Interdependence Between Tool Fracture and Wear

Interdependence Between Tool Fracture and Wear N. Alberti ( l ) , S. Noto La Diega, A. Passannanti, Dipartimento di Tecnologia e Produzione Meccanica, Universita di Palermo/ltaly

Wear and f r a c t u r e are t h e main causes o f t o o l scrapping. However f r a c t u r e plays a major r o l e f o r increasing values o f t h e hardness and b r i t t l e n e s s o f t o o l m a t e r i a l s o r when low-cobalt tungsten carbides a r e used o r i n i n t e r r u p t e d c u t t i n g c o n d i t i o n s where i t i s t h e most r e l e v a n t f a c t o r f o r t o o l scrapping. I n order t o o b t a i n t h e optimal values o f the c u t t i n g speed both these f a c t o r s should be considered. The hypothesis of stochastic independence among them s i m p l i f i e s the mathematical formulation of t h e o p t i m i z a t i o n problem; b u t experimental i n v e s t i g a t i o n s do n o t agree w i t h t h i s assumption and, as a matter of f a c t , the p r o b a b i l i t y d e n s i t y function of t o o l f r a c t u r e r e s u l t s t o be dependent on the wear conditions. I n t h e paper some experimental r e s u l t s w i l l be reported; these r e s u l t s are then applied t o t h e e v a l u a t i o n o f t h e optimal c u t t i n g speed and t o o l replacement p o l i c y .

INTRODUCTION I n t h e l a s t vears i t has been recoanized t h a t t h e Droaress i v e wear i s n o t - t h e o n l y mechanism t o o l f a i l u r e i n metal c u t t i n g ; f o r increasing values o f t h e hardness and b r i t t l e n e s s o f t o o l m a t e r i a l s , sudden t o o l f a i l u r e s can occur by f r a c t u r e o r by c h i p p i n g Ill,c21, 13). Several models have been proposed t o determine t h e optimum metal c u t t i n g c o n d i t i o n s when t h e t o o l l i f e d i s t r i b u t i o n i s a f f e c t e d by two o r more d i f f e r e n t f a i l u r e modes. The most used probability distribution functions t o define the tochastic phenomenon o f t h e f r a c t u r e a r e t h e exponential 145 and t h e Weibull [ S l w h i l e t h e log-normal d i s t r i b u t i o n i s u s u a l l y employed t o describe t h e collapse by wear. The o v e r a l l p r o b a b i l i t y d i s t r i b u t i o n o f t o o l l i f e , t a k i n g i n t o account f r a c t u r e and wear, i s always obtained under the hypothesis o f s t o c h a s t i c independence among t h e f a i l u r e modes o f t h e c u t t i n g edge. This assumption s i m p l i f i e s t h e mathematic a l f o r m u l a t i o n o f t h e o p t i m i z a t i o n problem but; f o r a m r e accurate a n a l y s i s , t h e i n t e r a c t i o n s between f r a c t u r e and wear must be taken i n t o account. Recently a p r o b a b i l i s t i c model, f o r t o o l f r a c t u r e , has been developed under t h e hypothesis t h a t t h e f r a c t u r e r e s i stance o f t h e c u t t i n t o o l i s a l i n e a r l y decreasing f u n c t i o n o f t h e c u t t i n g time [67, 173. The purpose o f t h i s paper i s t o present the r e s u l t s o f sev e r a l experimental t e s t s i n i n t e r r u p t e d c u t t i n g , c a r r i e d out using carbide i n s e r t s subjected t o d i f f e r e n t values o f wear. These t e s t s c o n f i r m t h a t t h e Weibull f u n c t i o n i s the best s u i t e d t o describe t h e f a i l u r e of t h e t o o l caused by f r a c t u r e , b u t show t h a t i t s scale parameter i s a f f e c t e d by t h e value o f t o o l wear. P a r t i c u l a r l y , t h e r e s u l t s i n d i c a t e t h a t the mean l i f e t o f r a c t u r e remains q u i t e constant f o r low values o f wear and, adversely, i t decreases f o r h i g h values o f the wear o f t h e c u t t i n g t o o l . This means t h a t i t can be assumed t h a t wear does n o t a f f e c t f r a c t u r e when t h e t o o l has c u t f o r a s h o r t time, w h i l e the f r a c t u r e resistance s t r o n g l y decreases when t h e t o o l has c u t f o r a h i g h f r a c t i o n o f i t s u s e f u l wear l i f e . L a t e r on, these r e s u l t s have been employed t o f i n d the optimal t o o l replacement p o l i c y and t h e optimal c u t t i n g speed developing a model which takes i n t o account t h e v a r i a t i o n s o f t h e l i f e t o f r a c t u r e due t o progressive wear.

OF

EXPERIMENTAL RESULTS AN0 ANALYSIS I n order t o determine t h e i n f l u e n c e o f wear on the stochas t i c behavior t o f r a c t u r e o f carbide i n s e r t s two d i f f e r e n t types o f t e s t s were c a r r i e d o u t under constant machining conditions: t e s t s t o f r a c t u r e on a l o t of carbide i n s e r t s as supplied; t e s t s t o f r a c t u r e on f i v e l o t s of carbide i n s e r t s w i t h d i f f e r e n t values o f wear. Sintered carbide i n s e r t s P10 and A I S I C1040 s t e e l were employed i n i n t e r r u p t e d t u r n i n using a workpiece holder a l l o w i n g f o u r shocks per r e v o l u t i o n q61. The f r a c t u r e o f the t o o l s was displayed by c u t t i n g f o r c e v a r i a t i o n s ; nevertheless i n some cases these v a r i a t i o n s were n o t evident; i n these circumstances t h e t e s t s were p e r i o d i c a l l y stopped i n order t o check t h e c u t t i n g edge; i f the c u t t i n g edge was broken, t h e exact number o f shocks before c o l l a p s i n g was ascertained through a more accurate exam o f t h e c u t t i n g f o r c e record. A l l t h e t e s t s were performed w i t h t h e f o l l o w i n g c u t t i n g parameters:

-

depth o f c u t - 1.5 mn; feed= 0.4 mn/rev; c u t t i n g speed= 180 m/min Using the same parameters i n continuous t u r n i n g , d i f f e r e n t values o f t h e p r e l i m i n a r y wear o f carbide i n s e r t s were obtained v a r y i n g t h e t u r n i n g time. A l o t of 55 edges as supplied and f i v e l o t s of 15 pre-worn i n s e r t s were t e s t e d i n i n t e r m i t t e n t c u t t i n g . The wear condit i o n s r e s u l t i n g from t h e p r e l i m i n a r y continuous t u r n i n g were checked using a contact surface t e s t e r and, f o r each value o f t h e t u r n i n g t i m e , t h e f o l l o w i n g mean values o f t h e c r a t e r r a t i o

Annals of the CIRP Vol. 34/1/1985

K were ascertained:

c u t t i n g time (min) crater ratio

Lot 2 1 0.004

Lot 3 5 0.025

Lot 4 10 0.045

Lot 5 15 0.076

Lot 6 20 0.10

The t o o l l i v e s ( i n minutes) o f t h e t e s t e d i n s e r t s are reported i n Tab. 1 and 2. Lot 1 0.5407 0.5751 0.6096 0.6199 0.6612 0.9436 0.9798 1.0434 1.2191 1.2225 1.3034 Tab. 1

1.3052 1.5789 1.7838 1.8011 1.8045 1.8252 1.8889 1.9113 2.0766 2.1007 2.1420

2.1437 2.2591 2.3417 2.3830 2.4381 2.4519 2.4795 2.5139 2.5242 2.6172 2.7171

2.7928 2.7946 2.9030 2.9995 3.1407 3.3128 3.3180 3.3352 3.4678 3.4850 3.6228

3.8001 3.8018 3.8449 3.9000 3.9465 3.9930 4.0722 4.1049 4.8797 5.2258 5.6855

- Tool l i f e (min) o f carbide i n s e r t s as supplied i n interrupted cutting.

Lot 2

Lot 3

Lot 4

Lot 5

0.5234 1.6461 1.9388 2.2969 2.4209 2.7756 3.0511

0.0344 0.7714 2.0387 2.5277 3.3335 3.7089 3.8432

0.5544 1.5187 1.6599 2.3865 3.2715 3.3576 3.4024

0.1481 0.4029 0.5889 1.7391 2.9547 3.0959 3.2749

0.3237 0.3754 0.4683 0.6199 1.0916 1.2569 1.3534

(1.7986) (1.8503) (1.9433) i2.0948j (2.5666j (2.7319) (2.8283)

3.8294 3.9671 4.6800 5.4238 7.7242

4.5353 4.6869 4.8694 4.9658 6.0058

3.7364 4.0291 4.7006 5.3928 5.5065

4.1841 4.2047 4.7661 5.1173 5.1380

2.5862 2.6999 5.3989 3.7295 4.1187

(4.0611) (4.1748) i4.8739j (5.2045) (5.5936)

Tab. 2

-

Lot 6

Tool l i f e (min) i n i n t e r r u p t e d c u t t i n g o f carbide i n s e r t s w i t h d i f f e r e n t values o f t h e wear time.

The a n a l y s i s o f these r e s u l t s using t h e t e s t developed by Quesenberry and Kent [81, [g] confirms t h a t t h e Weibull d i s t r i b u t i o n was t h e best s u i t e d f o r each l o t o f t e s t s , b u t d i f f e r e n t values of t h e Weibull's parameters were obtained. P a r t i c u l a r l y , f o r l o t s 2 i 5 s i g n i f i c a n t v a r i a t i o n s o f t h e shape parameter f3 were observed. The small v a r i a t i o n s obtained on t h e scale parameter suggested the idea t h a t t h e d i f f e r e n t l o t s belong t o t h e same population and t h a t t h e v a r i a t i o n s on the parameter were caused by t h e small number of t e s t s f o r each l o t . I n order t o prove t h i s hypothesis t h e Mann-Witney's t e s t [ l O ] was a p p l i e d t o l o t s 2 i 5 considered l i k e a s i n g l e sample; t h e value o f t h e f3 parameter obtained f o r t h e whole sample was very s i m i l a r t o t h a t one r e l a t e d t o t h e Weibull d i s t r i b u t i o n o f t h e i n s e r t s as supplied. On the basis o f t h i s observation, the i n v e s t i g a t i o n was extended a l s o t o l o t 6. Since f o r t h i s l o t t h e value o f A d i f f e r e d s i g n i f i c a t i v e l y from t h e corresponding values o f t h e o t h e r l o t s , i t was supposed t h a t , f o r t h i s l o t , t h e h i g h value o f wear was responsible o f t h e decrement o f while the variations o f were always a t t r i b u i t e d t o t h e small number o f t e s t s of l o t 6. Assuming t h a t t h e expected l i f e t o f r a c t u r e was a f u n c t i o n of t h e grade o f wear, each value o f t o o l l i f e o f l o t 6 was corrected adding t o each value the d i f f e r e n c e between t h e mean value o f t h e time t o c o l l a p s e o f l o t s 2 t 5 and l o t 6. The values so obtained a r e shown i n brackets i n Tab. 2. The Mann-Witney's t e s t s t i l l confirmed t h a t the corrected values o f l o t 6 belongs t o t h e same population o f l o t s 2 t 5. I t i s relevant t h a t t h e shape parameter p ( f3 = 2.21) i s equal t o t h a t r e f e r r i n g t o t h e carbide i n s e r t s as supplied ( l o t

x

61

l ) , as shown i n Fig. 1. Consequently i t i s p o s s i b l e t o a f f i r m t h a t t h e wear o f the t o o l a f f e c t o n l y the scale parameter and leaves unchanged the shape parameter. w i t h the value o f The v a r i a t i o n s o f t h e s c a l e parameter t h e wear time t are shown i n Fig. 2 which i n d i c a t e s t h a t a f t e r a few seconds o f continuous t u r n i n g the r e s i s t a n c e t o f r a c t u r e increases and then reaches a values t h a t remains q u i t e constant u n t i l the e f f e c t o f wear becomes so h i g h t o a f f e c t t h e l i f e t o f r a c t u r e . The sudden increase observed a t the beginning can be explained by the roundin of the edge between t h e face and t h e f l a n k o f the t o o l [ill,p121.

The minimum value of t h e u n i t production cost versus c u t t i n g speed w i t h d i f f e r e n t values of the Weibull parameters are shown i n Fig. 3. The associated value of the optimal t o o l replacement i n t e r v a l are reported i n Tab. 3.

100 125

200 225 250 275 300 325 350 375

j

where t i s a f r a c t i o n o f time T s t a r t i n g from which the wear a f f e c t the l i f e t o f r a c t u r e . It has been proved i n previous works 131, r131 t h a t , i n i n t e r r u p t e d c u t t i n g , i f the a c t u a l c u t t i n g time i s taken as an independent v a r i a b l e , the t o o l l i f e t o f r a c t u r e i s a random v a r i a b l e t h a t i s c h a r a c t e r i z e d by a Weibull d i s t r i b u t i o n whose parameters a r e independent by the c u t t i n g speed. Therefore i t i s reasonable t o admit, even i f r e s u l t s o f t e s t s f o r d i f f e r e n t values o f the c u t t i n g speed a r e n o t a v a i l a b l e , t h a t v a r y i n g t h e c u t t i n g speed. a t equal values o f t / T correspond the same value o f 1 according t o r e l a t i o n s h i p ( 1 ) . Under t h i s assumption i t i s p o s s i b l e t o f i n d the optimal t o o l replacement time and c u t t i n g speed. The research o f these optimal c o n d i t i o n s has been c a r r i e d o u t m i n i m i z i n g the u n i t production c o s t , t a k i n g i n t o account the p e n a l t y c o s t o c c u r r i n g when the workpiece must be r e j e c t e d because o f a t o o l f a i l u r e d u r i n g machining. P a r t i c u l a r l y , the scheduled t o o l replacement p o l i c y [14] was i n v e s t i g a t e d , assuming a d e t e r m i n i s t i c value o f t o o l l i f e T i n wear, according t o T a y l o r ' s law. Using t h i s s t r a t e g y t h e t o o l i s replaced e i t h e r i f i t has The t o o l replacement c u t f o r a f i x e d time o r upon f a i l u r e . i n t e r v a l has been chosen equal t o i n t e g e r m u l t i p l e s o f the machining time t L e t I t #e scheduled t o o l replacement i n t e r v a l ; d u r i n g the c u t o f ti& i - t h workpiece the t o o l i s c h a r a c t e r i z e d by a Weibull p.d.f. w i t h a s c a l e parameter obtained by equation I n these c o n d i t i o n s i t i s p o s s i b l e t o eva(1) f o r t = i.t l u a t e t h e e x p e c a d numbers of t o o l f a i l u r e s t h a t happen d u r i n g t h e c u t of t h e f i r s t workDiece as:

.

.

where g ( t ) i s t h e f a i l u r e r a t e given by:

(3) During the c u t o f t h e i - t h workpiece t h e expected number o f tool failures i s :

Using a t o o l replacement-time equal t o I ,t t e d values o f t o o l f r a c t u r e s i s :

Tab. 3

,

2 3 3 4 4 4 4 3

4

5 6

5

2 2

4 3 2 1

I

1

-

x,

= 1

*

2 3 3

1

A0

t /T = 0.2

1 1

,

= 40

t*/T = 1 9 12 14 17 19 13 8 5 4 3 2 1

ho =

4

t*/T = 0.2 9 12 14 13 11 8 6

5 3 3 1

1

Optimal values o f t h e t o o l replacement i n t e r v a l I a t d i f f e r e n t c u t t i n g speed.

.,

.f"<'Sl ' T 7

*

10

I t can be observed t h a t as much r e l e v a n t i s the i n f l u e n c e of wear as l e s s i s the value o f t h e optimal c u t t i n g speed.

; o = -ts $ T

5

t /T = 1

APPLICATION TO MACHINING OPTIMIZATION The above mentioned t e s t s c o n f i r m the i n f l u e n c e o f wear on fracture. P a r t i c u l a r l y , n e g l e c t i n g t h e v a r i a t i o n s t h a t occur i n the f i r s t seconds of c u t t i n g , according t o Fig. 2 , i t can be assumed t h a t the scale parameterX remains q u i t e constant u n t i l a f i x e d value o f wear i s reached; s t a r t i n g from t h i s p o i n t i t begins t o decrease and, f o r sake o f s i m p l i c i t y , i t i s supposed that i s a l i n e a r l y decreasing f u n c t i o n w i t h wear. Therefore, i f T i s the t o o l wear l i f e , the scale parameter i s a f u n c t i o n o f t h e r e s i d u a l u s e f u l l i f e , consequently, the f o l l o w i n g r e l a t i o n s h i p f o r the s c a l e parameter can be w r i t t e n :

x=x,

XI *

V

the o v e r a l l expec-

CONCLUSIONS The experimental i n v e s t i g a t i o n s have shown t h a t t h e two f a i l u r e modes o f t h e c u t t i n a t o o l s . wear and f r a c t u r e . a r e n o t s t o c h a s t i c independent pheiomena.. As a m a t t e r o f f a c t t h e t e s t s c a r r i e d o u t i n i n t e r m i t t e n t c u t t i n g on carbide i n s e r t s , p r e l i m i n a r y subjected t o d i f f e r e n t grade o f wear, i n d i c a t e d t h a t the f r a c t u r e r e s i s t a n c e o f t h e edge decreases w i t h prog r e s s i v e wear. It seems r e l e v a n t t h a t the wear a f f e c t s o n l y the s c a l e parameter o f t h e Weibull w h i l e leaves unchanged t h e shape parameter This r e s u l t s s i m p l i f i e s both t h e i d e n t i f i c a t i o n o f t h e Weibull p.d.f. of t h e worn t o o l and the research o f t h e o p t i mal machining c o n d i t i o n s . Consequently, i t was p o s s i b l e t o develop a p r o b a b i l i s t i c model f o r f r a c t u r e f a i l u r e s o f t h e t o o l s i n order t o evaluate t h e optimal t o o l replacement p o l i c y m i n i m i z i n g the u n i t production cost. This model shows t h a t t h e values o f t h e optimal t o o l replacement i n t e r v a l and c u t t i n g speed a r e as lower as stronger i s the i n f l u e n c e o f wear on f r a c t u r e .

.

NOMENCLATURE Expected value o f the u n i t production c o s t (M) T a y l o r ' s constant u n i t l a b o r and overhead c o s t (M/min) t o t a l c o s t p e r edge (M) expected value o f t o o l f a i l u r e f o r the scheduled t o o l r e placement i n t e r v a l I E w ( I ) expected value o f machined workpieces w i t h one t o o l f o r the scheduled t o o l replacement i n t e r v a l I g ( t ) f a i l u r e r a t e o f the t o o l t o fracture H t V I s@heduled t o o l replacement i n t e r v a l K crater ratio expected number o f t o o l f a i l u r e s i n machining t h e i - t h mi workpiece n exponent i n T a y l o r ' s equation P p e n a l t y c o s t f o r t h e r e j e c t e d workpiece (M) t c u r r e n t value o f machining time (min) t a u x i l i a r y time (min) ta t o o l replacement time (min) tCU machining time p e r workpiece (min) tm machining time l o s t f o r t h e r e j e c t e d workpiece (min) PT: t o o l l i f e t o wear (min) t l i m i t o f non i n f l u e n c e o f t h e wear time (min) V c u t t i n g speed (m/min) shape parameter i n t h e Weibull p.d.f. s c a l e parameter i n the Weibull p.d.f. (min) c C c co E:(I)

p

and the corresponding value o f t h e expected number o f machined workpieces i s :

REFERENCES

[ 11

T a y l o r J . , "Carbide C u t t i n g Tool Variallce and Breakage: Unknown Factors i n Machining Economics. , Proc. 8 t h I n t . MTOR Conference, 1967, pp. 487-504

I t i s now p o s s i b l e t o evaluate t h e l o n g r u n u n i t production c o s t f o r t h e t o o l replacement i n t e r v a l I-t, as:

[2] Ramalingam S.,

F i n a l l y , u s i n g r e l a t i o n s h i p ( 7 ) i t i s p o s s i b l e t o s e l e c t the optimal t o o l replacement i n t e r v a l and c u t t i n g speed. The above model was employed i n a t u r n i n g o p e r a t i o n char a c t e r i z e d by the f o l l o w i n g data:

[3] f f l b e r t i N., Noto La Oiega S., Passannanti A.,Carro-Cao G., The E f f e c t s o f the Fracture, Chipping and Wear o f Cement e d Carbide Tools on t h e Determination o f t h e Optimum Met a l - C u t t i n g Conditions", Annals o f t h e C.I.R.P., Vol. 30/1/1981, pp. 67-69

C = 400;

[ 41

n = 0.2;

H = 300; ,t

tCU = 1 min; ta = 1 min; t

mP

=

= H/V

0.5 ;,t

w i t h V = 100 i 400 m/min

P

=

10 co; cs/co = 5

Peng V., Watson J.O.,"Tool L i f e OistribuPart 3 Mechanism o f S i n g l e I n j u r y Tool F a i l u r e tions and Tool L i f e D i s t r i b u t i o n i n I n t e r r u p t e d C u t t i n g " , Trans. ASME, s e r i e B, May 1978, Vol. 100, pp. 193-200

-

-

Rossetto S . , L e v i R., "Fracture and Wear as Factors Affect i n g Stochastic Tool L i f e Models and Machining Economics", Trans ASME, s e r i e B, Feb. 1977, Vol. 99. pp. 281-286

[5) Lo Casto S.,

Passannanti A., R u i s i V . , "Influenza d e l l a v e l o c i t a d i t a g l i o s u i parametri d e l l a d i s t r i b u z i o n e d i p r o b a b i l i t a d i f r a t t u r a d i placchette d i carburi s i n t e r i r z a t i " , La Meccanica I t a l i a n a , N. 136, Jan. 1980, pp. 51-59

[6] L e v i R., Koren Y . , M a l k i n S . , Masory O.,"Probabilistic Model f o r C u t t i n g Tool Fracture Control", Proc. NAMRC I X , 1981, pp. 263-266

[ 7)

L e v i R., Koren Y.. M a l k i n S., Masory O., "Time and Fe:d Dependent Fracture o f C u t t i n g Tools A Stochastic Model Annals o f the C.I.R.P., Wol. 31/1/1982, pp. 41-43

-

,

[8] Quesenberry C.P.,

Kent J., S e l e c t i n g Among P r o b a b i l i t y D i s t r i b u t i o n Used i n R e l i a b i l i t y " , Technometrics, Vol. 24, N. 1, February 1982, pp. 59-65

:9]

Lo Casto S . , Passannanti A., Passannanti G . , " S u l l e d i s t r i b u z i o n i d i p r o b a b i l i t e d i f r a t t u r a dell; p l a c c h e t t e d i c a r b u r i s i n t e r i z z a t i nel tag1 i o i n t e r r o t t o , La Meccanica I t a l i a n a , N. 179, Jan.-Feb. 1984, pp. 43-47

[lo]

Guttman I . , Wilks ;.S., Hunter J.S., " I n t r o d u c t o r y Engin e e r i n g S t a t i s t i c s , Second E d i t i o n , John Wiley & Sons N.Y.

[ll]Ber A . , Kaldor S., "The F i r s t Seconds o f C u t t i n g , Wear Behavior", Annals o f the C.I.R.P., Vol. 31/1/1982, pp. 13-17 [12] Lo Casto S., Passannanti G . , "On the I n f l u e n c e o f t h e Radius b;tween Face and Flank on Tool L i f e o f Sintered 1985 Carbides , Submitted f o r p r e s e n t a t i o n a t C.I.R.P. (131 t;o Casto S . , Noto La Diega S . , Passannanti A., R u i s i V., Determinazione d e l l a v e l o c i t a economica d i t a g l i o med i a n t e sirnulazione", La Meccanica I t a l i a n a , N. 146, Dec. 1980, pp. 47-51

[14] La Comnare U., Noto La Diega S . , Passannanti A., "Optimum Tool Replacement P o l i c i e s w i t h Penalty Costs f o r Unforeseen Tool F a i l u r e " , I n t . Jour. o f Machine Tool Design and Research, Vol. 23, N. 4, 1983, pp. 237-243

50

100

200

300

V [ni/rnin]

400

8 -

-CCO 6

.

5 '

0.1

.01

Fig.]

-

1

10 0.1

----

Experimental r e s u l t s : A corrected: B l o t 1.

-

!O

1

-

4

"

3

.. I

l o t s 115 and 6

I

50 Fig.3

0 1 Fig.2

5

-

10 t8

200

300 Y [mirnin] 400

Expected values o f t h e machining c o s t versus V.

1

II

0

100

-

15

20 t [min]

Values o f the s c a l e parameter f o r l o t s 136.

63