Elastic contact model of elliptical parabolic asperity

To precisely describe the contact mechanics between two solid rough surfaces, a kind of elliptical parabolic elastic asperity contact model was proposed. Both top-top contact and shoulder-shoulder contact were considered in this model. Weingarten map was adopted to obtain the curvature of contact point, and Hertz surface contact theory was used to solve this model. Analytic formula was deduced to get contact displacement and contact area for shoulder-shoulder contact. The influence of relative location and ellipticity on contact area and contact displacement was discussed. Finite element model and the proposed model were compared. The result shows that the ellipticity exerts an obvious influence on the contact area and contact displacement; when ellipticity exceeds 0.9, the contact area and contact displacement of two asperities change drastically; the largest contact displacement error reaches 10%, and the largest contact area error reaches 6.2%. The proposed model is suitable for the other asperity models with second-order continuous partial derivatives.