Research on the loading–unloading fractal contact model between two three-dimensional spherical rough surfaces with regard to friction

A loading–unloading fractal contact model between two three-dimensional spherical rough surfaces with regard to friction is developed. The contact model of single asperity for the load–unload cycle with regard to friction is obtained. The expressions between contact load and real contact area in the loading and unloading processes in different deformation stages of three-dimensional spherical contact surfaces are deduced. The impacts of some parameters in the model are discussed by numerical analysis. The numerical results show that the critical contact load and the critical real contact area in different deformation stages of spherical contact surfaces with friction are positively related to the fractal dimension and the curvature radius, negatively correlated with the fractal roughness, influenced by the contact type. In the elastoplastic stage of spherical contact surfaces with friction, the real contact area in the unloading process is larger than that in the loading process with the same contact load; for a given contact load, the real contact area of the loading–unloading process, as well as the differences of the real contact area in the loading–unloading processes, increases with the increase in the fractal dimension and the curvature radius, decrease in the fractal roughness, or the substitution of internal contact for external contact.