同向夹持两点接触应力场特殊位置的极值应力

Stress Analysis of Two-Points Contact Gripping in the Same Direction in Some Special Places

夹持是一种依靠摩擦力工作的约束形式。法向力自身平衡,摩擦力与外力平衡。点接触夹持是最常见的夹持形式,也是研究线接触与面接触夹持的基础。点接触可以用集中力模型来模拟,在极限状态下点接触产生的摩擦力与法向集中力通过材料的摩擦系数相关联。摩擦力与法向集中力符合库仑摩擦定律。弹性理论中已经给出了半无限体受二维集中力作用模型应力场的公式,借助这些公式可以对点接触的夹持进行应力分析。本文从一点接触应力场的分布规律开始,对在摩擦极限状态情况下同向夹持两点接触应力场的分布进行了分析。并给出了若干特殊线、点的极值应力的大小和主方向。

Gripping is a restraint working by friction. The normal pressure is equilibrium by itself and friction by external force. Gripping in point contact is the common gripping and also is the foundation by which contacts in thread and on plane are studied. Point contact can be imitated by model of concentrated force, while the friction force and the normal concentrated force are related with the material friction factor under friction limit condition, which are accorded with the Coulomb＇s friction law. The formula of stress field under a concentrated force has been derived in two-dimension elastic theory by which stress analysis on gripping in point contact can be carried out. In this paper the stresses of two-points contact gripping in the same direction under friction limit condition have been analyzed from the results of one point contact model. Meanwhile, the values of main stresses and angles in some special lines or points of the contact model field have been proposed.