二维稳态热弹流润滑问题的近似、数值混合解

Approximate and Numerical Calculations to Two Dimensional Thermal EHL Problems under Steady Conditions

本文采用粘温系数β摄动法,将二维稳态热弹流问题的求解转化为等温弹流解与β各高阶解的叠加,极大地减小了计算工作量,对稳态热弹流润滑问题的求解有普遍意义。本文继而采用差分法建立了推导出的摄动解的求解公式,并以圆弧齿轮的热弹流润滑问题为例进行了计算。差分方程的建立过程中可以看到,在等温弹流解的基础上,β各高阶解可以很容易得到,并且各代数方程的系数矩阵均相同,显然给数值计算及编程带来了极大的方便。

In this paper, temperature-viscosity coefficient β perturbation method is adopted, by which calculations to two dimensional thermal EHL, problems are converted into the superpositions of iso-thermal EHL solution and higher grades of solutions of β. This reduces greatly the numerical calculating amounts, The method is of general significant to the calculations of thermal EHL problems. Then, numerical formulae are set up by finite difference method to the perturbation solutions obtained. As an example, thermal EHL problems of helical W-N gears are calculated. It could be seen during the set up of finite difference formulae that higher grades of solutions of β could be obatined easily based on iso-thermal EHL solutions, which could also reduce numerical calculation amounts greatly. Besides, all matrix of coefficients for different grades of solutions are the same except constant item. This is obviously of great convenient to numerical calculations and programs.