基于Hertz理论圆柱和平面之间的滑动接触分析  

Analysis of the Slipping Contact Between a Cylinder and a Plane on the Base of Hertz Theory

作　　者：冯剑军[1] 谭援强[1] 

机构地区：[1]湘潭大学机械工程学院,湖南湘潭411105

出　　处：《摩擦学学报》2009年第4期346-350,共5页Tribology

基　　金：国家自然科学基金资助项目(50875224);教育部新世纪人才培养计划资助项目(NCET06-0708)

摘　　要：当圆柱与平面之间产生摩擦滑动接触时,基于Hertz理论,推导了平面内应力分量的计算公式,分析了应力的分布,描述了应力分布的特点.在接触表面上,存在最大拉应力和最大压应力;最大拉应力出现在拖动边的边缘,而最大压应力发生在导向边的区域.因此,如果接触平面因拉或压应力引起失效,首先会出现在接触表面;第一型裂纹的产生及扩展首先会发生在拖动边的边缘.剪应力,主剪应力及Von-M ises等效应力(当摩擦系数较小时)的最大值均会出现在接触体内,存在于导向边.因此,塑性滑移开始首先会发生在接触体内,然后,才扩展到接触表面.这些结论为工程应用研究提供了依据.The expressions of the stress component in the plane （contacting body） are derived as the frictionally slipping contact arises between a plane and a cylinder on the basis of Hertz theory. Distributions of the stress in the plane are analyzed in detail, and their characteristics are presented. There exist the maximal tensile stress and the maximal compressive stress in the contacting surface. The maximal tensile stress occurs at the edge of the dragging side, and the maximal compressive stress takes place at the area of the leading side. Therefore, if the failure in the contact plane is induced by the tensile or compressive stress, it occurs firstly in the contacting surface; the first crack generation and propagation firstly take place at the edge of the dragging side. The maximums of the shear stress, the principal shear stress and the Von - Mises equivalent stress （ when the frictional coefficient is small） all occur inside the contacting body, and they all exist in the leading side. Therefore, The plastic slipping inception firstly takes place inside the contact plane, and then extends to the contacting surface. Those conclusions provide a base for the study of the engineering application.

关 键 词：摩擦滑动接触 等效应力 主应力 接触压力 剪切牵引力 

分 类 号：O31[理学—一般力学与力学基础]