The rough appearance of the tooth surface is random, and the geometric characteristics of the appearance are related to the cold working process or secondary finishing, as shown in Figure 1. It is obvious in the figure that the tooth surface processed by grinding has texture, and the surface roughness grade is less than the surface morphology after finishing. Improving the tooth surface finish can enhance the contact fatigue strength and load-bearing capacity of the tooth surface. Zhao Guanghui et al. Of the research group carried out detailed experimental research on the tooth surface characteristics of isotropic finishing and non finishing, and the research results show that finishing can improve the tooth surface roughness Contact fatigue strength. Because the geometric characteristics of micro surface topography of tooth surface are in micron or nanometer level, relative to the macro geometric size of tooth surface is negligible, and the tooth stiffness and matrix stiffness of gear meshing stiffness components are related to the geometric structure of gear. For the tooth surface with high surface accuracy, the micro surface topography has little effect on the tooth stiffness and matrix stiffness, so it can not be ignored However, when the tooth surface is damaged greatly (such as macro erosion, spalling, etc.), the change of the stiffness will be affected.

The contact stiffness is different from the tooth stiffness and the matrix stiffness. It is related to the micro effect of the gear interface characteristics. For example, the friction characteristics and intermolecular adsorption force of the interface under different surface morphologies are not consistent. Due to the limitations of early research methods and technical equipment, these performance characteristics have not been carefully studied by scholars. With the upgrading of modern technology and equipment and the advance of mathematics in micro scale space, the research on the mechanical properties of the interface is becoming more and more abundant.

Tian Hongliang et al. Established the mathematical / mechanical model of the rough surface of the fixed interface through the micro geometric morphology to study the effect of its normal contact stiffness; Geerke et al. Established the mathematical model and test of the normal fractal interface to analyze the bearing capacity of the contact surface, and analyzed the influence of different parameters (morphology, hardness, etc.) on the bearing capacity of the contact surface; pan et al. Studied the roughness Yuan et al. Proposed an improved M-B model of rough contact surface based on elastic-plastic theory, and Zhao Linlin et al. And Chen Qi et al. Qualitatively analyzed the contact strength and stiffness of tooth surface based on fractal theory. Zhao et al. Summarized the research characteristics, problems and challenges of fractal theory in engineering application of mechanical transmission. It can be seen that with the proposal and research of the basic theory of micro scale space, the system theory can be further improved to pave the way for the realization of engineering application. In this paper, the fractal theory of micro effect is used to analyze the contact stiffness between gear interfaces qualitatively and quantitatively to study the effect of roughness on the contact stiffness of gear dynamic characteristics.