Abstract:

According to the numerical calculation of the meshing angle the derivation of the meshing angle of transcendental equation was studied and the application of  Stephenson-Newton iterative method and Newton iterative method was put forward for the numerical calculation of the meshing angle,then more accurate meshing angle values were obtained，the elimination of shaving  “the flank concave” effect of  the process was carried out.Two methods of numerical calculation of meshing angle were analyzed through the error tolerance,iteration times and  the optimal solution value,Stephenson-Newtonian iterative method was compared with Newton iterative method,and can avoid differentiable numerical calculation inadequacy,with the advantages such as fast convergence,fewer iteration times,solving stability,optimal numerical solution etc..

Key words: shaving modification, meshing angle, numerical calculation, Stephenson-Newton iterative method, iteration times

摘要：

对啮合角的数值计算进行了深入研究,推导了啮合角超越方程，应用史蒂芬森-牛顿类迭代法和牛顿迭代法进行了啮合角的数值计算，得到了啮合角的最优解，有效保证了消除剃齿“齿形中凹”的工艺效果。通过误差容限、迭代次数和最优解对啮合角数值计算的两种方法进行了分析,
可知史蒂芬森-牛顿类迭代法能够避免牛顿迭代法中可微等数值计算的
不足,具有收敛快速、迭代次数小、求解稳定、数值解最优等优点。

关键词: 剃齿修形, 啮合角, 数值计算, 史蒂芬森-牛顿类迭代法, 迭代次数