Traction and wear of an elastomer in combined rolling and ...

LUBRICATION SCIENCELubrication Science 2016; 28:97–106Published online 27 May 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ls.1303

Traction and wear of an elastomer in combined rolling and sliding

Kyle G. Rowe, Alexander I. Bennett and W. Gregory Sawyer*,†

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA

ABSTRACT

Under combined rolling and sliding materials can experience millions of cycles as well as complex loadingand slip conditions, which can dramatically affect their friction and wear behaviour. It was shown that for acarbon black-filled natural rubber compound in combined rolling and sliding contact with a smooth aluminacoated disk, the traction coefficient, as a function of slip percent, was dependent upon the normal load andindependent of rolling velocity. The wear rate of this material pair was found to be independent of slippercentage as well as rolling velocity but dependent upon sliding distance. The wear rate was found to beapproximately the same for all tested cases (K~ 1× 10�4mm3·Nm�1). The worn profiles of the ball speci-mens showed that this wear occurred preferentially on the left side (inner radius) of the contacting area.Copyright © 2015 John Wiley & Sons, Ltd.

Received 5 January 2015; Revised 7 April 2015; Accepted 1 May 2015

KEY WORDS: traction; slip; rolling–sliding wear; elastomer

INTRODUCTION

The dynamic combined rolling and sliding contact involves a wide variety of conditions which canhave profound effects on friction, wear and lubrication. As such, it has been widely studied for a mul-titude of applications ranging from high performance bearing lubrication to automotive tires.1,2

Typically these materials will experience millions of cycles under complex loading and slip conditions.Elastomers are ideal materials for rolling elements due to their good fatigue resistance, highly elastic

and hysteretic behaviour, and varied friction coefficient.3–5 Because of their wide use as rollingelements a comprehensive understanding of how soft and highly elastic materials respond under thesecircumstances is necessary. Numerous studies on the contact mechanics and friction behaviour of thesematerials in pure sliding,5–14 rolling4,15–24 and combined rolling and sliding25–31 have been rigorouslyperformed for a variety of materials, surfaces, contact conditions and geometries. However, the wear ofsoft materials in combined rolling and sliding has primarily focused on abrasive surfaces, large slipangles and high slip velocities.2,25,26,29,32–42

*Correspondence to: W. Gregory Sawyer, Department of Mechanical and Aerospace Engineering, University of Florida,Gainesville, FL 32611, USA.†E-mail: [email protected]

Copyright © 2015 John Wiley & Sons, Ltd.

98 K. G. ROWE, A. I. BENNETT AND W. G. SAWYER

Iwai et al. performed well controlled combined rolling and sliding traction experiments with spher-ical elastomer specimens on a rotating glass disk.31 In their investigation they found that changes to theareas of the sticking and slipping regions in the rolling contact scaled directly with the imposed slippercent, with each area contributing to the measured traction response. Xu et al. performed combinedrolling and sliding experiments with a metal sphere rolling on various elastomer flats.29,39,41,42 Theyquantified the amount of material removed due to pure rolling conditions without imposing global slipwithin the contact.Here, a simple and unique instrument was designed for the tribological testing of materials in com-

bined rolling and sliding contact. In this configuration a driven sample is in a persistent state of rollingcontact with a smooth rotating disk. Using this instrument the tribological performance of a carbonblack-filled natural rubber compound was evaluated with an emphasis on the load and velocitydependence of the traction coefficient as well as the effects of slip on wear rate.

TRIBOMETER DESCRIPTION AND DESIGN

Experiments were performed on a ball-on-flat tribometer comprised of a rotary stage and spindlewhose rotational axes are aligned perpendicular to both each other and to gravity (Figure 1). A servomotor driven rotary stage holds and rotates the disk specimen from 1 to 1200 rpm±1 rpm with a radialrun-out< 8μm. Direct angular position measurements are made by an optical read head and a ringencoder with 0.002° resolution, capable of accurate measurements up to 1018 rpm. The sphericalsample and sample holder are clamped to the spindle and aligned by a machine-tool collet. Driving

Figure 1. Schematic of the combined rolling–sliding tribometer. Complex alignment schemes are circumventedby using a taper to align the sample with the spindle axis and by mounting the spindle directly to a six-channelload cell. Since all forces acting upon the sample must pass through the load cell, it is possible to simply move thespecimen to the pure rolling point without a priori knowledge of the contact location. The pure rolling point isidentically where all forces within the plane of contact cancel, resulting in a net-zero force.

Copyright © 2015 John Wiley & Sons, Ltd. Lubrication Science 2016; 28:97–106DOI: 10.1002/ls

99TRACTION AND WEAR OF AN ELASTOMER IN COMBINED ROLLING AND SLIDING

the assembly is an integrated, brushless, servo motor with rotational speeds up to 6000 rpm with a totalaxial error motion of <2μm and a radial error motion of <5μm; angular position is monitored by adirectly coupled rotary encoder.A six-channel load cell mounted directly under the spindle measures forces. The load cell is aligned

under the spindle such that all moments are zero while the sample is stationary and not in contact. Byisolating the spindle on the force transducer, it is possible to inferentially move the sample to the purerolling point by monitoring the force and moment channels without recourse to complex alignmentschemes and precision machining. Such a point occurs only when the losses due to rolling frictionare balanced with the losses due to sliding friction (slip), resulting in a net zero force within the planeof contact. This inference is possible since all forces acting on the sample must go through the load celland are therefore known. LabVIEW™ was used for experimental control and data acquisition. A 16bitanalog to digital acquisition device externally conditioned all force and position measurements; datawas acquired at 1000Hz.

MATERIALS AND EXPERIMENTS

Materials and sample preparation

Injection moulded carbon black-filled natural rubber spheres of 20mm diameter were used in thisstudy. The moulded rubber was conventionally vulcanised and had a composition similar to that ofa generic truck tire compound.43 This material had an elastic modulus of approximately 4.2MPa at10% extension and a density of 1200kg·m�3. The average surface roughness (Ra) and root meansquare roughness (RMS) of the moulded rubber were determined to be ≈800nm and ≈1000 nm,respectively, by scanning white light interferometer (Veeco Wyko NT9100). A machined 6061aluminum disk with an anodised coating, approximately 10μm thick, was used as the counter surface.An alumina coating was used to minimise the effects of surface chemistry on the wear and frictionmorphologies of the elastomer sample. The anodised disk had an average and root mean squareroughness of 460 nm and 590 nm, respectively.The elastomer specimens were initially cleaned with a mild detergent and deionised water, and

allowed to dry for 24 h before testing. A five-step solvent cleaning process was used to clean the diskbefore each test.44

Traction and wear experiments

Traction and wear experiments were conducted by affixing the sample to the spindle collet and loadingthe sample to the desired normal force. The sample and disk were set to the same rotational velocitybased on the measured track and sample radii; the sample was then adjusted to the pure rolling point.This was accomplished by moving both the spherical sample in x and y, as well as the rotational stagein z, and monitoring the forces along the load cell x-axis and z-axis as well as the moment about the y-axis. Where these forces and the moment simultaneously cross zero denotes the pure rolling point. Thevelocity of the disk was then set to the desired slip velocity (Vball�Vdisk) and the z-stage was adjustedto minimise cross slip within the contact (forces along x-axis).Traction tests were performed for a range of slip velocities from pure rolling to ±10% of the ball

velocity. This was repeated for four different ball velocities, Vb, of 100mm·s�1, 300mm·s�1,1000mm·s�1 and 3000mm·s�1 at a 10N normal load, as well as at different normal loads of 2N,



6N, 10N and 18N for an average ball velocity of 1000mm·s�1. During each test the disk velocity waschanged but the ball velocity remained constant.Wear rates were determined by mass loss measurements taken at regular rolling distance intervals.

The mass loss of the sample was converted into a volume loss and from this the wear rate of the sampleobtained.44 Wear experiments were performed at 1%, 3% and 5% slip for a ball velocity of1000mm·s�1; and at 3% slip for ball velocities of 300mm·s�1 and 3000mm·s�1.

RESULTS AND DISCUSSION

Traction experiments

The effects of ball velocity on the traction response, μ, of this material at various slip velocities areshown in Figure 2a. These tests were performed for one normal load of 10N, resulting in a nom-inal contact pressure of ≈0.47MPa. A marked change in the traction response was observed whenthe ball velocity was decreased by an order of magnitude (e.g. 1000mm·s�1 to 100mm·s�1) eventhough for all experiments the highest tested slip velocity corresponded approximately to the samedisk to ball velocity ratio. This data is plotted again in Figure 2b where the slip velocity has beenrecast as a slip percentage (Equation (1)), which is commonly expressed as a fraction and referredto as a slide-roll ratio (SRR) in literature. Using slip percent instead of slip velocity resulted in thecollapse of the traction data onto one curve that described the material’s traction response indepen-dent of rolling and slip velocities. There was also no observable traction maximum over this largerange of slip values, and at the tested velocities (both ball and slip) and corresponding rotationalfrequencies (≈5–50Hz) the traction coefficient remained unaffected, only being a function ofslip percent.

%slip ¼ Vball � Vdisk12 Vball þ Vdiskð Þ�100 (1)

The dependence of the traction coefficient on slip ratio is attributed to changes within thecontact during rolling with sliding. As the amount of imposed slip increases the contact dividesinto an increasingly slipping region and a decreasingly sticking region, an effect which has beenexperimentally verified.31 In this experimental configuration rolling losses have been cancelledthrough the zeroing of the instrument, but contributions to friction from material deformationsare still present. These include the shearing of material in the sticking region of contact as wellas asperity deformations of the material in the slipping region of contact. Increasing slip withinthe contact would result in an increase in the sliding distance and velocity of the slipping por-tion of the material as well as increase the amount of strain within the sticking portion. Both ofthese would alter the traction response, whether by energy dissipation due to asperity inducedmaterial deformations and oscillations or due to the shearing of the non-slipping area.Changing the applied normal load, and thus mean contact pressures, over a range of slip percent-

ages, did have an effect on the measured traction coefficient. Increasing the normal force resulted ina more shallow traction response (Figure 2c); however, increasing the normal force beyond a certainpoint (10N) had little effect. This suggests that the traction coefficient of rubber is closely related tocontact area in combined rolling and sliding. For small slips (micro-slip region) contact mechanics


Figure 2. (a) Traction coefficient versus slip velocity for a carbon black filled natural rubber sphere for differentball and disk velocities. (b) The same traction data as in 2a collapses onto a single curve when plotted againstpercent slip. (c) Effects of increasing normal load on the traction response of the filled rubber for variousslip percentages. (d) In the linear region of 2c (≈ ±4% slip) the traction coefficient scales with contact

area, or fn1/3.


predicts that the slip (s) in the contact is proportional to the tangential force (FT) over the square of thecontact radius (a), which gives the friction coefficient the form of Equation (2).

μ ¼ FT

Fn/ sa2

FN(2)

From Hertzian contact theory the normal force is proportional to the contact radius to the one-thirdpower (FN / a1/3). Using this relationship in Equation (2) predicts that the friction coefficient isproportional to the normal force to the negative one-third power (Equation (3)).

μ / FN�1

3 (3)



Within the ±4% slip region of the data plotted in Figure 2c the traction response is approximatelylinear for all normal loads considered in this investigation. Applying the relationship given in Equation(3) to the traction data from Figure 2c produced a single curve with a constant slope (Figure 2d);beyond this linear region the traction response no longer obeys this relationship. This agreementprovides reasonable evidence that with this material, and within the range of normal loads and slippercentages employed here, the traction coefficient is proportional to the real area of contact undercombined rolling and sliding conditions.

Wear experiments

The volume lost as a function of the product of the applied normal load, FN, and rolling distance, d, forthree different slip percentages (1%, 3% and 5%) is shown in Figure 3a. For a given rolling distance,higher slip percentages resulted in a greater volume of material removed; in fact, the slope of thesecurves linearly increased with slip percentage. However, when the slip within the contact, or sliding

Figure 3. (a) Volume loss as a function of rolling distance (d) for a ball velocity of 1000mm·s�1 at 1, 3 and5% slip. (b) Taking into account the sliding distance by including slip, the wear data collapse onto a singleline representing the sliding wear rate of the material (k≈ 1× 10�4mm3·Nm�1); a wear rate two orders of

magnitude greater than the rolling wear rate.

Table I. Rolling and sliding wear rates for different slip percentages and rolling velocities. Sliding wearrates were calculated by multiplying the rolling distance by the slip fraction.

Slip %Vb

[mm·s�1]Krolling

[mm3·Nm�1]u(Krolling)

[mm3·Nm�1]Ksliding

[mm3·Nm�1]u(Ksliding)

[mm3·Nm�1]

1 1000 1.2 × 10�6 4.0 × 10�8 9.7 × 10�5 8.7 × 10�6

3 1000 3.2 × 10�6 1.3 × 10�7 1.0 × 10�4 5.2 × 10�6

5 1000 5.5 × 10�6 3.8 × 10�7 1.0 × 10�4 8.0 × 10�6

3 300 2.4 × 10�6 1.2 × 10�7 7.5 × 10�5 6.6 × 10�6

3 3000 5.1 × 10�6 2.2 × 10�7 1.1 × 10�4 4.7 × 10�6



distance, was accounted for by multiplying the rolling distance by the slip fraction (% slip/100), it wasfound that a single wear rate could describe the material behaviour independent of slip condition(Figure 3b). This wear rate was determined to be ≈1×10�4mm3·Nm�1 compared to the rolling wearrates which were two orders of magnitude lower (Table I). This wear rate was also insensitive tochanges in rolling velocity. An order of magnitude change in the ball velocity from 300mm·s�1 to

Figure 4. Representative optical (a) and scanning electron micrographs (b) of the disk surface after1 000000 cycles at 3% driving slip show the presence of wear debris and material transfer. This debris mostprobably forms by the agglomeration of small wear particles that become entrained in the contact, creating therolled shapes shown here. The images show that this agglomerated debris exists on multiple length scales from~10μm up to 1–2mm. For the same experiment, optical profilometer scans (c) across the ~5mm wide weartrack on the ball specimen show that material removal was biased to the left side of the wear track (smaller diskradius); this behaviour was observed for all of the wear experiments and, due to the geometry of the experi-mental apparatus, is most likely where the slip gradient across the contact was the largest. A buildup of wornmaterial can be seen around the 2mmmark, and due to the leveling of the scans, appears as a large peak in thedata. These line scans have been curvature and tilt subtracted as well as shifted arbitrarily to show detail.



3000mm·s�1 resulted in sliding wear rates of 7.5 × 10�5mm3·Nm�1 and 1.1 ×10�4mm3·Nm�1,respectively. These relationships may not hold true for larger slip percentages where the tractionresponse is no longer linear and thermal effects may become dominant.The predicted energy dissipation in a rolling contact should scale with the applied normal force to

the two-thirds power. In these experiments, the majority of material removal was considered to bedue to the relative sliding between the elastomer ball and the rotating disk. It is for this reason thatthe wear data was presented as a sliding wear rate, and thus, a function of the normal force to the firstpower. Further investigations of the effects of normal force on volume loss would show whether or notthe worn volume scales with the predicted energy dissipation.Representative wear debris, generated during these experiments, is shown in Figure 4a–b. This

debris is most likely the result of small particles liberated from the sample surface that either stickto the disk and smear or agglomerate together and become entrained in the contact. Each successivepass of the sample over this material rolls the debris and causes more particles to become entrained,either from the disk or the rolling sample. These agglomerates eventually reach a critical size andare ejected from the contact, appearing on the edges of the wear track. This debris was observed torange in size from a few micrometers up to a few millimeters in length.Wear of the rolling sample was found to preferentially occur over a small portion of the contact

width (~2mm across the ~5mm wide contact), and its location on the ball did not change with anyof the different driving slip conditions, only its magnitude. Representative curvature subtracted linescans show material removal biased to the left of the sample center (smaller disk radius) (Figure 4c).For this material removal to occur there must exist a normal pressure and a sliding distance, in this caseslip, at this location. It is here that slip must be maximum, resulting in this locally increased materialremoval. Although the data presented here is for a wear test at 3% slip it is representative of all thewear tests in this investigation.

CONCLUSIONS

A simple instrument was created for the tribological testing of materials in combined rolling and slid-ing contact. Mounting the sample spindle directly to the force transducer made it possible to inferen-tially move the sample to the pure rolling point instead of relying on standard metrological methods.An illustration of the instrument’s function was given by the traction and wear testing of a compliantmaterial under a variety of load and slip conditions.Similar to the friction coefficient of elastomers under dry sliding, the traction coefficient of a carbon

black-filled natural rubber under combined rolling and sliding exhibited a dependence on both slipvelocity as well as contact area. For a given normal force, decreasing the ball velocity resulted in asteeper traction response over a range of slip velocities. A single traction curve could be used todescribe this effect independent of the ball and slip velocities when slip percent was used instead ofslip velocity. The traction coefficient was also shown to be proportional to the contact area of thesample (μ~FN

�1/3). Increasing the normal force resulted in a decreasing slope of the traction curve,but after a certain point this effect was minimal.Wear was found to be affected by the amount of global slip within the contact, with increasing

amounts of slip resulting in a greater volume of worn material, for a given distance. However, itwas found that a single parameter could be used to describe the material’s wear response indepen-dent of the slip condition when sliding distance, instead of rolling distance, was used to compute



the wear rate. This was the case over a range of slip percentages (1% – 5%) as well as rolling ve-locities (300mm·s�1 – 3000mm·s�1). Even though this material has a high sliding wear rate theconditions under which it is used are mild, resulting in low wear. This means that less wearresistant materials, although possessing other desirable tribological qualities (friction coefficient,corrosion resistance, etc.), may not be precluded from service as long as the contact conditionsunder which they are used are appropriate.

ACKNOWLEDGEMENTS

The authors would like to thank their collaborators at the University of Florida Tribology Laboratory for theirthoughtful comments and insight.

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