基于粗糙表面分形表征新方法的结合面法向接触刚度模型

如何有效预测结合面的接触刚度,是机械结构设计研究的一个重要课题。结合面接触刚度模型主要分为基于统计学特征参数的和基于分形参数的两类。前者依赖于粗糙表面形貌的测量尺度,后者与测量尺度无关。然而,多数研究者在利用分形理论进行建模时,以对应于微凸体接触面积a的尺寸l=a^1/2作为微凸体基底尺寸描述微凸体初始轮廓,给出了错误的微凸体变形机制和结合面接触刚度模型。提出了一种基于D,G和最大微凸体高度的粗糙表面轮廓分形表征新方法,探讨了微凸体接触变形机制,建立了与测量尺度无关的粗糙表面接触力学分形模型,揭示了接触刚度的变化规律。研究表明:接触载荷可用表达式F_c=F(E,D,G,h,a_L)描述;当结合面上的接触压力小于其屈服强度时,无论微凸体发生何种变形,结合面均因存在有弹性变形的接触点而具有一定的法向接触刚度。

A joint surface normal contact stiffness model based on a new rough surface fractal characterization method

It is an important topic in mechanical structure design study to effectively predict contact stiffness of a joint surface. Contact stiffness models of a joint surface are mainly divided into two types including one based on statistical characteristic parameters and the other based on fractal ones. The former depends on the measurement scale of rough surface topography and the latter is independent of measurement scale. When most of researchers used the fractal theory to model rough surface, the size l=a1/2, corresponding to the contact area of an asperity a, was taken as the base size of the asperity to describe the initial profile of asperities, and give incorrect asperities’ deformation mechanism and joint surface’s contact stiffness model. Here, a new rough surface fractal characterization method based on fractal dimension D, roughness parameter G and the maximum asperity height was proposed to explore asperities’ contact deformation mechanism, establish a rough surface contact mechanical fractal model independent of the measurement scale and reveal contact stiffness variation law. The study results showed that the contact load can be described with the expression Fc=F(E, D, G, h, aL);when the contact pressure on a joint surface is less than its yield strength, the joint surface has a certain normal contact stiffness due to the presence of contact points with elastic deformation, no matter what kind of deformation occurs in asperities.