Multi-stage contact model between fractal rough surfaces based on ellipsoidal asperity deformation

A multi-stage contact model between fractal rough surfaces based on the actual deformation of ellipsoidal asperity is proposed. Firstly, the equations for four deformation modes based on actual deformation of asperity are deduced, and the computational expressions for the contact characteristics of asperity are established. Secondly, the contact behavior of whole surface is divided into five contact stages according to the deformation stages of asperity and the contact degree of surface. Finally, the joint distribution function of base length and eccentricity is introduced, and the multi-stage contact model of surface is established by means of integration. Accordingly, the influences of different parameters (fractal dimension D, fractal roughness G and shape parameters τ, β) on the contact area and force are analyzed. The results show that the fractal dimension has a significant influence on the contact characteristics of surface; the contact area at the same force is related to the roughness of surface; The results obtained from the contact model based on ellipsoidal asperity are smaller than those obtained from the contact model based on spherical asperity. The results of proposed model are compared with the existing models and experiment data to verify the correctness and applicability of present model.