微动结合部的一次加载过程  

One loading process of fretting joint interface

作　　者：田红亮[1] 赵春华[1] 方子帆[1] 刘芙蓉[1] 朱大林[1] 

机构地区：[1]三峡大学机械与动力学院,湖北宜昌443002

出　　处：《振动与冲击》2014年第13期40-52,共13页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51275273);三峡大学博士科研启动基金资助项目(KJ2012B013)

摘　　要：根据赫兹弹性理论和分形几何理论,按照表面微凸体变形特点、表面微凸体承担法向接触载荷的光滑性与连续性条件,以及严格区分弹性变形与完全塑性变形,构建微动结合部的一种法向接触修正加载分形模型。给出Weierstrass-Mandelbrot分形函数不可微的条件。采取带随机相位Ausloos-Berman分形函数仿真各向异性非稳态三维随机表面形貌。提出表面微凸体法向弹性接触载荷与表面微凸体法向变形量之间的加载幂律关系形式,建立微动结合部两个微凸体之间互相影响的法向接触刚度的求导函数而非偏导函数计算方法。数字模拟结果显示:对于恒定的载荷,随着表面轮廓分形维数的增大,实际接触面积先增大后减小;实际接触面积随着法向接触载荷的增加而增加,但随着分形粗糙度的增加而减小;微动结合部法向接触刚度随着实际接触面积、法向接触载荷、相关因子和材料性能参数的增加而增加,但随着分形粗糙度的增加而减小;当表面轮廓分形维数较小时,微动结合部法向接触刚度随着表面轮廓分形维数从1变大而增加;当表面轮廓分形维数较大时,微动结合部法向接触刚度有时随着表面轮廓分形维数的增加逼近到2而减小。微动结合部法向接触修正加载分形模型的建立,可进一步分析微动两接触表面之间的卸载模型。Using the Hertz elastic theory and fractal geometric theory,a normal contact revised loading fractal model of fretting joint interface was proposed,in terms of the characteristic of surface micro bulge’s deformation and,the smooth and continuous condition of normal contact load acting on surface micro bulge based on strictly distinguishing elastic deformation and fully plastic deformation. The non-differentiable condition of Weierstrass-Mandelbrot fractal function was put forward.The anisotropic nonstationary three-dimensional random surface topography was emulated utilizing the Ausloos-Berman fractal function with a random phase.The power-law relationship between the normal elastic contact load on surface micro bulge and its normal deformation was brought forward.The calculating method of differential function （yet not partial differentiable function ）was established to solve the interacting normal contact stiffness between two micro bulges on the fretting joint interface.The numerical emulation results indicate that the real contact area first adds and then diminishes with the increase of fractal dimension of a surface profile under constant load.The real contact area increases with the increase of normal contact load,but decreases with the increase of fractal roughness.The fretting joint interface normal contact stiffness increases with increasing real contact area,normal contact load,relating factor and material property parameter,but decreases with the increase of fractal roughness.When the fractal dimension of the surface profile is smaller,the normal contact stiffness increases as the fractal dimension increases from 1;however,when the fractal dimension becomes larger,the normal contact stiffness at times decreases as the fractal dimension increases approaching 2.Constituting the normal contact revised loading fractal model of fretting joint interface helps to analyze the unloading model between two fretting contact surfaces.

关 键 词：微动结合部 随机相位 法向变形量 加载 法向接触载荷 法向接触刚度 表面轮廓分形维数 

分 类 号：TH113.1[机械工程—机械设计及理论]