Rubber friction on self-affine road tracks

A basic theoretical concept of rubber friction on rough surfaces is presented that relates the frictional force to the dissipated energy of the rubber during sliding stochastic excitations on a broad frequency scale. It is shown that this is of high relevance for tire traction and allows for a prediction of the likely level of friction of tread compounds on the basis of viscoelastic data.. The impact of both, the frequency dependent loss- and storage modulus on the frictional force during sliding of tires on rough tracks, is demonstrated quantitatively for different sliding velocities. The effect of the surface roughness of road hacks is described by three characteristic surface descriptors, i.e., the fractal dimension and the correlation lengths parallel and normal to the surface. These descriptors can be obtained from a fractal analysis of the road texture via stylus- or laser measurements. In particular, it is shown that the applied model of rubber friction is in agreement with the classical friction data of Grosch, who found a broad maximum for the friction coefficient with increasing sliding speed. The broadness of the friction maximum is shown to be directly related to the broadness of the roughness scale of the surface.