基于牛顿-拉普森及Hertz理论的轴承性能分析

Analysis of bearing performance based on the Newton-Rapson and Hertz theory

根据深沟球轴承的工作特点和负载条件,建立简化力学模型并定义载荷条件和边界条件,通过对模型的计算分析,找出深沟球轴承的最大应力位置和应力分布规律图。然后在由ANSYS转化成节点及元素组成的有限元模型中,运用完全牛顿-拉普森方法进行接触应力的静力学求解,最后根据Hertz椭圆形点接触理论,用微积分的方法求出轴承的刚度变形和应力与位移的关系。这种利用有限元分析软件与基础理论联合求解刚度的方法更精确、更有效、更实用可靠,为滚动轴承的选择和维护使用提供了更多依据,计算方法也便于工程应用。

According to the work of deep groove ball bearings characteristics and load conditions, it establishes the simplified mechanical model and defines the loads and boundary, and finds out the location of the maximum stress and stress distribution of figure in the deep groove ball bearings by calculating and analyzing the model. In the finite element model made of nodes and elements conversed by ANSYS, it uses the full Newton - Rapson method for solving the static contact stress. At last, it obtains the deformation and stiffness of the bearing relationship between the stress and displacement by the methods of calculus according to the elliptical point contact theory of Hertz. The method of combining finite element analysis software with the basic theory for solving stiffness of bearings is more accurate, more effective, more practical and reliable. The data have provided more guide for the select and preserve of rolling bearing. At the same time,the method is available for the engineering application.