Contact force resulting from rolling on a self-affine fractal rough surface

The time dependence of the contact force resulting from the rolling of a sphere on self-affine fractal rough surfaces was investigated using the method of reduction of dimensionality. The main focus was on the part of the spectrum corresponding to the short wavelength corrugation (with a wavelength much smaller than the nominal contact radius). It has been shown that in this domain, the spectral density of the normal force is a power function of frequency. This result can be used for calculation of high frequency acoustic emission of rolling contacts in various technical systems as well as for development of diagnostic systems.