基于分形理论的两粗糙表面接触的黏滑摩擦模型  

Modeling for fretting behavior of nominally flat rough surfaces based on fractal theory

作　　者：周华[1] 龙新华[1] 孟光[1] ZHOU Hua;LONG Xin-hua;MENG Guang(State Key Laboratory of Mechanical System and Vibration,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学机械系统与振动国家重点实验室,上海200240

出　　处：《振动工程学报》2022年第4期895-902,共8页Journal of Vibration Engineering

基　　金：国家重点研发计划重点专项(2018YFB2001300)。

摘　　要：两粗糙表面的接触本质上是大量微凸体的接触,具有复杂的力学行为,连接界面的力学建模是重要的科学问题。从微观角度出发,对单个微凸体进行接触分析,并考虑了微凸体相互作用造成的基底面的下降,根据分形理论积分,建立了整个接触面的法向接触模型。利用该模型,可确定在给定法向预紧载荷下微接触截面积的概率密度函数;根据Mindlin模型、Masing准则和分形理论,建立了两粗糙表面接触的切向载荷与切向位移的关系,并研究了不同参数对系统能量耗散的影响。数值仿真结果表明,能量耗散随分形维数D增大而增大,随分形粗糙度参数G及法向预紧力增大而降低。The contact between two rough surfaces is essentially the contact of a large number of asperities,which leads to a challenging scientific problem due to the complexity of interface behaviors.In this paper,the contact of an asperity and the asperity interactions are considered.The downward displacement of mean of asperity heights is used to represent the effects of the asperity interactions.The normal contact model can then be established by the summation integral based on fractal theory.Once the normal preload is given,the probability density function of truncated asperity contact area can be determined.Then the tangential load-displacement model of joint interface can be established by Mindlin theory,Masing’s hypothesis and fractal theory.The effect of different parameters on energy dissipation is studied by numerical simulation.The results show that the energy dissipation decreases with the fractal dimension D decreases,or with the fractal roughness parameter G increases.This means that the energy dissipation is lower when the rough surface is coarser.The energy dissipation will decrease with the normal preload increases.

关 键 词：分形接触模型 黏滑摩擦 粗糙表面 迟滞非线性 能量耗散 

分 类 号：O344[理学—固体力学] O322[理学—力学]