General theory of frictional heating with application to rubber friction

Empirical Models for the Viscoelastic Complex Modulus with an Application to Rubber Friction

Up-to-date predictive rubber friction models require viscoelastic modulus information; thus, the accurate representation of storage and loss modulus components is fundamental. This study presents two separate empirical formulations for the complex moduli of viscoelastic materials such as rubber. The majority of complex modulus models found in the literature are based on tabulated dynamic testing data. A wide range of experimentally obtained rubber moduli are used in this study, such as SBR (styrene-butadiene rubber), reinforced SBR with filler particles and typical passenger car tyre rubber. The proposed formulations offer significantly faster computation times compared to tabulated/interpolated data and an accurate reconstruction of the viscoelastic frequency response. They also link the model coefficients with critical sections of the data, such as the gradient of the slope in the storage modulus, or the peak values in loss tangent and loss modulus. One of the models is based on piecewise polynomial fitting and offers versatility by increasing the number of polynomial functions used to achieve better fitting, but with additional pre-processing time. The other model uses a pair of logistic-bell functions and provides a robust fitting capability and the fastest identification, as it requires a reduced number of parameters. Both models offer good correlations with measured data, and their computational efficiency was demonstrated via implementation in Persson’s friction model.

Effect of simulated tennis steps and slides on tread element friction and wear

In hard court tennis, players change direction by either stepping or sliding. The shoe–surface friction during these movements is crucial to player performance. Too little friction when stepping may result in a slip. Too much friction when attempting to slide could cause the player to move only a short distance, or to fail to slide. To understand the influence of tread design on shoe–surface friction in tennis, experiments were performed on individual shoe tread elements that replicated the tribological conditions typically experienced during hard court step and slide movements. Tread element orientation had no effect on the static friction in step movements, but longer tread elements (in the sliding direction) had 9% lower dynamic friction during slide movements (p < 0.001). The friction between tennis shoe tread and hard court tennis surfaces is also shown to be influenced by the tread’s sliding history, and the wearing pattern that forms on the surface of the rubber.

Rubber friction: The contribution from the area of real contact

There are two contributions to the friction force when a rubber block is sliding on a hard and rough substrate surface, namely, a contribution F_ad = τ_f A from the area of real contact A and a viscoelastic contribution F_visc from the pulsating forces exerted by the substrate asperities on the rubber block. Here we present experimental results obtained at different sliding speeds and temperatures, and we show that the temperature dependency of the shear stress τ_f, for temperatures above the rubber glass transition temperature T_g, is weaker than that of the bulk viscoelastic modulus. The physical origin of τ_f for T > T_g is discussed, and we propose that its temperature dependency is determined by the rubber molecule segment mobility at the sliding interface, which is higher than in the bulk because of increased free-volume effect due to the short-wavelength surface roughness. This is consistent with the often observed reduction in the glass transition temperature in nanometer-thick surface layers of glassy polymers. For temperatures T < T_g, the shear stress τ_f is nearly velocity independent and of similar magnitude as observed for glassy polymers such as PMMA or polyethylene. In this case, the rubber undergoes plastic deformations in the asperity contact regions and the contact area is determined by the rubber penetration hardness. For this case, we propose that the frictional shear stress is due to slip at the interface between the rubber and a transfer film adsorbed on the concrete surface.

Differences in Tribological Behaviors upon Switching Fixed and Moving Materials of Tribo-pairs including Metal and Polymer

The coefficient of friction (COF) between two materials is usually believed to be an intrinsic property of the materials themselves. In this study, metals of stainless steel (304) and brass (H62), and polymers of polypropylene (PP) and polytetrafluoroethylene (PTFE) were tested on a standard ball-on-three-plates test machine. Significantly different tribological behaviors were observed when fixed and moving materials of tribo-pairs (metal/polymer) were switched. As an example, under the same applied load and rotating speed, the COF (0.49) between a rotating PP ball and three fixed H62 plates was approximately 2.3 times higher than that between switched materials of tribo-pairs. Meanwhile, the COF between H62 and PTFE was relatively stable. The unexpected tribological behaviors were ascribed to the thermal and mechanical properties of tribo-pairs. Theoretical analysis revealed that the differences in the maximum local temperature between switching the fixed and moving materials of tribo-pairs were consistent with the differences in the tested COF. This result indicated the precise prediction of the COF of two materials is complexcity, and that thermal and mechanical properties should be properly considered in designing tribo-pairs, because these properties may significantly affect tribological performance.