Corrected power spectral density of the surface roughness of tire rubber sliding on abrasive material

Abstract

Various models describing the multiscale phenomena of contact mechanics and friction have been developed recently. The power spectral density (PSD) of three-dimensional (3D) surface topography is one of key elements used to formulate these mechanics models. However, the statistical variation of the PSDs of isotropic and self-affine fractal surfaces is not well understood. This paper presents a method to correct the PSD of 3D surface topography to perform statistical and spatial characterizations in a wavenumber space. To validate this data-processing methodology, we applied the areal-corrected PSD to numerical surface models and two real surface specimens made of abrasive grindstone and worn tire rubber and assessed the variation of surface roughness across scales through visual and statistical approaches.