计及摩擦的摆线轮齿与针齿的分形接触模型

Fractal Contact Model for Cycloid Tooth and Pin Tooth Considering Friction Factors

为综合体现摆线轮齿与针齿的宏观特征和微观特征对接触特性的影响,应用Weierstrass-Mandelbrot函数和矢量函数构建了摆线轮齿与针齿的表面形貌模型,应用MATLAB绘制了各向同性的粗糙针齿以及单个摆线轮齿的二维截面图,提出了摆线轮齿与针齿的接触比例系数,该接触比例系数始终小于1,且随啮合点的变化而变化,针齿与摆线轮齿的内凹部分接触时的接触比例系数远大于针齿与摆线轮齿外凸部分接触时的值。计及摩擦因素的影响,构建了单对摆线轮齿与针齿的分形接触模型,分析了摩擦因子、结合面的微观特征和宏观特征对接触特性的影响。研究结果表明,相同载荷下,接触面积随摩擦因子的增大而增大,随结合面粗糙度的增大先增大后减小,随针齿半径的增大而减小,随中心距的增大而减小,随针轮中心圆半径的增大而增大,随针轮齿数的增加而减小。

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.