圆柱形粗糙表面的弹塑性分形接触模型

An elastoplastic fractal model for cylinder in contact with a smooth plane

基于分形理论建立了圆柱形粗糙表面力学模型,采用W-M函数模拟了与分形维数D,形貌尺度参数G有关的圆柱形粗糙表面的等效轮廓.推导了单个微凸体弹性、弹塑性以及塑性变形的存在条件,得到了圆柱形粗糙表面均分份数与微凸体尺度的变化关系.对传统的微凸体面积密度分布函数进行改进,获得各频率指数微凸体的面积密度分布函数,最终得到整个圆柱形粗糙表面的无量纲接触载荷与无量纲真实接触面积之间的关系.研究结果表明:粗糙表面中微凸体的临界接触面积是尺度相关的,微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形.圆柱形粗糙表面的力学性能与微凸体的分布范围相关.当前6个频率指数的微凸体小于等于临界弹性频率指数,粗糙表面表现出近似的弹性性质,当前6个频率指数的微凸体处于临界弹性频率指数和临界塑性频率指数之间,粗糙表面表现出先弹性后弹塑性的性质.当前6个频率指数的微凸体大于临界塑性频率指数,粗糙表面呈现非弹性变形性质.

A mechanical model of which a cylinder-based fractal body in contact with a rigid plat surface presented based on fractal theory. The generalized Weierstrass-Mandelbrot function is employed to derive the formulae of fractal surface asperities formed a smooth cylindrical surface. The existing conditions of which a single asperity is in elastic, elastoplastic or full plastic deformation are derived. When the cylinder-based fractal rough is uniformly divided into N＇ subdivisions, a relation between the N＇ subdivisions and the asperity geometric dimensioning is obtained. A modified size distribution function is adopted to obtain the relation between the dimensionless contact load and the real contact area. The results show： the critical areas of a single asperity are scale dependent. With an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. The mechanical properties of the cylindrical rough surface are related to the range of the asperity frequency indexes. When the first six asperity frequency indexes are less than critical elastic frequency index nec, the rough surface appears to be elastic property under contact load. When the first six asperity frequency indexes are between the critical elastic frequency index noo and critical plastic frequency index npc, the rough surface appears to be elastic property and elastoplastic property, otherwise the rough surface appears to be of inelastic property.