Influence of self-affine roughness on the friction coefficient of rubber at high sliding velocity

Abstract

In this work we investigate the influence of self-affine roughness on the friction coefficient of a rubber body onto a solid surface at high speeds. The roughness is characterized by the rms amplitude $w$, the correlation length $\ensuremath{\xi}$, and the roughness exponent $H$. It is shown that the friction coefficient decreases with increasing correlation length $\ensuremath{\xi}$ and increasing roughness exponent $H$ for sufficiently large correlation lengths. However, for small correlation lengths the opposite behavior takes place because the system is within the strong roughness limit or equivalently average local surface slopes larger than 1. Moreover, direct plots of the friction coefficient as a function of the roughness exponent $H$ indicate that as the correlation length $\ensuremath{\xi}$ decreases, a maximum of the friction coefficient develops. The latter is followed by a continous increment of the friction coefficient with increasing $H$ and decreasing $\ensuremath{\xi}$.