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sliding contact
WEAR ELSEVIER
Wear 217 ! 1998) 95-103
Effects of pre-rolling and metal removal on the fatigue life of lubricated rolling/sliding contact Rong-Tsong Lee *, Yuang-ChemgChiou,J.H. Chang Deportment of Mechanical Engineering. Nationa! Sun Yul-Sen Universio', gm~hsiung 80424. Tuiwan
Received29 May 1997:accepted9 January 1998
Abstract In this experiment, after the test specimens are preloaded at different first-step rolling cycles, the ~rfacc layer of the lower speed roller is ground to different depths by a grinder along the radial direction. With a new higher speed roller, the effects of the ground depth and firststep rolling cycle on the fatigue life of lubricated rolling/slidingcontact are investigated using a 0.45% carbon steel pair. Remits .showthat the prerelling cycles with metal removal can improve the rolling fatigue life. It is found that when the surface hardness of the specimen starLs tO approximate the saturated value at the first-step roiling cycle with the ground depth to the position of its maximum ha~duess, the rolling fatigue life with this w¢loading operation is 3.3 times that with the normal operation for the ~coud-step load of 588 N. This increment in the rolling fatigue life can be reasonably explained by the measured plastic flow of the surface layer and the theoretical results of the residual stress below the contact surface. © 1998 El~vier Science S.A. All rights reserved.
Keywordw Plasticflow:Rollingfatiguelife:Premllingoperation:Metalremoval
!. Introduction Pitting often occurs on the machined surface of the lubricated rolling/sliding contacts, such as gears, roller, and hearings. The formation mechanisms of fatigue cracks have been investigated by many r e , a r c h reports. Merwin and Johnson [ I ] used the elastic-plastic theory to analyze the residual stress of contact surface layer. Results showed that the changes of the plastic flow had a significant effect on the rolling fatigue life. Shima et ai. [2l, and Chion and Hwang [ 31 investigated the effect of the plastic flow of the surface layer on the propagation of fatigue cracks. Broszeit and Zwirlein [4] investigated the effect of the residual stress on the fatigue life under various residual-stress distributions of the surface layer. Fujita and Yoshida [5] used the initial release of residual stress or the minimum value of the principal shear stress/hardness ratio to predict the location of the u n i t of fatigue cracks and the revolutions of rolling/sliding contacts. Muro and Tsushima [ 6 ] and Muro and Tokuda [ 7 ] indicated that the compressive residual stress was significantly influenced by the maximum shear stress of the contact surface at the beginning of the rolling/sliding contacts. Moreover, the residual stress was proportional to the hardness below the contact surface, lshibashi and Yokote [8 I, Kayaba and * Correspondingauthor,Tel.: + 880-7-531-6171: fax: + 886-7-551-8853. 0043-1648/98/$19.00 © 1998El~vicr ScienceS.A. All rightsrc~rvcd. PII S0043-1648 ( 98 ) 00146-X
Suzuki [9] had shown that the hardness in the surface layer incmlzsed gradually to a saturated value under rolling contacts with increasing loading cycle. Soda and Yamamoto ! I0] investigated that the plastic flow occurred on the surface layer due to the influence of shear stress. Futthenm~e, the change of hardness on the surface layer of material was cmvelated with the zone of the plastic flow. It has been known that compressive residual stres~s induced by plastic deformation on rolling contacL~ can increase the surface hardness and create microstruetural or geometrical changes. Hence. Cretu and Popinceanu [11| conducted rolling-fatigue tests where the residual stresses were induced by a Westressing operation using a small number of loading cycles so that the microstruc rural changes could be made apparent. Results showed that there existed an optimum distribution of the residual stress that was capable of leading to a maximum increase in the fatigue life of rolling contact. Yoshida and Fujita [ 12.13] investigated the effects of load and direction of surface rolling before fatigue test on the pitting failure and fatigue life of surface rolled steel rollers under various rolling-slidingconditions. Results showed that the fatigue life increased with increasing load of surface rolling, Fukui and Fujita [ 14] studied the influence of the pieloading driving before fatigue test on the rolling contact fatigue life of Austenitic stainless steel (SUS304.). After the
95
R. Lee el at / Wear 217119981 95-103
testing load was chosen to be a little less or larger than that of the endurance limit under a certain of loading cycles, the surface layer was ground to the depth of the maximum hardness, This procedure is called the preloading operation. Results clearly showed that this pretending operation could significantly improve the fatigue life, but they did not discuss the influence factors on the fatigue life by the preloading operation. Similar results wen: found by Zaretsky [ 15] that the Lundberg-Palmgren equation was modified to show the effects of surface removal, it has been a practice in the railway industry for extending rail life by grinding a portion of the stressed volume of the rail [ 16-18]. As mentioned above, the fatigue life is significantly increased by the processes of prerolling and metal removal. This technique can be widely applied in improving the roiling fatigue life by grinding a portion of the stressed volume of the contact surfaces before the pitting. Therefore, the effects of the ground depth and the first-step rolling cycle on the fatigue life of lubricated rolling/sliding contacts require elucidation. In this study, rolling contact lives under various test conditions are investigated theoretically and experimentally.
Vpulley ~
Inductionmotor Gem
~N~'~. i "\
bee
Testspecimens , ChonoeQeors
\\ Loodio9
" \ _ W " --"
Oil
lever
~ Coiledsgring ; {22.SNmm "t) 0""1~ . Hnndll
tonk
Fig. i. Schemalic diagram of Nishihara-type ~oller testing machine.
(a)
(b)
2. Experimental procedures and conditions The rolling fatigue test was conducted by using a Nishiham-type roller testing machine, which is described in detail elsewhere [3]. The schematic diagram of this machine is shown in Fig. I. In this figure, the higher and lower speed roller specimens were driven respectively by the induction motor through several stages of gears that are used to adjudge the slip ratio between the rollers. The normal load was applied on the roller specimen using a compressive coil spring with loading level. The circumferential speeds of the higher and lower speed rollers were 1,571 m s - l and 1.257 m s *, respectively, and its slip ratio between the rollers was 20%. In this paper, the rolling cycles oftbe higher speed roller were counted, The paraffin base oil. [SO 32 ( 30cSt at 40°C, 5.14cSt at 100°C), was supplied to the roller pair at a flow rate of 40 ml/min. The oil temperature was maintained at 25 + 5°C. The roller specimens were made of medium carbon steel ($45C). The size and shape oftbe test specimens are shown in Fig. 2. They were heated to 850°C for about 30 rain, and then cooled in the furnace slowly to room temperature. Alter heat treatment. they weft finished by a grinder and a grade-800 emery paper to remove the oxide layer, so that their surface roughness R~ was about 0.4/zm. The measurements of plastic flow, hardness, and SEM micrograph in the layer surface are given in a previous report [31, but the experimental process in this study is different in this paper. With the annealed, ground, and cleaned rollers, the rolling contact tests were conducted under the first-step load of 980 N orthe H e ~ i a n stress.p.= 1.235 GPa for three numbers of rolling contact cycles, 5 x l 0 4 . I.SX 10s, and 2.8x I0 ~ cycles. When the frictional coefficient is assumed to be 0.098 and the lubricant pressure is neglected, the subsurface stresses
dimensions in mm
(c) Higher speed roller
\
Lower speed roller Fig. 2. Dimensionsof test rollers: (a) lowerspeed roller; (hi higher speed roller; (c) variablesin the contactingcylinders,wherethe suffixi = I and 2 indicate without and whh grindingsafter the tirst-stcprolling cycles, can be obtained [ 19]. In the calculation of the maximum shear stress, the distribution of residual stress caused by repeated rolling contact was also neglected. The semiwidth of Hertzian contact was given by 0.168 ram, the maximum shear stress was 0.3047 p,, and the position of the maximum shear stress was located at 0.124 mm below the contact surlace. After a predetermined number of first-step rolling cycles were achieved, the lower speed roller was ground to different depths by a grinder along the radial direction to provide harder roller surface. The above operation is called the preloading operation in this paper. The test conditions for the preloading operation is given in Table I.
97
R Lee et al. / Wear217 (1998~95-103
Table I Experimentalcondilionsin the preloadingoperation Fi~t.steprolling cycles 5 x l(~ cycles 1,5xlO~cycles 2 , 8 x 10~ cycles
crack occurred on the contact surface in the second-step rolling test. Furthermore, the displacement of the plastic flow in the surface layer of the follower is also measured.
Grounddel~h.D(~m) 30
70
IlO
150
170
28O
50O
0 0 0
0 0 0
0
0 0 0
0
0 0 0
0 0
3. Esperimemal madls 3. i. CharacreristiL:l o f the surface layer after the preloading operation
It was discussed by Chiou and Hwang [3] thai the plastic flow of the lower speed roller moves towards the direction of
E .
rotation and thai of the higher speed roller .shifts towards the direction of friction force due to the action of the friction force during the rolling test. Moreover, the displacement of plastic flow for the higher speed roller is much smaller than that for the lower speed miler at all rolling cycles, and the initiation of a i~igue crack was not observed on the c o n t a c t surface of the higher speed roller. Hence, only the lower speed roller is investigated in this paper, Fig. 3 shows the typical profiles of the plastic flow on the surface layer of the lower speed roller (i.e., z = O in Fig. 2c) after the first-step rolling tests under three numbers of rolling c o n ' ~ t cycles, 5 x I04, 1.5x 105, and 2.8x 105. It is noted that the curves are symmetric along the centre line o r x axis and independent ofx. Fig. 4 shows the corresponding h a r d n e s s distribution below the contact surface taken from the centre of tl,~ Irack ( i.e., y = 0 in Fig. 2c). it is .seen from Figs. 3 and 4 that the plastic flow and the surface hardness increase with increasing number of rolling cycles, and they slat[ to approximate the satu-
2.80x10 ~
+ i.50xl0 s A 5,O0x104
.o 1.O i •~- 0.0
,
i ~ 1 , i - Z o - 1 'z - ! , 0 ~
,
i | ! 0.0 ~
~ i'W'nlm~ I I 1.0 l,S 2.0 2.5
Dis~lce fi'omcontactcenter, mm Fig. 3. Variationof the displaccraentof plasticflowwith the lir.~t-steprolling cycle.
The second-step rolling test implies that the hardened surface of the lower speed roller induced by the pre|oading operation was rolled with a new higher speed roller under the same test conditions (980 N, 1(300rpm, and 20% slip ratio). The fatigue life of the lower speed roller was defined as the number of rolling contact cycles until the pitting or the fatigue
x 2.80x 10 ~ A t.50xlO 5 [3 5.00x 10"
i x
350
x&
•r
~00
i 0 A&z O
6 x &
O Oo
X Q &
.o
t
ul .m
DO
2OO
G
x
t.
ooO'. •
ill
fi
150 0.0
Depth below the contact surface, Fig. 4. Varialionof microhardnesswiththe lirst-stcprollingcycle.
nun
R, Lee et ul. I Wear 217 ¢19981 95-103
98
rated values near !.5 X ! 0 s cycle. Table 2 shows the effect of the first-step rolling cycle for the lower speed roller on the rolled radius, r~, the displacement of the plastic flow on the center of contact surface,ft, and the depth range of the severe plastic flow below surface, zt"z,.. Here the criterion for severe plastic flow is judged from the optical micrograph of subsurface layer according to the conditions of deformation (Fig. 8 in Ref. 13l ). It is found from Table 2 that the rolled radius of the lower speed roller decreases slowly, and the plastic flow increases with increasing predetermined number of rolling cycles. However, the depth range of the severe plastic flow is insignificantly influenced by the predetermined number of rolling cycles. Therefore, the optimum predetermined number of rolling cycles should be 1.5× 105 where the surface hardness and the displacement of plastic flow were quite close to the saturated value. After the first-step rolling cycle achieved a predetermined number, the surface layer of the lower speed roller was removed to different depths by a grinder. The typical profile of hardness below the contact surface is shown in Fig. 5 for a first-step rolling cycle of 1.5× los under four ground depths. It is seen from Fig. 5 that the distributions of microhardness with the ground depths of 70, 150, and 280 pm are quite similar to that without grinding, but they move towards the left with increasing ground depth due to the removal of subsurface layer. This result indicates that the effect of the grinding process on the distribution of hardness below the contact surface is insignificant, but its distribution has been changed. Generally, the effect of work hardening on the
microhardness becomes signilic.~at for the ground depths of 70 and 150/~m. 3.2. Rolling-fatigue-life tests with preloading operation
In the process of preloading operation for three first-step rolling cycles. 5X 10~. 1.5× l0 s. and 2.8× los, the surface layer of the lower speed roller was removed to different depths by a grinder along the radial direction to provide harder roller surface, as shown in Table I. With a new higber speed roller, the second-step roiling test was conducted under the same operating conditions until the pitting or the fatigue crack occurred on the contact surface. Fig. 6 shows the relationship between the fatigue life and ground depth in three first-step roiling cycles. Results show that the fatigue life is insignificandy influenced by the ground depth, when the ground depth, D, is smaller than 30 ,am. However, the fatigue life increases with increasing ground depth for D > 30 pm, and the fatigue life achieves the maximum value for D = 150 #m. Moreover, the fatigue life decreases with increasing ground depth for D > 150/zm, and the fatigue life achieves a saturated value for D > 5 0 0 / z m . This saturated value is the same as that without the preloading operation, it is also seen from Fig. 6 that the first-step rolling cycle of 1.5 X IOs has a longer fatigue life than those of 5 x lif t and 2.8 × lOs cycles, when 10 "6
Q ao
8
a 2"8x10S o 1.5x10~ o 5.0xlO
a
Table 2 Changes in miler radius, r,, the displacement of plastic flow. f,, and the range of.~ver¢ phtsli¢ flow. :, ~ :.~. after the lirst-step rolling tbr the lower speed roller
x
6
a
:.= ,..r. 4
9
a
0
First-step roiling cycles
r, ( m m l
f, (/zml
:, ~ : : (/zm)
5 x 104 cycles 1.5 x Iff' cycles 2.8 x I0 :~cycles
14.957 14.950 14.937
330 390 410
811~ 170 .gO~ 180 80 ~ 180
o 21 n
,a.
o'°
t
,
J
1
2oo 3oo 400 Ground depth, l.mt
100
t
5oo
600
Fig. 6. Effects of first-step rolling cycle and ground depth oii the fatigue life of the second-step rolling contacl. 4OO 12
35o
Ground depth * O~ m
.P~-i O
/W~
\
-~
3°° /-~=-'o,."%,.
~
25f)
c=
x
.280 ~
o
8
9
s
o
b,.~
4. ~ o 2(10
~ r
~u.O
P 0.2
n
I 0.4
- - "~ u
3
a
.a Ig
a 2.8xt0 s o 1.5x I 0 f o 5,0xi0
~to
70/zrn
0
o o ._o
2 I
0
O.o
Delah below the contact surface, ram Fig.. 5. Microhardness changes resulting from the ground depth at the lirstsk-p rolling cycle of 1.5 x tO~'.
I IOO
,"
~o , ~ o '500
Ground depth, pm Fig. "7. Effects of ti~t-stcp rolling cycle and ground depth on total l'.tig.ue life.
R. Lee el al. / Wear 217 ( 1998195-103
99
Table 3 Effectof grounddeplh./3, on Ihecontactwidth. B,_,the radius,r,, the .semiwidthof Henziancontact,a. and the Ikfcziancontactpressure,p~.at different|ir..ctstep rollingcycles D
30 70 150 280
5 × lip cycles
1.5× I0s cycles
2.8 x IO"cycles
B;
e.
a
p,.
B:
r:
a
p.
B.
r;
a
p.
(rnm)
(mini
(pro)
IMPa~
imml
(mm~
(p.m)
IMPa)
(mm)
(romp
(#rn)
IMPal
3.36 3.47 3,47 3.30
14.93 14.89 14.81 14.68
159 156 156
1168
3,39 3.48 3,49 327
14.92 14.88 14,80 14.67
158 156 155 t60
1163 1149 1149
3.3"• 3.47 3.48 3,28
14.91 14.87 14.79 14,66
159 156 156
1167 1151 1151
160
1188
160
1151 1152 1184
the ground depth is larger than 30 btm. it should be noted that the fatigue life discussed above does not include the first-step rolling cycle. Fig. 7 shows the effect of ground depth on the total fatigue life with different first-step rolling cycles. In this figure, the total fatigue life is defined as the sum of the fatigue life for the first-step and the second-step rolling cycles, and zero ground depth indicates no prelo',gling or normal operation. In this figure, the total fatigue life under normal operation is about 3,2 × 105 cycles, and the total fatigue life is made dimensionless in the following manner, the ratio of total fatigue life to 3.2× IOs. it is seen from Fig. 7 that when the predetermined number of rolling cycles was i.5 × IOs or 2.8× 105, the total fatigue life for the ground depth of 150 /s,m was 3,3 times that for normal operation. As a whole, to improve the fatigue life of rolling contact by the preloading operation, the number of the first-step rolling contact cycles should reach 1.5 × l0 s. where the surface hardness starts to approach a saturated value, as shown in Fig. 4. Moreover, the ground depth is 150/zm, or 0.89a, or near the position of the maximum hardness below the contact surface, where a is the semiwidth of Hertzian contact. Under the above-mentioned preloading operation, the total fatigue life can be improved significantly.
4. IKscussion it has been seen from Fig. 6 or Fig. 7 that after the preloading operation, the fatigue life of the second-step rolling contact is significantly increased. Generally, this increment in the fatigue life can be reasonably explained as follows:
lltlO
life was insignificant [20]. However, the others [21,22] found that the fatigue life decreased with increasing hardness difference. Therefore. the hardness difference between the higher and lower speed rollers could not increase the fatigue life of rolling contact. 4.2. The effect o f contact pressure after preloading operation on the fatigue life
After the preloading operation, the radius of the lower speed roller, r_,, and the width along the contact. Bz, would be changed, .so that the Hertzian contact pressure, p~, and the Hertzian contact ~miwidth, a, are a l ~ changed, where the nomenclature is shown in Fig. 2c. Table 3 shows the data of the contact width. Bz, the radius, r_,,the semiwkhh of Hertzian contact, a, and the Hertzian contact stress, p~, after different preloading operations. Based on Hamrnck [ I91. the value and the position of the maximum shear stress can he easily obtained by a~suming the frictional coefficient of 0.098. The maximum shear stress has a value between 0.285, and 0.2938 Po and occurs at 0.87a>_x>__O.41a and O.'/2a_> :__>,0.45a for various preloading operations, it is.seen from Table 3 that the Hertzian contact pressure with various preloading operations quite approximates that with normal operation except that with the smaller amount of ground depth and the first-step rolling cycle. According to an investigation of the effect of load on the fatigue life by Chiou et al. [231. a little change on the Hertzian contact pressure can not improve the fatigue life significantly. 4.3. The effect o f plastic flow on the fatigue life at the conlac! ce~iter
4. I. The influence of hardness difference on the fatigue life
Because the surface hardness of lower speed roller is significantly increased by the preloading operation, the surface hardness between the higher and low speed rollers is different during the ~cond-step rolling contacts with a new specimen as the higher speed roller. Fujita and Yoshida 1201. Fujita and Fukui 1211, and Huang and Chen [221 experimentally investigated the effect of hardness difference on the fatigue life of rolling contact. Results showed that the pitting only occurred on the surface of the low speed roller [ 20-22 I, and the effect of hardness difference on the rolling contact fatigue
Fig. 8 shows the effect of ground depth on the displacement of plastic flow at the contact centre (i.e., y = 0 and z = 0 in Fig. 2c) in the ~cond-step rolling test under various firststep rolling cycles. It is ~en from Fig. 8 that when the gronnd depth, D, is larger than 100/zm, the. plastic flow increases with increasing ground depth under the .same first-step rolling cycle, and then approaches to a ~tumted value (410/zm) of plastic flow which is the same as that without the l~eloading operation. On the other hand, under the .same ground depth, it i.~ found that the effect of the first-step rolling cycle on the plastic flow is not .so obvious. Generally. the plastic flow with
R. la'e el al, I Wear217 ( 1098195-103
1110
Merwin and Johnson I I ] and Suh I24], it is found that the only possible state of residual stress reduces to
400
(o',.,)r=f(:), u 300
(fT.v).) r = v'f(~.). (a~:)r =(o',=),~0,
~" i,s~1o,'
o
:o E
o 5.0x10
o
~. ioo
I
O0
I00
I 200
i 300
i 400
l 500
600
Ground dcpzh, rum Fig. 8. Effectsof lirst-steprollingcycleand grounddeplh on displ~ceraent of plastic flow. the first-step rolling cycle of 1.5x 10s is quite close to that with 2.8× 105 cycles, but less than that with 5 × 104 cycles. This difference becomes quite clear for D >__150 p.m. It is seen from Table 2 and Fig. 4 that the severe plastic layer induced by various first-step rolling cycles is not ground lbr D = 30 /,Lmor just ground a little for D = 70 p,m. in other words, they still exist on the surface layer before the second-step rolling. However, most of severe plastic layers are ground away lot D>_ 150 p.m. or they almost do not exist before the secondstep rolling. Therefore, for D = 30 or 70 p.m, the total displacement of the plastic flow on the surface layer must include the displacement of the plastic flow induced by the first-step rolling cycle, as shown in Table 2, and that produced by the second-step rolling cycle, as shown in Fig, 8. However, for D > 150 p,m. the total displacement of the plastic flow on the surface layer is quite close to the displacement of the plastic flow in the second-step rolling cycle, because most of severe plastic layers are ground away, As mentioned above, it is found that the total displacement ot the plastic flow in the surface layer for D-- 150 p.m is near the minimum, so that its fatigue life is the maximum, as shown in Fi 8. 7.
where v is the Poisson's ratio, the residual stress is denoted by suffix r, and the stress components o',,+ ~r,.,, o;,=. and ~,: with their orientation of axes are shown in Fig. 2c. This equation indicates that the residual stresses are independent ofx and y, and only a function of z (i.e.,f(z)). It is also seen from Fig. 4 that when the loading cycle approaches 1.5 × I05, the hardness beneath the contact surface almost achieves a saturated value. Under this condition, the position of the m a y imum hardness agrees very well with the location of the maximum shear stress predicted by the elasticity analysis of contact mechanics. Hence. it is assumed that the equilibrium state is achieved at the position of the maximum hardness. As a result, there was no further change in (O',~)r and (o',.,.L. Consequently. the stress state in the position of the maximum hardness must obey yon Mises' or distortion-energy yield criterion. The appropriate von Mises criterion with the residual stress can be written as { I_ l(°',',' + (°',,')~-°'--)-" . . +{°'---°', . . . +Co',.,
Since a certain depth of surface layer is ground in the preloading operation, the change of the hardness distribution beneath the roller surface is observed belbre the second-step loading cycle, as shown in Fig. 5. In order to understand the influence of these changes on the fatigue life. the residual stresses are analyzed. It was discus~d by Muro and Tokuda 17 ] that the change in hardness. AH. is correlated with the change in the residual stress. Ao'~, beneath the roller surface. This relationship can be assumed to be linear as (i)
where C is a constant. According to the theoletical analysis of the compressive residual stress due to rolling contact by
, - (°', , ),)2
+(oT,.,)~-~.,.,.-(tr,.,.)r)'-+O(~r~:+~r~,
(3)
+ ~ r ~ , ) l ) " 2 = Vt'3k where k is the yield stress in simple shear. By making use of Eq. (2), Eq. ( I ) can be written as A(rr,, )~ =
C-AH v
A(~r,, ), = C.AH 4.4. The distributions o f hardness and residual stress below the contact surface after the prehmding operation
Atr,=C-AH.
(2)
2.8x10 s
~.2oo
(4)
Fujida and Yoshida [251 thought that the residual surface stresses of annealed rollers were almost zero in the virgin state. Hence, the change in the residual stress, Actr, beneath the roller surface is assumed to be equal to ~r, or A~r, =o',
(5)
For the case with the rolling cycle of 1.5 × l0 s, the change in the hardness, AH, is given as AH=H-H,
(6)
where H, = 187H, is the hardness of the virgin state and can be seen in Fig. 4 for => 1.2 ram. The subsurface stress analysis derived by Johnson [ 26 ] and Hamrock [ 19 j is used here to define the stress in various directions at the position of the maximum hardness. By substituting these subsurface stres~s and Eq. (4) into Eq. (3). the constant C gives about - 0.0003. After the constant C is calculated, the distribution
R. I~e el ,/. I Wear 217 ~1 ~ 8 ) 05-1#3
~r
1~b~low~contact~.
I01
z m"
~f
{
~:ii~;!iii~iiii',
•'. ~ :
.>:~..,:~:i~:;~.:::!~.~<: - ,-~::~:~:.~::-::~ ..............:-~ ~-z~::N.....
0.5 ~ 2 : ~"'."':" , J • '.~2'~2;'.;::.:i-~ :~ /."•;:::..... ' ~:N:"X.'.'.'::"?I;;~'×~I:'~ -" i~ -: ~h-::'";~
0.10
-l.O
100 .>o_
-~.~
-I.2;
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1.2.
'r,.t • '"
1.5
~.O
.~. I
*
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,
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I
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,
i
i
•
O
O'O00.O
0.$ 1.0 I.S 2.0 Dime~si~lessdeWh Ix:low dzccomz~:suKac¢, z / a Fig. 9. Residual stress distributions ( ( Act,, ),. axial: and 13,~,, p,,cireumferomial) due to the first-step rolling cycle of 1.5 x l(P.
2
°~ O.O
-I.B
of residual stresses, A(o;~,), and A(o',.,.), can be calculated from Eq. (4) by using the hardness distribution. Fig. 9 shows these typical distributions of residual stresses by using the hardness distribution shown in Fig. 4. it is noted that these residual stres~s are only a function of=. as shown in Eq. ! 2). To demonstrate this similarily, when the frictional coefficient (p.) was assumed to be 0.098 with r,= 0.3333. the maximum principal shear stress was found to be 0.281po at points (0.8 la, 0.49a). This resuh is in good agreement with Merwin and Johnson's results [ l l where the maximum principal shear stress was found to be O.281 p. at points (O.866a. 0.452a) for p = 0 . 1 and ~,=0.3. Hence, based on the procedure di~uss above, the residual stress distribution beneath the lower speed roller has been obtained, Moreover, differen! ground depths would result in the change of the residual stress distribution beneath the roller surface. As a result, the shear stress distribution beneath the roller surface is also changed before the .,~cond-step loading cycle. Fig. IO shows the contour of the shear sl~ss at the beginning of the second-step loading cycle after the first-step loading cycle of I.~ X IO"~under different ground depths 30 #m. 70 p.m. 150 p.m and 280 p.m. It is ~en from Fig. IO that the area enclo.~s by a curve of the principal shear stress. 7= 0.28pn, increases with increasing ground depth for D > 70 p.m,. This result is compared with the displacement of plastic flow. as shown in Fig. 8. A very good agreement is found where the displacement of plastic flow increa~s with the maximum shear stress or ground depth for D > 70 p.m. Furthermore, the shaded zone shown in Fig. IO shows that the severe plastic layer still exists after the preloading operation for D < 180 p.m. This zone moved towards the surface layer with increasing ground depth for D < 80 p.m. The shaded area decreases with increasing ground depth for D_>.80 p.m. It is seen from Fig. IOa and b that since the severe plastic layer keeps in the interior zone for D = 30 #m, the effect of work hardening on the surface hardness for D = 30 p.m is smaller than that for D = 70 p.m. Consequently, although the displacement of plastic flow for D = 30 pm is quite etose to that for D ~ 70 p.m after the second rolling, the fatigue life for D = 30
,.
"~:.i-'-'~::-,...-~"~<~.:~N~i'*:~"~::'~N-° :'~i:~i'i,g%,'-~ -I,'~
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.
041
Fig. IO. Contour~ of dirnensionles.'~ principal ...h~-arstr¢.~. ;'/p,, at [ha he[inning of th',~ ~cnnd-~tep rnlling cycle for II~ liz.~l-.~tep roiling cycle of I.SX 10', and I N gruund dcplhs. (a) .'g) pro. tb) 70pro. i c ) I.~O#m. and
(d) 2~I0p.m: wlvzre( + ) indicatesthe I~:ationot"the maximumprincipal shear stress, and the sh',aledzonerepre.,~n[~ihe .~vereplastic flowzoneduc Io the prcl~?ading op~ralion.
#m is much smaller than that for D = 70 #m. It is .seenfrom Fig, 10c that only about 30 pm .severe plastic layer (shaded zone) keeps at the roller surface for D = 1.50pm. However, this shaded zone is subjected to tbe lower shear stress during the ~cond-step rolling cycle, This implies that a harder surface due to the work hardening is subjected to lower loading cycle for D-- ! 50 pm. Moreover. the shaded zone for D = 70 pm is subjected to higher shear stress cycle. Hence, the fatigue life for D = 70 pm is much smaller than that for D = 1.50 pro. It is seen from Fig. 10d that no shaded zone is found in the roller zone f o r D = 280 p.m. that is, the effect of work hardening on the surface hardness can he ignored. Thcrelbre. its fatigue life is almost the same a.s that without preloading operation.
102
R. Leee7aL / Wear217 (1998) 95-103
4.5. The effect o f second-step hmd on the fatigue life
2000 First - step tolling cycle : [.5x10 s I
As mentioned above, the effect of work hardening due to the severe plastic layer on the fatigue life is significant. However, this severe plastic layer can not be subjected to a higher shear stress in the second-step loading cycle, Otherwise, it is easy to achieve a saturated value of the displacement of plastic flow. As a result, the fatigue crack is propagated into pitting at the severe plastic layer. It has been found that the best preloading operation is the loading cycle of 1.5 × l0 ~ under the load of 980 N with the ground depth of 150/zm. Using this preloading operation, the effect of the second-step load on the fatigue life is shown in Fig. I I. it should be noted that the fatigue life discussed in this figure does not include the first-step rolling cycle, it is seen from this figure that the fatigue life with preloading operation is larger than that without preloading operation. Moreover, this increment in the fatigue life decreases with increasing second-step load. it is found that the fatigue life with preloading operation is 3.3 times that without preloading operation for the second-step load of 588 N. Fig. 12 shows the changes in the displacement of plastic flow on the surface of lower speed roller for various second-step loads. It is seen from this figure that the displacement of plastic flow in the second-step rolling cycle increases with increasing load, and this displacement with preloading operation is smaller than that without preloading operation. This difference increases with increasing second-step load. However, it should be noted that the displacement ratio of plastic flow between preloading and normal operations increases with increasing second-step load. This implies that the smaller the displacement ratio, the larger the fatigue life with preloading operation. In particular, the displacement of plastic flow for the load of 588 N is approximated to zero, as shown in Fig. I I, so that it possesses the largest fatigue life with the preloading operation. Generally, this smaller displacement results from the work hardening in the surface layer by preloading operation.
O
15
u
o First- step rolling cycle : l.Sx10 s Ground depth : 150 pm o Normal operation
o o
o o
500
10CO Load, N
T500
8 2 ooo
Fig. I I. Effectof.,,ccond-stcploadon fatiguelifewhhpreloadingand normal operalions.
~ If~O0
Nomad
olm'auon
1000
~- soo ~x
el
0
500
10o0 Load,
1500
2000
N
Fig. 12. Effectof .~cond-step load on displacemen!of plastic flow with preloadingand normaloperations. 5.
Conclusions
The effects of prerolling and metal removal before the fatigue test on the rolling fatigue life are investigated under the lubricated rolling/sliding contacts using the specimens of medium carbon steel $45C. In this study, the test specimens are preloaded at the first-step rolling cycles, and then the surthce layer of the lower speed roller is removed to different depths by a grinder along the radial direction to provide harder roller surface. This procedure is called the preloading operation. With a new higher speed roller, the second-step rolling test is conducted under various operating conditions until the pitting or the fatigue crack occurs on the contact surface. From the experimental results with the theoretical analysis of the compressive residual stress, the following conclusions can be drawn. ( I ) The plastic flow and the surface hardness increase with increasing rolling cycle. The optimum first-step rolling cycle is found to be 1.5 X 10~ where the surface hardness and the displacement of plastic flow start to approximate the saturated value. (2) The optimum ground depth is found to be 150/,tin, or 0.89a, or near the position of the maximum hardness below the contact surface due to the first-step rolling cycle where only about 30/zrn severe plastic layer or O.18a is kept at the roller surface. Under this grinding process, the effect of work hardening on surface hardness is significant and this severe plastic layer is subjected to lower shear stress during the second-step rolling cycle. (3) The preloading operation can improve the fatigue life significantly. Under the optimum preloading operation, the fatigue life with preloading operation is 3.3 times thai without preloading operation for the second-step load of 588 N. (4) The smaller the displacement ratio of plastic flow between prcloading and normal ol~rations, the larger the fatigue life with preloading operation. The smaller the displacement of plastic flow, the larger the fatigue life with the preloading operation.
I?, Lee et al, I Wear 217 t 1998) 95--103
In general, this smaller displacement in the surface layer results from the work hardening by preloading opefatio~.
Acknowledgements The authors would like to express their appreciation to the National Science Council (NSC-80-O4OI-E110-09) in Tatwan, R.O.C., for the financial support.
References I I i J.E. Merwin. K.L. Johnson. An analysis of plgstic deformation in rolling contact. Prec. Inst. Moth. Eng, 177 (1963) 676-690, 121 M, Shima. Y. Kimum, T. Yamaoto. Mea.surement of subsurface plastic llow in rolling contact. J. JSLE 25 (1980) 817-822. 131 Y.C. Chiou. J.R. Hwang. Relationship between the propagation of fatigue cracks and the behavionr of plastic flow under rolling~sliding contacts---effect of slip ratio, Tribol. Int. 24 ( 1991 ) 101-107. 141 E, Broszeit. O. Zwirlein. Internal stresses and their inflnenee on material stresses in Hertzian contacts---calculations with different stress hypotheses, ASME J. Tribol. IO8 (1986) 387-393. [ 51 g. Fujita, A. Yoshida, The effect of changing the rolling direction on the rolling contac~ fatigue lives of annealed and case hardened steel rollers. Wear 43 I 1977) 301-313. 161 H. Muro. N. Tsushima. Microstructaral. microhardness and residual stress changes due to rolling contact, Wear 15 (19"/0) 309-330. 17 ] H. Muro, M. Tokuda, Residual stress due to rolling contact. J, ,ISLE 21 (9l ( 1976l 621-625 in Japane~. 181 A. Ishibashi, T. Yokote, Effect of number of revolutions and speed on pitting in rolling contact. Trans. JSME 16 ( 1971 ) 646-65,fi. 191 T. Kayaba. S. Suzuki, An investigation of surface damages by rolling contact. Technology Reports. Tohoku University. Japan. Vol. 41. 1976, pp. 2 !-46. I IOI N. Soda, T. Yamanmto, Effect of tangential traction and roughness on crack initiation/propagation during rolling contact, ASLE Trans. 25 12) (1980) 198-206.
103
I I I I Sp.S. Cretu. N.G. Popineeanu, The influence of residnal st~s.~s induced by plastic defomlation (m rolling con"tact fatigue. Wear 105 (1985) 153-170, 112] A. Yosbida, K, Fujita, Study on pitting of ~fface rolled steel rollers ( Ist report). J, JSLE 31 (1986) 276--283 in Japane~, [ 13] A. Yoshida. K. Fujita, Study on pitting of surface rolkd steel roller,~ (2nd report), J, JSLE 32 f 1987l 260-267 in Japane~. { 141 T, Fukui. T. Fujita. Influence of preload driving before fatigne test on the rolling contact fatigue strength of Austenilic slainlesssteel, J. iSLE 35 (1990) 202-206. 1151 E.V. Zaretsky, Effect of surface removal on rolling element fatigue. proc. Int. Conf. On Tribotogy--Eriction, Lubrication and Wear. Fifty Years On. Proc, IMechE. CI47/87. Ig89, pp. 829-.838. 116 [ R.K. Steele. The effect of metal removal, steel cleanliness and wheel load on the fatigue life of rail, Wear 144 ( 19911 7t-87. [ 17] J. Kalou~k, J.O. Igwemezic, Shell-like defecei "and microgeomct~ of griuding. Prue. Int. Conf. On Rail Steeb-DevelopmenL Manufacture and Performance. Pub. G, Kuhn. 1992, pp. 139-145. 1181 R.K, Stee½, Strategies for maximizing rail life. in: J J Kalker et al. ( Eds, ). Rail Quality and Maintenance for Modem Railway Operation. Kluwer Academic Publishers, 1993, pp. 78-97. [ 19l B.J, Hamro~k.FundamentalsofFluidFilmLn~ication.Mcgraw-HilL Chaps. 19aud 20. 1994. 120i K, Fujita. A. Yoshida. Effect of hardness difference on the surface durability and surface failure of steel rollers. Wear 67 { 1981J 187200. [ 21 ] T, Fujita. T. Fukui. Influences of ~hardacss of mating materials on rolling contact fatigue strength of the stainlesssteel. J. JSLE 32 ( 1987 ) 518-523. [ 22 | S.J. Huang. X.H. Chen. ~ influence of surface hardness difference on the contact fatigue strength. Pent. JSLE ;ntere~iorral Tribology Conference. Tokyo. Japan, i983. pp. 91%922. 1231 Y.C. Chiou. R.T. Lee. J.H. Chang. Relation,,hip between propagation of fatigue retook, and behaviou: ~f plastic flow umler rolling/sliding conPact.~---effectof load. Chin. J. Mech.. Taiwan 9 ( 1993 } 17-25. 124 ] N.P. Sah. Surface Interactions. in: P.B. Scnholzi ( Ed. ). Tfibology Technology. Vol. I. Marinus Nijhoff Publishers. 1982. pp. 110-167. [ L51 K. Fajida. A. Yoshida. Macroscopic and microscopic changes in the surface layers of annealed and ca.~-hardened steel rollers due to roiling contact, Wear 43 (1977) 3OI-313. i261 K,L. Johnson. Contact Mechanics. Chap. '). Camh'idge Univ. Press. 1985. pp. 102-104 aud 285-295.
Wear 217 ! 1998) 95-103
Effects of pre-rolling and metal removal on the fatigue life of lubricated rolling/sliding contact Rong-Tsong Lee *, Yuang-ChemgChiou,J.H. Chang Deportment of Mechanical Engineering. Nationa! Sun Yul-Sen Universio', gm~hsiung 80424. Tuiwan
Received29 May 1997:accepted9 January 1998
Abstract In this experiment, after the test specimens are preloaded at different first-step rolling cycles, the ~rfacc layer of the lower speed roller is ground to different depths by a grinder along the radial direction. With a new higher speed roller, the effects of the ground depth and firststep rolling cycle on the fatigue life of lubricated rolling/slidingcontact are investigated using a 0.45% carbon steel pair. Remits .showthat the prerelling cycles with metal removal can improve the rolling fatigue life. It is found that when the surface hardness of the specimen starLs tO approximate the saturated value at the first-step roiling cycle with the ground depth to the position of its maximum ha~duess, the rolling fatigue life with this w¢loading operation is 3.3 times that with the normal operation for the ~coud-step load of 588 N. This increment in the rolling fatigue life can be reasonably explained by the measured plastic flow of the surface layer and the theoretical results of the residual stress below the contact surface. © 1998 El~vier Science S.A. All rights reserved.
Keywordw Plasticflow:Rollingfatiguelife:Premllingoperation:Metalremoval
!. Introduction Pitting often occurs on the machined surface of the lubricated rolling/sliding contacts, such as gears, roller, and hearings. The formation mechanisms of fatigue cracks have been investigated by many r e , a r c h reports. Merwin and Johnson [ I ] used the elastic-plastic theory to analyze the residual stress of contact surface layer. Results showed that the changes of the plastic flow had a significant effect on the rolling fatigue life. Shima et ai. [2l, and Chion and Hwang [ 31 investigated the effect of the plastic flow of the surface layer on the propagation of fatigue cracks. Broszeit and Zwirlein [4] investigated the effect of the residual stress on the fatigue life under various residual-stress distributions of the surface layer. Fujita and Yoshida [5] used the initial release of residual stress or the minimum value of the principal shear stress/hardness ratio to predict the location of the u n i t of fatigue cracks and the revolutions of rolling/sliding contacts. Muro and Tsushima [ 6 ] and Muro and Tokuda [ 7 ] indicated that the compressive residual stress was significantly influenced by the maximum shear stress of the contact surface at the beginning of the rolling/sliding contacts. Moreover, the residual stress was proportional to the hardness below the contact surface, lshibashi and Yokote [8 I, Kayaba and * Correspondingauthor,Tel.: + 880-7-531-6171: fax: + 886-7-551-8853. 0043-1648/98/$19.00 © 1998El~vicr ScienceS.A. All rightsrc~rvcd. PII S0043-1648 ( 98 ) 00146-X
Suzuki [9] had shown that the hardness in the surface layer incmlzsed gradually to a saturated value under rolling contacts with increasing loading cycle. Soda and Yamamoto ! I0] investigated that the plastic flow occurred on the surface layer due to the influence of shear stress. Futthenm~e, the change of hardness on the surface layer of material was cmvelated with the zone of the plastic flow. It has been known that compressive residual stres~s induced by plastic deformation on rolling contacL~ can increase the surface hardness and create microstruetural or geometrical changes. Hence. Cretu and Popinceanu [11| conducted rolling-fatigue tests where the residual stresses were induced by a Westressing operation using a small number of loading cycles so that the microstruc rural changes could be made apparent. Results showed that there existed an optimum distribution of the residual stress that was capable of leading to a maximum increase in the fatigue life of rolling contact. Yoshida and Fujita [ 12.13] investigated the effects of load and direction of surface rolling before fatigue test on the pitting failure and fatigue life of surface rolled steel rollers under various rolling-slidingconditions. Results showed that the fatigue life increased with increasing load of surface rolling, Fukui and Fujita [ 14] studied the influence of the pieloading driving before fatigue test on the rolling contact fatigue life of Austenitic stainless steel (SUS304.). After the
95
R. Lee el at / Wear 217119981 95-103
testing load was chosen to be a little less or larger than that of the endurance limit under a certain of loading cycles, the surface layer was ground to the depth of the maximum hardness, This procedure is called the preloading operation. Results clearly showed that this pretending operation could significantly improve the fatigue life, but they did not discuss the influence factors on the fatigue life by the preloading operation. Similar results wen: found by Zaretsky [ 15] that the Lundberg-Palmgren equation was modified to show the effects of surface removal, it has been a practice in the railway industry for extending rail life by grinding a portion of the stressed volume of the rail [ 16-18]. As mentioned above, the fatigue life is significantly increased by the processes of prerolling and metal removal. This technique can be widely applied in improving the roiling fatigue life by grinding a portion of the stressed volume of the contact surfaces before the pitting. Therefore, the effects of the ground depth and the first-step rolling cycle on the fatigue life of lubricated rolling/sliding contacts require elucidation. In this study, rolling contact lives under various test conditions are investigated theoretically and experimentally.
Vpulley ~
Inductionmotor Gem
~N~'~. i "\
bee
Testspecimens , ChonoeQeors
\\ Loodio9
" \ _ W " --"
Oil
lever
~ Coiledsgring ; {22.SNmm "t) 0""1~ . Hnndll
tonk
Fig. i. Schemalic diagram of Nishihara-type ~oller testing machine.
(a)
(b)
2. Experimental procedures and conditions The rolling fatigue test was conducted by using a Nishiham-type roller testing machine, which is described in detail elsewhere [3]. The schematic diagram of this machine is shown in Fig. I. In this figure, the higher and lower speed roller specimens were driven respectively by the induction motor through several stages of gears that are used to adjudge the slip ratio between the rollers. The normal load was applied on the roller specimen using a compressive coil spring with loading level. The circumferential speeds of the higher and lower speed rollers were 1,571 m s - l and 1.257 m s *, respectively, and its slip ratio between the rollers was 20%. In this paper, the rolling cycles oftbe higher speed roller were counted, The paraffin base oil. [SO 32 ( 30cSt at 40°C, 5.14cSt at 100°C), was supplied to the roller pair at a flow rate of 40 ml/min. The oil temperature was maintained at 25 + 5°C. The roller specimens were made of medium carbon steel ($45C). The size and shape oftbe test specimens are shown in Fig. 2. They were heated to 850°C for about 30 rain, and then cooled in the furnace slowly to room temperature. Alter heat treatment. they weft finished by a grinder and a grade-800 emery paper to remove the oxide layer, so that their surface roughness R~ was about 0.4/zm. The measurements of plastic flow, hardness, and SEM micrograph in the layer surface are given in a previous report [31, but the experimental process in this study is different in this paper. With the annealed, ground, and cleaned rollers, the rolling contact tests were conducted under the first-step load of 980 N orthe H e ~ i a n stress.p.= 1.235 GPa for three numbers of rolling contact cycles, 5 x l 0 4 . I.SX 10s, and 2.8x I0 ~ cycles. When the frictional coefficient is assumed to be 0.098 and the lubricant pressure is neglected, the subsurface stresses
dimensions in mm
(c) Higher speed roller
\
Lower speed roller Fig. 2. Dimensionsof test rollers: (a) lowerspeed roller; (hi higher speed roller; (c) variablesin the contactingcylinders,wherethe suffixi = I and 2 indicate without and whh grindingsafter the tirst-stcprolling cycles, can be obtained [ 19]. In the calculation of the maximum shear stress, the distribution of residual stress caused by repeated rolling contact was also neglected. The semiwidth of Hertzian contact was given by 0.168 ram, the maximum shear stress was 0.3047 p,, and the position of the maximum shear stress was located at 0.124 mm below the contact surlace. After a predetermined number of first-step rolling cycles were achieved, the lower speed roller was ground to different depths by a grinder along the radial direction to provide harder roller surface. The above operation is called the preloading operation in this paper. The test conditions for the preloading operation is given in Table I.
97
R Lee et al. / Wear217 (1998~95-103
Table I Experimentalcondilionsin the preloadingoperation Fi~t.steprolling cycles 5 x l(~ cycles 1,5xlO~cycles 2 , 8 x 10~ cycles
crack occurred on the contact surface in the second-step rolling test. Furthermore, the displacement of the plastic flow in the surface layer of the follower is also measured.
Grounddel~h.D(~m) 30
70
IlO
150
170
28O
50O
0 0 0
0 0 0
0
0 0 0
0
0 0 0
0 0
3. Esperimemal madls 3. i. CharacreristiL:l o f the surface layer after the preloading operation
It was discussed by Chiou and Hwang [3] thai the plastic flow of the lower speed roller moves towards the direction of
E .
rotation and thai of the higher speed roller .shifts towards the direction of friction force due to the action of the friction force during the rolling test. Moreover, the displacement of plastic flow for the higher speed roller is much smaller than that for the lower speed miler at all rolling cycles, and the initiation of a i~igue crack was not observed on the c o n t a c t surface of the higher speed roller. Hence, only the lower speed roller is investigated in this paper, Fig. 3 shows the typical profiles of the plastic flow on the surface layer of the lower speed roller (i.e., z = O in Fig. 2c) after the first-step rolling tests under three numbers of rolling c o n ' ~ t cycles, 5 x I04, 1.5x 105, and 2.8x 105. It is noted that the curves are symmetric along the centre line o r x axis and independent ofx. Fig. 4 shows the corresponding h a r d n e s s distribution below the contact surface taken from the centre of tl,~ Irack ( i.e., y = 0 in Fig. 2c). it is .seen from Figs. 3 and 4 that the plastic flow and the surface hardness increase with increasing number of rolling cycles, and they slat[ to approximate the satu-
2.80x10 ~
+ i.50xl0 s A 5,O0x104
.o 1.O i •~- 0.0
,
i ~ 1 , i - Z o - 1 'z - ! , 0 ~
,
i | ! 0.0 ~
~ i'W'nlm~ I I 1.0 l,S 2.0 2.5
Dis~lce fi'omcontactcenter, mm Fig. 3. Variationof the displaccraentof plasticflowwith the lir.~t-steprolling cycle.
The second-step rolling test implies that the hardened surface of the lower speed roller induced by the pre|oading operation was rolled with a new higher speed roller under the same test conditions (980 N, 1(300rpm, and 20% slip ratio). The fatigue life of the lower speed roller was defined as the number of rolling contact cycles until the pitting or the fatigue
x 2.80x 10 ~ A t.50xlO 5 [3 5.00x 10"
i x
350
x&
•r
~00
i 0 A&z O
6 x &
O Oo
X Q &
.o
t
ul .m
DO
2OO
G
x
t.
ooO'. •
ill
fi
150 0.0
Depth below the contact surface, Fig. 4. Varialionof microhardnesswiththe lirst-stcprollingcycle.
nun
R, Lee et ul. I Wear 217 ¢19981 95-103
98
rated values near !.5 X ! 0 s cycle. Table 2 shows the effect of the first-step rolling cycle for the lower speed roller on the rolled radius, r~, the displacement of the plastic flow on the center of contact surface,ft, and the depth range of the severe plastic flow below surface, zt"z,.. Here the criterion for severe plastic flow is judged from the optical micrograph of subsurface layer according to the conditions of deformation (Fig. 8 in Ref. 13l ). It is found from Table 2 that the rolled radius of the lower speed roller decreases slowly, and the plastic flow increases with increasing predetermined number of rolling cycles. However, the depth range of the severe plastic flow is insignificantly influenced by the predetermined number of rolling cycles. Therefore, the optimum predetermined number of rolling cycles should be 1.5× 105 where the surface hardness and the displacement of plastic flow were quite close to the saturated value. After the first-step rolling cycle achieved a predetermined number, the surface layer of the lower speed roller was removed to different depths by a grinder. The typical profile of hardness below the contact surface is shown in Fig. 5 for a first-step rolling cycle of 1.5× los under four ground depths. It is seen from Fig. 5 that the distributions of microhardness with the ground depths of 70, 150, and 280 pm are quite similar to that without grinding, but they move towards the left with increasing ground depth due to the removal of subsurface layer. This result indicates that the effect of the grinding process on the distribution of hardness below the contact surface is insignificant, but its distribution has been changed. Generally, the effect of work hardening on the
microhardness becomes signilic.~at for the ground depths of 70 and 150/~m. 3.2. Rolling-fatigue-life tests with preloading operation
In the process of preloading operation for three first-step rolling cycles. 5X 10~. 1.5× l0 s. and 2.8× los, the surface layer of the lower speed roller was removed to different depths by a grinder along the radial direction to provide harder roller surface, as shown in Table I. With a new higber speed roller, the second-step roiling test was conducted under the same operating conditions until the pitting or the fatigue crack occurred on the contact surface. Fig. 6 shows the relationship between the fatigue life and ground depth in three first-step roiling cycles. Results show that the fatigue life is insignificandy influenced by the ground depth, when the ground depth, D, is smaller than 30 ,am. However, the fatigue life increases with increasing ground depth for D > 30 pm, and the fatigue life achieves the maximum value for D = 150 #m. Moreover, the fatigue life decreases with increasing ground depth for D > 150/zm, and the fatigue life achieves a saturated value for D > 5 0 0 / z m . This saturated value is the same as that without the preloading operation, it is also seen from Fig. 6 that the first-step rolling cycle of 1.5 X IOs has a longer fatigue life than those of 5 x lif t and 2.8 × lOs cycles, when 10 "6
Q ao
8
a 2"8x10S o 1.5x10~ o 5.0xlO
a
Table 2 Changes in miler radius, r,, the displacement of plastic flow. f,, and the range of.~ver¢ phtsli¢ flow. :, ~ :.~. after the lirst-step rolling tbr the lower speed roller
x
6
a
:.= ,..r. 4
9
a
0
First-step roiling cycles
r, ( m m l
f, (/zml
:, ~ : : (/zm)
5 x 104 cycles 1.5 x Iff' cycles 2.8 x I0 :~cycles
14.957 14.950 14.937
330 390 410
811~ 170 .gO~ 180 80 ~ 180
o 21 n
,a.
o'°
t
,
J
1
2oo 3oo 400 Ground depth, l.mt
100
t
5oo
600
Fig. 6. Effects of first-step rolling cycle and ground depth oii the fatigue life of the second-step rolling contacl. 4OO 12
35o
Ground depth * O~ m
.P~-i O
/W~
\
-~
3°° /-~=-'o,."%,.
~
25f)
c=
x
.280 ~
o
8
9
s
o
b,.~
4. ~ o 2(10
~ r
~u.O
P 0.2
n
I 0.4
- - "~ u
3
a
.a Ig
a 2.8xt0 s o 1.5x I 0 f o 5,0xi0
~to
70/zrn
0
o o ._o
2 I
0
O.o
Delah below the contact surface, ram Fig.. 5. Microhardness changes resulting from the ground depth at the lirstsk-p rolling cycle of 1.5 x tO~'.
I IOO
,"
~o , ~ o '500
Ground depth, pm Fig. "7. Effects of ti~t-stcp rolling cycle and ground depth on total l'.tig.ue life.
R. Lee el al. / Wear 217 ( 1998195-103
99
Table 3 Effectof grounddeplh./3, on Ihecontactwidth. B,_,the radius,r,, the .semiwidthof Henziancontact,a. and the Ikfcziancontactpressure,p~.at different|ir..ctstep rollingcycles D
30 70 150 280
5 × lip cycles
1.5× I0s cycles
2.8 x IO"cycles
B;
e.
a
p,.
B:
r:
a
p.
B.
r;
a
p.
(rnm)
(mini
(pro)
IMPa~
imml
(mm~
(p.m)
IMPa)
(mm)
(romp
(#rn)
IMPal
3.36 3.47 3,47 3.30
14.93 14.89 14.81 14.68
159 156 156
1168
3,39 3.48 3,49 327
14.92 14.88 14,80 14.67
158 156 155 t60
1163 1149 1149
3.3"• 3.47 3.48 3,28
14.91 14.87 14.79 14,66
159 156 156
1167 1151 1151
160
1188
160
1151 1152 1184
the ground depth is larger than 30 btm. it should be noted that the fatigue life discussed above does not include the first-step rolling cycle. Fig. 7 shows the effect of ground depth on the total fatigue life with different first-step rolling cycles. In this figure, the total fatigue life is defined as the sum of the fatigue life for the first-step and the second-step rolling cycles, and zero ground depth indicates no prelo',gling or normal operation. In this figure, the total fatigue life under normal operation is about 3,2 × 105 cycles, and the total fatigue life is made dimensionless in the following manner, the ratio of total fatigue life to 3.2× IOs. it is seen from Fig. 7 that when the predetermined number of rolling cycles was i.5 × IOs or 2.8× 105, the total fatigue life for the ground depth of 150 /s,m was 3,3 times that for normal operation. As a whole, to improve the fatigue life of rolling contact by the preloading operation, the number of the first-step rolling contact cycles should reach 1.5 × l0 s. where the surface hardness starts to approach a saturated value, as shown in Fig. 4. Moreover, the ground depth is 150/zm, or 0.89a, or near the position of the maximum hardness below the contact surface, where a is the semiwidth of Hertzian contact. Under the above-mentioned preloading operation, the total fatigue life can be improved significantly.
4. IKscussion it has been seen from Fig. 6 or Fig. 7 that after the preloading operation, the fatigue life of the second-step rolling contact is significantly increased. Generally, this increment in the fatigue life can be reasonably explained as follows:
lltlO
life was insignificant [20]. However, the others [21,22] found that the fatigue life decreased with increasing hardness difference. Therefore. the hardness difference between the higher and lower speed rollers could not increase the fatigue life of rolling contact. 4.2. The effect o f contact pressure after preloading operation on the fatigue life
After the preloading operation, the radius of the lower speed roller, r_,, and the width along the contact. Bz, would be changed, .so that the Hertzian contact pressure, p~, and the Hertzian contact ~miwidth, a, are a l ~ changed, where the nomenclature is shown in Fig. 2c. Table 3 shows the data of the contact width. Bz, the radius, r_,,the semiwkhh of Hertzian contact, a, and the Hertzian contact stress, p~, after different preloading operations. Based on Hamrnck [ I91. the value and the position of the maximum shear stress can he easily obtained by a~suming the frictional coefficient of 0.098. The maximum shear stress has a value between 0.285, and 0.2938 Po and occurs at 0.87a>_x>__O.41a and O.'/2a_> :__>,0.45a for various preloading operations, it is.seen from Table 3 that the Hertzian contact pressure with various preloading operations quite approximates that with normal operation except that with the smaller amount of ground depth and the first-step rolling cycle. According to an investigation of the effect of load on the fatigue life by Chiou et al. [231. a little change on the Hertzian contact pressure can not improve the fatigue life significantly. 4.3. The effect o f plastic flow on the fatigue life at the conlac! ce~iter
4. I. The influence of hardness difference on the fatigue life
Because the surface hardness of lower speed roller is significantly increased by the preloading operation, the surface hardness between the higher and low speed rollers is different during the ~cond-step rolling contacts with a new specimen as the higher speed roller. Fujita and Yoshida 1201. Fujita and Fukui 1211, and Huang and Chen [221 experimentally investigated the effect of hardness difference on the fatigue life of rolling contact. Results showed that the pitting only occurred on the surface of the low speed roller [ 20-22 I, and the effect of hardness difference on the rolling contact fatigue
Fig. 8 shows the effect of ground depth on the displacement of plastic flow at the contact centre (i.e., y = 0 and z = 0 in Fig. 2c) in the ~cond-step rolling test under various firststep rolling cycles. It is ~en from Fig. 8 that when the gronnd depth, D, is larger than 100/zm, the. plastic flow increases with increasing ground depth under the .same first-step rolling cycle, and then approaches to a ~tumted value (410/zm) of plastic flow which is the same as that without the l~eloading operation. On the other hand, under the .same ground depth, it i.~ found that the effect of the first-step rolling cycle on the plastic flow is not .so obvious. Generally. the plastic flow with
R. la'e el al, I Wear217 ( 1098195-103
1110
Merwin and Johnson I I ] and Suh I24], it is found that the only possible state of residual stress reduces to
400
(o',.,)r=f(:), u 300
(fT.v).) r = v'f(~.). (a~:)r =(o',=),~0,
~" i,s~1o,'
o
:o E
o 5.0x10
o
~. ioo
I
O0
I00
I 200
i 300
i 400
l 500
600
Ground dcpzh, rum Fig. 8. Effectsof lirst-steprollingcycleand grounddeplh on displ~ceraent of plastic flow. the first-step rolling cycle of 1.5x 10s is quite close to that with 2.8× 105 cycles, but less than that with 5 × 104 cycles. This difference becomes quite clear for D >__150 p.m. It is seen from Table 2 and Fig. 4 that the severe plastic layer induced by various first-step rolling cycles is not ground lbr D = 30 /,Lmor just ground a little for D = 70 p,m. in other words, they still exist on the surface layer before the second-step rolling. However, most of severe plastic layers are ground away lot D>_ 150 p.m. or they almost do not exist before the secondstep rolling. Therefore, for D = 30 or 70 p.m, the total displacement of the plastic flow on the surface layer must include the displacement of the plastic flow induced by the first-step rolling cycle, as shown in Table 2, and that produced by the second-step rolling cycle, as shown in Fig, 8. However, for D > 150 p,m. the total displacement of the plastic flow on the surface layer is quite close to the displacement of the plastic flow in the second-step rolling cycle, because most of severe plastic layers are ground away, As mentioned above, it is found that the total displacement ot the plastic flow in the surface layer for D-- 150 p.m is near the minimum, so that its fatigue life is the maximum, as shown in Fi 8. 7.
where v is the Poisson's ratio, the residual stress is denoted by suffix r, and the stress components o',,+ ~r,.,, o;,=. and ~,: with their orientation of axes are shown in Fig. 2c. This equation indicates that the residual stresses are independent ofx and y, and only a function of z (i.e.,f(z)). It is also seen from Fig. 4 that when the loading cycle approaches 1.5 × I05, the hardness beneath the contact surface almost achieves a saturated value. Under this condition, the position of the m a y imum hardness agrees very well with the location of the maximum shear stress predicted by the elasticity analysis of contact mechanics. Hence. it is assumed that the equilibrium state is achieved at the position of the maximum hardness. As a result, there was no further change in (O',~)r and (o',.,.L. Consequently. the stress state in the position of the maximum hardness must obey yon Mises' or distortion-energy yield criterion. The appropriate von Mises criterion with the residual stress can be written as { I_ l(°',',' + (°',,')~-°'--)-" . . +{°'---°', . . . +Co',.,
Since a certain depth of surface layer is ground in the preloading operation, the change of the hardness distribution beneath the roller surface is observed belbre the second-step loading cycle, as shown in Fig. 5. In order to understand the influence of these changes on the fatigue life. the residual stresses are analyzed. It was discus~d by Muro and Tokuda 17 ] that the change in hardness. AH. is correlated with the change in the residual stress. Ao'~, beneath the roller surface. This relationship can be assumed to be linear as (i)
where C is a constant. According to the theoletical analysis of the compressive residual stress due to rolling contact by
, - (°', , ),)2
+(oT,.,)~-~.,.,.-(tr,.,.)r)'-+O(~r~:+~r~,
(3)
+ ~ r ~ , ) l ) " 2 = Vt'3k where k is the yield stress in simple shear. By making use of Eq. (2), Eq. ( I ) can be written as A(rr,, )~ =
C-AH v
A(~r,, ), = C.AH 4.4. The distributions o f hardness and residual stress below the contact surface after the prehmding operation
Atr,=C-AH.
(2)
2.8x10 s
~.2oo
(4)
Fujida and Yoshida [251 thought that the residual surface stresses of annealed rollers were almost zero in the virgin state. Hence, the change in the residual stress, Actr, beneath the roller surface is assumed to be equal to ~r, or A~r, =o',
(5)
For the case with the rolling cycle of 1.5 × l0 s, the change in the hardness, AH, is given as AH=H-H,
(6)
where H, = 187H, is the hardness of the virgin state and can be seen in Fig. 4 for => 1.2 ram. The subsurface stress analysis derived by Johnson [ 26 ] and Hamrock [ 19 j is used here to define the stress in various directions at the position of the maximum hardness. By substituting these subsurface stres~s and Eq. (4) into Eq. (3). the constant C gives about - 0.0003. After the constant C is calculated, the distribution
R. I~e el ,/. I Wear 217 ~1 ~ 8 ) 05-1#3
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~f
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~:ii~;!iii~iiii',
•'. ~ :
.>:~..,:~:i~:;~.:::!~.~<: - ,-~::~:~:.~::-::~ ..............:-~ ~-z~::N.....
0.5 ~ 2 : ~"'."':" , J • '.~2'~2;'.;::.:i-~ :~ /."•;:::..... ' ~:N:"X.'.'.'::"?I;;~'×~I:'~ -" i~ -: ~h-::'";~
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~.O
.~. I
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,
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0.$ 1.0 I.S 2.0 Dime~si~lessdeWh Ix:low dzccomz~:suKac¢, z / a Fig. 9. Residual stress distributions ( ( Act,, ),. axial: and 13,~,, p,,cireumferomial) due to the first-step rolling cycle of 1.5 x l(P.
2
°~ O.O
-I.B
of residual stresses, A(o;~,), and A(o',.,.), can be calculated from Eq. (4) by using the hardness distribution. Fig. 9 shows these typical distributions of residual stresses by using the hardness distribution shown in Fig. 4. it is noted that these residual stres~s are only a function of=. as shown in Eq. ! 2). To demonstrate this similarily, when the frictional coefficient (p.) was assumed to be 0.098 with r,= 0.3333. the maximum principal shear stress was found to be 0.281po at points (0.8 la, 0.49a). This resuh is in good agreement with Merwin and Johnson's results [ l l where the maximum principal shear stress was found to be O.281 p. at points (O.866a. 0.452a) for p = 0 . 1 and ~,=0.3. Hence, based on the procedure di~uss above, the residual stress distribution beneath the lower speed roller has been obtained, Moreover, differen! ground depths would result in the change of the residual stress distribution beneath the roller surface. As a result, the shear stress distribution beneath the roller surface is also changed before the .,~cond-step loading cycle. Fig. IO shows the contour of the shear sl~ss at the beginning of the second-step loading cycle after the first-step loading cycle of I.~ X IO"~under different ground depths 30 #m. 70 p.m. 150 p.m and 280 p.m. It is ~en from Fig. IO that the area enclo.~s by a curve of the principal shear stress. 7= 0.28pn, increases with increasing ground depth for D > 70 p.m,. This result is compared with the displacement of plastic flow. as shown in Fig. 8. A very good agreement is found where the displacement of plastic flow increa~s with the maximum shear stress or ground depth for D > 70 p.m. Furthermore, the shaded zone shown in Fig. IO shows that the severe plastic layer still exists after the preloading operation for D < 180 p.m. This zone moved towards the surface layer with increasing ground depth for D < 80 p.m. The shaded area decreases with increasing ground depth for D_>.80 p.m. It is seen from Fig. IOa and b that since the severe plastic layer keeps in the interior zone for D = 30 #m, the effect of work hardening on the surface hardness for D = 30 p.m is smaller than that for D = 70 p.m. Consequently, although the displacement of plastic flow for D = 30 pm is quite etose to that for D ~ 70 p.m after the second rolling, the fatigue life for D = 30
,.
"~:.i-'-'~::-,...-~"~<~.:~N~i'*:~"~::'~N-° :'~i:~i'i,g%,'-~ -I,'~
--=.6
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c
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--Ldl
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.
.
--0.I
"~'....M///A {I~
.
.
.
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.
~.I
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.
041
Fig. IO. Contour~ of dirnensionles.'~ principal ...h~-arstr¢.~. ;'/p,, at [ha he[inning of th',~ ~cnnd-~tep rnlling cycle for II~ liz.~l-.~tep roiling cycle of I.SX 10', and I N gruund dcplhs. (a) .'g) pro. tb) 70pro. i c ) I.~O#m. and
(d) 2~I0p.m: wlvzre( + ) indicatesthe I~:ationot"the maximumprincipal shear stress, and the sh',aledzonerepre.,~n[~ihe .~vereplastic flowzoneduc Io the prcl~?ading op~ralion.
#m is much smaller than that for D = 70 #m. It is .seenfrom Fig, 10c that only about 30 pm .severe plastic layer (shaded zone) keeps at the roller surface for D = 1.50pm. However, this shaded zone is subjected to tbe lower shear stress during the ~cond-step rolling cycle, This implies that a harder surface due to the work hardening is subjected to lower loading cycle for D-- ! 50 pm. Moreover. the shaded zone for D = 70 pm is subjected to higher shear stress cycle. Hence, the fatigue life for D = 70 pm is much smaller than that for D = 1.50 pro. It is seen from Fig. 10d that no shaded zone is found in the roller zone f o r D = 280 p.m. that is, the effect of work hardening on the surface hardness can he ignored. Thcrelbre. its fatigue life is almost the same a.s that without preloading operation.
102
R. Leee7aL / Wear217 (1998) 95-103
4.5. The effect o f second-step hmd on the fatigue life
2000 First - step tolling cycle : [.5x10 s I
As mentioned above, the effect of work hardening due to the severe plastic layer on the fatigue life is significant. However, this severe plastic layer can not be subjected to a higher shear stress in the second-step loading cycle, Otherwise, it is easy to achieve a saturated value of the displacement of plastic flow. As a result, the fatigue crack is propagated into pitting at the severe plastic layer. It has been found that the best preloading operation is the loading cycle of 1.5 × l0 ~ under the load of 980 N with the ground depth of 150/zm. Using this preloading operation, the effect of the second-step load on the fatigue life is shown in Fig. I I. it should be noted that the fatigue life discussed in this figure does not include the first-step rolling cycle, it is seen from this figure that the fatigue life with preloading operation is larger than that without preloading operation. Moreover, this increment in the fatigue life decreases with increasing second-step load. it is found that the fatigue life with preloading operation is 3.3 times that without preloading operation for the second-step load of 588 N. Fig. 12 shows the changes in the displacement of plastic flow on the surface of lower speed roller for various second-step loads. It is seen from this figure that the displacement of plastic flow in the second-step rolling cycle increases with increasing load, and this displacement with preloading operation is smaller than that without preloading operation. This difference increases with increasing second-step load. However, it should be noted that the displacement ratio of plastic flow between preloading and normal operations increases with increasing second-step load. This implies that the smaller the displacement ratio, the larger the fatigue life with preloading operation. In particular, the displacement of plastic flow for the load of 588 N is approximated to zero, as shown in Fig. I I, so that it possesses the largest fatigue life with the preloading operation. Generally, this smaller displacement results from the work hardening in the surface layer by preloading operation.
O
15
u
o First- step rolling cycle : l.Sx10 s Ground depth : 150 pm o Normal operation
o o
o o
500
10CO Load, N
T500
8 2 ooo
Fig. I I. Effectof.,,ccond-stcploadon fatiguelifewhhpreloadingand normal operalions.
~ If~O0
Nomad
olm'auon
1000
~- soo ~x
el
0
500
10o0 Load,
1500
2000
N
Fig. 12. Effectof .~cond-step load on displacemen!of plastic flow with preloadingand normaloperations. 5.
Conclusions
The effects of prerolling and metal removal before the fatigue test on the rolling fatigue life are investigated under the lubricated rolling/sliding contacts using the specimens of medium carbon steel $45C. In this study, the test specimens are preloaded at the first-step rolling cycles, and then the surthce layer of the lower speed roller is removed to different depths by a grinder along the radial direction to provide harder roller surface. This procedure is called the preloading operation. With a new higher speed roller, the second-step rolling test is conducted under various operating conditions until the pitting or the fatigue crack occurs on the contact surface. From the experimental results with the theoretical analysis of the compressive residual stress, the following conclusions can be drawn. ( I ) The plastic flow and the surface hardness increase with increasing rolling cycle. The optimum first-step rolling cycle is found to be 1.5 X 10~ where the surface hardness and the displacement of plastic flow start to approximate the saturated value. (2) The optimum ground depth is found to be 150/,tin, or 0.89a, or near the position of the maximum hardness below the contact surface due to the first-step rolling cycle where only about 30/zrn severe plastic layer or O.18a is kept at the roller surface. Under this grinding process, the effect of work hardening on surface hardness is significant and this severe plastic layer is subjected to lower shear stress during the second-step rolling cycle. (3) The preloading operation can improve the fatigue life significantly. Under the optimum preloading operation, the fatigue life with preloading operation is 3.3 times thai without preloading operation for the second-step load of 588 N. (4) The smaller the displacement ratio of plastic flow between prcloading and normal ol~rations, the larger the fatigue life with preloading operation. The smaller the displacement of plastic flow, the larger the fatigue life with the preloading operation.
I?, Lee et al, I Wear 217 t 1998) 95--103
In general, this smaller displacement in the surface layer results from the work hardening by preloading opefatio~.
Acknowledgements The authors would like to express their appreciation to the National Science Council (NSC-80-O4OI-E110-09) in Tatwan, R.O.C., for the financial support.
References I I i J.E. Merwin. K.L. Johnson. An analysis of plgstic deformation in rolling contact. Prec. Inst. Moth. Eng, 177 (1963) 676-690, 121 M, Shima. Y. Kimum, T. Yamaoto. Mea.surement of subsurface plastic llow in rolling contact. J. JSLE 25 (1980) 817-822. 131 Y.C. Chiou. J.R. Hwang. Relationship between the propagation of fatigue cracks and the behavionr of plastic flow under rolling~sliding contacts---effect of slip ratio, Tribol. Int. 24 ( 1991 ) 101-107. 141 E, Broszeit. O. Zwirlein. Internal stresses and their inflnenee on material stresses in Hertzian contacts---calculations with different stress hypotheses, ASME J. Tribol. IO8 (1986) 387-393. [ 51 g. Fujita, A. Yoshida, The effect of changing the rolling direction on the rolling contac~ fatigue lives of annealed and case hardened steel rollers. Wear 43 I 1977) 301-313. 161 H. Muro. N. Tsushima. Microstructaral. microhardness and residual stress changes due to rolling contact, Wear 15 (19"/0) 309-330. 17 ] H. Muro, M. Tokuda, Residual stress due to rolling contact. J, ,ISLE 21 (9l ( 1976l 621-625 in Japane~. 181 A. Ishibashi, T. Yokote, Effect of number of revolutions and speed on pitting in rolling contact. Trans. JSME 16 ( 1971 ) 646-65,fi. 191 T. Kayaba. S. Suzuki, An investigation of surface damages by rolling contact. Technology Reports. Tohoku University. Japan. Vol. 41. 1976, pp. 2 !-46. I IOI N. Soda, T. Yamanmto, Effect of tangential traction and roughness on crack initiation/propagation during rolling contact, ASLE Trans. 25 12) (1980) 198-206.
103
I I I I Sp.S. Cretu. N.G. Popineeanu, The influence of residnal st~s.~s induced by plastic defomlation (m rolling con"tact fatigue. Wear 105 (1985) 153-170, 112] A. Yosbida, K, Fujita, Study on pitting of ~fface rolled steel rollers ( Ist report). J, JSLE 31 (1986) 276--283 in Japane~, [ 13] A. Yoshida. K. Fujita, Study on pitting of surface rolkd steel roller,~ (2nd report), J, JSLE 32 f 1987l 260-267 in Japane~. { 141 T, Fukui. T. Fujita. Influence of preload driving before fatigne test on the rolling contact fatigue strength of Austenilic slainlesssteel, J. iSLE 35 (1990) 202-206. 1151 E.V. Zaretsky, Effect of surface removal on rolling element fatigue. proc. Int. Conf. On Tribotogy--Eriction, Lubrication and Wear. Fifty Years On. Proc, IMechE. CI47/87. Ig89, pp. 829-.838. 116 [ R.K. Steele. The effect of metal removal, steel cleanliness and wheel load on the fatigue life of rail, Wear 144 ( 19911 7t-87. [ 17] J. Kalou~k, J.O. Igwemezic, Shell-like defecei "and microgeomct~ of griuding. Prue. Int. Conf. On Rail Steeb-DevelopmenL Manufacture and Performance. Pub. G, Kuhn. 1992, pp. 139-145. 1181 R.K, Stee½, Strategies for maximizing rail life. in: J J Kalker et al. ( Eds, ). Rail Quality and Maintenance for Modem Railway Operation. Kluwer Academic Publishers, 1993, pp. 78-97. [ 19l B.J, Hamro~k.FundamentalsofFluidFilmLn~ication.Mcgraw-HilL Chaps. 19aud 20. 1994. 120i K, Fujita. A. Yoshida. Effect of hardness difference on the surface durability and surface failure of steel rollers. Wear 67 { 1981J 187200. [ 21 ] T, Fujita. T. Fukui. Influences of ~hardacss of mating materials on rolling contact fatigue strength of the stainlesssteel. J. JSLE 32 ( 1987 ) 518-523. [ 22 | S.J. Huang. X.H. Chen. ~ influence of surface hardness difference on the contact fatigue strength. Pent. JSLE ;ntere~iorral Tribology Conference. Tokyo. Japan, i983. pp. 91%922. 1231 Y.C. Chiou. R.T. Lee. J.H. Chang. Relation,,hip between propagation of fatigue retook, and behaviou: ~f plastic flow umler rolling/sliding conPact.~---effectof load. Chin. J. Mech.. Taiwan 9 ( 1993 } 17-25. 124 ] N.P. Sah. Surface Interactions. in: P.B. Scnholzi ( Ed. ). Tfibology Technology. Vol. I. Marinus Nijhoff Publishers. 1982. pp. 110-167. [ L51 K. Fajida. A. Yoshida. Macroscopic and microscopic changes in the surface layers of annealed and ca.~-hardened steel rollers due to roiling contact, Wear 43 (1977) 3OI-313. i261 K,L. Johnson. Contact Mechanics. Chap. '). Camh'idge Univ. Press. 1985. pp. 102-104 aud 285-295.