依据各向异性分形理论的固定结合面椭圆弹塑性法向接触刚度建模及仿真分析  

Modeling and Simulation Analysis of Elliptic-plastic Normal Contact Stiffness of Joint Surface Based on Anisotropic Fractal Theory

作　　者：谭文兵 兰国生[1] 张学良[1] 孙万 温淑花[1] 陈永会[1] Wenbing Tan;Guosheng Lan;Xueliang Zhang;Wan Sun;Shuhua Wen;Yonghui Chen(College of Mechanical Engineering,Taiyuan University of Science and Technology,Taiyuan,030024)

机构地区：[1]太原科技大学机械工程学院,太原030024

出　　处：《固体力学学报》2021年第1期63-76,共14页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(51275328);山西省自然科学基金项目(201601D011062);山西省“1331”工程重点学科建设项目资助。

摘　　要：依据各向异性分形几何理论,将结合面接触点拓展为椭圆形,结合微凸体接触点面积大小分布函数以及概率论相关理论获得关于椭圆形接触点接触面积以及离心率的二维联合分布密度函数,应用赫兹接触理论,进而建立了依据各向异性分形理论的结合面椭圆弹塑性法向接触刚度模型,并采用MATLAB软件对影响结合面法向刚度的相关因素进行了数值仿真及结果分析.结果表明:结合面椭圆形接触点离心率分布情形对结合面总刚度具有明显影响,结合面总刚度随形状参数α的增大而增大,却随着形状参数ε的增大而减小;结合面法向刚度随法向载荷的增大而增大;在同一载荷作用下,结合面法向接触刚度随塑性指数增大而增大,随分形粗糙度的增大而减小,但是随分形维数的增大而先增后减.该模型对模型优化进而提高计算精度提供了一定的理论依据.Establishing a more realistic contact model of joint surfaces is one of the key way to explore the variation law of stiffness characteristics.Firstly,according to the anisotropic fractal geometry theory,this paper equates the micro-convex body on the joint surface to an ellipsoid;Secondly,the two-dimensional joint distribution density function of the micro-contact area and eccentricity of the elliptical contact point was obtained by combining the micro-contact area distribution function and the related theory of probability theory;Finally,based on the Hertz theory,the elliptic elastoplastic normal contact stiffness model of the joint surface was established,and the related factors affecting the normal stiffness of the joint surface were numerically simulated and analyzed using MATLAB software.The results show that the eccentricity distribution of the elliptical micro-contact points on the joint surface has a significant effect on the total rigidity of the joint surface.The total stiffness of the joint surface increases with the increase of the shape parameterα,but decreases with the increase of the shape parameterε;The normal stiffness of the joint surface increases with the increase of the normal load.When the load is constant,the normal contact stiffness of the joint surface increases with the increase of the plastic index and decreases with the increase of the fractal roughness,but increases first and then decreases with the increase of the fractal dimension.This model provides a certain theoretical basis for model optimization to improve calculation accuracy.

关 键 词：各向异性 结合面 椭圆接触点 法向接触刚度 弹塑性 分形模型 

分 类 号：TH114[机械工程—机械设计及理论] TP391.9[自动化与计算机技术—计算机应用技术]