Contact Mechanics Analysis of Fractal Surfaces Considering Elliptical Asperity with Elliptical Geometry

The purpose of this paper is to present a fractal model of normal contact stiffness of joint surfaces based on elliptical asperity. The effects of normal contact load, fractal dimension, fractal roughness and elliptical eccentricity on the normal contact stiffness of the joint surfaces were investigated by numerical simulations. This article equates the shape of the asperity on the joint surface to a more practical ellipse, including the elastic, elastic-plastic, and fully plastic deformation stages of the asperity. Additionally, a fractal model of the normal contact stiffness of the joint surface is established to investigate the influence of the relevant parameters of the joint surface on the normal stiffness. The results indicate that there is a nonlinear relationship between the dimensionless normal contact stiffness and the normal load when D < 2.4. When D > 2.4, the normal contact stiffness is approximately linearly related to the normal load, and as it increases, the linear relationship becomes increasingly apparent. When 2.1 ≤ D ≤ 2.6, the normal contact stiffness increases with increasing fractal dimension; when 2.6 ≤ D ≤ 2.9, it decreases as the fractal dimension increases. The normal contact stiffness of the joint surface increases with increasing contact load, decreases with increasing fractal roughness, and increases with the increase of eccentricity. Comparison of the simulation results between the theoretical model and the experimental model in this paper shows that the theoretical stiffness of the proposed model in this paper is greater than that of the experimental results, and the maximum error between them is 18.7%.This verifies the correctness and validity of the present model, which can better predict the normal contact stiffness of the fixed joint surface, and also demonstrates that the shape of the asperity on the rough surface has an important influence on the normal contact stiffness of the rough surfaces.