An Analysis of Conical Drill Point Grinding - the Generation Process and Effects of Setting Errors

J. D. Wright, Engineer, Government Aircraft Factory, Melbourne; E. J. A. Armarego (1). University of Melbourne/Australia

The f i n a l d r i l l p o i n t geometry g e n e r a t i o n p r o c e s s f o r g e n e r a l p'urpose t w i s t d r i l l s u s i n g t h c popular c o n i c a l g r i n d i n g method is d e s c r i b e d and model led. Based on t h e " i d e a l " c a s e a n a l y s i s pre*--iously r e p o r t e d , t h e fundamental c lements of t h i s p r o c e s s a r e i d e n t i f i e d and ana lysed . Far t h i s " i d e a l " ( d e s i g n ) c a s e , t h e g r i n d e r d e s c r i b e d c m producc a l l t h e recommended s p e c i f i e d d r i l l p o i n t f e a t u r e v a l u e s f o r a range of g r i n d i r g cone angles . The i n t r o d u c t i o n of g r i n d e r s e t t i n g a c v i a t i o n s from t h e " i d e a l " c a s e ( s e t t i n g e r r o r s ) s e v e r e l y compl ica tes t h e a n a l y s i s and t h e genera ted curved l i p d r i l l p o i n t shape. m e t r i c a l f e a t u r e s and t h e " a c c e p t a b l e g r i n d e r c r i t e r i a " had t o be e s t a b l i s h e d . The e f f e c t s of d e v i a t i o n s i n s i x g r i n d e r s e t t i n g s and two d r i l l f l u t e - f e a t u r e s have been s t u d i e d f o r 80 g e n e r a l purpose combinat ions of d r i l l p o i n t f e a t u r e v a l u e s . d r i l l shapes occur f o r 2 6 combinat ions. l i p s a r e o b t a i n e d a l though t h e ranges between t h e d e s i g n and g e n e r a t e d f e a t u r e s can d i f f e r s u b s t a n t i a l l y . The dominant s e t t i n g e r r o r s and t h c s u s c e p t i b l e genera ted f e a t u r e s a r e i d e n t i f i e d . T h i s s t u d y high- l i g h t s t h e d i f f i c u l t i e s ic a c h i e v i n g and c o n t r o l l i n g t h e s p e c i f i e d geometry i n p r a c t i c e .

N e w d e f i n i t i o n s f o r t h e geo-

I t is shown t h a t even w i t h smal l d e v i a t i o n s , unacceptab le Fcr t h e remaining 5 4 combinat ions e s s e n t i a l l y s t r a i g h t d r i l l

INTRODUCTION

The g e n e r a l g e o n e t r y of t h e c o n v e n t i o n a l t w i s t d r i l l h a s been d e s c r i b e d i n numerous tex tbooks and handbooks E1-31. Cons iderable i n t e r n a t i o n a l agreement on t h e nomenclature and s p e c i f i c a t i o n of t h e s a l i e n t g e o m e t r i c a l f e a t u r e s of t w i s t d r i l l s is a l s o e v i d e n t i n handbooks and Standards [2-71. F u r t h e r , it has been recognised t h a t t h e geometry a t t h e d r i l l p o i n t , where c u t t i n g o c c u r s , a f f e c t s t h e impor tan t machining per - formance c h a r a c t e r i s t i c s such a s f o r c e s , power and d r i l l l i f e . Through decades of developn.ent and e x p e r i m e n t a t i o n , recommendations f o r t h e v a l u e s o f s p e c i f i e d d r i l l p o i n t f e a t u r e s f o r optimum d r i l l per- formance when machining d i f f e r e n t work m a t e r i a l s have been g i v e n i n handbooks [ 2 , 3 ] . Recommendations f o r g e n e r a l purpose d r i l l s , r e p r e s e n t i n g a compromise optimum geometry f o r machining a range of common work m a t e r i a l s have a l s o been quoted [ 2 , 3 , 7 ] and compared [81.

D e s p i t e t h e accumulated knowledge of t w i s t d r i l l s t h e r e is r e l a t i v e l y l i t t l e d e t a i l e d i n f o r m a t i o n about t h e p r e c i s e geometry of t h e d r i l l p o i n t and t h e assoc- i a t e d sharpening method. There i s ev idence to suggest t h a t t h e c o n i c a l g r i n d i n g method i s commonly used i n p r a c t i c e [9] a l though o t h e r methods have been noted i n t h e l i t e r a t u r e [lo-121. I n a d d i t i o n t h e ' a s measured' g e o m e t r i c a l v a r i a b i l i t y of nominal ly i d e n t i c a l manuf- a c t u r e d d r i l l s h a s been shown t o be e x c e s s i v e [13-161 and c o n t r i b u t e s s i g n i f i c a n t l y t o t h e s c a t t e r i n t h e d r i l l i n g f o r c e s [14,15] and d r i l l l i f e [1G,17]. The s e l e c t i o n of t h e d r i l l p o i n t sharpening method, t h e d r i l l p o i n t f e a t u r e v a l u e s and t h e q u a l i t y c o n t r o l procedures f o r g e n e r a l purpose d r i l l s h a s been t h e r e s p o n s i b i l i t y of t h e d r i l l manufac turers . I n r e c e n t y e a r s , r e s e a r c h workers have developed a keen i n t e r e s t i n t h e s e impor tan t a s p e c t s of t w i s t d r i l l s . A number of i n v e s t i g a t i o n s of t h e d r i l l g e o m e t r i c a l v a r i a b i l i t y o b t a i n e d d u r i n g manufacture have h i g h l i g h t e d t h e s o u r c e s of v a r i a t i o n s and t h e s i g n i f i c a n t r e d u c t i o n s i n v a r i a b i l i t y p o s s i b l e through improved q u a l i t y c o n t r o l procedures [18-20]. A s e r i e s of s t u d i e s of t h e popular c o n i c a l and some o t h e r d r i l l p o i n t sharp- en ing methods have a l s o been made i n an a t t e m p t t o a r r i v e a t an optimum d r i l l p o i n t geometry [13,16,21-231. The i n v e s t i g a t i o n s o f d r i l l p o i n t sharpenin? methods c a r r i e d o u t a t t h e U n i v e r s i t y of Melbourne have been aimed a t o b t a i n i n g a deeper unders tanding of t h e g e n e r a l purpose d r i l l geometry and p l a u s i b l e d r i l l p o i n t g r i n d e r s c a p a b l e of a c h i e v i n g a d e s i r e d opt imal geometry w i t h a view to improve t h e v a r i a b i l i t y of nominal ly i d e n t i c a l d r i l l s [24-271.

f i n a l d r i l l p o i n t geometry g e n e r a t i o n p r o c e s s f o r g e n e r a l purpose d r i l l s is p r e s e n t e d . The a n a l y s i s is a f u r t h e r development of e a r l i e r s t u d i e s based on t h e " i d e a l " c o n i c a l g r i n d i n g method. D e t a i l e d a n a l y s e s of g r i n d i n g methods have shown t h e c o n i c a l g r i n d i n g method t o be most promising a s a means of g e n e r a t i n g t h e reconmended range o f d r i l l p o i n t f e a t u r e v a l u e s f o r g e n e r a l purpose d r i l l s [26]. I n t h i s p r e s e n t a n a l y s i s t h e g e n e r a t e d shape and d r i l l p o i n t f e a t u r e v a l u e s w i l l be cons idered both i n t h e absence ( i . e . ' i d e a l ' c a s e ) and presence of g r i n d e r s e t t i n g errors.

I n t h i s paper an a n a l y t i c a l i n v e s t i g a t i o n of t h e

-- FINAL DRILL POINT GEOMETRY GENERATION_ PROCESS - IDEAL CASE

I n deve loping an a n a l y s i s of t h e f i n a l d r i l l p o i n t geometry g e n e r a t i o n p r o c e s s , i t is necessary t o con- s i d e r t h e g e o m e t r i c a l i n t e r a c t i o n between t h e d r i l l and t h e g r i n d i n g s u r f a c e . From a p r a c t i c a l p o i n t of view, t h i s i n v o l v e s f o u r major e lements t h e s e being t h e s e l e c t i o n of an i n i t i a l d r i l l p o i n t geometry: t h e

s e t t i n g of t h e d r i l l i n a g r i n d e r ; t h e g r i n d e r a c t i o n d u r i n g which t h e i n i t i a l geometry is p r o g r e s s i v e l y removed; and t h e s e l e c t i o n of an end p o i n t a t which t h e d e s i r e d f i n a l d r i l l p o i n t geometry i s g e n e r a t e d ( i . e . " i d e a l " f i n a l l o c a t i o n ) . For each of t h e s e e lements of t h e g e n e r a t i o n p r o c e s s , mathematical r e l a t i o n s h i p s need to be e s t a b l i s h e d which l i n k t h e g r i n d e r s e t t i n g para- meters t o t h e g e n e r a t e d d r i l l p o i n t geometr ic f e a t u r e s . The common approach i n e a r l i e r a n a l y t i c a l s t u d i e s [13, 21,22,24-261 has been t o develop t h e s e types of math- e m a t i c a l r e l a t i o n s h i p s when t h e d r i l l i s p o s i t i o n e d i n t h e " i d e a l " f i n a l - l o c a t i o n and t h e i n i t i a l geometry h a s been f u l l y removed. These a n a l y s e s have provided i m - p o r t a n t i n s i g h t s i n t o t h e p o t e n t i a l of t h e g r i n d i n g methods a s a s s e s s e d by " a c c e p t a b l e g r i n d e r c r i t e r i a " [2G]. Thus they r e p r e s e n t an e s s e n t i a l s t a r t i n g p o i n t for t h e broader a n a l y s i s i n c o r p o r a t i n g a l l e lements o f t h e g e n e r a t i o n p r o c e s s .

The g e n e r a l geometry of t h e c o n i c a l g r i n d i n g method wh'en t h e d r i l l i s i n t h e ' i d e a l ' f i n a l l o c a t i o n i s shown i n F i g . 1. I n a d d i t i o n t o assuming t h a t t h e i n i t i a l geometry i s f u l l y removed, i t has a l s o been assumed [24 ,26] t h a t :

!a) The d r i l l geometry is symmetr ical about t h e d r i l l a x i s .

T 1 C*

SECTION A-A

Annals of the ClRP Vol. 32/1/1983 1

( b ) The p o r t i o n o f t h e f l u t e s u r f a c e which f o r m s e a c h l i p i s a " r u l e d " s u r f a c e ( d e v e l o p a b l e a n n u l a r h e l e c o i d ) .

( c ) The d i s t a n c e be tween e a c h s t r a i g h t l i n e f l u t e g e n e r a t o r i n ( b ) and t h e d r i l l a x i s is h a l f t h e web t h i c k n e s s (W) and t h e a c u t e a n g l e between t h e skew g e n e r a t o r and t h e d r i l l a x i s i s h a l f t h e p o i n t a n g l e ( p ) .

F o r t h i s g r i n d i n g method, t h e d r i l l f l a n k s a r e gen- e r a t e d by two r i g h t c i r c u l a r g r i n d i n g c o n e s symmetr ic- a l l y l o c a t e d a b o u t t h e d r i l l a x i s w i t h e a c h cone gen- e r a t i n g o n e f l a n k . The c o n e and d r i l l axes l i e i n p a r a l l e l p l a n e s w i t h t h e cone a x e s d i s p l a c e d by a d i s - t a n c e C from t h e d r i l l a x i s . The a c u t e a n g l e s b e t - ween t h g skew d r i l l and cone a x e s a r e e a c h y w h i l e t h e semi -cone a n g l e f o r e a c h cone is b. I f t h e g e n e r a t e d l i p i s t o b e s t r a i g h t , t h e ' i d e a l ' f i n a l l o c a t i o n o f t h e d r i l l mus t be s u c h t h a t a s t r a i g h t l i n e g e n e r a t o r o f e a c h f l u t e ( t a n g e n t i a l to t h e d r i l l core d i a m e t e r ) i s c o i n c i d e n t w i t h a c o r r e s p o n d i n g s t r a i g h t l i n e c o n e g e n e r a t o r . The a n g l e between t h e p r o j e c t i o n s o f t h e cone g e n e r a t o r t h r o u g h t h e l i p and t h e c o n e a x i s i n t h e p l a n e no rma l t o t h e d r i l l a x i s i s A . The cone a p i c e s , a t o r i g i n s 0 and 0 are d i s p l a c e d by C , C and C w i t h r e s p e c t to o r i g i n 0 on t h e d r i l l a x r s as shdwn i n F i g . 1. A number o f t h e g r i n d i n g p a r a - meters ? , ~ , A , V , C ~ , C , C z a r e i n t e r r e l a t e d by [ 2 4 ] ,

t a n v = - Y

s inxcosxsec ' e - g ' s e c 2 i (cos2 i(sec'1:-1) + s i n ' x s e c 2 ,2 (1-cos? ysec2 9)

(1) ( 2 ) Cx = C tanA - W/cos;i

Y and Cz = C t a n v . ( 3 ) Y Thus from t h e geomet ry i n F i g . 1 and t h e above e q u a t - i o n s , f o u r g r i n d i n g p a r a m e t e r s a r e s u f f i c i e n t t o f u l l y d e s c r i b e t h e geomet ry w i t h t h e d r i l l i n t h e ' i d e a l ' f i n a l l o c a t i o n [26 ] . As w i l l be n o t e d l a t e r , t h e f o u r g r i n d i n g p a r a m e t e r s o , x , i and Cx p r o v i d e a u s e f u l p r a c t i c a l s e l e c t i o n .

The e q u a t i o n s f o r g r i n d i n g cone 1 w i t h respect to t h e o r i g i n 0 o n t h e d r i l l a x i s h a s b e e n e x p r e s s e d as ~ 2 4 1

( 4 )

A similar e q u a t i o n f o r cone 2 c a n a lso h e found [24 ] .

g e n t i a l t o t h e d r i l l cone d i a m e t e r ) p r o j e c t e d i n t h e x-y p l a n e are:

The e q u a t i o n s f o r t h e l ips ( f l u t e g e n e r a t o r s t a n -

f o r L i p 1 : x = y t a n i - W/COSA f o r L i p 2 : x = y t a n i + W/COSA

The r e l e v a n t p o r t i o n o f t h e c h i s e l e d g e e q u a t i o n i n t h e x-y p l a n e c a n b c found by s G l v i n g t h e two c o n e e q u a t i o n s w i t h r e s p e c t t o o r i g i n 0 on t h e d r i l l a x i s

i f rom which [24]

F o r t h e c u r v e d c h i s e l edge , the c h i s e l e d g e a n g l e $ is b a s e d on t h e t a n g e n t t o t h e c u r v e i n t h e x-y p l a n e a t x=y=O, t h u s from F i g . 1

where

t a n $ ' = -

$ = 1800 - A - $ 1 (7)

[ s i n 2 9 - s i n x c o s x L i n 2 ci - ( cx/c ) ( cod -cog 3

(CX/C )( cos~e-cos7x) ( 8 ) Y

t h e p o i n t a n g l e 2p and l i p c l e a r a n c e a n g l e CP are also r e l a t e d t o t h e g r i n d i n g p a r a m e t e r s [ 2 4 ] 20 t h a t

and

t a n c s = -cos ( & # - A ) [ t a n A + t a n ( ~ - 1 ) ( c o s 2 x - s in7 Xtan2 9) -tanvtan(w-i)sinycosxsec20]

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

cospcosx + s i n p s i n x c o s ~ - c o s e = 0 ( 9 )

i [ t a n " ( s i n 2 x -cos2 ,q t a n 2 o ) - s inxcosXsec2 D I ( 10) where t h e web a n g l e w is d e f i n e d a s

, = s i n - l ( w / r ) (11)

A t t h e o u t e r c o r n e r , r = D/2 and ,: = .,, , so t h a t t h e l i p c l e a r a n c e a n q l e C : c a n be found f?om E q u a t i o n (101 by u s i n y . , f rom EquatTon (11).

E q u a t i o n s (1) t o (11) p r o v i d e t h e m a t h e m a t i c a l r e l a t i o n s h i p s be tween t h e g r i n d i n q p a r a m e t e r s and t h e commonly s p e c i f i e d d r i l l p o i n t f e a t u r e s 2p , Cv , ' v , 2W and D . f e a t u r e s 2p. C! and i:' a r e g e n c r a t e d on :he f l u t e d body w i t h known'features 2W and D . A s n o t e d earlier and e v i d e n t from E q u a t i o n s (1) t o (11) t h e f o u r nec- e s s a r y g r i n d i n g p a r a m e t e r s s u c h a s '1, Y , and C h a v e t o be found from t h e t h r e e e q u a t i o n s i n v o l v i n g t#e g e n e r a t e d f e a t u r e s 2p, Ci and I ( E q u a t i o n s ( 7 ) , (9) and (10). Thus tine d r i l l O g e o m e t r y i s u n d e r s p e c i f i e d a l t h o u g h a l l t h e d r i l l p o i n t f e a t u r e s c a n b e independ- e n t l y s e l e c t e d and g e n e r a t e d by t h i s g r i n d i n g method p r o v i d e d one g r i n d i n g p a r a m e t e r s u c h a s '4 is p r e - s e l e c t e d [24 ,26 ] . F u r t h e r i t h a s p r e v i o u s l y b e e n shown t h a t t h e c o n d i t i o n $1 .. '< mus t a p p l y t o e n s u r e t h a t t h e d r i l l r e m a i n s w i t h i n t h e g r i n d i n g cone and h e n c e c a n b e f u l l y g round [24 ] . I n a more r e c e n t work by t h e a u t h o r s [26] a comprehens ive set o f " a c c e p t a b l e g r i n d e r cri teria" h a v e b e e n e s t a b l i s h e d and a p p l i e d to t h e c o n i c a l . g r i n d i n g method. I t was found t h a t a t a l l c o m b i n a t i o n s o f t h e recommended d r i l l p o i n t f e a t u r e v a l u e s f o r g e n e r a l p u r p o s e d r i l l s , t h e d e s i r e d geomet ry was g e n e r a t e d and t h e a v a i l a b l e r a n g e w i t h i n wh ich ( ' u ) c o u l d be s e l e c t e d was o n l y m a r g i n a l l y r e s t r i c t e d [26] .

The r e m a i n i n g e l e m e n t s o f t h e g e n e r a t i o n p r o c e s s need t o b e c o n s i d e r e d i n o r d e r t o p h y s i c a l l y p o s i t i o n t h e d r i l l i n t h e ' i d e a l ' f i n a l locat ion shown i n F i g . 1 and t h u s a c h i e v e t h e d e m o n s t r a t e d p o t e n t i a l o f t h i s g r i n d i n q method f o r g e n e r a l p u r p o s e d r i l l s h a r p e n i n g . The g r i n d e r shown i n F i g . 2 , h a s b e e n d e s i g n e d f o r t h i s p u r p o s e . I t i s n o t e d t h a t t h e g r i n d e r a l l o w s f o r t h e f a c t t h a t t h e i n i t i a l s e t t i n g s w i l l o c c u r when t h e d r i l l i s d i s p l a c e d from i ts f i n a l l o c a t i o n w i t h r e s p e c t to t h e g r i n d i n g s u r f a c e . Thus , a l t h o u g h o n l y f o u r g r i n d i n g p a r a m e t e r s are needed to d e s c r i b e t h e geomet ry i n t h e " i d e a l " f i n a l l o c a t i o n , more g r i n d e r s e t t i n g p a r a m e t e r s may b e needed t o a c h i e v e t h i s c o n d i t i o n . N e v e r t h e l e s s , a n a t t e m p t h a s b e e n made t o maximize t h e u t i l i z a t i o n o f t h e g r i n d i n g p a r a m e t e r s i n t h e above a n a l y s i s . F o r example , t h e g r i n d e r s e t t i n g p a r a m e t e r s 9 and :< are d i r e c t p h y s i c a l r ep - r e s e n t a t i o n of t h e cor-res o n d i n g r i n d i n g p a r a m e t e r s i n t h e a n a l y s i s . S i m i l a r P y by m J i n g t h e v e e g r o o v e

Dur ing p o i n t s h a r p e n i n g t h e t h r e e s p e c i f i e d

o, coneapex * ab"G, bc-cp

ac = cq

FIGURE 2

2

i n which t.he d r i l l is h e l d s y n m e t r i c a l wi th r e s p e c t t o t h e p l a n e p a r a l l e l t o t h e d r i l l and g r i n d i n g cone ax is , t h e g r i n d i n g parameter C can be d i r e c t l y set on t h e g r i n d e r ( F i g . 2 ) . The d iHect U S E of t h e g r i n d i n g para- meters C z and C a s g c i n d e r s e t t i n g parameters p r e s e n t problems s i n c e These a r e d i s t a n c e s between o r i g i n s 0: and 0 i n space when t h e d r i l l i s i n t h e ' i d c a l ' f i n a l l o c a t i o n . By a n t . i c i p a t i n g t h e f i n a l l o c a t i o n o f t h e o u t e r c o r n e r of t h e d r i l l wi th r e s p e c t to t h e p i v o t p o i n t on t h e g r i n d e r a t tachment , t h e s e t t i n g parameter d i s t a n c e L a long t h e d r i l l a x i s can he e s t a b l i s h e d . T'ne d i s t a n g e normal t o t h e g r i n d i n g wheel s u r f a c e L may b e used t o d e s c r i b e t h e r e l a t i o n s h i p between t h g g r i n d e r p i v o t p o i n t and t h e g r i n d i n g s u r f a c e i n t h e ' i d e a l f i n s 1 l o c a t i o n . These s e t t i n g parameters , shown i n Fig. 2 , may be usea instDad of C z and C and

L~ = c (co t%-tan . , ) t ( D / 2 ) ( co tycosecv- tan . Jcos ic , , - . ) ) and Ls = (C + ( D / 2 s i n ~ ) ) s i n ~ i c o s ~ c o s e c ' ~ (13) wherc is h a l f t h e vee groove a n g l e . The i n i t i a l nnqular s e t t i n g of t h e d r i l l i n t h e vee groove t o achieve t h e g r i n d i n g p a r m e t e r 1. depends on t h e i n i t - i a l d r i l l p o i n t geometry and i t s r e l a t i o n t o t h e f l u t e g e n e r a t o r in tended t o f o r n t h e l i p when t h e d r i l l i s i n i t s ' i d e a l ' f i n a l p o s i t i o n . T h i s angular g r i n d e r s e t t i n g parameter may be made e q u a l tc t h e g r i n d i n g parameter i by c a r e f u l l y s e l e c t i n g t h e i n i t i a l d r i l l p o i n t geometry.

The d e s i g n of t h e i n i t i a l d r i l l p o i n t qenmetry c o n s t i t u t e s t h e f i r s t impor tan t e lement of t h e f i n a l d r i l l p o i n t g e n e r a t i o n process . The i n i t i a l d r i l l p o i n t geor ,e t ry should s i m p l i f y t h e s e t t i n g of t h e d r i l l i n t h e g r i n d e r (second e l e m e n t ) , should e n s u r e t h a t t h e i n i t i a l d r i l l p o i n t geometry is f u l l y rem- oved a t t h e g r i n d e r a c t i o n end p o i n t (e lement f o u r ) , should n o t i n v o l v e e x c e s s i v e m a t e r i a l removal d u r i n g p o i n t g r i n d i n g and should h e a n easy shape t o be produced.

The i n i t i a l p o i n t geometry c o n s i s t i n g of a r i g h t c i r c u l a r cone c o a x i a l w i t h t h e d r i l l a x i s can s a t i s - f y a l l t h e above c r i t e r i a when a s u i t a b l e semi-cone a n g l e '3 is s e l e c t e d . I t is a p p a r e n t t h a t t h i s i n i t i a l D p o i n t geometry is easy t o produce and h a s a geometry which roughly approximates t n e f i n a l p o i n t georretry so t h a t t h e amount of m a t e r i a l t o be removed is n o t e i tcess ive . F u r t h e r t h e c i r c u m f e r e n t i a l c l e a r - ance a n g l e Ct [24,26] is z e r o on t h e i n i t i a l c o n i c a l f l a n k s so t h a f e x c e s s m a t e r i a l is a v a i l a b l e a t t h e f l a n k s i n c e C e 0 on t h e s e s u r f a c e s fcr t h e f i n a l p o i n t geometryCO F u r t h e r t h e s o l i d cone i n t h e web ( c o r e ) r e g i m a l s o p r o v i d e s excess m a t e r i a l which e n a b l e s t h e c h i s e l edge to be formed by t h e g e n e r a t i o n process . The c o n d i t i o n s i n t h e v i c i n i t y of t h e event - u a l l i p can be s t u d i e d from t h e yrometry of t h e inLer- s e c t i o n of t h e i n i t i a l d r i l l p o i n t cone and t h e f l u t e s u r f a c e . I t i s found t h a t vhen 9 is s e l e c t e d such t h a t a s i n g l e flute g e n e r a t o r i n t g r s e c t s t w o cone g e n e r a t o r s a t t h e o u t e r and core r a d i i , r e s p e c t i v e l y , t h e i n t e r s e c t i o n c u r v e has an ex t remely s m a l l convex c u r v a t u r e when viewed i n a p l a n e normal t o t h e d r i l l axis (x-y p l a n e ) . Thus t h e i n i t i a l c o n e - f l u t e i n t e r - s e c t i o n c u r v e v e r y c l o s e l y approximates t h e s i n g l e f l u t e g e n e r a t o r c o n s i d e r e d a l though a s l i g h t amount of m a t e r i a l is a v a i l a b l e f o r removal when t h e f l u t e g e n e r a t o r is chosen a s t h e e v e n t u a l l i p of t h e sharp- ened d r i l l . The r e q u i r e d i n i t i a l d r i l l semi-cone s i n g l e 4 is found to depend on t h e p o i n t a n g l e 2p and web t h i c a n e s s t o d i a m e t e r r a t i o 2W/D [27] i . e .

a r e expressed by [ 1 2 ] , Y

Y ( 1 2 )

Y

From t h e above e q u a t i o n i t is c l e a r t h a t 5 w i l l be less t h a n t h e " i n t u i t i v e " c h o i c e of 9 i n i t i a l geometry, t h e i n t e r s e c t i o n o f D t h e i n i t i a l d r i l l cone and f l u t e may be used t o i d e n t i f y t h e f i n a l l i p and o u t e r c o r n e r which s i m p l i f i e s t h e i n i t i a l s e t t i n g of t h e d r i l l i n t h e g r i n d e r , i . e . s e t t i n g s Lc and 1 .

ing t h e i n i t i a l p o i n t geometry a t t h e a p p r o p r i a t e 0 (Equat ion (14)) and s e t t i n g O , x , C ,L and ,I on t h e g r i n d e r a t tachment . The d r i l l i s x t h & p o s i t i o n e d i n i t s ' i d e a l ' f i n a l l o c a t i o n by g r a d u a l l y incrementing t h e g r i n d e r a t tachment i n t h e L d i r e c t i o n w h i l e O s c i l l a t i n g a b o u t t h e g r i n d i n g done a x i s u n t i l t h e

i n i t i a l geometry is f u l l y removed i . e . L i s s a t i s - f i e d .

T h i s a n a l y s i s h a s demonstrated t h a t t h e s tudy of t h e d r i l l p o i n t g e n e r a t i o n p r o c e s s i s more i n t r i c a t e t h a n t h e a n a l y s i s f o r t h e d r i l l i n t h e ' i d e a l ' f i n a l l o c a t i o n d e p i c t e d by F i g . 1. However by a d e t a i l e d c o n s i d e r a t i o n of t h e v a r i o u s e lements t h e g e n e r a t i o n p r o c e s s can be s i m p l i f i e d and t h e p o t e n t i a l scope of t h i s g r i n d i n g method noted e a r l i e r [26] achieved when s e t t i n g e r r o r s a r e ignored .

= pp With t h i s

The g e n e r a t i o n p r o c e s s t h e r e f o r e c o n s i s t s of gr ind-

FINAL IIRILI. POINT GEOMETRY - GEWERATION PROCESS - SETTING ERRORS

I n a t t e m p t i n g to a c h i e v e t h e d e s i r e d f i n a l d r i l l p c i n t geometry, e r r o r s a r e p o s s i b l e i n s e t t i n q each of t>e f i v e main g r i n d e r parameters ( i . e . a , A , . + , C , and L 1 . A d d i t i o n a l l y , t h e i n i t i a l geometry may c 8 n t a i n f f r o r s i n 2W and i , i rh i le t h e d r i l l may be moved Loo f a r towards t h e g r i n d i n g wheel by an amount dt, d u r i n g the g r i n d e r a c t i o n element of t h e g e n e r a t i o n process . With such numerous p o t e n t i a l soi i rces of error, it i s d o u b t f u l i n o r a c t i c e i f a l l t h e s e e r r o r s can be e l i m - i n a t e d . T h e i r n e t e f f e c t w i l l be t o make i t impract- i c a l tr) p o s i t i o n t h e d r i l l i n t h e " i d e a l " f i n a l l o c a t - i o n . S o a l though t h e f i n a l g e n e r a t e d d r i l l p o i n t geometry w i l l have c o n i c a l f l a n k s i t s l i p s must be curved because u n l i k e t h e " i d e a l " c a s e i l l u s t r a t e d i n F i g . 1, t h e l i p s a r e n o t formed by a s i n g l e g r i n d i n g cone g e n e r a t o r . Thus t h e need is c r e a t e d f o r an extended a n a l y s i s t o s tudy t h e i n f l u e n c e of e r r o r s on t h e g e n e r a t e d geometry.

The a n a l y s i s p r e s e n t e d i s based on t h e " i d e a l " case and accommodates t h e g r i n d e r s e t t i n q , i n i t i a l geometry, and g r i n d e r a c t i o n errsrs d i s c u s s e d above. I t a l s o i n c l u d e s a s u i t a b l e d e f i n i t i o n of t h e g r i n d e r a c t i o n rnd p o i n t . F u r t h e r , t h e " a c c e p t a b l e g r i n d e r c r i t e r i a " e s t a b l i s h e d f o r t h e " i d e a l " c a s e [26] a r e reviewed and modi f ied . F i n a l l y , r e v i s e d d e f i n i t i o n s of t h e s p e c i f - i e d d r i l l p o i n t f e a t u r e s a r e developed and a means of measuring t h e amount of l i p c u r v a t u r e determined.

For t h e purpose Of t h e a n a l y s i s , t h e o r i g i n i s t a k e n t o be t h e p o i n t 0 on t h e d r i l l a x i s a s shown i n F i g . 1. The i n t r o d u c t i o n of s e t t i n g and g r i n d e r a c t i o n e r r o r s w i l l l e a d t o t h e d isp lacement of bo th t h e d r i l l and cone a x e s away from t h e " i d e a l " f i n a l l o c a t i o n . When t h e g r i n d e r j i g is p o s i t i o n e d a d i s - t a n c e L t r . away from t h e g r i n d i n g wheel p l a n e , t h e equat io j l s f o r t h e d isp lacement between t h e o r i g i n 0 on th? d r i l l a x i s and t h e cone apex become: C X ' = cx t dCx ( 1 5 )

C ' = C s i n ( d 0 t d x ) + C c o s ( d * + d r ) Y Z Y

t 2C s in[%]cos[$+ 5]+ 2C s i n [ Z ! c o s [ x + d i : - . ' t ~ ] dB

- (G,singI- L ) ( c o t $ - c o t ( 1 j t d 9 ) ) s in!HtiAdatdu)

t s i n ( y t d x ) c o s e c ( e + do) . \ (16)

P 2 2 q

Cz' = Cz cos(d0 + d i ) - C s i n ( d . 1 + dX) Y

(20)

I t is noted t h a t i n t h e " i d e a l " c a s e when do, d r , dCx, dLc and A e o u a l z e r o , Equat ions ( 1 5 ) - ( 1 7 ) r e v e r t , a s expec ted , t o Cx '=Cx , C '=C

The e q u a t i o n s f o r a p o i n t x , y , z on t h e g r i n d i n g cone 1 can then be detgrmised from:

and C z ' = C z . Y Y

x = ( y , + c ' ) t a v A ' - cx' ( 2 2 ) Y zc = (yc + C y ' ) t a n v ' - C Z '

where t h e a n g l e s > ' and Y ' can b e i n t e r r e l a t e d u s i n g a modif ied v e r s i o n of t h e " i d e a l " c a s e Equat ion (1) and s u b e t i t u t i n g 4 + dq and x + d i f o r 9 and x r e s p e c t i v e l y .

A t a r a d i u s r , a p o i n t x on a g e n e r a l f l u t e g e n e r a t o r may be d e t e g h i % %om t h e fo l lowing e x p r e s s i o n s ( w i t h r e f e r e n c e t o o r i g i n 0 on t h e d r i l l axis) : xf = r s i n ( i t 9 + dh - 6)')

yf = r cos()i t h t d i - i u ' )

zf = (Wtanh + rcos , , , ' )cotp + [*$]cot(6,t dS)

(23)

(24) (25)

(26) where, s inw' = W 7- t dW

and G r e p r e s e n t s t h e i n c l i n a t i o n between t h e p r o j e c t - i o n s of t h e g e n e r a l and r e f e r e n c e f l u t e g e n e r a t o r s i n a p l a n e normal t o t h e d r i l l a x i s . The r e f e r e n c e f l u t e g e n e r a t o r i n t u r n r e p r e s e n t s t h e g e n e r a t o r i n c l i n e d by t h e error a n g l e dA t o t h e g e n e r a t o r which forms t h e

s t r a i g h t l i p when t h e d r i l l i s p o s i t i o n e d i n t h e " i d e a l " f i n a l l o c a t i o n .

d r i l l cone g e n e r a t o r t R e '8' e u a t 'f ons t a k e t h e form: xD = r s i n e

yD = CoSE zD = r c c t 9

where i~.' i s found by s u b s t i t u t i n g r = D i n Equat ion (27) and E is t h e a n g l e between t h e p r o j e c t i o n s of t h e g e n e r a l i n i t i a l d r i l l cone g e n e r a t o r and t h e y- a x i s i n a p lane normal t o t h e d r i l l a x i s .

p o i n t can b c e s t a b l i s h e d and t h e r e s u l t a n t f i n a l d r i l l p o i n t geometry found. I t i s a p p a r e n t t h a t t h e s e e q u a t i o n s a r e f a i r l y complex and i n v o l v e v a r i a b l e s which a r e d i f f i c u l t t o s e p a r a t e . Hence i t was necess- a r y t o u s e i t e r a t i v e s o l u t i o n s e a r c h techniques t o de termine t h e g r i n d e r a c t i o n end p o i n t . The l a r g e number of c a l c u l a t i o n s involved was expedi ted by developing and us ing a s u b s t a n t i a l computer programme

I n broad terms, t h e method of de te rmining t h e g r i n d e r a c t i o n end p o i n t i s t o f i r s t select v a l u e s of t h e commonly s p e c i f i e d d r i l l p o i n t f e a t u r e s t o g e t h e r w i t h s i z e s of t h e g r i n d e r s e t t i n g , i n i t i a l geometry, and g r i n d e r a c t i o n errors. The " i d e a l " c a s e g r i n d i n g and g r i n d e r parameter v a l u e s a r e t h e n c a l c u l a t e d from Equat ions (1) - (13) and t h e i n i t i a l d r i l l semi-cone a n g l e 8 de te rmined u s i n g Equat ion ( 1 4 ) . Equat ions (28)-(3B) a r e used t o s e l e c t a p o i n t on t h e i n i t i a l d r i l l cone. The p o i n t on t h e g r i n d i n g cone a t which x =x and y =y i s then found from Equat ions ( 1 5 ) - ( 2 3 ) . Tfiesg two g h B s of e q u a t i o n s a r e i t e r a t e d f o r . ? t ill t h e c o n d i t i o n z =z is s a t i s f i e d . By r e p e a t i n g t h e above s t e p s forCa Eomprehensive g r i d of p o i n t s on t h e i n i t i a l d r i l l cone a minimum v a l u e of.! can be e s t a b - l i s h e d . T h i s r e p r e s e n t s t h e l a s t p o i n t on t h e i n i t i a l d r i l l cone removed by t h e g r i n d i n g cone. S u b t r a c t i n g dA from t h e minimum h v a l u e g i v e s t h e g r i n d e r a c t i o n end p o i n t when errors o c c u r .

The f i n a l d r i l l p o i n t geometry genera ted a t t h e g r i n d e r a c t i o n end p o i n t must , i n a s i m i l a r f a s h i o n t o t h e " i d e a l " c a s e , m e e t c e r t a i n shape c o n s t r a i n t s i f i t s g e n e r a l appearance i s t o be cons idered accept - a b l e . With e r r o r s p r e s e n t , t h e seven " a c c e p t a b l e

g r i n d e r criteria" e s t a b l i s h e d 1261 a r e reduced to t h e fo l lowing f i v e c r i t e r i a :

F i n a l l y , a p o i n t x , on t h e g e n e r a l i n i t i a l

+ WtanAcotp + n(cosh:co tp - c o t c D ) (30) D 2

Using Equat ions ( 1 5 ) - ( 3 0 ) , t h e g r i n d e r a c t i o n end

~ 2 7 1 .

1.

2.

3 .

4.

5.

The d r i l l p o i n t r e g i o n should be symmetr ical about t h e d r i l l a x i s . The d r i l l f l a n k s u r f a c e bounded by t h e l i p , c h i s e l edge , d r i l l p o i n t h e e l , and f l u t e d land should be a cont inuous s u r f a c e . The c h i s e l edge should j o i n t h e l i p a t t h e c h i s e l edge c o r n e r . The c l e a r a n c e a t a l l p o i n t s on t h e angular f l a n k r e g i o n between t h e o u t e r c o r n e r and t h e c h i s e l edge c o r n e r should be s u f f i c i e n t t o p r e v e n t i n t e r f e r e n c e w i t h t h e t r a n s i e n t s u r f a c e d u r i n g d r i l l i n g . C o n d i t i o n s (1) t o ( 4 ) should be s a t i s f i e d when a t t e m p t i n g to achieve t h e recommended ranggs of t h e s p e g i f i e 8 d r i l l g o i n t f e a t u r s i.e. 2p=118 ; Q= 120 -135 : CLn=8 -16'; 6,,=2C -32O; 2W/D=12%-20%. %

- The modes of f a i l u r e of t h e above c r i t e r i a a r e

i d e n t i c a l t o t h e " i d e a l " c o n i c a l g r i n d i n g method [26] w i t h t h e e x c e p t i o n s t h a t c r i t e r i o n 3 may be f a i l e d by t h e c h i s e l edge i n t e r s e c t i n g t h e d r i l l p o i n t h e e l and c r i t e r i o n 4 may n o t be m e t due t o t h e l i p c l e a r r n c e angrle becoming n e g a t i v e .

e r a t e d a t t h e g r i n d e r a c t i o n end p o i n t , co-ord ina tes f o r p o i n t s on t h e d r i l l f l a n k were found from Equat- i o n s ( 1 5 ) - ( 2 3 ) . Combining t h e s e e q u a t i o n s w i t h Equat ions ( 2 4 ) - ( 2 7 ) f o r t h e d r i l l f l u t e and i t e r a t i n g f o r $ till t h e c o n d i t i o n z =z w a s s a t i s f i e d , t h e d r i l l l i p co-ord ina tes w e & e s t a b l i s h e d . F i n a l l y , t h e c h i s e l edge c o - o r d i n a t e s were found from Equat ion (23) and a modif ied v e r s i o n of t h e " i d e a l " c a s e Equat ion ( 6 ) w i t h C x ' , C I , R + d B , and x+dx s u b s t i t u t e d f o r Cx, C

With t h e g e n e r a t e d l i p s being curved , r e v i s e d d e f i n i t i o n s w e r e needed f o r t h e g e n e r a t e d p o i n t f e a t u r e s such as t h e p o i n t angle . Three r e v i s e d d e f i n i t i o n s were d e r i v e d us ing t h e concept of an "average" d r i l l l i p formed by j o i n i n g t h e o u t e r and c h i s e l edge c o r n e r s w i t h a s t r a i g h t l i n e . The aver - age p o i n t a n g l e 2p d i r e c t l y based on t h e "average" l i p w h i l e t h e average c h i s e l edge a n g l e $ was a l s o r e q u i r e d u s e of modif ied v e r s i o n s of Equat iohs ( 7 ) and ( 8 ) developed f o r t h e " i d e a l " c a s e . S i m i l a r l y , t h e c l e a r a n c e a n g l e CZ ' was obta ined us ing a modif ied v e r s i o n of t h e " i d e a l " c a s e Equat ion (10). I n both c a s e s , t h e m o d i f i c a t i o n s involved s u b s t i t u t i n g t h e error c a s e f o r t h e " i d e a l "

I n d e s c r i b i n g t h e f i n a l d r i l l point-geometry gen-

a , and y r e s p e c t i v e l y . Y '

and average l i p spac ing 2WA were

c a s e va lues c .g . $',+dt. f n r t i . F i n a l l y , t h e l i p curva t - u r e was determined i n t h e x-y p lane (,',xy) and y-z p lane (!.yz) by e s t a b l i s h i n g t h e amount of d e p a r t u r e of t h e curved l i p from t h e "average" l i p . Scope of Conica l Grinding w i t h Errors

The " a c c e p t a b l c g r i n d e r c r i t e r i a " w e r e used t o a s s e s s t h e g e n e r a t e d f i n a l d r i l l p o i n t geometry f o r a l a r g e number of g e n e r a l purpose combinat ions of d r i l l p o i n t f e a t u r e v a l u e s . A s i n d i c a t e d i n t a b l e 1, 80 combinat ions of 0 , CI , 2W/D and h e l i x a n g l e x . were t e 8 t e d t o g e t h e r wi th 9 0 v a l u e s of 2 over t h e range 31 -50° ( i . e . lo i n t e r v a l s ) . T h i s gave a t o t a l of 80120 = 1 6 0 0 combinat ions which were examined. The combined e f f e c t s of t h e 8 e r r o r s a<,, dw, d ; , dC , dL , d a , dW and d i , were s t u d i e d by s imul taneous ly a5plyifig t h c worst c a s e l i m i t s f o r each error. The f i g u r e s s e l e c t e d f o r t h e 8 errors were dil, d:? t .5O: d l ! 2O; dCx, dL I .002", dh + .002"; dW 1 .0013": and d t : 1C28O. The g r i n d e r s e t t i n p and p o s i t i o n i n g ergors were d e r i v c d f r o n c o n s i d e r a t i o n of t h e r e l e v a n t s e t t i n g mechanisms w h i l e t h e i n i t i a l geometry e r r o r s wcre obta ined from an e a r l i e r p r o c e s s c a p a b i l i t y s tudy 1191. From t a b l e 1 it i s a p p a r e n t t h a t i n con- t r a s t t o t h e " i d e a l " c a s e ( i . e . z e r o e r r o r s ) , a t 26 ( o r 32%) of t h e 80 geometr ic combina t ions , no accept - a b l e f i n a l d r i l l p o i n t geometry could be produced t h u s f a i l i n g c r i t e r i o n 5. For t h e remaining combinat- i o n s , upper l i m i t s for fi were g e n e r a l l y due t o t h e f a i l u r e of c r i t e r i o n 4 i n t h a t t h e c i r c u m f e r e n t i a l c l e a r a n r e a n g l e C1 [ 2 4 ] was inadequate w h i l e t h e l o w e r l i m i t s w e r e &own t o r e s u l t from e i t h e r no or a second c h i s e l edge c o r n e r be ing g e n e r a t e d Thus n o t meet ing c r i t e r i o n 3. I n t o t a l , of t h e 1600 combinat- i o n s cons idered , a t some 688 (or 435) t h e d r i l l p o i n t geometry g e n e r a t e d was unacceptab le . Hence t h e presence of r e l a t i v e l y smal l e r r o r s has been demon- s t r a t e d t o s u b s t a n t i a l l y reduce t h e scope of c o n i c a l g r i n d i n g and p l a c e s i g n i f i c a n t r e s t r i c t i o n s on t h e v a l u e of .? which may be s e l e c t e d . L i p Curva ture and Prominent D r i l l P o i n t F e a t u r e s

The combined e f f e c t s of errors on t h e genera ted l i p c u r v a t u r e and d r i l l p o i n t f e a t u r e v a l u e s have been examined f o r s e v e r a l combinat ions of t h e spec- i f i e d d r i l l p o i n t f e a t u r e s and g r i n d e r semi-cone a n g l e 4 a t which t h e " a c c e p t a b l e g r i n d e r c r i t e r i a " w e r e s a t i s f i e d . A sample of t h e s e r e s u l t s is i l l u s t - r a t e d i n t a b l e 2 . For each of t h e 11 geometr ic combinat ions l i s t e d , t h e combined w o r s t c a s e l i m i t s

TABLE 1. Combined e f f e c t s of d e v i a t i o n s on scope of c o n i c a l d r i l l F o i n t g r i n d e r model led. (2p = 118O i n a l l c a s e s ) IDEAL CASE ( i . e . z e r o errors)

D = 1" D = 1 / 2 "

$\cyo 8 10 1 2 1 4 16

125 * * 130 * * * 135 ,34 .33 ,31 * *

120 * * r-T--T-

D = 1 / 4 "

g\"'o 8 10 1 2 1 4 16 120 * * * * * 125 * * * * * 130 * * * * 1 3 5 i 3 3 * * *

COMBINED EFFECTS

D = 1" D = 1/2"

, >v 'o 8 10 12 1 4 16 b\"o 8 10 11 1 4 16 1 2 0 <43 <42 e42 d 4 0 e35 120 .45 ~ 4 5 <45 e45 ~ 4 2 125 <48 <49 -50 * * 125 -50 ~ 5 0 * * * 130 n 34-37* * * 130 n 33-42* * * 1 3 5 n n n n n 135 n n n n n

D = 1 / 4 " D = 1/8" v\'*o 8 1 0 12 14 16 b\"o 8 10 1 2 14 16

120 *46 .46 <47 .47 *47 120 ~ 4 5 .46 *47 .48 ~ 4 9 125 <SO * * * 125 <50 * * * * 130 n n * * * 130 n n ~ 4 8 * * 1 3 5 n n n n r . 1 3 5 n n n n n

-

---

Symbols: * - combinat ion a c c e p t a b l e ( a l & g r i n d e r

n - combinat ion unacceptab le Agrindgr c r i t e r i a m e t , ti = 31° - 50 ) .

c r i t e r i o n n o t m e t , r) = 3 1 - 50 ) .

= 32O- f o r D = $", 2W/D = 14% and 6 " = 30°:

D = k " , 2W/D = 17% and 6 " = 26O: and fo r

When D = 1". 2W/D = 1 2 % and F

f o r D = 2W/D = 20% and"b3 = 2bo.

4

o f t h e 8 errors c o n s i d e r c d i n t h i s i n v e s t i g a t i o r were appl ied a t t h e levels l i s ted p r e v i o u s l y . From t a b l e 2 i t c a n b e s e e n t h a t t h e l i p c u r v a t u r c ? i s i n a l l cases q u i t e smal l . A s t h e maxim!im m a g n i t u d e o f t h e c u r v a t u r c componen t s was J mere .003 ( f o r ' > x y / D ) , t h e g e n e r a t e d l i p s c a n f o r p r a c t i c a l p u r p o s e s b e r e g a r d e d as s t r a i g h t l i n e s . Gi7Jen t h a t a l l t h e " a c c e p t a b l c g r i n d e r criteria' are a l s o s a t i s f i e d , t h e s e r e s u l t s s u g g e s t t h a t t h e g e n e r a l a p p e a r a n c e of t h e g e n e r a t e d p o i n t g e o m e t r y is n o t a r e l i a b l e i n d i c a t o r o f t h e p r e s e n c e o r e f f e c t s of g r i n d e r s e t t i n g errors.

The l i m i t e d Lip c u r v a t u r e a l s o i m p l i e s t h a t t h e g e n e r a t e d p o i n t f e a t u r e s c a n b e t reated as p h y s i c a l r e p r e s e n t a t i o n s o f t h e i r " i d e a l " case c o u n t e r p a r t s . From t a b l e 2 it is a p p a r e n t t h a t t h e combined errors s u b s t a n t i a l l y a f f e c t t h e v a l u e s o f t h e g e n e r a t e ? p o i n t f e a t u r e s . F o r i n s t a n c e i n a l l 11 cases, t h e r a n g e o f 2p r e a c h i n g 6.9'. v a l u e s is a s i g n i f i c a n t 4 .8 . :mWAseems p a r t i c u l a r l y s e n s i t i v e to errors . I n 3 of the 11 cases i i l u s t r a t e d , t h e g e n e r a t e d r a n g e o f i exceeded t h e recomnended q e n e r a l p u r p o s e r a n g e f o r A t h i s f e a t u r e o f 15' (12Oo-13So) w h i l e t h e naximum r a n g e of v c o n s i d e r e d ? ,, t o d . b u t s u r ~ r i s i n g l y i t d ; . S i m i l a r l y , d ; a n d d; h a d t h e a n t i c i p a t e d major i n f l u e n c e on 2p w h i l e dW s i g n i f i c a n t l y a f f e c t e d 2W ' . The r e s u l t s i n A t a b l e 2 show t h a t t h e g e n e r a t e d d r i P l p o i n t f e a t u r e r a n g e s s t r a d d l e t h e c o r r e s p o n d i n g " i d e a l " s p e c i f i e d v a l u e s . However , d i f f i c u l t i e s a re l i k e l y t o b e e n c o u n t e r e d i n t h e a c h i c v e m e n t and con t ro l o f a p a r t i c u l a r set of recommended g e n e r a l p u r p o s e f e a t u r e v a l u e s . F u r t h e r when t h e nomina l d e s i g n v a l u e s d i f f e r f rom b a t c h t o b o t c h t .he t o t a l sca t te r i n t h e q e n e r a t e d p o i n t f c a t u r e v a l u e s c a n b e e x t r e m c l y w i d e . F o r e x a n p l e , f r o g tab&' 2 , when I is s e l e c t e d w i t h i n t h c l i m i t s 120 -130 t h e g g n e r a t c d va lue o f 3.) a r a n g e o f 28 .3 . I t s h o u l d be n o t c d t h a t a s f a i r l y l o w l e v e l s o f errors h a v e b e e n c o n s i d e r e d i n t h i s i n v e s t i g a t i o n , t h e s u b s t a n t i a l p o i n t f e a t u r e v a r i a t . - i o n s shown i n t ab l e 2 may w e l l b e c o n s e r v a t i v e w h i l e t h e g e n e r a l p u r p o s e scope i l l u s t r a t e d i n t a b l e 1 c o u l d be e v e n f u r t h e r r e d u c e d .

v a l u e s e x c e e d s 46 w i t h t h e maximum r a n g e S i m i l a r l y , &he maximum r a n g e o f C .

A l t h o u g h t h e r a n g e s o o f ' i D are f a i r l y moderate ( i . e . 2 .6% max.; t h e a n g l e

'

w a s a s h i g h as 16.6O. Of t h e 8 errors was found t o b e , as e x p e c t e d , s e n s i t i v e

w a s e v e n more s e n s i t i v e t o

is shown t o v a r y f rom 112 .4 -138 .7

TABLE 2 . Combined e f f e c t s of d e v i a t i o n s on s a l i e n t f e a t u r e s of f i n a l d r i l l p o i n t g e o m r t r y .

MAX PlAX

A D 2p 1, C ! *y/3 fyz /D 2pA , -_----I - ---__ll----___l

f 1 1 8 1 2 0 8 42 Hi .001 - 1 2 0 . 1 128 .2 9 . 5 L-.OOl - 1 1 5 . 7 112 .4 6 . 9 R 4 .4 15 .8 2.6

3 1 H+.001 - 1 2 0 . 1 126 .5 l G . 2 L-.OO2 - 1 1 5 . 7 113 .7 6 . d R 4.4 12 .9 3 .8

f 1 1 8 1 2 0 1 6 42 H i . 0 0 2 + .001 1 2 0 . 5 125 .7 17 .4 L - . 0 0 2 - . 001 115 .0 1 1 4 . 2 14 .7 R 5 . 5 1 1 . 5 2 .7

31 Hi.002 - 1 2 0 . 5 124 .7 1 7 . 3 L-.002 - . 001 114 .9 1 1 5 . 1 15.0 R 5 . 6 9 .6 2 .3

$j 1 1 8 130 16 42 H+.COl - L-.002 -.001 R

L-.002 - . 001 R

1 118 120 8 42 €1+.002 - L-.002 - R

3 1 H+.001 - L-.002 -.OOl R

1 118 120 16 3 1 Hc.002 +.001 L-.003 - . 001 R

1 118 130 16 42 H+.OOZ +.001 L- .003 - . 0 0 1 R

3 1 H+.OO2 +.OOl L-.003 -.OOl R

31 H+.OOl -

1 2 0 . 5 138 .4 114 .9 121 .9

5.6 1 6 . 5 1 2 0 . 5 1 3 6 . 8 1 1 4 . 8 123 .5

5.7 1 3 . 3

1 2 0 . 3 127 .6 1 1 5 . 7 1 1 3 . 3

4.6 1 4 . 3 120 .4 125 .3 1 1 5 . 7 1 1 5 . 0

4 .7 1 0 . 3

120 .7 123 .6 114 .6 116.0

6 . 1 7.6

120 .6 138 .7 114 .6 1 2 2 . 1

6 .0 16.6 120 .8 136 .4 114 .6 124 .0

6 . 2 1 2 . 4

18.0 1 4 . 4

3.5 18 .7 1 4 . 1

4 .6

9 .4 6 . 8 2.6

1 0 . 2 6 .0 4 . 2

17 .O 15 .2 1.8

1 7 . 8 14 .4

3 .4 18 .6 13 .8

4 .8

2WI;/D

1 8 . 2 15 .9

2 . 3 1 8 . 1 1 5 . 8

2 . 3

1 8 . 2 15 .8

2 .4 1 8 . 2 1 5 . 8

2 .4

1 8 . 3 1 5 . 8

2 . 5 18 .3 1 5 . 7

2.6

12 .3 1 1 . 7

.6 1 2 . 3 11 .7

.6

1 2 . 3 11 .7

.6

1 2 . 3 11 .7

.6 1 2 . 3 11 .7

.6

Note: When D = f " , 2W/D=171 and A =26O and when D = l " , 2W/D=12?: a n d 4::=32O

H - maximum v a l u e o f g e n e r a t e d f e a t u r e L - minimum v a l u e o f g e n e r a t e d f e a t u r r R - r a n q e of n e n e r a t e d f c ~ 3 t u r c s .

c o ~ c L , v s I o r ; s

The f i n a l d r i l l p o i n t g e o m e t r y g e n e r a t i o n p r o c e s s for g e n e r a l p u r p o s e t w i s t d r i l l s u s i n g t h e p o p u l a r c o n i c a l g r i n d i n g method h a s 'm3en a n a l y s c d b o t h i n t h e a b s e n c e ! i . e . " i d e a l " case) and p r e s e n c e of g r i n d e r s e t t i n g e r r o r s . I t i s shown t h a t t h e a n a l y s i s f o r r e l a t i n y t h e s p e c i f i e d d r i l . 1 p o i n t f e a t u r e s t o t h e g r i n d i n g p a r a m c t e r s when t h e d r i l l i s i n t h e " i d e a l " f i n a l 1 . o t a t i o n r e p r e s e r . t s o n l y p a r t o f t h e g e n e r a t i o n p r o c e s s . The i n i t i a l d r i l l p o i n t g e o m e t r y , t h e s e t t i n g o f t h e d r i l l i n t h e g r i n d e r , t h e g r i n d e r a c t i o n d u r i n g wh ich t h e i n i t i a l g e o m e t r y is removed a n d t h e i d e n t i f i c a t i o n o f t h e g r i n d e r a c t i o n e n d p o i n t c o n s t i t u t e t h e f o u r m a j o r e l e m e n t s wh ich c o n t r i b u t e t o t h e c o m p l e x i t y 3f t h e d r i l l p o i n t g e n e r a t i o n process. The d e t a i l e d a n a l y s i s o f t h e s e e l e m e n t s r e s u l t e d i n a n i n i t i a l d r i l l p o i n t g e o m e t r y and g r i n d e r d e s i g n c a p a b l e o f p r o d u c i n g a l l t h e r eco rn tend- e d s p e c i f i e d d r i l l p o i n t f e a t u r e xvalues fo r t h e " i d e a l " case of z e r o s e t t i n q errors.

The nore complex a n a l y s i s a n d g e n e r a t e d d r i l l po in t s h a p e d u e to t h e i n t r o d u c t i o n o f s e t t i n g errors n e c e s s i t a t e d r e a p p r a i s a l of " a c c e p t a b l e y r i n d c r c r i te r ia" and d r i l l p o i n t f e a t u r e d e f i n i t i o n s . The p r e s e n c e o f r e l a t i v e l y s m a l l g r i n d e r s e t t i n o errors l e a d t o a s i g n i f i c a n t r e d u c t i o n i n t h e s c o p e of c o n i c a l g r i n d i n g f o r g e n e r a l p u r p o s e d r i l l s . Of t h e 80 g e n e r a l p u r p o s e c o m b i n a t i o n s of d r i l l p o i n t f e a t u r e v a l u e s ?.n a c c e p t a b l e s h a p e is o n l y g e n e r a t e d a t 54 ( i . e . 68%) c o m b i n a t i o n s . W i t h i n t h e r e d u c e d scope, t h e amoullt of l i p c u r v a t u r e f o r a c c e p t a b l e d r i l l p o i n t s h a p e s was shown to b e n e g l i g i b l e a l t h o u g h s m a l l s e t t i n g errors r e s u l t e d i n wide v a r i a t i o n s i n t h e v a l u e s o f t h e g e n e r a t e d f e a t u r e s ! e g 1.6.6" for r a n g e ) . i l ence i t h a s b e e n d e m o n s t r a t e d t h a t i n i t s e l f t h e q e n e r a l a p p e a r a n c e of t h e g e n e r a t e d p o i n t g e o m e t r y is a n u n r e l i a b l e i n d i c a t o r o f t h e p r e s e n c e or e f f e c t s o f s e t t i n g errors f o r u s e i n q u a l i t y c o n t r o l . F u r t h e r , t h P g e n e r a t e d p o i n t f e a t u r e s h a v e b e e n shown to b e p a r t i c u l a r l y s e n s i t i v e to a number o f s e t t i n g errors.

T h i s s t u d y h a s h i g h l i g h t e d t h e c o m p l e x i t i e s o f t h e g e n e r a t i o n p r o c e s s and t h e a t t e n d a n t d i f f i c u l t i e s i n a c h i e v i n g and c o n t r o l l i n g t h e s p e c i f i e d d r i l l p o i n t geornc t ry n o t e d i n p r a c t i c e .

A

1.

2.

3 .

4 . 5 .

6 . 7. 8 .

9 .

10 . 11. 1 2 .

1 3 .

1 4 .

1 5 .

1 6 .

1 7 .

1 8 .

19.

2 0 .

2 1 .

22 .

2 3 .

2 4 .

25 .

26 .

27 .

REFERENCES

C. DONALDSON, G . H . Le CAIN a n d V.C. GOULD, " T o o l D e s i g p " , McGraw-Hill , N e w J e r s e y (1969) . A. S .T.M.E., " T o o l E n g i n e e r s ' IIandbook" , McGraw-11111, N e w Y o r k , ( 1 9 5 8 ) . METAL CUTTING TOOL INSTITUTE, "Metal C u t t i n q T o o l Handbook", ( 1 9 6 9 ) . AMERICAN STANDARD, USAS, H94-11-1967. BRITISH STANDARD INSTITUTION, B .S .328 , P a r t I- 1959 . AUSTRALIAN STANDARD, A.S.2438-1981. G . M . H . STANDARD, " C u t t i n g T o o l s " , ( 1 9 6 8 ) . E . J . A . ARMAREGO and J . D . WRIGHT. J. Engg. P r o d . , 2 . 1. ( 1 9 7 8 ) . . . c. ROHLKE, W e r k s t a t t s t e c h n i k and Masch inenbau , 47 , 5 , ( 1 9 5 7 ) . M . D . K I N M A N , M a c h i n e r y , 102, ( 1 9 6 3 ) . W . D . ARNOT, M e c h a n i c a l World, 1 1 4 , March ( 1 9 5 2 ) . E . J . A . ARMAREGO a n d A. ROTENBERG, 1 n t . J . M a c h . T o o l D e s . R e s . , 13, 1 8 3 , ( 1 9 7 3 ) . D.F. GALLOWAY, T r a n s . Amer. SOC. Mech. E n g r s . , 7 9 , 1 9 1 , ( 1 9 5 7 ) . G.F. MICflELETTI a n d R . LEVI, P r o c . o f 8 t h I n t . M.T.D.R. C o n f . , U n i v e r s i t y o f N a n c h e s t e r , S e p t . , ( 1 9 6 7 ) . fl. MALKIEWTCZ, M.Enq.Sc. T h e s i s , U n i v e r s i t v o f

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Melbourne ( 1 9 7 3 ) . S . KALDOR a n d E . LENZ, A n n a l s o f t h e CIRP, 2, 1, ( 1 9 8 0 ) . C .S . OXFORD J N R , A.S.T.E. c o l l e c t e d p a p e r s , 2, ( 1 9 5 9 ) .

J . D . WRIGHT, M.Eng.Sc. T h e s i s , U n i v e r s i t y o f M e l b o u r n e , ( 1 5 7 5 ) . E.J.A. ARMAREGO and J . D . WRIGHT, J . Cngg. P r o d . 2 , 2 , ( 1 9 7 8 ) . I. MUSHTAQ, M.Ena.Sc. T h e s i s , U n i v e r s i t y of Melbourne ( 1 9 8 0 ) . S. F U J I I , M.L. DeVRIES a n d S.M. W U , J. o f Eng. I n d . , 92, ( 1 9 7 0 ) .

I n d . , 9 3 , ( 1 9 7 1 ) . W . D . TSAI a n d S.M. WU, I n t . J . Mach. T o o l D e s . R e s . , 1 9 , 9 5 , ( 1 9 7 9 ) . E.J.A.-jiRMAREGO a n d A . ROTENBERG, I n t . J. Mach. T o o l Des. R e s . , 2, 155 a n d 1 6 5 , ( 1 9 7 3 ) . F.K.T. Y A N , M . Eng. Sc . T h e s i s , U n i v e r s i t y of H e l b o u r n e ( 1 9 7 4 ) . E .J .A. ARMAREGO a n d J.D. WRIGHT, Annals of t h e CIHP, 2, 1, ( 1 9 8 0 ) . J . D . WRIGHT, Ph.D. T h e s i s , i i n i v e r s i t y of Melbourne ( 1 9 8 1 ) .

S. F U J I I , M.L. DCVRIES a n d S.M. WU, J. of Eng.

5