关键词: 摆线针轮, 分形接触模型, 宏观特征, 微观特征

Abstract: In order to comprehensively reflect the influences of macroscopic and microscopic characteristics of cycloid teeth and pin teeth, the surface topography model of cycloid teeth and pin teeth was established by Weierstrass-Mandelbrot function and vector function. The section plots of pin tooth and cycloid tooth with obvious fractal characteristics were described using MATLAB. In order to confirm the contact area between rough surfaces, the parameter called contact proportionality coefficient was proposed and the relations among the coefficient and fractal dimension, characteristic scale, center distance, radius of pin tooth, number of pin wheel were analyzed. The analyses indicate that the coefficient is less than 1 in any case and the values of inner contacts are larger than that of outer contacts. The fractal contact model with friction was set up. The model shows that the relationship between the contact load and area is affected by gross characteristics, and by the microscopic characteristics of the contact surfaces. It may be indicated by the analyses of the contact characteristics of the model, that the contact area in the same load increases with the increases of friction factors, increases at first and then decrease with the creases of surface roughness, decreases with the decreases of radius of pin teeth, decreases with the decreases of center distance, increases with the decreases of radius of pin wheel and decreases with the decreases of number of pin teeth.

Key words: cycloidal-pin wheel, fractal contact model, gross feature, microscopic characteristics