Simulation of a wear experiment

J. Anderssona,, A. Almqvista,, R. Larssona,

aDivision of Machine Elements,Lulea University of Technology, Sweden

Abstract

By using a deterministic FFT-accelerated contact mechanical tool to calculate pressure and elastic-plastic deformation, a wear model is utilized to simulate the time dependent wear from a sphere onflat contact. The results of the simulated wear are compared to experimental results form a SRV ballon disk tribometer, from which worn surfaces are optically measured. The conditions of the simulationand the experiments are independently adjusted to match. Agreement and diversity shows upon theusefulness and limitation of wear modeling of this type.

1. Introduction

The prediction of wear and scuffing risk inmetallic contacts is an important task. Influentialfactors such as temperature, elastic-plastic defor-mations, wear, surface topography, material prop-erties and chemistry all contribute to the complexcontact conditions.

Because of the complexity of the system, anexperimental approach is often chosen. While anexperimental approach is necessary, the underly-ing mechanisms behind the wear can prove dif-ficult to probe by just analyzing wear scars andno information can be obtained in situ. There-fore, numerical predictions and matching againstsimulations is good complement to find out moreabout governing factors causing wear.

Early models for determination of wear, uti-lizing the Archard wear equation, used the ini-tial pressure distribution throughout the wear life.This was found to give results that diverted fromreality [1].

Numerical methods to study wear has beenused by Podra and Andersson [2], incorporating asimple and numerically efficient contact mechan-

Email addresses: joel.andersson@ltu.se(J. Andersson), andreas.almqvist@ltu.se(A. Almqvist), roland.larsson@ltu.se (R. Larsson)

ics model known as the Winkler surface model.Using this model, Flodin and Andersson [3] sim-ulated wear of helical gears. Another exam-ple of using the same model is by Spiegelbergand Andersson [4] simulating wear in the valvebridge/rocker arm pad of a cam. As the modelworks well numerically, its simplicity carries thedrawback that neighboring surface patches deflectindependent of each other. This is only true forvery special materials, under limited constraints.

More sophisticated mechanical contact modelsinvolving the interaction between contact pointson each surface is used here by implementation ofthe DC-FFT method described Liu et al [5]. Theplastic deformation is included by the methods ofSahlin et al. [6, 7]. This deformation behaviorcorrespond to an ideal plastic behavior of ductilematerials, such as steel.

In this study influence of elastic perfectly plas-tic deformations and wear is simulated for twosurfaces. Under consideration of the surface as-perities mutual influence by FFT-accelerated nu-merical methods, deeper insight into the wearmechanism of a tribosystem is expected. Numeri-cal simulations of a sphere on a flat are comparedto experimental assessments of the reciprocatingmotion of a ball on a disk.

April 29, 2010

2. Wear model

Holm [8] introduced the concept of wear volumeper sliding distance, Q, being proportional to thenormal force for each material pair according to

Q = KF

H. (1)

Where H is the hardness. The wear constant Kwas interpreted as number of abraded atoms peratomic collision. Archard [9] improved the the-ory behind Eq. (1) which is known as the “Ar-chard wear equation”. The wear constant wasinstead interpreted as the probability that an as-perity collision would lead to the formation of awear particle. The model has been used to pre-dict wear in several different systems, thus beingused as a rough universal wear volume predictor.In this work the Archard wear equation will be in-terpreted as contribution to wear from tangentialstresses and sliding at the micro scale. Of partic-ular interest is wear depth at each point on thesurface, h. Rewriting Eq. (1) results in

h = kps. (2)

Here, the dimensional Archard wear coefficientk = K/H is used as the proportionality constantto the pressure p times the sliding distance s. Alocalized discrete version of Eq. (2) is used. Thiswill mean that the wear rate is constant duringthe sliding. by assuming lateral wear to occur ata point subjected to the pressure p over a slidingdistance ∆s at a magnitude of ∆h.

∆h = kp · ∆s. (3)

3. Numerical model

The numerical model has been set up to reflectthe experiments that will be described under ex-perimental details.

3.1. Contact mechanics

As real materials experience plastic flow at highpressure, plastic deformation is included in thissimulation. To maintain necessary numerical effi-ciency the transition to fully plastic flow is imme-diate above yield pressure. Yield pressure is set

to the same magnitude as the hardness, H. Elas-tic deflection due to contact between two surfaceshas been solved by a fast DC-FFT method [5].The methods of [6] and [7] are implemented forthe perfectly plastic flow.

For numerical simulations the surfaces are as-sumed to be isotropic infinite half-spaces. Thetop surface is a half space shaped like a spherewith a radius of 5 mm and the opposing surfaceis a perfectly flat half-space. Both surfaces haveelastic moduli of 207 GPa, Poisson ratios of 0.3and a hardness of 4 GPa. The simulated load is100 N.

3.2. Wear modelling

As the simulations are to be compared to anexperiment described under experimental details,a specification of the movement is necessary. Herea wear model is used to represent the movement.Time and velocity is simulated by discrete timeincrements of ∆T = 0.25 s at a fictional velocityv = 0.1 m/s. A wear constant is chosen resultingin the same wear volume as in the experiments,k = 3.11 · 10−16 Pa−1.

Since the pressure on any contact point on thedisk in the experiment changes with time rela-tive to any coordinate system in the bulk of thedisk, the material removal is distributed over theflat. This distribution of the wear is what willrepresent the relative movement of the surfaces.To achieve the distribution, a sliding direction ischosen. Along this sliding direction the wear mustfollow Eq. (3), considering that the pressure is dif-ferent in each contact point. Figure 1 illustrateshow a pressure distribution across the contact issmeared out in the sliding direction.

The pressure in each individual point on theflat will change as the sphere moves across theflat. The points close to the centre of the trackon the flat would be expected to initially experi-ence pressure for a longer time at each passing,and also experience a different pressure distribu-tion due to the shape of the sphere. If the pres-sure is assumed constant during the time step ∆Tand the frequency f(here f = 25) of the move-ment at constant velocity is chosen as an integervalue of the time step, every worn point in the

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Figure 1: In order to simulate wear across the flat surface,the momentary pressure is spread out over the wear regionbefore it is used to calculate wear in Eq. (3), giving a timeavarage wear. The red shaded zone represents a possiblepressure distribution at one time step. The correspondingwear on the flat would be distributed across the shadedblack area, in this case resulting in more wear at the centreof the wear zone.

y-direction on the flat can be assumed to experi-ence the whole pressure spectrum. Therefore, thetime avarage pressure is equal to the geometricallyavarage pressure over the whole contact region.

Shortly, the pressure average over one time stepPp(y) in each contact point on the flat, choosingthe sliding direction as x in Fig. 1 is determinedby

Pp(y) =1

N

∫ L

0

P (x, y)∂x. (4)

Here, L represents the length of the entire windowof the flat which is worn. In the current case thiswindow is set to 2 mm. The resulting wear height∆h(y) on the flat over the timestep ∆t is givenby combining Eq. (3) with Eq. (4), that is

∆h(y) = k · 1

N

∫ L

0

P (x, y)∂x · ∆t · v. (5)

Equation (5) is implemented at each timestepwith the a pressure distribution.

For the spherical surface the local pressuresare used directly to calculate wear according toEq. (3) with the same s and k. The wear is dis-tributed equally between the surfaces.

The resulting numerically convenient model de-scribes an ideal process of wear and deformationfor a sphere moving on a flat. The model corre-sponds to the conditions in the middle of the disk,

so the simulation should be compared to the cen-tre of the wear scar on the disk.

4. Experimental details

Before and after experiments the contactingsurfaces were measured with an optical profilome-ter, WYKO NT1100, manufactured by PhoenixArisona USA. Measurements were taken at threedifferent magnifications, rendering samples of size1.24mm × 0.94mm, 0.62mm × 0.47mm and0.31mm × 0.24mm. This was achieved using a10× mirau objective with three variations of thefield of view lens; producing measurements at 5×,10× and 20× magnification.

The experiments are conducted with a slidingreciprocating rig, Optimol SRV reciprocating fric-tion and wear tester. The rig is used to estimatesurface behavior at reciprocating wear, see e.g.Hardell et al. [10].

A ball sliding on a disk, both of AISI25100steel are the samples used in the reciprocatingwear tester. The contact is lubricated with 99%pure hexadecane. The hexadecane has low polar-ity and should minimize chemical interaction (seee.g. Kajdas et al. [11, 12, 13] or Naveira-Suarez etal. [14]) with the surface and still reduce the fric-tion to boundary lubrication levels. The radiusof the ball is 5mm. The temperature is preset to90℃ before the samples are loaded with 100 Nand the ball is slid on the disk by a frequency of25 Hz. A stroke length of 2 mm giving an av-erage velocity of 0.1 m/s is chosen. The test isterminated after 1 hour of sliding.

Before and after the experiment the contactingbodies were weighed in order to measure the wear-volume.

5. Results and discussion

5.1. Experimental

The weight of the disk before and after the ex-periment was measured to 27.6445 g and 27.6443g respectively, i.e. a weight change of around 0.2mg. The corresponding change of the balls weightwas around 2 mg. This indicates a difference be-tween fundamental assumptions of the numerical

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model and the experiment, implying that the wearis 10 times greater on the ball than on the disk.The resulting dimensional Archard wear coeffi-cient, using the density of the steel 7850 kg/m3,is calculated to K = 3.11 · 10−16 Pa−1.

Surface metrology measurements of the disksurface with the interferometer resulted in Ra val-ues ranging from 6.7 − 10.8 nm, calculated byVeeco’s software Vision 32. The variations dueto magnification were small, which indicates nounwanted curvature on the disk surface. The factthat we have variation in Ra value is the normaldependence on spot, resolution, measured areaand measurement quality.

A surface roughness measurement of the disk isdisplayed in Fig. 2. Figure 3 shows the ball sur-face before the test. After running the test for

Figure 2: The roughness of the disk surface before wear.

Figure 3: The ball surface before wear.

one hour, under the severe wear conditions de-scribed under experimental details, the surfaceswere once again analyzed by the optical profilersystem. The worn ball can be seen in Fig. 4 and

Figure 4: The wear scar on the ball.

Figure 5: The wear scar on the disk.

the wear scar on the disc is depicted in Fig. 5.Severe plastic flow combined with wear has pro-duced chaotic roughness levels. Except for theroughness there are some interesting phenomenaor specific patterns, that can be seen in the wearscar, which demand an explanation.

Comparing the surface profile parallel with andperpendicular to the wear scar clearly illustratessuch a pattern. Figures 6 and 7 shows worn pro-files of the ball in the perpendicular and paralleldirections to sliding direction respectively. FromFig. 6 it can be seen that the shape of the ballhas been worn down to be almost flat, the vari-ation in height between the end of the wear scarand the highest roughness peaks being about 1µm. The profile seen in Fig. 7 has retained amore circular shape, with a corresponding differ-ence in wear scar depth of about 10 µm. Twogrooves has formed on each side of the centre ofthe wear scar. The corresponding roughness onthe flat conforms as far as the wear scar is con-cerned, compare Fig. 5.

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Figure 6: A typical profile of the ball parallel to the wearscar.

Figure 7: A typical profile of the ball perpendicular to thewear scar.

If intrinsic properties of the system consideredin the numerical simulations bring about the wearin the experiments, we should find identifiablesimilarities. In other words, how well does theArchard wear equation applied as in the numeri-cal model describe the wear mechanism.

5.2. Numerical

The simulation of the contact between thesphere moving on the flat is described in the sec-tion numerical model. Analysis of the simulatedworn profiles show both interesting similaritiesand differences compared to the experiment.

The contact pressure during sliding can not eas-ily be followed in an experiment. This real timepressure is one of the advantages of using a numer-ical model compared to experiments. An image ofthe full in-contact pressure distribution after 200s is shown in Fig. 8. Curves illustrating a crosssection of the initial pressure, and the pressureafter 200 s, 500 s, 1500 s and 3600 s are depictedin Fig. 9.

As can be seen the load is spread out over alarger area as the surfaces wear, leading to a lower

Figure 8: The complete pressure in the contact betweenthe sphere and flat after 200 s.

Figure 9: The pressure as it changes over time during thesimulation.

more even pressure distribution with time. Wecan also see that the magnitude of the pressureis not high enough to cause plastic flow. For im-provement of the model, the local pressures dueto roughness should be investigated since they arelikely to induce plastic flow.

Figures 10 and 11 show the wear profiles per-pendicular and parallel to the sliding direction.It can be seen, by comparing to the experimentalprofiles, that the numerical wear model producesa profile somewhat different from that observedin the experiment on the ball. No sings of thetwo grooves perpendiuclar to sliding direction areseen. The basic shape of the wear scar, on theother hand, is similar in experiment and simula-tion. The similarity lies within the flatness seenin profiles in line with sliding, compared to thecurved shape that appears perpendicular to thesliding direction. In the experiment this differ-ence is clear comparing the y-scale in Fig. 7 andFig. 6. It seems like the pressure distribution andthe sliding distance are factors influencing wearand that the Archard model can be used to givean idea of were there is risk for wear locally.

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Figure 10: Profiles of a sphere being worn by a numericalmodel in line with the simulated sliding direction. The topcurve shows the unworn surface, with profiles after 200 s,500 s, 1500 s and finally 3600 s of wear following beneathit.

Figure 11: Profiles of a sphere worn being worn by a nu-merical model perpendicular to the simulated sliding di-rection. The top curve shows the unworn surface, withprofiles after 200 s, 500 s, 1500 s and finally 3600 s of wearfollowing beneath it.

6. Conclusions

Experimental results from a ball and disk righave been compared to a simulation of the contactmechanics of a spherical and a flat surface. Aroughness increase, i.e. an increase in Ra, wasobserved in the surface metrology measurement ofthe real worn surfaces. The wear process was alsoanalyzed by an evaluation of the artificially wornsurfaces resulting from the numerical simulations.

A direct conclusion from the experiment fromthe quantitative wear 10 times larger on the ballcompared to the disk. It could be explained by awear temperature dependence, since the ball isconstantly in contact and will experience morefriction heating and less time for recovery com-pared to the local parts of the disk in contact.

Simulations with the Archard wear equationwas found to match to some degree with thewear on a ball and a flat. The difference on thewear scar on a ball between sliding direction andperpendicular direction was found to be intrinsicproperties of the system, i.e. the pressure cal-culated by contact mechanical methods has beenshown to have an effect on the wear. Indeed, sim-ulations may serve as a feasible analytical tool tounderstand, predict and prevent wear. Still, wearmodelling of this type is in an infant stage andadditional effects must be added. Some examplesof such effects are those from temperature andlubrcant-surface interaction.

References

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[3] A. Flodin and S. Andersson. A simplified model forwear prediction in helical gears. Wear, 249(3-4):285–292, 2001.

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Appendix A. Nomenclature

The meaning of letters used to describe vari-ables are sumarized here.Q = Wear volume per sliding distance[m3/m]K = Dimensionless wear constant.H = Hardness[Pa].FN = Normal force[N].k = Dimensional wear constant K/H[Pa−1].p = Pressure[Pa].s = Sliding distance[m].∆s = Sliding distance[m].h = height change due to wear[m].∆t = The size of one timestep[s].v = Velocity[m/s].L = The length of the evaluation window [m]

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