ign i f i cant l y improv ing s tab i l i t y

of the isolated object . The increased dis tances be-

twe en isolators can be achieved by instal l ing isola-

tors under a plate or ra i ls at tached to the bed.

Smal le r prec i s ion mach ines usua l l y do not re-

qu i re the add i t i on o f a foun dat ion for enhanc ing

r ig id i ty o f the i r f rames , whereas la rger mach ines

(e .g . , mach ine too l s we igh ing over ten tons ) usu-

al ly do, unless they are spec ial ly des igned to be

mounted on three po in ts (k inemat i c mount ing) . In

ma ny cases , and p ar t i cu lar ly fo r mach ines o f i n ter-

media te weight (10-20,000 Ibs ) , j ud i c ious p lace-

me nt o f the i so la t ion mo unts ma y reduce sta t ic de-

f lec t ions of the machine bed, thus in ef fect , making

i t act as i f i t we re m ore r ig id. For the large Schau dt

AR-1500 cy li ndr i ca l g r i nder , fo r exa mple , fo r wh ich

the manufac turer recommended ins ta l l a t i ons on 15

r ig id wedge-mounts p laced in the l ocat ions i nd i -

cated by circles in Figure 14 i t was found that the

use of 7 mounts placed as indicated by pluses in

the f igure resul ted in a s igni f ican t ly greate r effec-

t ive r ig id i ty , 4 ma king i t poss ible to ins tall th is ma-

ch ine on i so la t i on mo unts w i tho ut u s ing a s t if fen-

ing foundat ion. Another way o f s t i f fen ing mach ine

frames is to at tach them to r ig id plates.

Because the proper se lec t i on o f the number

and the l ocat ion o f the mount ing po in ts i s impor -

tant , bo th for reduc ing rock ing and for i nc reas ing

the e f fec t ive r i g id i ty o f the m ach ine s t ruc ture , th i s

prob lem genera l l y deserves par t i cu lar a t tent i on .

Designers rarely give th is the cons iderat ion i t de-

serves.

Conclusions

1. Param eters o f f loo r v ib ra t i ons i n var ious m an-

ufac tur ing p lants f i t i n to con s tant d i sp lace-

m en t am p l i t ude pa t te r ns f o r a l im i t ed fr e -

q u e n c y r a n g e ( d i f f e r e n t f o r v e r t i c a l a n d

hor izontal v ibrat ions) . Use of these pat terns

a l l ow us to fo rmula te ob jec t i ve spec i f i ca t i ons

for parameters o f v ib ra t i on i so la t i on sys tems.

2 . S e n s i t iv i t y o f p r o d u c t i o n a n d m e a s u r i n g

* - O O O O

~- 3834 mm

I

F i gu r e 14 Loc a t i ons o f m o un ts unde r bed o f

Schaudt AR-1500 prec i s ion gr inder (O- -as recom-

m ended by m anu fac tu re r ; + - - f a v o r a b l e i nsta ll a -

t i on determ ined as resu l t o f r i g id i ty eva luat ion)

equ ipment to ex terna l v ib ra t i ons can be s ig-

ni f icant ly reduced b y a tho ug ht fu l s t ructural

design.

3. N atural f requen cies of v ibrat ion isolat ion sys-

tems for prec i s ion equ ipment un i ts (and, con-

sequ ent ly , s ti ffnesses of v ibra t ion isolators)

can be inc reased by enhanc ing the damping

of isolators.

4 . Res i l ien t m a te r i a l s f o r v i b r a t i on i s o l a to r s

shou ld be selected in accordance wi th prevai l -

i ng ampl i tudes o f f l oor v ib ra t i ons i n accor -

dance w i th the proposed c r i te r i on .

5 . Man y h igh-prec i s ion produc t ion and measur -

ing machines can be successful ly ins tal led on

pass ive v ibrat ion isolators hav ing high damp-

ing, w i th active pn eum at ic /electronic isolators

being needed only in except ional cases.

6. Constant natural f requency isolators can sub-

s t a n t i a l l y s i m p l i f y d e s i g n o f a v i b r a t i o n -

isolated instal lat ion and, at the same t ime, no-

t i ceab ly improve i t s per formance.

7. Rock ing and reduct ion of effect ive s t i ffness o f

v ibra t i on - i so la ted ma ch ines can be s ign i f i -

cant ly al lev iated by judic io us s elect ion of the

number and locat ion of isolators , as wel l as of

their st i f fness character ist ics.

cknow l edgmen t

S uppor t f r om Na t i ona l S c i enc e Founda t i on and

f rom Wayne S ta te Univers i ty Ins t i tu te o f Manufac -

tur ing Research is grateful ly acknowledged.

References

1 R i v in , E. I . R ev i ew o f v i b ra t i on i nsu l a t i on mou n t i ngs fo r

m a c h i n e t o o l s ,

Mach and Toot ing,

1965, 8 , 37-4 6

2 D eB ra , D . B . V i b ra t i on i so l a t ion o f p rec is i on mach i ne too l s

a n d i n s t r u m e n t s ,

Ann of the C/RP,

1992, 41 /2, 7 11-71 8

3 Rivin, E. I . Act ive Servo-Contro/ /ed) Vibro iso/ators and

M o u n t i n g S y s t e m s f o r M a c h i n e r y ,

M o s c o w : N I I M A S H ,

1971, p. 80 ( in Russian)

4 R i v in , E . I. V i b ra t i on iso l a t i on o f p rec i s i on ma ch i ne ry , S/V

Sound and V /b,

1979, 8 , 18-2 3

5 H e g a r t y , G . P . A m b i e n t f l o o r v i b r a t i o n s u r v e y , R e p t

122888 o f Jan 28, 1988, Fabreeka Products Company

6 F l oo r v i b ra t i on tes t i ng repo r t o f fu tu re s ite o f a p roduc t

l in e , G e n e r a l M o t o r s C o r p o r a t i o n , P r iv a t e c o m m u n i c a t i o n ,

1990

7 G o r d o n , C . G . G e n e r i c c ri t e r ia f o r v ib r a t i o n - s e n s i t i v e

e q u i p m e n t , i n

Vibrat ion Co ntrol in Microelectronics, Op-

t ics and Metro logy , SP IE Proceedings,

Vol . 1610, Nov. 1991

8 Ungar , E . E ., S turz , D . H . and Amick , C . H . V ib ra t ion contro l

des i gn o f h i gh techn o l ogy fac i l it i e s , S/V Sound and V ib,

1990, 7 , 20-27

9 R iv in , E . I . P r inc ip les and cr i te r ia o f v ib r a t io n i so la t ion o f

m a c h i n e r y ,

A S M E J o f M e c h D e s ,

1979 , 101 ,682 -692

10 S no w don , J . C . H a ndb ook o f v i b ra t i on and no i se con t ro l ,

T he P ennsy l van i a S ta te U n i ve rs i t y , 1979

11 R i v in , E. I . P ass i ve eng i ne mo un ts - -D i rec t i o ns fo r fu tu re

d e v e l o p m e n t ,

SAE Transactions,

1985, 3 , 582-5 92

12 R iv in , E . I . So m e issues o f v ib r a t ion i so la t ion o f mach ine

too l s , i n

Dinamika Mash in ,

Moscow : N auka , 1969 , pp .

229-238 ( in Russian)

13 R i v in , E . I . D es i gn o f v i b ra t i on i so l a t i on sys tems fo r fo rg i ng

h a m m e r s , S/V Sound and V ib , 1978, 12 , 12-15

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Vibration Isolation of Precision Machines