Tangential stiffness model of the joint surface considering contact angles between asperities based on fractal theory

Based on fractal theory, the tangential contact model for a joint surface, taking into account the contact angle between asperities, was developed by incorporating Gorbatikh's contact angle probability distribution function. Mathematical expressions for the stages of a single asperity and the entire joint surface were derived. The quantitative effects of fractal parameters, friction coefficient, material properties, normal and tangential loading forces, and repeated loading on tangential stiffness were analyzed theoretically, and a dedicated testing platform was constructed to validate the accuracy of the model. The results show that the proposed model enhances stiffness prediction accuracy. The increase in contact stiffness is primarily determined by the fractal dimension and the number of repeated loadings. Tangential contact stiffness initially increases and then decreases with the fractal dimension D, reaching its maximum value when D = 2.6. Multiple loadings significantly improved stiffness, which gradually stabilized. After three loading cycles, the stiffness reached over 90 % of the maximum value, stabilizing at 1.21 times the initial loading stiffness when D > 2.6. This study provides a systematic analysis of the quantitative effects of various factors on tangential contact stiffness, offering both a theoretical foundation and practical guidance for optimizing the assembly process.