Sliding friction surface contact mechanics model based on fractal theory

According to fractal theory, the sliding friction surface contact mechanics model considering the influences of the asperity's deformation and friction is established. The relationship of elastic-plastic deforming asperity's contact pressure and contact area is expressed by a cubic polynomial, by which the continuous and smooth conditions of transformation of asperity contact area and contact pressure at the critical point of transition of distorting state are obtained. The mathematical expressions of critical elastic deformation micro contact area, critical plastic deformation micro contact area, dimension 1 real contact area of sliding friction surface are deduced. Theoretical calculation results show that real contact area increases with the increases of the load when the surface topography is constant. Real contact area decreases with the increases of characteristic length scale, and increases at first and then decreases with the increases of fractal dimension when the load is constant. Friction factor ha