Investigation on Mathematical Model of Electric Contact Based on Fractal Geometry

Electrical contact is an important part of electromechanical equipment. The performance of electrical contact has an important impact on the overall reliability of the system. Based on the study of the topological characteristics of fractal rough surfaces and the elastic–plastic deformation behavior of rough bodies, a theoretical model of electric contact is established by introducing a mathematical description of contact resistance which takes into account the effect of nano-scale. The corresponding relationship among contact area, contact pressure and compression displacement of asperities is obtained. The accuracy of fractal electrical contact model has been greatly improved. It is satisfactory in the field of precision instruments and analysis of the microscopic mechanism of electrical contacts. The model is used to qualitatively analyze the influence of different factors on contact resistance. The results show that the fractal parameters of rough surfaces influence the electrical contact according to some general rules. The mechanism of influencing factors is analyzed.