A method of modeling residual stresses in superfinish hard turning

WEAR ELSEVIER

A method of modeling residual stresses in superfinish hard turning S. Mittal. C.R. Liu * S~.h,,,,I ol huht~lri¢d En~im.~,rme. t',rdu,, I "mv,'r~tt~. 12.~7 (;,t,,,,,,l tt, dl. U ,.~! I.,it,txette. I.'~147t,~17.12,~¢Z I ' S A

Rc~:ct~cd 15 [~'ccmbcr It~tl7:ac~ opted 2r NI.tr~:h Itl¢~.~

Abstract It has recently been proven that it is fea~,ible h~ u',e hard turning in ,,elected ¢onditi~n~ to ~uperlinish sul'l~aces, hardened n) 64 Re. to surface linish of 2 /.tin.. thus making it possible to eliminate the need for ~eparate gnndmg and abrasive-based superfinish in a broad range of production activities involving hardened workpicc¢~. The ~url'ace intc~rit', afler fnachinin.~ hardened steel is ~,uperior and more consistent than ground and superfinished surfaces IC.R. Liu. S. Mittal. J. MFg. S~t. 14 I 2~ I I~)05~ 129-133]. It is also known that hard turning produces compressive residual stresses [C.R. Liu, S. Minah Robotic, C~mtput. Integr. Manuf. 12 ( I ) I I t S ) 15-27l and that machining parameter such us speed, feed and depth of cut effect the residual ~tress distribution, h b, prnposed that the residual stress profile is a deterministic function of the machining parameters. It is postulated that lhc residual q r e ~ prolile along the depth is a polynomial function of the depth and the coefficients of thb, polyllomial are in turn tunction,, of the machining parameters. The m~.lel, with some refinements, ha.,, been develnped in this paper and has been checked I'lwa¢curac.~. ~: 19t)8 Elsc'.ier Science S.A. All fights re,,er'.'ed. Keyword.~:

Supertinishmg:Hard lUtnin~: Rc~,idu~l, .e~ modeling: tlardcncd bearing q¢cl

i. I n t r o d u c t i o n This age of stringent consumer demands in a competitive market environment necessitates the production of goods which are not only aesthetically appealing but possess a high degree of surface integrity as well. In the case of roller bearings, primary component of sud",,ce integrity is the nature of residual stresses existing at the surface of contact and in the layer close to the surface. The profile ( magnitude and direction along the depth) of the residual stresses can greatly enhance or reduce the fatigue life of a roller bearing. It is believed that compressive residual stresses are more faw~ra* hie for rolling contact fatigue life than tensile residual stresses. Therefore. it is imporlant that the effect of the tinishing process on the residual stress profile he determined, and subsequent to this, such machining parameters he chosen which would enhance latigue life by inducing lavorable residual stresses. To determine the machining parameters which would enhance fatigue life. the procedure shown in Fig. I should be adopted. This paper concentrates on modeling the effect of machining parameters on residual stresses. Majority of the research existing in literature on the efl~zct of machining parameters on residual stress proliles have been * Cortesp~)ndin[,'author. Tel.: + I 765 4L)45413: fax: + t 765 494 544~: liu¢h¢~'een.purdue.edu

e-mail:

experimental in r,ature. Very few analytical models are available. Barash and Schoeeh [ I ] used the slip line theory to predict the plastically deformed layer ( corresponding to the depth t o which residual stresses are existent ) beneath t h e metal surface machined by orthogonal cutting. Liu and Bara~,h 12.3 1 explained the formation of residual stres~s by considering the stress strain history that the surface layer experienced due to the movement of the cutting tool. Matsumoto et al. [4] observed compressive residual stres~s while machining hardened steel and explained their formation with the help of a model proposed earlier by Merwin and Johnson ] 5 ] to explain the formation of residual stresses in roller bearings. Lin et al. [ 6 ] used Finite Element techniques to determine residual stress profiles in orlhogonal machining. Wu and Matsumoto [71 also u.~d finite elements to determine factors which affect residual stress formation in hardened steel machining. Ahhough these models provide useful insights to the basic residual stress fi)rmation mechanism, they are unsuccessful in predicting actual residual stress profiles for particular machining conditions. This is mainly due to: ( I ) residual stress formation is a complex mechanism and the theory of plasticity is not developed enough to enable accurate prediction of residual stresses: ( 2 ) all required material properties are not accurately known. Due to this. experimental models could he used more effectively for prediction of residual

0043-1648198 I $ - see IYnnt unatter ,~) I tY)8 Eb,evicr Science S.A. All rights re~,er',ed. PIt s o n 4 3 - I (148 ( 9 8 ) n n 2 n L -4

S. MitmL C.R. Liu / W e , r 2 1 8 (1(~8) 21-33

to Induce favorablere4dduel ~

crlll~ll =tressfor givenservice/ No

tonal.lone)

I i,htddnl~ pemmetor8me

I

/

~1

Yes

Yes

No

I 8udeealexlure°' mechk~

Note :The Conceptand Method shownhereis partof a Roller Beedngs wllh choNn

machk31ng~ndlYons Fig. I. Flowc.'hanIor manuPacmuringcustomizedroller hearings. stresses for particular situations. Experimental techniques have been used successfully for too! life application [ 81 and for surface roughness predictions I 9 I. Devarajan et al. [ 10 I constructed an experimental model for prediction of the surface residual stress. Although the surface residual stress is important, in most roller bearing applications, the subsurface residual stresses are at least equally important. Jang I I I I proposed a model to predict the surface residual stress, the maximum residual compressive stress and the maximum tensile residual stress. This model is more useful as it provides an insight as to the effect of machining parameters on some useful residual stress profile parameters, but is still inadequate due to the lack of knowledge of the location of these maximum stresses and the depth to which residual stresses exist. This paper introduces a more comprehensive experimental model to predict entire residual stress profiles in precision facing of hardened steel. With the help of this knowledge it will become possible to optimize machining parameters such that the surface integrity of the machined component is maximized under service conditions.

2. Proposed

functions of the machining parameters. A triaxial stress state is assumed, i.e., neither of o',. rr,. or 0.. ( stresses in the circumferential and radial direction and along the depth. respectively ) are necessarily zero. T o reduce the number of unknown variables, two new variables are introduced defined as l'ollows~: ~'ri = 0.. - 0.: . and 0" 2 = 0 . , - 0 . : .

The model assumes that profiles of or, and ~r. along the depth are polynomial functions of the depth. The proliles can be represented as li)llows: For ( ) < z < Z , . , . , :

0., = , ' o , + ( ' , , z + t ' 2 , z

~-+ . . . + c , , , z " .

For z>--Z,m,,~: ( r , = t ) . where: 0., = residual stress in direction I. i = I circumferential direction, i = 2 radial direction, c,,, = cocl'licient o f Ibe nth order term o f p o l y n o m i a l , z = depth. Z,,,,,,. = depth to w h i c h (r, is distributed,

model

The proposed model postulates that the residual stress prolile as well as the depth of residual stress distribution arc

i Not only d~:~, tills, lranM~irnlalion reduce the number Ill" variable~,, it aho ease~,the calculations, invoh'cd in ~xpcrhnenlally dclermhling Ihe residual ~,lr¢~s¢~.by Ihe X-ra), Diffraction iit~:thod.

Further. it is proposed that the coefficients o f the polynomial are individual functions of the machining parameters. T h e relation of the coefficients to the machining parameters. is as follows: c.

= h.,~ + h, ,, r + h w .I'+ h,o, d + I,,,,, 41'+ h, ,, <1'+ h, r0, i'll.

where: % = coefficient of polynomial for residual stress profile in the ith direction, h , , = effect of factor (or interaction of factors ) x. r = I ( 2( V - V,,,,, ) ) / ( V,,.,, - V.,., ) } + 1. f = {(2(F-F,.~..))/(F,.,,.-F,,,,,,)} + I. d = ( ( 2 ( D - I ) , , , . , . ) ~/ ( D,,,~,. - D,,.. ) } + I. V.F.D = speed, teed and depth o f c t u for which residual stress proliles have to he determined. V....... F, ...... D,,,,, m a x i m u m values of speed. Iced and depth of cut used for constructing the model. V.... F,,,,,. D,,,,. minimuna values of speed, feed and depth of cut used for constructin[: the model. A similar model is constructed for the depth of distribution:

Zi,,,ax=tl(i,+~l,,t'+tlt,./'+tt,t,d+U,h,~['+tt,

Tahlc

[.e~el~ of machinin,_,parameter., for comhinaliom, u~d in experiment S[M~ed

Feed

Depth ol cut

I

ti~

V, ....

F, .....

I;' ......

4 5

v,,.,,, V...... V,..... V.....

F,,.... F...... F,..... F,.....

D...... D...... D...... I)......

7

V......

x

v, .....

/- ...... F. .....

D..... D ......

('olnJ~illdli¢lll no.

t,t'f+tl ,/,t d.

T h e values of a,,s and h,,,s are determined experimental b . T h e procedure is as follows. ( I ) Eight specimens are cut using difl'ercnl combinations ( I ) o f V,, ..... V..,,. Y,,,.,,. F ....... D ...... a n d I),,,,,, as s h o w n in Table

I.

The residual stress profiles and depth o f distribution lor each specimen are determined. ( 3 ) Polynomials of a pre-dccided degree are litted to the residual stress profiles for each specimen for both directions ( 4 ) The coefficients ( ru,,s ) o f these polynomials are then used to determine the values of I,,,s ~,,ith the help of the following expressions: (2)

bO. = rl. + r2. + r~. + Ih. + r~. + I".. +

c~o

"rod r , ~ , w ~

U~l~

T~

~t,~l e l m coy ~

O0~QUEST ~

s u ~ )

~ y He~t~le)

r 7 t , ~- 1"st,,

h, i,=

rll. - r2. + r~,. - lh, , + r%, + r~.. + rT,,+ r~..

hi# =

- rl u - 1"2a + r ~1, + t'4t, + r~t, + f % , + rT, , +

i'~,,,

vm~ .aso

~

W i r e . 200 ~ m .

Fml~. ~ .

e . e u ~ , Om~. O,O e l l ~ .

Lem~h

O e l ~ . e.OUll~l~

Fi'.'. 2. ~;tk'~.'iI11t'n~,and machining conditions u~,:d Ior e'~perimenl~..

b,t. = - r~i, - r. i, - r ~t, - th ,, + r:,, + 6,,, + rT, + i"~,. l~,lli' =

rll , ~- l% l, -- r~H -- i[11, -- r4l , -- fhl , -~- 1"71 ' ~- r~p,

b. I,, = -- rll, +

r:.

h . dli = -- rl i,+

1"2t,-- r ~t,+

+ i.~. - 14, - ~k,,+ 1;.,.+ r~,. ~- ti,,. tht , + lkl, -- 6,. +

r7u -- l~,,.

( 5 ) Similar calculations are m a d e tot a,,s. except that instead o f values o f r,,,s, the values of pt,s are used where I'~, is the depth of distribution d e t e r m i n e d for combination / in direction L

was used with CrK,, radiation tube. T h e voltage applied was 50 K V P with a m p e r a g e 20 m A . T h e sin-'~,method as detailed in Ref. I 121 was used in these experiments. A triaxial stress state was assumed. Fifteen readings were taken for each layer of e v e r y specimen. Layers o f approximately 0 . 0 0 5 - 0 . 0 2 0 in. were r e m o v e d with the help o f electropolishing. Layers were r e m o v e d until the residual stress state b e c a m e negligible. The residual stress profiles obtained are shown in Fig. 3a and h.

2. I. E.werimental l,,',,ce~h,'e 2.2. Co,strucfion ol'the model T h e dimensions of the m a c h i n e d specimens as well as other m a c h i n i n g conditions used in the experintcnts ~,re shown in Fig. 2. T h e specimens were m a c h i n e d using 2 ' experimental design as detailed above, A new insert was used fi~r each experiment. T h e residual stress m e a s u r e m e n t s were done using X-ray diffraction techniques. A G E XRD-5 X-Ray Diffractometer

A visual inspection of the profiles obtained warranted that at least a fourlh degree polynomial would be regarded as sufficient to lit the profile. Preliminary results with a fourth degree polynomial ,~tere not encouraging: therefore, it was decided to use tilth degree polynomials to represent the residual stress pmliies, T h e coefficients (rl,,s) corresponding to

24

S. MitmL C.R. Lht / Wear 218 (199N) 21-.¢.¢

8pets 1-4:8|gm81

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Dep|h (0.001 Inch)

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8

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Specs 1-4: Slgm~ 2

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Depth (0.001 inch) Fig. 3. (a) Rc~,idual ',trc~.'. pn~lih.'s mca~.urcd fi-om machined spt.'ci11101l~(Sigma I I. (h) Rc~,idual ~.trc~.~. pmtile~, mea~,ured from machined specimens ( Sigma 2 ~.

the closest tit with filth degree polynomials are shown in Table 2a and b. Using the model, the values of a,,s and h,,,s were determined. The calculated values ofa,,s are shown in Table 3 and those of h,,,.¥ are shown in Table 4a and b. The a,,s were used to predict the values of Z,,~,,. The h,l,s were used to predict

(.,,s. Ihe v.'tlues or which are shown for various cutting conditions in Table 5a and h. Plots of the original titled curve ( dashed line ) and the predicted curve ( dolled line ) are shown in Figs. 4 and 5. As can be seen from the figures, the model is accurate for smaller values of depth of cut. but tail in cases where the

25

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Fig. 4. Polynomials titled 1o residual ~,tre,.~,p r o l i l c , ( d;ishud l i , c , ) and re,idual ,trc,s prolik,~ predi¢lcd by original model ( dotted lines ) ( Sigma ! ).

.~/. Mitud. C.R. Liu I We,r 21~ (lOOt';) 21-33

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--.,

1"10

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S. Mittal. C.R. I.iu / n'ctlr 21B I/q9,% 21 .¢.,' Table 2 ( a I Coeflicicnts of lifth polynomial lifted u, data oh,ained ill experinlents I ilriginal model - - thrccllon I Combination no. ( I I

Direction I il

('ocflicient~ ,11 cxperimenlalb determined pnh lllmllal t , 0

I

I

I (circ.~

4O.(,6672O 44.750455 - {)6.44992.1 f~4.856945 - 17.2.";17')2 4().162147 -74.712271} -31,.S 1782 ~

I

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1

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2cll gs5~45 If,¢,. ~442~S 1711 Iqllq()o 10&52412fi 7,% ~42~74 0S.571117S Ii} 7~ }TSt II ,~155t1(I

- n)5.448940 - sg. i 54OO6 - q9.864113 - 69. I2879 I - 26.19528 I) - 37.572728 - 2.971~23 - l).693701

1.4811694 1.2158711 1.425195 - 1.0.M577 -n.331561

21.3(R~63 17.X01~)71

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20.64341(I 14.750247 6.(,556,49 5.21 g29g 1.291945 1.94~36

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- 11.241n56 - I).0R 1122

0.11,5337

( b ) C,~'..'l'licienls of li flh p*fl', nomial lilled to dakt oblairlcd i,~ ¢xpcruuent, ! original model --d,rcclion 2, I

2 I ,';td. ~

3 4 5 g

2 2 2

7

2

54t.t11722

N

2

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-- 9ktl~Xl t4 - 52 I)11111)6 ~s.12)5 5 2,1 1111215 I ()t,j)211h I S tJi) s5s~9

~ 115.2 ~2ns9 I It) 5 lat,at, 124 r l 2 7 2 I t~4 521,3-11 f ( II}.,IN217(,

I t',1).704442 -- 145.3315IN - 142.7015n5 - 135.8(,5522 - 13.22765O - 28.242917 - 28.9331119 - 31.875256

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Tuhle 3 Calculated ~;,tues ()11¢l.. Fac,t,r,,r interaction ql I

El'l~:cl ol ~ on llCplh ,~1 re,ldU.fl .trc., dl,lrlhuluul I ,; , l)ir~'clnon I i )

t Ii

- 11.11251)()1) i).os75(x)()

c

1.5(l(xR)o

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df

(). 1251111(I (I.D/5I)IR } I[I)125IS)

{I 1751)Xl 11.1111511tl II q1(~2~11l}

*/ id

q).qlh25qRRI q). 175(~R)

( 3 ) "[he u n i t s o f z w e r e c h a n g e d

r e s i d u a l s t r e s s e s a r e d i s l r i b u t e d d e e p e r . T h e s e restnlts i n d i c a t e t h a t s o m e I t : m s f o r m a t i o n is n e c e s s a r y to o b t a i l l m o r e a c c u r a t e

i n c h ( O.(X)I

results.

S u c h that t h e v a l u e In z w a s b e t w e e n

in. ) t o t e n - t h o u s a n d t h s

from thou~ndths

o f an

o f an i n c h ( 0 . 0 0 0 1 in. ). I and 6 for reasonable

: d u e , o f d e p t h o f r e s i d u a l stress d i s t r i b u t i o n

in hard turning.

The rctincd model was used to predict the residual stresses.

2.3. R
T h e n e w ~ a l u e s o f r.,s a r e g i v e n in T a b l e 6 a a n d b. h,,.s a r e shown To transform

of the depth

the magnitude

model, three changes

in I h c o r i g i n a l

(2)

The

0.000271

i.e.. t h = c . , + c , l n z + c J n polynomial

was

7 a a n d b a n d c,,v in T a b l e 8 4 a n d b. T h e

p h , t s a r e s h o w n in F i g s . 6 a n d 7.

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

( I ) The natural logarithm of z was used instead of : in the polynomial,

in T a b l e

corresponding

were made

r;4lc I b r ;all ~.alues O f t .

z-' + . . . + c , , I n :"'.

valid only

finn( a depth

of

in. d o w n . T h e s u r l ' a c e s t r e s s e s w e r e c a l c u l a t e d t=sing

a separate model

( s i m i l a r to t h e m o d e l

assumed

at s m a l l e r v a l u e s o f z. In : w o u l d a s s u n l c

because

negative values of high magnitude its accuracy.

f o r Z,,.,, ). T h i s w a s

and the model would lose

3.

Discu,~sion

and

The underlying

summary

assumption

ual stresses p r o d u c e d

in t h e e n t i r e m o d e l is t h a t r e s i d -

by identical conditions

are also fairly

S, Mitl, I. C.R. Lit~ / Wear 218 (1998) 21-33

28

Spec 1: Sigma 1 0r

Spec 2: Sigma 1 501 . . . . . . . . . . . . .

~35.7

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sol,,/. ................ ~................... .l~s.~ ~ !

• 35.7

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100

Spec 6: Sigma 1 35.7 __~. 501"................... ":'................... J35.7

oll

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Spec 8: Sigma 1

501"................... "~ /'-. ~................... .13§.7~ "~

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|

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-100 t ................ 127,p.m ......... - ' " t -71.4 0 50 100 Depth (0.0001 inch)

Fi~.6. Polyn.miuhfiucd to residual~,lrc~,~.pr.lilc~,( da~,hL'dline,.) and re~,idual~.ffe~.~.pmlil¢,,predicledhy relim:dmi}d,:lI dolledlint:~.) ( Sigma I I.

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Spec 3: Sigma 2 50~ .................... ;................... ~35.7 ~

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33

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50 Depth (0.0001 Inch)

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Fi~. 7. P.iynonfiM~, filled h) rc',idual ~tre~ prolil¢~ ~daqlcd tmcs ) and rcsitJtlil] ~Irc+,s pr~+tilc, prcdi,+:tcd hy r~llncd m(Kl+l
S. Mittal, C.R. Liu / Wear 218 ( 10981 21-33

30

Table 4 (a) Calculated values of b., (original model---direction Factor or interaction (x)

Direction ( i I

I

E fleet of ~. ( h,,, ) On coefficient (jl 0

(circ.)

-51.139766 -5.9117917 -- 15.5744.79 10.3'41252 3.547941 - 12.878938

- 15458798

17.703534

98.965309 5.37677 - 36.745347 - 62.6'45840 - 14.441715 2.123319 - 18.85(1199

- 56.387832 13.868570 - 39.2611315 72.223246 -23.522596 3.8659(X1 4.959163

159.824325 -2.7O4O53 12.943906 - 112.335621 18.169222 - 3.52{b174 - I n.334648

4.1110364 52.181671 31.8116117 14.842288 6.587168

(1.739394

-56.253658 -4.866331 111.83'411811 34.(~53112 4.4365711 - 1.136957 6.891233

11.138627 1.184239 - 1.4774'43 - 7.511116711 -11.5311523 0.122303 - 1.139399

-0.739427 - n.n'4(1215

11J177870 11.54'4658 ([111866'4 - 0.(X)1385 01173643

( b ) Calculated values of b,,, ( original m o d e l ~ i r e c t ion 2 )

2 ( rad. ) 2 2 2 2

- 611.878185 - 12.74811611 27.60260 -7.8(19468 8.149248 - 0.201971 - (I.239956

2

Table 5 ( a ) Predicted valuer; of c,, ( original model---direction Combination nu. t I )

I

Direction It)

t (circa I I I i I I [

3 4 5 6 7 8

- 86.'47772'4 - 1.663926 2.148'4n2 61.408(116 -6.983328 0.675490 6.1533(12

17.'493684 11.721'.137 - 1.3811272 - 13.827614 1.473423 0.069221 - 1.3926',)4

- 1.298893 - 11.U73346 n. 141886 1.083427 -11.124353 - 11.(118747 (1.1(11(202

I )

Coefficients of plflynomial:, predicted h', model (c,,) n

I

2

3

-36.256'47114 - 48.560223 - 1110.25969 -6t.114718'4 -21.1191557 -36.352391 - 7([902513 - 34.64759

- In4.714642 -64.493962 - 16.861537 - 2.989532 -35.37'4916 -65.9733757 I I 1.842344 54.'41111211

2(16.068444 16t.861127 165.7n7820 113.11117223 71.85'479 1113.1153277 - 26.267696 - 3.5674'43

- 1(17.'422t18t) - 86.681)865 -97.3011973 - 71.6111'42'4 -33.722148 -411.1145867 - 5.444761) - 7.22nf~,'4

21.79fi6o2 17.393931 211.1472711 15.255385 5.55'4511'4 5.714437 1.7881183 1.4537'47

- 1.51o75"4 - 1.18581 - 1.395129 - i .nf4.ff-12 -11.31114'46 -.11.271122 - t). I I I 187 ~ 0.n75272

-

36.72114o6 32.629584 31.151458 26.783749 3.332'44o 4.812898 3.657685 4.86o757

-2.811363 -2.485758 - 2.316377 - 13}15785 -11.17'43'47 - 11.2866113 ~11.181824 .-11.214041

( b ) Predicted values of c, ( original model--direction 2 I 2 3 4 5 6 7

2 ( rad. 2 2

8

2

2 2

-84.8282115 -611.21593 -46.325437 -20.905284 - 117.225553 - '41 653463 -46.125791 - 19.745813

-

1117.829857 117.91686'4 131.573492 157.124107 '43.581111~. 63.6564'4t} -24.253864 -6t.l.fi41133

288.53634o 266.2341'48 271.(84756 262.824515 6.857345 25.s'4371-~'4 62.042654 95.1611111'4

166.0n|7nl 149.025261 146.395257 132.111778 - 16.9213'4'4 - 24.54'4171 -25.239273 -35.56'411116

identical. To check this repeatability, two more specimens

w a s d e e m e d s u l l i c i e n t . T h e p r o l i l e s a r e s h o w n in F i g . 8. T h e

were machined using the following conditions:

residual stress proliles predicted by the original as well as the

V= 425 sfpm (or 21.7 m/s).

r e l i n e d m o d e l for t h e s a m e c u l l i n g c o n d i t i o n s a r e a l s o s h o w n in t h e l i g u r e .

F=0.00275 D=0.0125

ipr ( 1.08 m m / r e v ) . in. (5 mm).

Models with the capability of predicting residual stresses in l i n i s h m a c h i n i n g

o p e r a t i c m s a r e t h e c r i t i c a l l i n k in t h e

development of ntorc complex models which can enable the The variability of the proliles could be checked with stan-

concept of "custom manufactured" roller bearings. Once such

dard variance techniques, but for this paper, a visual check

m o d e l s a r e k n o w n , t h e y c a n b e u s e d in c o n j u n c t i o n w i t h o t h e r

s. ?.littal. C R. L I . / I,'ear 21 '~ t 1 9 1 ~ 21 ¢.¢ Table 6 I a ) Coel'licienls of lillh pd_~ nomial litlcd Io dala l~blaJncd in c~pcrillldlh I relined l l l o d d - - d l r c d l u h I i £ ' . m b i n a t i . n no. I I )

Directi.n I il

C ~ : l l i c i c n h ol cxp,:rmlcnlall~, determined p,,l~, n,,lni,tl i ,- , I

11

I Icircn I I I I

1158.765543 1303.7112(,7 1180.9124~17 ¢~38.23~1252 529.85274(~ IlOfl4llL~l)2 • .:,81 15~C27 871 6¢~7'125

I

I I

2

l t B s f~44t2¢, t4 ~,4 fill6fit ,~ M t17. I f,gtm [ 1817314ogl) 1476.8257xf~ 29111.H81174 1155 *152271 2412.71}71116

1 - ~165 If~ffla7 ~'~21 "11117t l ~'~ I" ~272"~ I 21 ~2 t~17736*~ 1f,[711s5 It)S 3 6 1 "'~ 68"~ 14117 ~.845114 2508 ~22116'~

15311.397984 1690.694270 1787.6210M 1142. ! ! ! ! ] ! 818.31011..I.9 1398.668498 ,~1-4.786352 1274.865294

-345.25199q - 379.174370 -417.4851211 - 277.772122 - 190.275999 -305.852461 -2117.724667 -287.(169O96

29.329122 32.064436 36.319419 24.9218112 16.361657 24.972162 18.3114906 23.882499

I b I Cocflidcnt~ of liflh pd.'.mm,al hucd t,~ dala oblaincd in c \ p c n m c n h ~rctmcd m~,d¢l - d:rcch,m 2 2 Irad.~ 2 2 2 2

f,31.11421,7 583.38 C 2 3 - 724.73L~fil) I112.518~s 273 5 4 s 1 4 7 - 277.8(~(q ]t~ - 1086.245,";72 t122.8¢,¢,7 ~0

2 2

17111.7¢,L4111 1~+~3772811 2042 5741 ~(1 21 t B qfi'll ",l 747 ~,~47g4 821.84"=,':, I~ 2852.18¢~¢~"1 2447 81161151

2r127 13n~ ~,~ 1,~2~ 2 Ifl C(I 21=11 ()~ ~47,~ ~0*~5 4,1fl42,1 1l~7h ~X5~1~4 I 1:',2 ~ 7 7 5 3 IS t C 2 6 m 2478 (),', ~ I'),

11113.915189 1022.226170 1161.364{'178 1475.7(MI43 655.167872 715.869312 1372.7274112 1166.303009

-271.401282 -247.396942 - 272.~M.96~ -325.692169 -- 169.47772-1. h~t.926537 -297.04.5663 - 25d.93D31

24.554929 22.198147 23.878274 26.%4O29 15.524771 16.t,~9992 23.926524 211.844066

Table 7
I)irectiLul I t )

]:llc¢l ul i I h,,. ) 1111 ,;octhdcnl i/) i)

t d J

I ~circ. I I 1 I

df U'

I I

id

I

0

•- 8 % . 3 ~t1538 838~7716 12,";.345494 174.11678~t) -- 32.4857711 96.708 [I)3 183.11111~51~7

2431 84057~ 209.61~3371 -286.0118028 - 4 4 5 117311 X3.f,5~1431~ 2411.4203-13 - 4~11.641 t}~l

2625.45:d22 1761189826 1~1.22flt183 4~,tL41,17¢~7 6~. ~ ~S(IIL~ 241L4fii)211~ 4 U . ~ I 1 ~8

1310.973510 -65.694635 - 48.5442~-J -226.815942 24.212484 119.4691147 - 186.914711

-301.325714 11.141282 3.812977 53.5115173 -3.479303 - 26.23M25 37.588939

25.769511) -11.6911735 0.087667 -4.889205 0.125729 2.145718 - 2.856288

1084.i67114 -10.873436 2119.872586 -1116.650323 82.125720 -16.120331 47.3114174

- 252.972152

21.857591 0.113533 2.[}45631 -2.541253 1.023325 -0.114357 0.295776

t b) ('alculated ~alues . f h,,, ( relined m , d e l - - d i r e c t i o n 2 ) 2 Irad. I

701.5t4118 22.(~24¢~74 - 2~O.IN~(~)I fil.4112341~ I04.31~577 U.477812 - 62.3899fil

2 2 2 2 2

models protile

which

provide

that would

and the bearings This

paper

the capability

infixmalion

be most

introduces of predicting

turning. The relined model

about

favorable

can be machined

the residual

in service

to maximize

an experimental

IqJ8.71 7 0 M - 72.6tJ2727 ~75.32725 ~) 191.61 ~521 257.571~0711 -63.'161075 155 4511982

stress,

conditions, filtigue life.

model

which

r e s i d u a l s t r e s s e s in p r e c i s i o n

has hard

litted the original dala with a high

- 212t318¢~U8 4x3143128 56g.721 114 2073}7t~tH 5 2153C5418 47.4 ~0,235 132.4410-11

degree of accuracy, cations.

A future

0.2{14742

- M.67[530 26.376688 - 14.7218112 2.403624 -6.930972

which should be sufficient for most applipaper

[ 131 by the authors

details on how this model

is used to determine

parameters

enhance

which

would

will provide the machining

fatigue life. Its procedure

is ~ , h o w n in F i g . I. T h i s p a p e r c o n c e n t r a t e s

on modeling

effect of machining

stres~s.

parameters

on residual

the

S. Mittal. CR. Liu / Wear 218 (199¢¢) 21-33

32 Table 8 (a) Predicted values of G, I refined m o d t . l ~ i r e c t i o n I I Combination no. ( I )

Direction (i)

I 2 3 4 5 6 7 8

I (circ.) I I I I I I I

Cot.flicit.nt!, o f polynomials predicled by n.+del I c,, )

0

I

2

3

4

5

- 1233.962273 1228.514719 -11(]5.71594t -713.435957 -454.656175 -1181.607026 -456.352934 -796.471354

3257.152617 3236.1198184 2998.658368 21115.922521 1278.317213 31)99.826547 1354.460707 2214.288626

-3351.544329 -3337.322115 -3331.348554 -2319.285485 - 143(I.7064.55 - 3147.128835 - 1683.862712 -2402.444237

1612.297190 161)8.795138 1705.7219(81 1224.343635 736.410889 1480.567701 926.685543 I It)2.%6143

-362.427403 -361.998941 - 41Xl.309692 -294.947524 - 173.11X)564 -323.027864 - 224.9(X~168 -269.89366

3(I.716612 30.676943 34.931926 26.309381 14.974164 26.359652 19.692395 22.495(XI6

1518.377721 1846.760992 2225.957938 2810.18552(I 930.918426 637.461754 2668.803028 263 I. 190668

- 1843.222571 --2111.118443 - 2453.941555 -2911.582379 - 126n.293953 - 998.425648 -2734.714633 - 2662.59128()

It)21.l)13288 11(15.127849 1244.266359 1392.862249 738.116953u 632.967388 1289,825504 1249.21)4691

- 254.f+U7()21 - 264.1912()3 - 289.699229 - 308,8979111 - 186.271981 - 168.132272 -280.25141)3 - 271.726192

23.31)8652 23.444424 25.12455 I 25.717751 16.7711)47 15.723714 22.681)247 22.1190343

( b ) Predicted values of c,, ( relined mt)d¢l--dircclitm 21

l "~ 3 4 5 6

2 (rad.) 2 2 2 2

7 8

2 2

-555.712214 -658.78586[) - 800.131438 -11)37.116341 -348.95(]261 - 202.464055 - 1010.843824 - 998.268873

Specs T1 and T2: Sigma 1 + + o ~

me

..................

o

I. ..................

! ...................

, ...................

' ................

:

!

i:~

::

,!,

i ....

o

~

-"100~" . . . . . . . . . . . . . . . . . . ; . . . . . . . . . . . . . . . . . . . . . +Al'"m"....... Jl'~J'.'~+". """~"........ i ................. -1.7.1.4

o

~o

40

eo

eo

Depth (0.0001 Inch)

lOO

Specs T1 and T2: Sigma 2 _-+

++

..................

+°f

~ ..................

: ...................

+,..................

~ ....

........ i .................. i..............:::il ................. i................. 1

-~oof ..................

0

: ...................

". . . . . . . . . . . . . . .

20

~,~'+

....... '+/'~'~+"

40 60 Depth (0.0001 inch)

......... ~ . . . . . . . . . . . . . . . . .

80

4-~1-+

1O0

Fig. 8. Measurt.d plols ( ,,ulid lint.~,l, prt.dic'tilm by original inotlcI I dolled lint.~, ) and prediclion b', rc.lincd inodu.I ( dashed line~, I for SpL'u'hllcll,, r l ulld T2.

Acknowledgements The

senior

author

for the preparation

wa~ supported

by NSF

DMI

9612022

of the manuscript.

References I I I M . M . Barash. W.J. Schoech. A semi+anal)Ileal modt.I tll Ihe residual ~.lre~,s zone in orthogtmal machining, in: Advance~. in Machine Tool Dt.sign and Rt.~,t.arch. 197 I. pp. 6 0 3 - 6 1 3 .

121 C . R . l . i u . M . M . Bara~ll, The itlu'challi¢~) Mule t,J the , u N a + e r ul +i surface gt.ncrated b 3` chip-rt.nloxa] pruce~,, palls I alld 2. J. ling. hid. 98 141 11976~ 1195-120~. I 3 ] C.R. lAu. M . M . Baranh. Variahlc,, (;oxt.ming Palt,.'rll~, l}t Mechanical Residual StrL,~n in a Machined Surluc¢, Technical Report .~2+Pmd-X. A S M I - . 345 IL 471h St.+ New Ytlrk. N Y lIH)17. It~X2. 141 Y. Matnuntoh>. M . M . Bara~.h. C R . I.iu. I-I'llrct tll hardne,,~ on lilt' ~,urfaet. inlcgrit~ o l A I S I 4340 ',1~:¢1+ J. I-n~. Ind. 10~ I 1 ~ 6 1 169175. [51 J.E. Mt.rwin, K.I+. Jtlhnson. All analyst, i~l' pla,tic dcti~rnl~ltion ill rolling c~mtact. I'n~c. InMn. Mech. I:,ngr,. 177 125 ) 119631 fi7fi-690.

I t~J z.-c. I_in. Y.-Y. I.in. C.R.I.iu. [~lfL'clUI Ihcrm~d It,rid and mcchantc;d load on the residual slrt',s t,la m;t,:hined ~ ~+lkpi¢ce+lilt. J. %lech. S~:I 33 141419911 263-278. I 71 S.W. Wu. Y. Matr,urntlto+ The effect ol hardllc,, Oil rc,ldu,tl ,trc,,,cin onho~mal machining ol AISI 434O Mccl. J [~llg Ind. I [ 2 ~ It)tit) + 245-252. I S ] S.M. Wu. Tool lilc It,ring b.~ re~pon~c ,url:lcc tllcihlltlc~h~. - :!t, I and 2. J. l-ng. Ind. SO I I tl64. p 11)5- I 16. I¢)1 R.P. Bandyopadh~l). I'.t'l. Too...\pplicati~,n i,I Cx~l~Cl'llllClllill ht~h speed turning, in: the ProL:ccdll~g~~)[ Mzlnu fztclklrin~ hltcrr~atil,nal "t~l). Vol. 4. pp 3-8. [IO1 N.t)¢~.lr~tiZlll. M.K.,.\~ulldl. S. SOlllZl~und.lralil. I;x~rttll~:Zlldllllet]tl,d for prediclin~ residual ,trc,~e, due t,, turnill; ill ,t,lllll¢~, ,loci. ~.\1 ~ Tcch. S 119841 22-26. I I I I D.Y. J~lIl~. Unified optitlli/atit,n model ol ~l IlI,Aehllllll~ prt~¢,, 1,11" ,pccitietl CtllldilJons t~l rTlgtc[lincd~url~cc dnd pr,,tc,, rcrlt,rnlal~tc. Int. J. Prod. Res. 30 t 3 ~ t It)t)21 b47 -(~t~~,. I ] 21 I.('. No,an. LB. ('t~hcn. Rt'~lthlal S~rc~,: XlCdMIrt.'lllt'll[h~. I)lllr~lCll,,h dlld |llterprelztlitln. Sprin~cr-Vcrla~. Ncx~ ~l'~,lk. I tl~T [131 ('.R. l-iu. S. Mittal. Oplin~:d l~rc-,trc~lt~, ti~c ~,url.lcc ,,I ,,(',~mp,~ll~'nt bx Supcrtirllsh I-lard Turllin~ I~,r ~.|~l~.lllltlll/ I,tli~tl~ III R,,IILII~(.'till tact. t~ ~lppcar in Weal

Biographies Dr. Shridhar Mittal r e c e i v e d an M S in indu,,triat e n g i n e e r i n g f r o m the State University o f N e w York at Buffalo in Augu,,t 1990. H i s M S thesis w o r k w a s on just-m-tinac production s y s t e m s . Subsequently. Mr. Mittal enrolled in the P h D prog r a m in the School o f Industrial E n g i n e e r i n g at Purdue

L'nixer~it.x xs here he xsorked on application o f precision hard turnin.S. In 19t)3. he began w o r k with the manul~acturing Proccs,, D e s i g n G r o u p o f Ford Electronics. He c o m p l e t e d hi,, P h D in 19t)6. Currently. he is a consultant with i2 Technologies, a compan.~ ,pecializing in the d e v e l o p m e n t and application o f intelligent planning and scheduling software. Dr. C.R. [.iu i~ a Fellow o f the A m e r i c a n Sex:iety o f Mechanical Engineers ( A S M F ), has serx'ed as a m e m b e r o f the editorial board of Robiotics and C o m p u t e r Integrated Manufacturing and a,, a r e v i e w e r for the N S F E C R p r o g r a m . the N S F regular p r o g r a m s , the U.S. A i r Force M a n T e c h prog r a m . and ~c~ entl technical journals. He has published more thzm I I0 rclcrccd papers and edited four books. Dr. L i u ' s czlrl~ re~earch x~ith a large c o m p a n y in M i c h i g a n resulted in a maior breakthrough and induced a further U S $ 1 0 0 million d c x e l o p m e n t p r o g r a m in the c o m p a n y . T h e technology w a s a majtlr inllueucc in the d e v e l o p m e n t o f a product with US$1 billion per 3 e~tr x olume. He later received, a m o n g others, the ..\SME Blackall A ~ ard for his surface integrity w o r k and the IR IO0 A ~ a r d I ioint ) lk~r his w o r k on error c o m p e n s a t i o n of m a c h i n e tool,. He initiated the o n g o i n g Superfinish Hard T u r n i n g P r o g r a m :it Purdue Uni~,ersity in 1990. H i s main rc,,curch dircction~ ,ire agile single-step Iinishing o f difficultto-cut matcrial~, m~lchine tool accuracy and C A D / C A M / C I M . [te ha~, 6 .~eztrs industrial experience and is n o w a Profc,,,,or ol nlanulLIcluring s y s t e m s e n g i n e e r i n g in the Scht~ol of hldu,trial E n g i n e e r i n g at Purdue University.