基于分形理论的粗糙表面接触力学模型  

Contact mechanics model of rough surface based on fractal theory

作　　者：成雨[1] 原园[1] 

机构地区：[1]西安理工大学机械与精密仪器工程学院,西安710048

出　　处：《中国科技论文》2016年第16期1850-1854,共5页China Sciencepaper

基　　金：国家自然科学基金资助项目(51105304;51475364);高等学校博士学科点专项科研基金资助项目(20116118120004);陕西省自然科学基础研究计划资助项目(2015JM5212)

摘　　要：依据分形理论,考虑微凸体的等级及变形特征的影响建立了粗糙表面间的分形接触模型。确定了粗糙表面中单个微凸体弹性变形、弹塑性变形及完全塑性变形的存在条件,推导出3种变形阶段的临界接触面积的表达式。在此基础上应用海洋岛屿面积分布规律,获得了接触表面上接触载荷与真实接触面积之间的解析式。数值仿真结果表明:单个微凸体的接触面积是和微凸体的等级相关的,随着微凸体等级的增大而减小;微凸体的临界弹性、临界弹塑性接触面积由顶端曲率半径与分形参数共同确定;接触面积一定时,轮廓分形维数增大,接触载荷减小。According to the fractal theory, the fractal contact mechanics model considering the influences of asperity＇s level and asperity＇s deformation is established. The criteria of elastic deformation, elastic-plastic deformation and fully plastic deformation of a single asperity on the rough surface are developed, and the expressions for the critical contact area in the three regimes are derived respectively. Considering the size distribution function, the analytic expression for the total contact load and the real con- tact area is obtained. Simulation results show that the critical contact area of a single asperity is related to scale, and it reduces while the level of asperity increases. The elastic and dastic-plastic critical contact area of a single asperity relate not only with the radius of curvature, but also the fractal parameters. The total contact load decreases with the increase of fractal dimension when the real contact area is fixed.

关 键 词：粗糙表面 微凸体 真实接触面积 接触模型 

分 类 号：TH117.1[机械工程—机械设计及理论]