高速四点接触球轴承力学模型的数值求解算法  

A Numerical Solution Algorithm for Mechanical Models of High-Speed Four-Point Contact Ball Bearings

作　　者：路春雨[1] 刘少军[1] 戴瑜[1] 

机构地区：[1]中南大学机电工程学院∥高性能复杂制造国家重点实验室,湖南长沙410083

出　　处：《华南理工大学学报（自然科学版）》2016年第1期123-130,共8页Journal of South China University of Technology(Natural Science Edition)

基　　金：国防预研项目(81302XXX);湖南省研究生创新项目(CX2014B060)~~

摘　　要：文中根据Hertz弹性接触理论分别建立了零转速和高速工况下四点接触球的力学模型;针对高速四点接触球轴承力学模型数值求解初值难以确定和不易收敛的问题,提出了一种基于Newton-Raphson理论的高速四点接触球轴承力学模型的数值求解算法,并给出了迭代变量取值范围及收敛因子的选取原则.为了降低求解难度,文中通过对高速四点接触球轴承力学模型进行数学变形,使得未知量的个数减少了一半.为了解决求解规模较大非线性方程组时经常出现卡死现象的问题,文中通过优化算法解决卡死现象,并提高了计算效率.文中算法计算结果与Jones程序结果的比较表明,调整收敛因子可控制文中算法的收敛性和收敛速度,从而验证了文中算法的正确性.On the basis of the Hertz contact theory, the mechanical models of high-speed four-point contact ball bearings in the cases of high speeds and zero-speed are constructed respectively.In order to solve the problems that the initial values of the constructed mechanical model at high speeds is undeterminable and their convergence is dif-ficult, a numerical solution algorithm for the constructed mechanical model at high speeds is proposed on the basis of the Newton-Raphson theory, and the range of iteration variables and the selection principle of convergence factors are presented.For the purpose of reducing the solving difficulty, the number of unknown variables is reduced by a half through the mathematical transformation of the constructed mechanical model at high speeds.In order to tackle the stuck phenomenon of the program for larger-scale nonlinear equations, the proposed algorithm is optimized and the computational efficiency is improved.Finally, the results of the proposed algorithm are compared with those of Jones’ program.It is found that the convergence and convergence rate of the proposed algorithm can be controlled by adjusting the convergence factor.Thus, the proposed algorithm is proved to be correct.

关 键 词：球轴承 载荷分布 拟静力学 数值求解 

分 类 号：TH133.334[机械工程—机械制造及自动化]