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A Common Denominator for Optimal Cutting Tool Geometry
S. Ksldor. A.D.A., M.O.D., Rsfsel/lsrsel - Submitted S. Mslkin (1). Technion/lsrsel
Sul.urg: Prcvloua invcmt iga t ion i of c u t t i n g tool ~ e m e t r i m s have m h m t h a t for ~ r u x i n u ~ r w l l i f e rhcrc i s rn optirml c l e a r a n c e angle which vmrirm r i g n i f i c a n r l y far d i f f r r c n t t y p r r uf c u t t i n g tool#. 7hr incrcare i n to01 I i f c nip ti? I h r o p t i n m c l e a r a n c e angle i m rmlated to l o i r f lank wei r by # l i d i n # . Abuve the opriral clrmranc. angle i n c r c r i e d f l a n k w a r and shortmr tool l i f e is often asmociatcd with a greater tendsney for nicrarh ipping . l lwrerorm, u t r e s r e s locnred in rhc v i c i n i t y of t h e c u t t i n g ednr might be responnib le f o r t h e decreasu i n too l l i f e at I r r s r r elemraneu nny lea and for rhr eximtancm of an optimal clrarancm anglo. c l e a r m r anglc found for di iKerent rypur of hiph mperd srcrl currinW t u o l i have n i t rcsm r r l a t e d cumon dcnominator. A m i q l i f i m d loaded cut t ing tool m d r l wsm used t o d e a r r i b r the stremmmm i n the tool wedgc. r u b s t a n t i a l l y d i t f c r c n t ryprn of r u t t i n s tools inc luding end n i l l m , f l y CutlcrN J3d d r i l l s were fuud to have rllmrt the i d e n t i c a l mtrmsa v a l u e r on t h e roo; rrkr face- . T h i n r e a l t volrld .ern tu bu particular!:# tirrful iar o p r i r u l duripn and r e l e e t i o n of tool r e m r r i c a .
The p r e i e n t i n v e n t i r a t i u n warn undertaken to e x a r i n e wh-rher the optimr
Optimal g m t r t e r for
K m m c l a t u r e
a depth of cut
b u n i t width af cut
0 d i . w l r r
F frud
FC cul t inn forcm
Ff feed f o r c e \ c u t c i n ~ rrmrnt
n mubmcript re tmrr inp t u n o w 1 plane
0 s u b s c r i p t r e f u r r i n g LO urrhopnal plane
P. PI. P2 f o r c e corponenrn Pn. 1. n o m l and ciirtinR ednr planus
P x "Per iphera l M i l l i n s Curve" nmmu
b r sw- 1
VC
Y
n
P 1
0 . 9'
'I
r c a i n t n n r r 10 brcmkaRr
co-ordlnmte ax in n u of d r i l l p r o w t r y
c u t t i n g vmlocitv
width of c u t t i n g . d i e
clmarmce angle
tool w d l e m g l e rnol rmkr nnnlc
c w r d inmtr ax i s tool c u t t i n g edge i n r l i n m t i m
"r r a d i a l mtremm or!, mr2 r a d i a l strrmm colponeots
C C
n g e o a e r r i c a l rxpremmiom
I . In t roduct ion
I h m g . g t v of c u t t i n u tools bam a s i ~ i t i c m n t e f f e c t on r c h i o i n # pmrfo-c. I t is g e n e r a l l y fwad t h a t charm is M o p t h l tool gmmtry f o r r r i u r lifm of cutting t o o l s . tbm various g e a a t r i c p a r w t m r m . on. of the most important and often n-lmctad I m t h e c l e a r a n c e angle.
lo p r w i o u s invamtigarlonm with und mills. fly cuttarn and d r i l l # . i t h s b..n .houn t h a t t h e r e i e i n each cam. a p a r t i c u l a r rlmarmncm -1. uhich in c d i n a t i m wi th othmr g a a a t r i c a l pmr.rtmrn of t h e p a r t i c u l a r c u t t i n g opmration yloldr a u x i n u n tool llfm [ l . 2.11. The y m r a l k h v i o r is i l l u m t r r r e d in Fia.1 I l l .
l l w p a r t l c u l u c i e s r m c e annie corrruponding to the u x i u m tool 111. 1s rdarrad t o as t h e optimal clsarmcm angle. optin1 c l e a r a n c e mglm, Dorm1 allding m a r im obmervrd on tbm tool flank. A t larger clmarmem mylam c o r r c r p o n d i y to mullmr -a -lei (waker toold. war i m oftmn aecorpanimd by breakage or chipping. mhorter tool lifm is llkmly to be a m u x i a r r d wi th microchipping. S ince tool l ih r d u c t l o n a t h igher than tha optimal c l e a r a n c e mnglem appaarm to k rmlatmd to chipping a t t h e c u t t i y adge. t h m a t remi in t h e tool -a im mmsumed t o reach cri t ical valumr at t h e ch ipping location. The tendency for microchipping m y be obsmmd mmpmclallg in t h e w r y e a r l y s t q r s of c u t t i l y . and nuch microchlpping can account tor a shortrr tool l l f e I&] . stream at tbm p a r t i c u l a r po in t of chipping i n i t i a t i o n u y tbermform be eonmidrrrd am a pommiblm c u n denominator uhich could mecount f o r thm particular o p t l r l geomcriem obtminrd with various types of toolm.
- u n d i r n m i o l u l radial mtress valnm
Belw tbm
In t h i s ragion. i t -Id - t h a t t h m
The
2. S i m l i f i e d Strmmm %dul
?or r h r purpose of analyzing rhe tuo l s t r a i n . a s i q r l i f i c d rodel i a adopted as sl~um in Fiq.2. s i m i l a r to one i n ref 151 . The bruit- aruumptlnnr fur t h i r andel a r e a s follows:
a . 'ihr luul hns a p c r f t w t l y i h a r p c u t t i n u UJKU with a - inRlu furca F, a c t i n s in t h e c u t t i n g nprrd d i r u r t i o n .
b. Ihr gourntry anr lyrcd i n chnscn in each came nt chat arra on thc e i i r r inp rdpe uhcrc r h r wqt s r v c r r f a i l u r r x c u r n .
U. Pracrurc o r chipping is l o c a l i z e d c l u s c t u t h e curr im( cdno wheru t h e tml q r o a e t r y i - n i n p l i f i r d Ln a p r i m a t i c shape.
d. Tlir anslor .ire def ined in the n n n u l p lane Pn and in thc c u t t i n e r d y p l a n r Pl 161.
V . r e n i i l r ntrussuli on the r r k r :ace a r e r n w r d t o bu the r n i n caiiac ior frnctiwe.
Thu loadod r u t t i n g too l wedge Lrmutry a c c a r d i n s L O thw d c l i i def ined in a Rrnvral form af an ubl ique p r i m n s d r p i c t c d in Fiy.2. A r u r d i m e n r i o m l - t r e s s a n a l y r i i i n carriwd uut i n rtw nurmal plane rur uhicll rlir f o r c e i s t r a n n f a r s d b i r p l y Lhrouqh t h r angle '.. Thr unit width uf cur b la n l m mffecicd by I ~ P Lranufornarion t o t h e norrarl plane. Fnr y n m c i r i c a l m d unmyrmetricrl loodine. r e r p e r r i v e l y . the rndia l r f rewes a r e given by 17::
hrrm: and ~~2 - r d i a l mtremm c m p o n c n t s
r . 3 ' and 4 - pnlar er rord ina tem r1 and PI - force corgomnrm Y
I - urdne englc - width of the c u r c i n e edvu
Ihr anelm 3 in Eq.1 and . I ' In Eq.2 mre both wamured f r m t h e linc of action of the force. ~ I C co-ordinmtr mymtem as 9 by:
The angle 3 ' ern b. t r a n s t o m d t o the
mo that Eq.2 can br w r i t t e n an: P2 s i n ?
rtdf+ - 4 min 2 ) 'r1 3
Tbe c u t t i n 8 foreu Fc i m m e p r r a t d i n t o PI and 12 bv t h r followin# clpremmionm :
P i - Frcnm ),corn (a ?/Z) P2 - Cccos 1, sin ( 1 il2)
After t rmnmforur lon the width of t h e c u t t i n g cdae k c a e a :
Y - blcon )I
Suprrpomine rhm a t r e a w n uf Eq.1 and 2 yie ld#:
'r 'KI 'r2
and cod#inin# Eq.1.0.5.b.7 mnd 8 Leads to:
F, tor' i qr . -2. r
b r h a r e :
1 9 )
41 Annals of fhe CIRP Vd. ss/l/lm
sin(o+ij/2) sins ( ~ / 2 + 4 sin8 )-cos(a+3/2) cos 3 ( 2 / 2 - 1 sins) P = (10)
( P / z ) ? - ( i sins)'
For convenience a normalized stress 5, is detined:
- ?,br/FC ( 1 1 )
Furthermore according to assumption ' e ' 9 is equal to 2 1 2 . Therefore the final result for the nomlized stress is:
Eq. 12 is a purely geometrical relationship which depends only on the tool clearance angle 1. rake angle 7 and cutting edge inclination Is. The wedge angle 2 is given by:
-I + 3 + -' - 90" (13)
Eq.12 is also presented in the form of a nomogram in Fig.3. The stress is obtained by starting with a horizontal line from to the appropriate Yn curve. the ' in curve, a vertical line is drawn up to the line representing J S . A horizontal line on the upper part of the nomagram back to the ordinate leads to the G, value.
From the point of intersection on
3. Optimal Tool Geometries
In this section the simplified stress model is applied to previous results obtained for optimal cutting tool geometries. i.e. drilling. end milling and fly cutting [1-3]. Other geometries are also evaluacrd for standard tools. which m y or may not be optimal. It should be mentioned that the angles I, I and B in the previous section are all measured i n the normal plane, but for simplicity the subscript ' n ' has been omitted. When dealing with actual cutting tools these angles are measured in the orthogonal plane. In order to calculate the stress cr the angles lo and orthogonal plane must be transfomed to che normal plane accorti- ing to the relationships:
in the
(14)
( 1 5 )
- I - in * tan [tan ~,,lcos Is]
i - i n - tan-l[tan i o n cos i s ]
3.1 Optimized Drilling Geometry
A new twist drill point geometry SRP-I was evaluated I l l and the test results are shown in Fig.4. For all feeds used in these tests the optimal geometry was found to be virtually the same. This new drill point shape gave a much longer tool lire than convent iona 1 point shapes . The test conditions were n s follows:
cutting tool: work material: AlSI 4140, 266 WE cutting conditions:
coolant: none The optimal tool angles were:
1 I O m m . M7 HSS. jobber drills
vc = 40 mlmin E, = 0.065, 0.09 and 0.125 mmltooth
=o = 3 deg., lo = 32 deg. and and Is - 7.3 deg.
The corresponding dimensionless stress factor is ;r = 2.43.
3 . 2 Optimized Fly Cutting
As part of an investigation into end milling clearance geometry [ I ] . a special series of cutting tools was prepared and tested. Two types of clearance profiles were compared: comnon flat flank and eccentric flank face. Both types are comrcially used. The results are shown in Fig.5.
The test conditions were as follows:
cutting tool: 4 2Omn,!42 HSS work material: EN-19, 300 HB cutting conditions: vc - 40 mlmin
fz - 0 . 0 5 , 0.08 and 0.1 w/tooth orthogonal cutting
coolant : none The optimal toolangles for the flat flank were:
so - 10 deg., Yo - 5 deg. and A s = 0 deg.
,x0 = 14 deg.. Yo = 5 deg. and is - 0 deg. -
and for the eccentric flank were:
The corresponding average stress factor is gr - 2.32. 3.3 Optimized End nilling
A variety of different makes of end mills were ground to form test groups each having a different clearance angle [ 3 1 . Test results in Fig.6 clearly define an optimum angle and the transi- tion from wear failures Lo chipping.
The test conditions were as follows:
cutting tool: a lOmm, 32 HSS, end mill vork material: EN-24. 340 HE cutting conditions: vc - 30 mlmin
f, = 0.025 m/tooth coolant: oil emrlsion, 1:20 dilution.
The optimal angles were: q, - 16 and 20 deg. for flank and corner wear,respectively, Y o - 10 deg. and I, - 30 deg.
The corresponding average stress factor is Cr - 2.65. 3.4 Assumed Optimal Geometries
(a) A turning geometry with HSS tools was proposed by IS0 for tool life tests [ a ] . The tool geonetry is:
L~ - 5 deg., (D = 25 dog. and A s - 0 deg. The stress value for these angles is Cr = 2.86.
No uention was made whether this geometry was optimized. but it is likely that an efficient shape was chosen to minimize wear rate9 for a standard testing setup in order to include testing for a large range of workpiece materials.
(b) Cutoff or parting cools are often reground by hand on both the rake and flank faces. A c o m w n method is to have a circular groove ground on the rake. like a chip breaker, which forms at the same time a relatively large rake angle. The clearance angles are mostly kept small. Measurements have shown that average angles are ?o = 5 deg., lo = 25 deg. and is - 0 deg. stress value is a, = 2.42.
3.5 Other Published Values
A large number of recommended tool geometries are f w n d in hand- books, cutting data books and manufacturers literature 19-111. In most cases, the geometries are chosen to cover a large range of applications at the expense of efficiency, and it would there- fore bc expected to find that the angles are not necessarily optimal. for strength to avoid breakage, and Cr values should therefore be below optimal. Typical angles for turning toola are [ll]:
= 7 - 9 deg.. Yo - 8 - 12 deg. and A s - 0 - 12 deg. The corresponding stress values are in the range: ?,. - 1.98-2.23. Drills on the other hand are difficult to form with a required clearance angle. ln order to ensure sufficiently large clearance angles near the drill web, it is generally necessary with conical point grinding to have excessively large clearance angles at the periphery [ 1 , 1 2 , 1 3 1 . This should yield high 5, values for standard drills and increase the tendency for breakage or severe wear propagation at the corners. For standard conical drills at the periphery: a0 - 10 - 14 deg.. ' I , 32 deg. and a s - 7 deg. The corresponding stress values are: or - 3.78-4.90. 3 . 6 Theoretical Limiting Geometries
The total possible range for the dimensionless stress factor Cr can be obtained from two imaginary geometries. "he first is a flat plate pressed against a w v i n g workpiece. This represents a "tool" having a clearance nngle rto = 0 deg., rake angle Yo - -90 deg., and A s = 0. This "tool" will never cut but it represents the lowest limiting stress factor, which was calculated as 7 , - 0.63. The second imaginary tool chosen was a kind of scraper having a minimum wedge angle and oriented perpendicularly to the workpiece. The angles no. respectively. about the upper limit for the worst or "weakest" tool geometry.
4. Discussion and Conclusion A11 the results in the previous section are suwarized in Table 1 and in Fig.7. different tools from high speed steel, the diwnsionless stress factor always resulted in a cumnon value zr 1 2 . 5 . standardorrecomnended geometries for high speed steel tools cover a broader range 1.5 < Gr < 5 . For carbide cutting tools it can be seen that the stress range is usually 1 5 Cr < 2 .
Deviations from the optimal value of 2 . 5 were noted as follows: end mills and turning tools tend to have "stronger" shapes with stress factors of 1.80 and 2.15 respectively. Standard drills having a conical geometry show an or value of 3.8 to 4.9, and they have shown a lnrch lower tool life than the optimal SRP-1 drills. Conical drill points have a relatively large clearance angle at the periphery. which is unavoidable because of the conical grind- ing method. Improvement of this geometry may be possible by geometric modifications of the angle As. drill corners up to 35 - 4 5 deg. will reduce the stress factor from 4 to 2.5 . Such modification necessitates an alteration in the flute profile. which will result in a curved cutting edge as seen in Fig.8.
Two imaginary "cutting tools'' were assumed as limits of the total range of possible stress factors. The lower limit obtained from the geometry of a flat plate pressed against the work piece is
The upper limit was obtained from a very small wedge angle uhich may represent a "raser blade" geometry. with a rake angle of 0 deg. the "weakest" configuration is
The corresponding
hrning tools and similar cutters are usually designed
and X, are 89 deg.. 0 deg., and 0 deg. The stress for this case is & - 2.104 vhich is
It can be seen that with optimal geometries for
Other
An increase in is at the
* 0.63. For this tool
42
obtained yielding a stress value of Cr - 2.104. These results can be applied to designing better and more efficient tool geometries.
1.
2.
3.
4 .
5 .
6 .
7 .
8.
9.
10.
1 1 .
12.
13.
References
Kaldor, S. and Lenz, E., "Drill Point Geometry and Optimization", Trans. ASME Eng. for Industry, Vol. 104. Feb. 1983.
Kaldor, S., Trendler. P. H. H. and Hodgson. T.."Investigations into the Clearance Geometry of End ?(ills". Annals of the CIRP, Vol. 33/1/1984.
Kaldor. S . . Trendler. P. H. H. and Hodgson. T.."Investigation and Optimization of the Clearance Geometry of End Mills", Annals of the CIRP. Vol. 34/1/1985.
Ber, A . and Kaldor. S.. "The First Seconds of Cutting, Wear Behavior". Annals of the CIRP. Vol. 31/1/1982.
A m r e g o . E. J. A . and Brown. R. H., The Machining of Hetals Prentice-Hall. Engleuood Cliffs, 1969.
IS0 3002/1. Geometry of the Active Part of Cutting Tools - Part 1: General Terms. Reference System, Tool and Working Angles, 1977 (El. Timoshenko. S. P. and Goodier. J. N.. Theory of Elasticity!. .XcCrau-Hill, Third Edition. New York. pp 109-112. 1970.
ISO, Draft International Standard, DIS 3685. "Tool Life Testing with Single-Point Turning Tools".
Tool and Manufacturing Engineers Handbook, Vol. 1 , Machining, SHE Publications, Dearborn. Xichigan. Fourth Edition, 1980. Manuel de Donnees Technologiques D'Usinage en iraisage CETIX, Departement Pub1 icat ions, Sen1 is, France.
0 1 0 2 0
jo
0% Technical Guide End Hilling. 0% Mfg Company, Toyokawa. Japan, 1982.
Kaldor. S . , "~nvestigation of Machining Parameters in Drilling", D.Sc. Thesis, Technion - Israel Institute of inclination angles, respectively. Techno1 ogy , 1980. Kaldor, S., Xoore, K. and Hodgson, T., "Drill Point Designing by Computer". Annals of the CIRP, Vol. 32/1/1983.
- Fig.3: Nomogram shoving the stress value o r on the tool rake
face: an. Yn and A s are the clearance. rake and
I
Fig.1: Typical tool 1ifevs.clearance angle [ l ]
Fig.2: Simplified cutting model for sharp tools i n planes Pn and Ps. Fig.5: 1001 lifevs. clearance angle in single point peripheral
milling [2].
43
[PRS s h s . I
6 t 6 .
4 . ./
. rn
' I EN 2 4 340 BCN rn
I I 0' . 10 20 30
Fig.6: Tool l i f e vs. clearance angle in end rniLling [ j ! .
n
Fiy.8: Propored improved cuttinq rdpe shape for d r i l l < .
mu &(,, I0 P 7 IO.07 81.8 1.m , +& Ib P 7 1b.l 11.8 4.W
7 1 a I 8 1.u B I 2 I 2 1.2 11.1 2.28 9
Fig.7: Dimensionless stress values from Table I . r-4 Note the following stress l e v e l s : optimized tools 2 . 5 , minimum level 0.63 and the region in which fractures are expected.
-10 II smmm .I -it. r r mid n-8 r r m 'r
44
