Contact Characteristics Analysis of Tooth Surface Microscopic Morphology Based on the Fractal Theory

How to effectively calculate the contact stiffness of the joint surface and analyze the influence of the joint surface stiffness on the dynamic characteristics of the overall structure is one of the important subjects in the study of mechanical structures. However, at present, the fractal theory is simply applied to the calculation and analysis of the joint surface stiffness, and it is difficult to comprehensively analyze the microscopic contact characteristics. Therefore, it is urgent to propose a new method to calculate the contact stiffness of the tooth surface and to analyze the microscopic contact characteristics. Based on the W-M （Weierstrass-Mandelbrot） function, a three-dimensional solid model of the microcosmic joint surface of the tooth surface was constructed, and a new method for fractal representation of the rough surface profile based on the fractal dimension <italic>D</italic> and the tooth surface roughness was proposed, considering the influence of roughness on the stiffness. The contact deformation mechanism of asperities was discussed, and the law of contact stiffness changing with the deformation of asperities was revealed. The research shows that in the same roughness of the micro-joint surface, when the asperity deforms to the same level, the larger the fractal dimension <italic>D </italic>is, the greater the contact stiffness will be. In the joint surface with the same fractal dimension and different roughness, the smaller the roughness of the joint surface is, the greater the contact stiffness will be.