A Novel Contact Resistance Model for the Spherical–Planar Joint Interface Based on Three Dimensional Fractal Theory

In order to obtain the contact resistance of relay contacts more accurately, a novel contact resistance model for the spherical–planar joint interface is constructed based on the three-dimensional fractal theory. In this model, three-dimensional fractal theory is adopted to generate a rough surface at microscopic scale. Then, using contact mechanics theory, the deformation mechanism of asperities on rough surfaces is explored. Combined with the distribution of asperities, a contact resistance model for the planar joint interface is established. Furthermore, by introducing the surface contact coefficient, cross-scale coupling between the macro-geometric configuration and micro-surface topography is achieved, and a contact resistance model for the spherical–planar joint interface is constructed. After that, experiments are conducted to verify the accuracy of the proposed model, and the maximum relative error of the proposed model is 8.44%. Ultimately, combining numerical simulation analysis, the patterns of variation in contact resistance influenced by factors such as macroscopic configuration and microscopic topography are discussed, thereby revealing the influence mechanism of the contact resistance for the spherical–planar joint interface. The proposed model provides a solid theoretical foundation for the optimization of relay contact structures and improvements in manufacturing processes, which is of great significance for ensuring the safe and stable operation of power systems and electronic equipment.