Hysteresis friction of sliding rubbers on rough and fractal surfaces

The friction force generated between sliding rubber and rough surfaces has two components commonly described as the adhesion and hysteretic components, respectively. Under wet conditions, the adhesion component of the total friction is drastically reduced, whereas the hysteresis loss remains largely unaffected. Such situations arise in daily life during blocked wheel braking where tire treads slide over wet road asperities. The situation becomes more complex in Anti Blocking System (ABS) braking on wet roads where both adhesion and hysteresis components of the friction force act. We present a new model of the hysteretic friction coefficient of a sliding rubber sample over a rough or even fractal surface. The model uses the basic assumption that the damping properties of the dynamically strained rubber depend on specific properties of the surface profile through its power spectral density. This assumption is based on recent findings that the fractal texture model is the only one developed to date to successfully address the complete multiscale behavior of paved road surface texture. The spectral density depends on the 'topothesy' k of the surface and scales with the spatial frequency f according to a power law. The corresponding power is related to the surface fractal dimension D. The quantities k and D are scale-independent parameters that characterize the multiscale self-affine topography of road surfaces in the characteristic length scale range of interest. The influence of surface roughness on the frictional properties of the rubber depends on the sliding velocity and is described through a retarded coupling between relaxational modes of the polymer network and roughness modes of the surface. The results of the theory are discussed in comparison with recent experimental results of Grosch. Finally, we demonstrate how the fractal descriptor parameters of different test road pavements are used to compare tire traction measurements performed on wet test roads.