wear experiment and model of rolling balls in sliding
TRANSCRIPT
Mechanics & Industry 18, 511 (2017)© AFM, EDP Sciences 2017https://doi.org/10.1051/meca/2017039
Mechanics&IndustryAvailable online at:
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REGULAR ARTICLE
Wear experiment and model of rolling balls in sliding-rollingconditionsJianfei Xi, Xuejin Shen*, and Xiaoyang Chen
Department of Mechanical Automation Engineering, Shanghai University, Shanghai 200072, PR China
* e-mail: e
Received: 14 June 2017 / Accepted: 23 October 2017
Abstract. When the rolling bearing is working, sliding and rolling always exist in the friction pairsimultaneously. The operating condition is complicated and fickle. For these kinds of behaviors, it is necessary tosimulate the bearing sliding-rolling ratio (SRR), load, speed and other operating parameters in the wear-testingresearch between the rolling elements and the inner or outer ring. By the improvement of the transmission,measurement, and control system of an existing pure rolling contact fatigue test rig for bearing ball with threecontact points, the simulation of bearing balls would be more realistic and test parameters are close to actualoperating conditions. The rolling ball wear experiments were carried out under different SRRs operationconditions. By analyzing test data, the calculation model of wearing rate under the operation condition ofsliding-rolling was established based on Archard model.
Keywords: Wear test / rolling ball / sliding-rolling ratio / wear performance model
1 Introduction
As an important part of rolling bearing, rolling ballcontacts with its friction pairs frequently, the wear in theprocess of contacting has great effect for the assemblyprecision of bearing [1,2]. During the running of rolling ball,it not only rotates alone the inner or outer ring but alsoslides when the friction of contact point between rolling balland its friction pairs is not enough, which is called thesliding-rolling state [3]. Cheng et al. [4] established a modelfor calculating surface friction heat in slide state. Byanalyzing factors which affect the part temperature incontact point, the variation trends of surface temperaturewas obtained. Sundar et al. [5] measured vibration toestimate coefficient of friction and a mechanical systemwith combined rolling-sliding contact. An empiricalrelationship for the coefficient of friction is suggestedbased on a prior model under a mixed lubrication regime.Šperka et al. [6] put forward amplitude decay theory,established a model of predicting tribology performanceaccording to surface roughness, and analyzed howroughness would affect tribology performance at sliding-rolling state using optical interference film test rig. Ciulliet al. [7] measured film thickness of point contacts understeady state and transient conditions at different sliding-
-mail: [email protected]
rolling ratios (SRRs). The experiments proved that undertransient conditions, high slide-to-roll ratios seem to reducethe squeeze effect on the film thickness.
Although studies about bearing tribology performancein sliding-rolling state exist, researches only involved withwear performance of rolling ball are not sufficient [8,9]. Themain contribution of our work lies on the experiments, bycollecting real time wear identification with variation ofSRRs, load and rotate speed based on self developed testrig. The wear performance in different states has beendiscussed. The calculation model of wearing rate under theoperation condition of sliding-rolling was established basedon Archard model.
2 Experiment rig and method
2.1 Experiment rig and material
Figure 1 shows the test rig instrumentation and controlsystem.
Test rig is the self designed and developed three-pointcontact bearing ball fatigue life testingmachine [10], and itsstructure is shown in Figure 2.
Motor 1 connects support wheels 2, 3, 4 with cog belt.Support wheels as middleware transmit velocity to slaverollers 5, 6. The driven wheel 9 transmit velocity betweenload wheel 8 and driver 10 which connects with motor 1. Inthis condition, the rolling ball 7 contacts with slave roller 5,6 and load wheel 8 in three points.
Fig. 1. Test system at the laboratory.
Fig. 2. Structure of three-point contact bearing ball fatigue lifetesting machine.
2 J. Xi et al.: Mechanics & Industry 18, 511 (2017)
For implementing sliding-rolling state and collectingreal time wear volume, test rig has been improved. Bychanging transmission ratio between driven wheel 9 anddriver 10, the velocity of load wheel 8 can be different fromslave rollers 5, 6. At this time, the velocities of three contactpoints in rolling ball are not same anymore, rolling ball is ina certain sliding-rolling state. Adjusting the transmissionratio between driven wheel 9 and driver 10, SRR can becontrolled. Displacement sensor 11 is placed above loadwheel 8.With proceeding of wear in rolling ball, diameter ofrolling ball 7 is smaller and smaller, the change reflects indistance between sensor 11 and wheel, distance data arecollected online using DAQ card and calculated to realitywear volume in Labview.
2.2 Experiment method
Operation condition is shown in Table 1.A simple sliding-rolling condition is described by two
speeds.
va ¼ vu � vd ð1Þ
vr ¼ vu þ vd2
ð2Þ
where vu, vd are speeds of friction pair and counter-pairin sliding-rolling (m·s�1), va is sliding speed (m·s�1), vr isrolling speed (m;·1)
SRR [11] is defined as the ratio of slide velocity to rollingvelocity:
S ¼ vavr
¼ 2ðvu � vdÞvu þ vd
ð3Þ
The SRRs in three contact points, S1, S2, S3, are definedas:
S1 ¼ 2ðv1 � vballÞv1 þ vball
ð4Þ
S2 ¼ S3 ¼ 2ðvball � v2Þvball þ v2
¼ 2ðvball � v3Þvball þ v3
ð5Þ
where v1, v2, v3 are the velocities in three contact points,respectively (m·s�1), vball is velocity of test ball (m·s�1),shown as Figure 3.
The angles of contact points in v1 and v2 or v1 and v3 arebig (≥160°). For calculating the sliding-rolling simply, eachangles are assumed to be 180°, relationship among speeds intest ball is shown in Figure 4.
Due to the existent of sliding, a part of speedtransmitted to test ball may lost.
v01 ¼ v1 � vs1 ð6Þ
v02 ¼ v2 � vs2 ð7Þ
where v01 is the real speed what v1 transmits to test ball
(m·s�1), v02 is the real speed what v2 transmits to test ball
(m·s�1), vs1 is the slide speed in point v1 (m·s�1), vs2 is theslide speed in point v2 (m·s�1).
During the experiment, centre of test ball is fixed, so thespeed of centre of test ball is zero called instantaneouscenter of velocity. It means the values of v
01, v
02 need to be
equal, and the directions of v01, v
02 are opposite. According
to equations (6) and (7), we can get
vs1 ¼ vs2 ð8Þ
Fig. 3. Velocities in three points.
Table 1. Operation condition.
Operation condition Parameters
Material of rolling ball GCr15Diameter of rolling ball 6.35mmRa of rolling ball 0.0054mmLoad 50–150NMaximum contact stress 2.545–3.846GPaRotate speed 1000–3000 r·min�1
Sliding-rolling ratios 0.05–0.15Lubricant 32# engine oilSupply quantity of lubricant 150mL·min�1
Lubricant supply state ContinuousTime 96 h (5760min)
Fig. 4. Relationship among speeds in test ball.
Fig. 5. Effect of sliding-rolling ratio for wear volume.
J. Xi et al.: Mechanics & Industry 18, 511 (2017) 3
According to the equations (1)–(3):
S1 ¼ S2 ð9ÞSimilarly, S1=S3Assuming S1=S2=S3, vball is defined as:
vball ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv1 � v3
p ¼ 2pffiffii
p � rsvs60
ð10Þ
where i is transmission ratio, rs are radius of slave rollersand load wheel (mm), vs are speeds of slave rollers and loadwheel (m·s�1).
SRR S is defined as:
S ¼ 2ðv1 � vballÞv1 þ vball
¼ 2ð1� ffiffii
p Þð1þ ffiffi
ip Þ ð11Þ
Therefore, the SRR in experiment can be obtained bycalculating the transmission ratio.
Due to the existent of vibration and thermal expansion,measured movement of load wheel by displacement sensoris not the real change of rolling ball. By some calibrationexperiments, real variation of rolling ball in radius is fittedusing distance changes of load wheel, and relationshipbetween them is defined as:
Drt ¼ 0:38927DLþ 0:01283 ð12Þ
where Drt is the real measured variation of rolling ball inradius (mm), DL is the measured movement of load wheel(mm).
Wear volume is calculated by Dr as follows:
DV ¼ 4
3p½rt3 � ðrt � DrtÞ3� ð13Þ
whereDV is the real wearing volume (mm3), rt is the radiusof tested rolling ball (mm), Drt is the real measuredvariation of rolling ball in radius (mm).
Wear rate is calculated as follows:
V ¼ DV
tð14Þ
where V is the wearing rate (mm3·min�1), DV is the realwearing volume (mm3), and t is the wearing time (min).
3 Results and discussion
3.1 Wear performance in different SRRs
Figure 5 gives results of wear volume of different SRRs in50N and 3000 r·min�1.
As shown in Figure 5, when SRR is 0, tested ball is inpure rolling state, wear volume is only 7� 10�5mm3, and itis hard to observe different wear stages at this condition.When SRR is 0.05, compared with pure rolling state, thewear volume increases to 0.0034mm3, although SRR is stilllow. At the same time, different wear stages are obvious.
Fig. 7. Effect of sliding-rolling ratio in different loads.A1
Fig. 6. Effect of sliding-rolling ratio for wear rate.
4 J. Xi et al.: Mechanics & Industry 18, 511 (2017)
From 0 to 1000min, the wear volume appears very highincrease. Within 4000min, wear volume increases continu-ally but growth rate is lower, and this period is calledrunning-in period. In running-in period, asperity-peak ofcontact zone is worn or flatted due to local high pressure.Surface topography of friction pairs is improved gradually[12]. After 4000min, wear level is changed into stabilizationperiod. When SRRs are increased to 0.095 and 0.15, wearvolumes are 0.0078mm3 and 0.01745mm3, respectively.According to equation (3), the slide velocity is proportionalto SRR. So in the same wear time, slide distance isproportional to SRR. According the model described byArchard, wear volume is proportional to slide distance.Therefore, the wear volume is proportional to SRR.
Figure 6 gives results of wear rates of different SRRs in50N and 3000 r·min�1.
As shown in Figure 6, when SRR is 0 called pure rollingstate, wear rate is only 10�12mm3·min�1, and variation ofwear rate is not obvious during process of wear. When SRRis 0.05, stabilization wear rate is 4.1� 10�10mm3·min�1,and much larger than the wear rate in pure rolling period.In the beginning of wear, for forming a favourable surfacequality which is suitable for operation condition such assurface pressure and friction coefficient, wear rates arelower and lower and tend to be in stable state. It’s calledstabilization period. Compared with pure rolling condition,wear rate in SRR is 100 times than one in pure rolling state.In 0.095 and 0.15 SRRs, stabilization wear rates are5.3� 10�10mm3·min�1 and 6.1� 10�10mm3·min�1, respec-tively. As shown in Figure 6, greater the SRR is, theduration reaching stabilization wear stage is shorter, butthe stabilization wear rates are almost same. It means thatin the same operation condition and tribology performanceof surface, wear rate is independent of SRR.
3.2 Effect of SRR in different loads
Figure 7 give results of wear rates of different SRRs in3000 r·min�1 and different loads.
As shown in Figure 7(a), when load is 50N, due to lowload, stabilization wear rates, about 5.9�10�10mm3·min�1, are close for three SRRs. The mainwear behavior is slight abrasive wear as shown in Figure 8(a).
In Figure 7(b), when load is elevated to 100N,stabilization wear rates in 0.05 and 0.095 SRRs are5.9� 10�10mm3·min�1 and 6.1� 10�10mm3·min�1, andthey are similar with the operation condition in 50N.WhenSRR increases to 0.15, wear rate is stable at 8.4�10�10mm3·min�1. It can be seen in Figure 8(b), the wearbehavior in this condition is not only abrasive wear but alsoslight adhesive wear in area A1. Adhesive wear is not a wearperformance appearing on oxide layer. Adhesion pointbreaks the surface of material [13], and metal inside isexposed in air, so wear rate is increased.
As shown in Figure 7(c), when load is changed to 150N,stabilization wear rate in SRR 0.05 is 5.8�10�10mm3·min�1, and surface is still in slight wear likecondition in load 100N. In 0.095 and 0.15 SRRs,stabilization wear rates are 1.12� 10�9mm3·min�1 and1.43� 10�9mm3·min�1, respectively. It can be seen inFigure 8(c) which is divided into area B1 and B2. Becauseof high contact stress, compared with normal contactsurface B2, area B1 presents obvious depth differences,called plastic deformation appearance. Plastic deformation
Fig. 9. Effect of sliding-rolling ratio in different rotate speeds.C2
Fig. 8. SEM images from sliding-rolling ratios in different loads.
J. Xi et al.: Mechanics & Industry 18, 511 (2017) 5
causes cold-work hardening in metal [14], and surface ofmetal is more andmore fragile. This characteristic results inthat it is easier to formabrasive particles in surface.With theincrease of abrasive wear, the wear rate is higher and higher.
The conclusion of these experiments is described. In lowload condition, effect of SRR in different load is notobvious. With the load increased, the SRR has a greatsignificance for wear rate. Compared with operationcondition in low load, wear performance and shapes insurface are changed from abrasive wear to adhesive wear,and the surface area presents plastic deformation gradual-ly. All changes above reflect in the increase of wear rate.
3.3 Effect of SRR in different rotate speeds
According to effect of SRR in different loads, load is higherand the degree of wear is severer. For avoiding adhesivewear, the experiments about wear rates of different SRRs invarious rotate speeds are carried out in load 50N.
As shown in Figure 9(a), when the rotate speed is1000 r·min�1, with the SRR increasing, the wear rateachieves the stable state more quickly. All wear still occuron oxide layer with slight abrasive wear, as shown inFigure 10(a). Therefore, three stabilization wear rates, allabout 5.7� 10�10mm3·min�1 in three different SRRs, aresimilar.
In Figure 9(b), the variation of SRR affects wear rate in2000 r·min�1. The stabilization wear rates of SRR 0.05,0.095, 0.15 are 4.9� 10�10mm3·min�1, 5.9�10�10mm3·min�1 and 6.1� 10�10mm3·min�1, respectively.In Figure 10(b), compared with low speed, although thespeed is twice as much as before, wear volume didn’tmultiply as speed, and wear performance of this conditionare also slight abrasive wear. With elevated speed,performance of abrasive wear do not be worse. It meansthat because of limited abrasive particles, in high rotatespeed, most of abrasive particles formed by slide wear arethrew away by rolling of ball. All of characters result in thephenomenon that wear performance and wear rate are notchanged obviously.
In Figure 9(c), the variation of SRR affects wear rate in3000 r·min�1 before 6000min. The stabilization wear ratesin three SRRs are 5.6� 10�10mm3·min�1, 6.3�10�10mm3·min�1 and 6.5� 10�10mm3·min�1, respectively.Compared with the experiment results in 1000 r·min�1 and
Fig. 11. Relationship between corrected load and SRR.
Fig. 12. Relationship between corrected speed and SRR.
Fig. 10. SEM images from sliding-rolling ratios in differentrotate speeds.
6 J. Xi et al.: Mechanics & Industry 18, 511 (2017)
2000 r·min�1, wear rates are changed a little with increaseof rotate speeds. Within the range of the temperaturewhich wouldn’t influence surface tribology performance[15,16], the increase of rotate speed can only cause thedecline of ability of heat dissipation on surface [17] and thenaffect the wear rate. But in this experiment, the influence islimited.
In the process of rolling-wear, the main failure mode isfatigue failure in high stress cycles. So in this favorableoperation condition, time of experiment is lengthened toresearch the relationship between sliding-rolling andfatigue failure.
As shown in Figure 9(d), experiments data are all after60 000min. In 0.15 SRR, wear rate keeps stable before66 000min. After 66 000min, wear rate has a suddenincrease from 6.2� 10�10mm3·min�1 together with theincrease of temperature. At this time, the surface of testedball presents obvious spalling appearance, called fatiguewear phenomenon. In 0.095 SRR condition, wear rate ischanged in 87 720min suddenly. Compared with conditionin 0.15 SRR, time of appearing fatigue wear phenomenon is21 720min longer. In 0.05 SRR, required duration time ofappearing phenomenon of fatigue wear is too long, so thisexperiment is terminated. As seen in Figure 10(c), fatiguespalling [18] can be observed in surface area C1 in highstress cycles. Around the spalling area, surface of ball ishard to be observed the obvious wear performance in areaC2. Unless fatigue wear occurs, otherwise fatigue spallingdata is not easy to obtain from variation of wear rates.
According to experiment results, in normal wearcondition, SRR affects the wear rate a little, but has asignificant influence for the time of fatigue wear. With theincrease of SRR, sliding friction accelerates crack formationand crack propagation on ball surface, and shortens thetime of occurring fatigue wear.
4 Wear performance model
By analyzing the experiment data, a model of variation ofwear rate with time in sliding-rolling condition can beestablished. According to the conclusion of experimentsabove, variation of wear rate is divided into two periods,running-in period and steady-state period. Firstly, theinfluence of SRR to steady wear rate needs to be figuredout.
4.1 Steady wear rate model based on Archard
According to Archard theory [19]:
DV
L¼ ks
W
3sSð15Þ
where L= ∫ vadt, DV= ∫VAdt. v and VA is constant atsteady state, so L= va ∫dt, DV=VA ∫dt. Equation (15) ischanged to:
V A ¼ ksWva3sS
ð16Þ
whereDV is wear volume (mm3), L is wear distance (m),Wis load (N), ss is yield strength of softer material (Pa),VA istheoretical wear rate (mm3·min�1), t is wear time (min), vais slide speed (m·s�1), andKs is coefficient of adhesive wear.Assuming K ¼ KS
3sS; equation (16) is changed to:
V S ¼ V A ¼ KWva ð17Þ
J. Xi et al.: Mechanics & Industry 18, 511 (2017) 7
where VS is steady wear rate (mm3·min�1). Wearcoefficient in lubrication condition is Ks = 10�7, yieldstrength ss=518.42MPa, so K=6.43� 10�17.
4.2 Corrected steady wear rate model
Archard theory is adhesive wear theory [20], due to theexistence of SRR in these experiments, wear performance isnot adhesive wear any more, and it is changed with thevariations of load, speed and SRR. Even so, Archard modelis able to expound the relationships among factors affectingwear rate [21]. Considering this, the equation (17) iscorrected in sliding-rolling operation condition.
According to experiment result above, with the increaseof load, wear performance is changed from abrasive wear toadhesive wear, and the wear rate is enhanced gradually, butthe rate of increase is lower and lower. The approximatetrend is shown in Figure 11.
The load W is corrected with adding SRR S:
W 0
W¼ ae�bS þ c ð18Þ
whereW0 is the corrected load (N),W is the real load (N), Sis SRR, a, b, c are related correct coefficient.
At S=0, equation (18) is defined as:
W 0
W
� �0
¼ aþ c; ð19Þ
where W 0W
� �0is the ratio of corrected load to real load at time
zero.At S=∞, equation (18) is defined as:
W 0
W
� �∞¼ c; ð20Þ
where W 0W
� �∞ is the ratio of corrected load to real load at
steady state.So a ¼ W 0
W
� �0� W 0
W
� �∞; c ¼ W 0
W
� �∞; equation (18) is
changed to:
W 0
W¼ W 0
W
� �0
� W 0
W
� �∞
� �e�bS þ W 0
W
� �∞: ð21Þ
According to the experiment result about effect of SRRsin different rotate speeds, rotate speed has a little influenceto wear rate in low load condition. Some of wear particlesformed in sliding wear the surface twice, called three-bodyabrasive wear, so wear rate is increased. But with theincrease of rotate speed, most of wear particles are threwout, and variation trend is not obvious any more. Withcontinuous increase of speed, high temperature caused byhigh speed may make the state of contact area [22] worse,and the wear rate increases substantially. The approximatetrend is shown in Figure 12.
This experiment is not in very high speed. Therelationship between SRR S and v0r
vris assumed to be linear
simply. The rotate speed v is corrected with adding SRR S:
v0rvr
¼ dS þ f ð22Þ
where v 0r is the corrected rotate speed (r·min�1), vr is the
real rotate speed (r·min�1), S is SRR, d and f are relatedcorrect coefficient.
The speed vr is not the slide speed directly in thisexperiment. The slide speed needs to be calculatedindirectly, according to equation (4).
vball ¼ ð2� SÞv12þ S
ð23Þ
va ¼ v1 � vball ¼ 2S
2þ S
� �v1 ¼
2p 2S2þS
vrrs
60ð24Þ
va0 ¼
2p 2S2þS
vr
0rs
60; ð25Þ
where vball is speed of test ball (m·s�1), S is SRR, v1 is speedof slave pairs (m·s�1), va is sliding speed (m·s�1), vr is realrotate speed (r·min�1), rs is radius of slave roller (mm), va0is corrected sliding speed (m·s�1), vr0 is the corrected rotatespeed (r·min�1).
Wear rate equation, equation (17) after being correctedis:
V S ¼ V A ¼ KW 0va0 ð26ÞEquation (26) is fitted using experiment data by least
square method. Known from equation (17), K=6.43�10�17. The wear rate equation is corrected as:
V s ¼ ð�281:7e0:00377S þ 282:7ÞW � ð0:699Sþ 0:068Þ 2þ S
2S
� �60va2p
� 10�14 ð27Þ
or the equation can be described with rolling speed vr in thisexperiment as:
V s ¼ ð�281:7e0:00377S þ 282:7ÞW � ð2:22Sþ 0:216Þvr � 10�14 ð28Þ
4.3 Verification of steady wear rate model
The accuracy of the corrected model of steady wear rate isverified using relative error:
d ¼ jV f � V tjV t
� 100% ð29Þ
where d is relative error, Vf is predicted wear rate, Vt is realmeasured wear rate.
Test operation condition is shown in Table 2.Comparison of relative errors between Archard model
and corrected model are shown in Figure 13.Using root-mean-square error as standard of model-
error, Archard model’s error is 3.775, and correctedmodel’s error is 1.197. As shown in Table 2 and Figure 13,in low load, predictions of two models are both accurate.
Table 2. Test operation condition.
Group 1 2 3 4
Load (N) 50 100 100 150Rotate speed (r·min�1) 1000 2000 3000 3000Sliding-rolling ratio 0.15 0.095 0.05 0.095Real measured wear rate (10�10mm3·min�1) 2.38 7.71 10.25 19.23Steady wear rate base on Archard (10�10mm3·min�1) 2.51 7.92 12.24 22.56Corrected steady wear rate (10�10mm3·min�1) 2.30 7.67 9.28 17.27Relative error of Archard model 0.054 0.027 0.194 0.173Relative error of corrected model 0.033 0.005 0.094 0.101
Fig. 13. Comparison of relative errors between Archard modeand corrected model.
Fig. 14. The variation of wear rate with time.
Table 3. Model verification operation condition.
Group 1 2 3 4
Load (N) 50 100 100 150Rotate speed (r·min�1) 1000 2000 3000 3000Sliding-rolling ratio 0.15 0.095 0.05 0.095Relative error 0.112 0.097 0.195 0.107
8 J. Xi et al.: Mechanics & Industry 18, 511 (2017)
With the load increasing, considering the influence of SRRto contact area, the corrected model is more precise thanArchard model. Therefore, the corrected model is moreeffective in sliding-rolling condition, and wear rate ofcorrected model is applied to be the steady wear rate inwhole model next.
4.4 Relationship between wear rate and time
The variation of wear rate with time is shown schematicallyin Figure 14. Initially the wear rate is high which reducesexponentially with time and reaches steady-state aftersome time. This trend is expressed mathematically asfollows [23]:
V ¼ ðV 0 � V SÞe�ht þ V S ð30Þwhere V is wear rate (mm3·min�1), V0 is wear rate at timezero (mm3·min�1), VS is wear rate at steady state(mm3·min�1), t is time of wear (min), and h is relatedcoefficient.
The equation (30) is fitted using experiments data byleast square method, and related correct coefficienth=0.0009. The wear rate changed with time is definedas follows:
V ¼ ½ðV 0 � V SÞe�0:0009t þ V S� � 10�10 ð31Þ
4.5 Model verification
Model verification operation condition is shown in Table 3.As shown in Table 3, average relative errors of four
groups are not larger, all errors are under 0.2, so it can beidentified that fitting results are credible. The specificfitting results are shown in Figure 15.
In Figure 15, overall, fitting curves are similar with thereal wear rate. Especially in steady wear period, precision ishigher. Due to variation of machine or unstable state ofball’s rolling in the beginning of experiment, the wear rateat time zero is hard to be obtained accurately, and thefitting results at the beginning of experiments or running-inperiod are barely satisfactory.
Fig. 15. Specific fitting results.
J. Xi et al.: Mechanics & Industry 18, 511 (2017) 9
The corrected model may be unable to be applieddirectly in complex practical production, but it describesthe change trend of wear rate and the relationship amongload, rotate speed and SRR. By amending the relativecoefficient of equation (31), the corrected model can beapplied in other operation condition with sliding-rollingstate.
5 Conclusion
–
A test rig is designed and improved. SRR can be changedand wear data is collected online.–
Compared with pure rolling state, even though in lowspeed, wear rate of sliding-rolling state is considerablyhigher than pure rolling state. Sliding-rolling statepresents obvious running-in wear and stable wearperformance.–
Within the certain range of speed, in low load, SRRaffects the wear rate in a low extent. With load increase,SRR has a significant influence for wear rates. High SRRand heavy load change the form of contact area from onlyabrasive wear to adhesive wear, and the wear rateincreases obviously.–
In non-heavy load condition, variation of SRRs andvelocities have a limited influence for wear rate, but has agreat effect for time of fatigue wear appearance. Theincrement of SRR accelerates crack formation and crackpropagation on ball surface, and shorten the time offatigue wear appearance.–
According to the relationship among load, velocity, SRR,a wear rate prediction model based on Archard model iscorrected in sliding-rolling state. The veracity ofcorrected model shows great improvement over Archardmodel.Nomenclature
a, b, c, d, f, h
Related correct coefficient i Transmission ratio rs Radius of slave rollers and load wheel (mm) rt Radius of tested rolling ball (mm) t Wear time (min) va0 Sliding speed (m·s�1) v a Corrected sliding speed (m·s�1) vball Velocity of test ball (m·s�1) vr0 Rolling speed (r·min�1) v r Corrected rotate speed (r·min�1) vs Speeds of slave rollers and load wheel(m·s�1)
vs1 Slide speed in point v1 (m·s�1) vs2 Slide speed in point v2 (m·s�1) vu, vd Speeds of friction pair and counter-pair insliding-rolling (m·s�1)
v1, v2, v3 Velocities in three contact points, respec-tively (m·s�1)
v01 Real speed what v1 transmits to test ball(m·s�1)
v02 Real speed what v2 transmits to test ball(m·s�1)
Ks Coefficient of adhesive wear L Wear distance (m) S Sliding-rolling ratio S1, S2, S3 Sliding-rolling ratios in three contactpoints, respectively
V Wear rate (mm3·min�1) Vf Prediction wear rate (mm3·min�1) Vt Real measured wear rate (mm3·min�1) VA Theoretical wear rate (mm3·min�1)
10 J. Xi et al.: Mechanics & Industry 18, 511 (2017)
VS
Wear rate at steady state (mm3·min�1) V0 Wear rate at time zero (mm3·min�1) W Load (N) W0 Corrected load (N) Drt Real measured variation of rolling ball inradius (mm)
DL Measured displacement of load wheel (mm) DV Real wearing volume (mm3) ss Yield strength of softer material (Pa) d0� �
Relative error WW 0Ratio of corrected load to real load at timezero
W 0W
� �∞
Ratio of corrected load to real load atsteady state
Acknowledgments. This work was carried out with financialsupport from the National twelfth five-year project of China forscience and technology under Contract D.50-0109-15-001.
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Cite this article as: J. Xi, X. Shen, X. Chen,Wear experiment andmodel of rolling balls in sliding-rolling conditions, Mechanics &Industry 18, 511 (2017)