Prediction of the friction coefficient of filled rubber sliding on dry and wet surfaces with self-affine large roughness

The friction of filled rubber on a rough surface is mainly determined by the rubber viscoelasticity and the surface property of multiple-scale asperities that can be represented by the power spectral density of the surface profile (i.e., power spectrum of surface roughness). This paper investigates a prediction model of rubber friction on dry and wet surfaces with large roughness under lightly squeezing, and finds a high stationary friction coefficient that depends on sliding speed. To this end, we demonstrated friction testing at low velocities with carbon-black-filled rubber and a hard substrate having self-affine surface roughness. From the experiment results, we estimated the hysteresis friction coefficient related to energy dissipation resulting from cyclic deformations of the viscoelastic rubber by applying the theory developed by Persson [(J. Chem. Phys. 115, 3840 (2001)]. We discussed the additional factor, an adhesion force, which also increases the friction coefficient. We concluded that the hysteresis loss of rubber viscoelastic deformation contributes most of the friction force, accounting for the nonlinear viscoelastic behavior of filled rubber, and that the operative surface wavelength extends to the order of micrometers.