A fractal contact model of rough surfaces considering detailed multi-scale effects

In order to analyse and study the dynamic contact performance of engineering surfaces, a fractal contact model of rough surfaces (isotropic and non-Gaussian) was proposed considering the scale-dependence of both the asperities’ critical contact parameters and the size distribution of contact spots. Considering multi-scale effects, the deformation modes of a single asperity at each scale were discussed, and a new piecewise and scale-dependent size distribution of contact spots was derived. Then, the contact stiffness and load of the entire joint surface were calculated by integrating and summing the piecewise size distribution of the contact spots for each scale. The contact characteristics depend significantly on the scale parameter, surface topography, and material properties. The contact characteristics of asperities with a range of scales in the lowest ten grades significantly contribute to those of the entire joint surface. The change in topography and material properties was mapped to the critical frequency index and critical contact parameters—both related to the transition of the asperity deformation mode, which subsequently mapped to the contact characteristics; the influences of topography and material properties on the contact characteristics were thus revealed.