Scale Dependence of Fractal Contact Mechanics Model for Friction Surface

Abstract

According to the fractal theory, the normal contact mechanics model for friction surface considering the asperity level and the various hardness of material has been established. The mathematical expressions of critical contact areas and critical levels of a single asperity are derived respectively from the deformation mechanism of a single asperity. Based on the micro-contact area distribution function, the relationship between the total normal contact load and the total real contact area is obtained. The numerical results show that the critical contact areas of asperity on friction surface are scale dependent, they reduce while the asperity level increases; for determined material properties of friction surface, the critical elastic level and the critical plastic level of asperity are decided by the value of fractal parameters; when fractal parameters of certain friction surface are constant, the elastic contact area ratio which manifests the wear resistance of the friction surface decreases with the raising of asperity level. The fractal contact mechanics model produces a theoretical foundation for further study of the wear mechanisms of friction surface.