变双曲圆弧齿线圆柱齿轮接触面切向刚度分形模型研究  

Research of Fractal Model of Tangential Stiffness for Contact Surface of Cylindrical Gear with Variable Hyperbolic Circular-arc-tooth-trace

作　　者：白青松 侯力[1] 吴阳[1] 罗岚[1] 魏永峭 Bai Qingsong;Hou Li;Wu Yang;Luo Lan;Wei Yongqiao(School of Manufacturing Science and Engineering,Sichuan University,Chengdu 610065,China;School of Mechanical and Electronical Engineering,Lanzhou University of Technology,Lanzhou 730050,)

机构地区：[1]四川大学制造科学与工程学院,四川成都610065 [2]兰州理工大学机电工程学院,甘肃兰州730050

出　　处：《机械传动》2018年第8期11-16,共6页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51375320)

摘　　要：基于Hertz接触理论和分形理论,提出利用两椭圆体的表面接触系数对微凸体分布函数进行修正,引入微凸体的临界弹塑性变形接触面积,推导出变双曲圆弧齿线圆柱齿轮接触面切向刚度的分形模型。通过数值仿真论证了表面接触系数的合理性,并分析出主要参数(法向载荷、分形维数、粗糙度幅值、切向载荷、材料特性参数)对切向刚度的影响。结果表明,法向载荷与切向刚度成正比关系,但当分形维数的取值范围不同时,两者的变化规律有着较大的差别。当分形维数增大时,切向刚度先增大后减小,在分形维数为1.85时达到最大值。切向刚度随着粗糙度幅值和切向载荷的增大而减小,随着材料特性参数的增大而增大。该模型的建立为研究变双曲圆弧齿线圆柱齿轮接触面的切向刚度提供了理论依据。Based on the fractal theory and Hertz contact theory,the establishment of fractal model for tangential stiffness for contact surface of cylindrical gear with variable hyperbolic circular-arc-tooth-trace（ VH-CATT） is presented. This model is obtained by introducing the equation of critical contact area of elastic and plastic deformation of asperity and employing the surface contact coefficient of two ellipsoids to modify the asperity distribution function. The rationality of the surface contact coefficient is proved by numerical simulation,and the influence of the main parameters（ such as normal load,fractal dimension,roughness amplitude,tangential load,material propertied parameters） on the tangential stiffness is analyzed. The results are as follows,the normal load is proportional to the tangential stiffness,but when the fractal dimension is not the same,there is a big difference between them. The tangential stiffness first increases and then decreases with the increasing of the fractal dimension,and reaches the maximum when the fractal dimension is 1. 85. The tangential stiffness decreases with the increasing of the roughness amplitude and the tangential load,and increases with the increasing of the material propertied parameters. The model provides a theoretical basis for the further study of the tangential stiffness for contact surface of VH-CATT.

关 键 词：分形理论 HERTZ接触理论 变双曲圆弧齿线圆柱齿轮 切向刚度 数值仿真 

分 类 号：TH132.41[机械工程—机械制造及自动化]