自仿射接触点及其在分形接触理论中的应用

Self-Affine Contact Spot with Applications in Fractal Contact Theory

为了深入研究分形方法在接触理论中的应用,利用数值模拟实验研究了分形粗糙表面的接触机理,并提出了自仿射接触点的概念。该概念充分利用分形函数自仿射的优点,改善了传统分形接触理论中微凸体不满足分形特性的缺陷,去除了接触理论中微凸体相互作用无法考虑等假设。将自仿射概念应用于分形接触理论中,建立了新的接触模型。模型基于粗糙表面均为各向同性的无润滑表面且可以利用W-M函数模拟的假设,利用接触中接触点最大变形量与接触面积的关系,对分形接触模型进行修正,得到更符合实际情况的分形接触理论。与经典的统计及分形接触模型进行对比,结果表明:G-W模型是一个弹性模型,较少考虑塑性接触,因此G-W模型在整体上会低估粗糙表面的接触压力;M-B模型利用单个余弦函数模拟微凸体,得到的最大接触变形量偏小,且微凸体尺寸分布函数的使用也不准确,M-B模型高估了接触压力;提出的基于自仿射接触点的分形接触模型利用自仿射接触点代替微凸体进行理论推导,能更准确地计算出接触压力;在相同的接触面积下,粗糙表面分形维数越大或分形特征尺度越小,接触压力越小。

The numerical simulation for contact essence between fractal rough surfaces is conducted,and a concept of self-affine contact spot is introduced to propose a new fractal contact model.Compared with the asperity in classical fractal contact model,the self-affine contact spot better describes the process of fractal contact.The self-affine contact spot now gets fractal,and the assumption of no interaction between asperities is unnecessary.Under the assumption that the rough surfaces are all unlubricated isotropic surfaces,this model can be simulated by W-M function.Making use of the relationship between the maximum deformation and contact area of contact spot,the classical fractal contact model is modified to further approach the engineering practice.It is found that G-W model ignores plastic deformation of contact spot thus to underestimate the contact load of rough surfaces;M-B model leads to a smaller maximum deformation to difficultly use size-distribution function and overestimates the contact load.The self-affine contact spot instead of asperity enables to accurately evaluate the contact pressure,The more the fractal dimension（or the less the fractal characteristic scale）,the less the contact pressure is needed for same contact area.