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M e a s u r e m e n t o f h a l f - b o r ea n d l a r g e - b o r e f e a t u r e sM . S . S h u n m u g a m *C e r ta i n e n g i n e e r i n g c o m p o n e n t s h a v e h a l f - b o r e a n d l a r g e -b o r e f e a tu r e s w h o s ed imen s ions have to be c r i ti ca l l y con t ro l l ed du r i ng manu fac tu re . The p resen twork dea l s w i th t he measu remen t de ta i l s sys tema t i ca l l y and b r i ngs ou t t hecha rac te r i s ti c s o f t hese measu remen ts . The desc r i p t i ons o f t he me asu r ingdev i ces a re a l so i nc luded .K e y w o r d s : d imens iona l measu remen t , bo res , bo re measu remen t dev i ces

T h e m e a s u r e m e n t o f t h e i n n e r d im e n s i o n s o f h o l e s isa l w a y s m o r e d i f f ic u l t t h a n t h e m e a s u r e m e n t o f t h ee x t e r n al d i m e n s i o n s a n d t h e m e a s u r e m e n t o f l a r g e-bores a lso has spec i f ic prob lems 1 '2 .Compared to the measuremen t o f f u l l - f ea tu res ,the measuremen t o f segmented fea tu res posesd i f f e ren t k inds o f p rob lems as d iamet r i ca l l y oppos i tepo in ts a re non-e x i s ten t . A few a t tempts have beenmade to deve lop measur ing dev i ces fo r cy l i nd r i ca land spher i ca l segments us ing su i tab le l i nkages 3'4 bu tno such a t tempts have been made fo r t he case o fha l f -bo re fea tu res .Eng ineer ing i ndus t r i es engaged in them a n u f a c t u r e o f c o m p o n e n t s f o r e a r th m o v e r s ,m a t e ri a l h a n d l i n g e q u i p m e n t a n d o t h e r s i m il a rdev i ces , o f ten face p rob lems re la t i ng to ha l f -bo re o rl a r g e -b o r e m a n u f a c t u r e . A l t h o u g h t h e sem e a s u r e m e n t s c a n b e c o n v e n i e n t l y c a rr ie d o u t o n ac o o r d in a t e m e a su r in g m a c h in e ( C M M ) , t h ew o r k p i e c e h a s t o b e r e m o v e d fr o m t h e m a c h i n e t o o lfo r such measuremen ts . I n such cases , t he rese t t i ngo f t h e w o r k p i e c e o n t h e m a c h i n e to o l f o r r e - w o r kposes p rac t i ca l p rob lems . There fo re , anym e a s u r e m e n t c a r ri e d o u t o n t h e w o r k p i e c e w h e n i ti s o n t h e m a c h i n e to o l w o u l d b e o f im m e n s e v a l u eto the opera to r .A t y p i c a l c o m p o n e n t h a v i n g a h a l f - b o r e fe a t u rei s shown in F ig 1 . The bo re -s i ze and the he igh t o fi t s cen t re above the su r face shown a re impor tan t t oi t s f unc t i on . Cer ta in CNC mach in ing cen t res a rep r o v i d e d w i t h p r o b e h e a d s t o c h e c k t h e w o r k p i e c ed i m e n s i o n s w i t h o u t d i s t u r b i n g i t s p o s i t io n . F o rm a c h i n i n g o p e r a t i o n s ca r ri e d o u t o n c o n v e n t i o n a lm a c h i n e s o r C N C m a c h i n e t o o l s w i t h o u t t h ep rob ing fac i l i t y , t he re i s a need fo r a measur ingdev i ce . I n the case o f a ha l f -bo re , d iamet r i ca l l yoppos i te po in ts a re no t ava i l ab le and th i s makesd i rec t measuremen ts d i f f i cu l t . A su i tab le measur ingdev i ce i s necessary to tack le th i s p rob lem . Su ch adev i ce i s a l so necessary fo r l a rge bo re ma ch in in gw i t h c l o se r c o n t r o l o f d i m e n s i o n .Th is pa per p resen ts the the o re t i ca l bas i s fo r t hemeasuremen ts o f ha l f -bo re and l a rge bo re . The

* D e p a r t m e n t o f M e c h a n i c a l E n g in e e r i n g In d i a n I n s t i t u t e o fT e c h n o lo g y , M a d r a s - 6 0 0 0 3 6 , I n d i a

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F i g 1 A t y p i c a l c o m p o n e n t w i t h h a l f - b o r e f e a tu r e

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F i g 2 B o r e - d e p t h m e a s u r e m e n t : e x t e r n a l s u r fa c e a sd a t u m ( a ) S c h e m a t i c o f d e v i c e ; ( b ) G e o m e t r i c a lp r i nc ip le

PREC IS ION ENG INEERIN G 014 1-63 59 /8 9 /01 001 5-04 /$03 .00 1989 Bu tterwor th & Co (Pub li shers ) L td 15

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Shu nm ugam --meas urem ent of hal f -bore and large-bore features

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l o c a t i o n o f t h e b o r e - c e n t r e . H o w e v e r , a m e a s u r i n gd e v i c e w h i c h t a k e s th e b o r e s u r fa c e a s a d a t u md o e s n o t s u ff e r f r o m t h i s d r a w b a c k . F i gs 4 ( a ) a n d5 ( a ) s h o w t w o s u c h d ev ic e s. T h e d e v ic e s u s er o ll e r s as l o c a t in g e l e m e n t s : s o m e t i m e s e d g e s c o u l db e e m p l o y e d f o r t h is .

C h o r d a l l en g t h m e a s u r e m e n tW i t h r e fe r e n c e t o F i g 4 ( b ) , t h e f o l l o w i n g r e l a ti o nca n b e d e r i ve d

L 2 = ( D - d - H ) Hd i f fe re n t ia t i n g E q 8 a n d re a r ra n g in g th e te rmsp r o d u c e s

d L / d D = (1 - k ) H / 2 Lw h e r e k = d / D a s d e f in e d in th e e a r l i e r se c t io n ,

( 8 )

( 9 )

S o lv in g E q 8 fo r H a n d su b s t i t u t i n g in to E q 9 ,d L / d D = [ ( 1 - k ) / 2 { [ ( 1 - k ) / 2 ] O / L

+ ( [ ( 1 - k ) / 2 1 2 [ ( O / L ) 2 - 1 ] )1 /2 }( 1 0 )

L e t d L / d D = M , t h e m e a s u r e m e n t s e n s i ti v it y , a n d f o ra sp e c i f i e d M E q 1 0 ca n b e so lve d fo r L in te rms o fD . T h e n E q 9 y ie ld s th e ch o rd a l h e ig h t .H = 2 M L / ( 1 - k ) ( 1 1 )

F ig 4 ( c ) s h o w s t h e c h a r a c t e ri s t ic s o f th e m e a s u r i n gd e v ice .C h o r d a l h e ig h t m e a s u r e m e n tF o r t h e d e v ic e s h o w n i n F ig 5 ( a ) a n d th ec o r r e s p o n d i n g g e o m e t r y i n F i g 5 ( b ) , t h ech a ra c te r i s t i c e q u a t io n i s th e sa me a s E q 8 .D i f fe re n t ia t i n g E q 8 a n d re a r ra n g in g th e te rms

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S h u n m u g a m - - m e a s u r e m e n t o t h a l t - b o r e a n d l a r g e - b o r ep r o d u c e s

d H / d O = - ( 1 - k ) H / [ ( 1 - k ) O - 2 H ] ( 1 2 )w h e r e k = d / D . T h e n e g a t i v e s ig n s h o w s t h a t a ninc rease i n t he d iame te r (D ) resu l ts in a reduc t i on o fcho rda l he igh t (H ) . The cha rac te r i s t ics o f t h i sm e a s u r i ng d e v i ce a re s h o w n i n F i g 5 ( c ) .

I f t he measu remen t sens i t i v i t y - ( d H / d D ) isrep resen ted by M, then the cho rda l he igh t i sH = M ( 1 - k ) O / [ 2 M + (1 - k ) ] ( 1 3 )

F rom Eq 8 , t he cho rda l l eng th can be ob ta ined asL = H ( 1 + (1 - k ) / M ) 1 / 2 ( 1 4 )

L a r g e - b o r e m e a s u r e m e n tThe measu remen ts o f f u l l - bo re s i ze do no t gene ra l l ypose p rob lems , as the measu r ing i ns t rumen t canc o n t a c t t h e d i a m e t r i c a l ly o p p o s i t e p o i n t s o n t h e b o r esu r face . Somet imes , a c lose r t o le rance i s ma in ta inedon l a rge -bo res . A measu r ing dev i ce wh ich magn i f i esthe dev ia t i on i n t he va lue o f t he d iame te r i s h igh l ydes i rab le i n t h i s s i t ua t i on . O f t he two measu r ingdev i ces tha t use the bo re su r face as da tum, thed e v i c e c h e c k i n g t h e c h o r d a l h e i g h t ( F i g 5 ) h a s t h ei n h e r e n t m a g n i f i c a ti o n .R e s u l t s a n d d i s c u s s i o nFor the pu rpose o f d i scu ss ion , l e t us assume thef o l l o w i n g d i m e n s io n s

D + t d a s 60 _+ 0.1 mmC + t c a s 3 + 0 . 2 m m

f o r t h e c o m p o n e n t s h o w n i n F i g 1 .F o r t h e b o r e - d e p t h m e a s u r e m e n t ( F i g 2 ( a ) )the nomina l va lue o f H i s 57 mm. The va r ia t i on i n Hva lue i s due to the va r i a t i on in d iame te r ( D ) andloca t i on ( C ) . I f t he l oca t i on i s c lose l y con t ro l l ed( t c - ~ 0 ) , a u n i t c h a n g e in t h e d ia l r e a d in g s h o w s t h eu n i t c h a n g e i n r a d i u s ( i e t w i c e t h e d i a m e t e r ) v a l u e .F o r t h e d e v i c e s h o w n i n F i g 3 ( a ) , l e t t h e b a l ld iame te r be D / 1 0 = 6 mm . A se ns i t i v i t y o f M = 0 .5w o u l d m e a n t h a t th e d i a m e t r i c a l ly o p p o s i t e p o i n t sa re con tac ted . As th i s cond i t i on i s no t poss ib le , asen s i t iv i ty o f M = 1 is chos en. From Eq 5, L is13 .5 mm and Eq 7 y ie lds H as 20 .38 3 mm. A un i tchange i n d ia l r ead ing (on a cho rda l l eng th o f 2L )c o r r e s p o n d s t o a c h a n g e o f a h a l f - u n i t i n d i a m e t e rva lue , assuming tha t t c i s neg l i g ib le . I ns tead o f ab a l l -e n d e d p r o b e , a d i s c - t y p e p r o b e ( d = 0 ) c o u l dbe used . Imper fec t i ons on the d i sc edge , however ,wo u ld a f fec t adve rse l y t he measu remen t resu lt s .Fo r dev ices tha t res t on the bo re -su r face , t heloca t i on C has no e f fec t on the measu remen ts . Theuse of an edge ins tead of a ro l le r as a locat inge l e m e n t i n t h e s e d e v i c e s ( F i g s 4 ( a ) a n d 5 ( a ) ) ,su f fe rs f rom the same d rawback men t ioned above .Wi th re fe rence to F ig 4 (a ) , i t can be seen tha t asens i t i v i t y o f M = 0 .5 i s poss ib le on l y w he n themeasurem en t i s a long the d iam e t r i ca l l i ne . The re fo re ,M i s t aken to be 0 .25 . As sum ing the ro l l e r rad ius tobe D / I O (6 ram) , L i s ca l cu la ted f rom Eq 10 as0 .382 D , i e 22 .92 mm. Eq 11 y ie lds 12 .733 mm fo rthe H va lue . A un i t change i n t he d ia l r ead ings

teatures( w h i c h i s o n a l e n g t h 2 L ) r e p re s e n ts a c h a n g e o ftwo un i t s on the d iame te r va lue .

T h e d i m e n s i o n s o f th e d e v i c e s h o w n i nF ig 5 ( a ) , f o r a s e n s i t i v it y o f M = - 1 a n d w i t h t h eo the r cond i t i ons rema in ing the same, a re ca l cu la tedf rom Eqs 13 and 14. H is 18.62 mm and L is25 .666 mm. In th i s case , t he re is a on e - to -on ec o r r e s p o n d e n c e b e t w e e n t h e c h a n g e i n t h e d ia lread ing and the change i n t he bo re d iame te r . Themeasureme n t and the d iame te r a re re la ted l i ke theve rn ie r ca l i pe r /m ic romete r measu remen ts o f a fu l l -bo re . The changes a re, howeve r , i n t he op pos i tesense , i ea un i t r educ t i on i n H de no tes a un i tincrease in the d iameter va lue and v ice versa.Fo r the m easu remen t o f a l a rge bo re hav ing as i ze o f 750 _+ 0 .02 mm, the dev i ce m easu r ing thec h o r d a l h e i g h t ( F i g 5 a ) c a n b e d e s i g n e d w i t h asens i t i v i t y o f 5 o r more . Fo r examp le , a sens i t i v i t y o f5 e f fec t ive ly increases the d ia l read ing to + 0 .1 mmwh en the d iame te r va r i a t i on i s _+ 0 .02 mm.C o n c l u s i o n sThe dev i ces desc r ibed i n t h i s pape r cou ld bese lec ted fo r t he measu remen t o f ha l f -bo re fea tu resacco rd ing to the deg ree o f con t ro l o f t he d imens ion .The dev i ces us ing the bo re -su r face as da tum a rebe t te r su it ed fo r t he co n t ro l o f t he bo re -s i ze .H o w e v e r , a n y d e p a r t u re f ro m r o u n d n e s s w o u l din f l uence the read ings ob ta ined .The cha rac te r i s t i cs i nc luded i n t h i s wo rk pe rm i t sthe des ign o f t hese dev i ces w i th p rede te rm inedsens i t i v i t y . Such an app roach makes thein te rp re ta t i on o f t he d ia l r ead ings much s imp le r andmean ing fu l . An a rb i t ra ry des ign o f t he dev i cesr e q u ir e s a c h a r t s h o w i n g t h e c o r r e s p o n d e n c ebe tween the d ia l r ead ing and the d iame te r va lue .

The app roach p resen ted he re requ i res on l y al i nea r d ime ns ion to be se t. Fo r examp le , t he dev i ces h o w n i n F ig 4 ( a ) r e q u ir e s o n l y t h e c h o rd a l l e n g t hto be se t and any s tanda rd i ns t rum en t cou ld be usedfo r t h i s pu rpose . An a rb i t ra ry des ign may necess i ta tethe use o f se t t i ng b locks hav ing ha l f -bo re fea tu res a tt h e i r l i m i t in g c o n d i t i o n s .T h e i n h e r e n t m a g n i f i c a ti o n o f t h e m e a s u r in gd e v i c e s h o w n i n F i g 5 ( a ) a l so p e r m i ts a c l o s ercon t ro l o f t he d iame te r o f l a rge -bo res .A l t h o u g h t h e m e c h a n i c a l - ty p e d i a l h as b ee nshown in a l l app l i ca t i ons , su i t ab le d i sp lacemen tt ransduce rs based on i nduc tance , capac i tance o ro the r p r i nc ip les cou ld be used a long w i th a d ig i t a ld i sp lay .R e f e r e n c e s1 Y a n u s h k e v i c h , E . P . Im p r o v i n g t h e a c c u r a c y o f m e a s u r in gthe i nne r d i ame te r o f ho l es , M easur em e nt Techn i ques , 1970 ,1 3 , N o. 3 , 6 5 6 - 5 9 .2 Ru b i n ov , A . D . T he e f f ec t o f e las t i c de fo r m a t i on o f i ns idemi c r ome te r s on t he ac c u r ac y o f m eas u r i ng l a r ge in te r na ld i mens i on , M easur em ent Techn i ques , 1983 , 1 6 , No, 12,1801 - 1803.3 Ya k i r i n , R . V . Pos s i b i li t ies o f des i gn i ng ins t r umen ts hav i ngl i nea r s c al es f o r t he meas u r em en t o f r ad i i o f c y l i nd r i c a l an ds phe r i c a l s egmen ts , M easur em ent Techn i ques , 1973 , 1 6 , N o. 3 ,3 4 2 - 3 4 64 Ya k i r i n , R . V . Meas u r i ng r ad i i o f c y li nd r i c a l and s phe r ic a ls egmen ts . M easur em en t Techn i ques , 1976, 1 9 , N o. 11 , 1567

1 8 J A N U A R Y 1 9 8 9 V O L 11 N O 1