New analytical model of elastic-plastic contact for three-dimensional rough surfaces considering interaction of asperities

The contact calculation of three-dimensional real rough surfaces is the frontier field of tribology and surface science. In this study, we consider the interaction and elastic-plastic deformation characteristics of asperities and further, propose an analytical contact calculation method for rough surfaces considering the interaction of asperities. Based on the watershed algorithm, the rough surface is segmented and the asperities are reconstructed into ellipsoids. According to the height relationship between the asperities, the definition of the deformation reference height of the matrix between each couple of asperities is provided. Subsequently, the calculation formula of the substrate deformation is provided according to the local contact pressure considering the elastic-plastic deformation of the asperity, and the contact state under a specific load is determined using the iterative correction method. The results correspond with those of finite element numerical calculation and the study reveals the following: (1) compared with the results obtained without considering the asperity interaction, contact area, distance, and stiffness will be reduced by 6.6%, 19.6%, and 49.5%, respectively, when the influence of asperity interaction is considered; (2) the interaction of the asperities has the greatest influence on the surface contact distance and stiffness. Under the same load, the existence of asperity interaction will reduce the contact distance, area, and stiffness; (3) considering the interaction of the asperities, the higher asperity will bear more load, but it will simultaneously reduce the contact of the surrounding area and increase that of the distant area. The calculation method proposed in this study has the advantages of high calculation efficiency and accuracy, thus, providing the calculation basis and method for subsequent studies on service performance of rough surfaces, such as the calculation of contact stiffness and fatigue performance analysis of rough surfaces.