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.

In this paper, a novel fractal model for the contact resistance based on axisymmetric sinusoidal asperity is proposed, which focuses on the resistance characteristics of the rough interface at a microscopic scale. By introducing the unique geometric shape of axisymmetric sinusoidal asperity, and combining it with a three-dimensional fractal theory, the micro-morphology characteristics of the rough interface can be characterized more precisely. Subsequently, by conducting a theoretical analysis and numerically solving the deformation mechanisms of asperities on the rough interface, a refined model for contact resistance is constructed. This research comprehensively employs theoretical analysis, numerical simulation, and experimental testing methods to deeply explore the current transmission mechanisms during the contact process of the rough interface. The findings suggest that the proposed model is capable of precisely capturing the intricate interplay of various factors, including contact area, contact load, and material properties, with the contact resistance. Compared to the existing models, the presented model demonstrates significant advantages in terms of prediction accuracy and practicality. This research provides an important theoretical basis and design guidance for optimizing the electrical performance of the rough interface, which has great significance for engineering applications.