A Novel Three-Dimensional Fractal Model for the Normal Contact Stiffness of Mechanical Interface Based on Axisymmetric Cosinusoidal Asperity

A novel three-dimensional fractal model for normal contact stiffness is proposed in this paper. First of all, a hypothetical surface based on axisymmetric cosinusoidal asperity is established. Then, based on the hypothetical surface, the analytical expressions for the contact stiffness and contact load are derived by combining the three-dimensional fractal theory with the contact mechanics theory. In addition, the simulation results of the presented model and the Pan model are compared with the experimental results. The comparison results show that the maximum relative error of the Pan model is 29.58%, while the maximum relative error of the presented model is 4.35%. Ultimately, the influence of different fractal parameters on contact stiffness is discussed. Under the same contact load, the normal contact stiffness first increases and then decreases with the increase of the fractal dimension D, while the normal contact stiffness monotonically decreases with the increase of scale coefficient G. The results are explained from the perspective of the shape of the asperity. This study provides a novel model for the calculation of normal contact stiffness, which provides a model basis for the study of contact properties for the mechanical interface.