圆柱齿轮啮合过程齿根应力数值计算方法研究

本文提出了一套在微机上计算机直齿与斜齿圆柱齿轮啮合过程齿根应力分布的方法。使用者只需输入一对齿轮副的几何参数和结构参数，计算机将自动完成齿轮副的三维有限无风格部分。通过齿面坐标系及坐标变换矩阵，一次求出核齿轮副的齿向载荷分布齿间载荷分本。一步运用 齿根局部网络密化，可详细研究轮在啮合过程中的齿根应力分布。编制的软件配有较强的数据前，后处理手段，便于使用。文中以一对斜齿轮副为例进行了说明，计算结果与

On Numerical Method for Calculation of Root Stresses of Cylindrical Gears in Meshing

Oda in 19801] and Oda2] and Ueno3] in 1984 presented their research results on the various factors influencing the distribution of root bending stresses of helical gears in meshing.Simon in 19884] presented calculating factors for computing such bending stresses.None of them considered effect of gear structure sizes on root stresses of gears.In this paper,the authors believe that they succeed in giving such effect ade- quate consideration. To give adequate consideration of such effect,it is necessary to overcome essentially two difficulties. One difficulty is the simultaneous consideration of many contact lines to minimize the possibility of miss- ing the maximum root stress.In the case of load distributions along the contact lines,the problem was solved by the first author in a previous paper5].But in the case of calculating root stress distribtuions un- der different contact loads,the mesh needs to be much finer.This requires greatly increased amount of computation.Herein lies the second difficulty. The main contribution of this paper is to propose a mesh refinement model only locally on root re- gion of gear tooth.In this way,root stresses of spur or helical gears during the engagement period can be accurately determined with only a small increase in amount of computation. As a numerical example,a pair of helical gears is taken.Comparison of computed results with test da- ta shows that local mesh refinement of tooth root can reduce the error of computing the maximum root stress from about 25% to about 6%.