Friction and universal contact area law for randomly rough viscoelastic contacts

Abstract

We present accurate numerical results for the friction force and the contact area for a viscoelastic solid (rubber) in sliding contact with hard, randomly rough substrates. The rough surfaces are self-affine fractal with roughness over several decades in length scales. We calculate the contribution to the friction from the pulsating deformations induced by the substrate asperities. We also calculate how the area of real contact, A(v, p), depends on the sliding speed v and on the nominal contact pressure p, and we show how the contact area for any sliding speed can be obtained from a universal master curve A(p). The numerical results are found to be in good agreement with the predictions of an analytical contact mechanics theory.

Rubber Friction on Ice: Experiments and Modeling

“…In the absence of frictional heating of the rubber, the theory predicts that the viscoelastic contribution to the friction coefficient is independent of the nominal contact pressure (or normal load), unless the pressure is so large as to give rise to a contact area approaching complete contact [29], which is not the case in the present study. However, including frictional heating results in a rubber friction coefficient which depends on the nominal contact pressure.…”

“…We have derived a set of equations describing the viscoelastic contribution to the friction force acting on a rubber block squeezed with the stress p 0 against a hard randomly rough surface [7,23,27,29]. In the following, we summarize the basic equations: …”

“…As for the evaluation of the test series, we first fit an empirical friction formula after [13] and [12], in order to reproduce the measurements and to provide interpolations between tested scenarios, such as required for numerical simulations supporting the development of winter tires. The macroscopic and phenomenological nature of the fitting function is the motivation to extend our theoretical analysis toward the micromechanical Persson rubber friction and contact theory [7,23,24,29]. The latter envisions two essential contributions to rubber friction on ice: (1) a contribution from the viscoelasticity of the rubber activated by ice asperities scratching the rubber surface, and (2) an adhesive contribution resulting from shearing the area of real contact under the real contact pressure.…”

“…The formula depends on the hardness of the rubber compounds, the roughness of the ice surfaces, the ambient air temperature, and the nominal contact pressure [12,13]. In order to gain a deeper insight into microscopic processes determining rubber friction on ice, we employ the Persson rubber friction and contact mechanics theory [7,23,24,29]. This model accurately takes into account the viscoelastic contribution to the friction force, and also determines the area of real contact A 1 which is needed for quantifying the adhesive contribution to the friction.…”

Multiscale physics of rubber-ice friction

“…In the theory of Persson, the friction force acting on a rubber block squeezed with the stress p 0 against a hard randomly rough surface is given by 24,29,39 µ visc ≈ 1 2…”