Abstract:

Based on the Hertz contact and rigid races theory,a quasi-static model of angular contact ball bearing was established,and the nonlinear equations for the model were obtained.Reducing equation number and introducing iteration step length adjustment factor were proposed to prevent the non-convergence and oscillation problems for solving those established nonlinear equations by using Newton-Raphson iteration method.Through analyzing the geometrical meanings of those iteration variables,a method of constraining the variables during iteration process to solve the difficulty to determine the initial iteration variables.Finally,the calculation results were compared  separately to the results using the TABACY method proposed by SKF and the experimental results to verify the correctness of the improved iteration method.The results show that adopting appropriate step length adjustment factor and constraining some variables can improve the calculating convergence rate and efficiency without influencing the result correctness.

Key words: angular contact ball bearing, quasi-static method, numerical solution, step length adjustment factor, variable constraint

摘要：

根据Hertz接触理论和刚性套圈理论,建立了角接触滚珠轴承的拟静力学模型，得到了针对该模型的非线性方程组。针对传统Newton-Raphson迭代方法对所建立的非线性方程组求解过程中的不收敛和振荡问题，提出了减少非线性方程和引入迭代步长调节因子的方法。通过对迭代变量几何意义、物理意义的研究,提出了一种对迭代变量进行约束的方法来解决迭代算法中初始变量难以确定的问题。最后分别将改进后算法的计算结果与SKF公司TABACY方法的计算结果和轴承加载实验结果进行对比,验证了算法的正确性。结果表明：选取合适的步长调节因子和对一些变量施加约束能在保证计算结果正确性的前提下，提高非线性方程组求解的收敛率和效率。

关键词: 角接触滚珠轴承, 拟静力学模型, 数值求解, 步长调节因子, 变量约束