基于数值方法的内超环面齿轮齿廓离散建模

Discrete Modeling of the Tooth Profile of the Stationary Internal Toroidal Based on Numerical Method

超环面行星蜗杆传动系统中的关键零件内超环面齿轮的齿面是一种复杂的空间曲面。为了实现复杂曲面的数控加工和采用有限元方法对其进行接触分析时,能否获得精确的内超环面齿轮的实体模型是解决问题的关键。本文针对内超环面齿轮数字化建模问题,根据内超环面齿轮的数学模型,对其螺旋齿面进行网格划分,提出基于数值方法的内超环面齿轮离散建模方法。该方法采用截平面蔟将内超环面齿轮模型离散成数据点云,从而获得内超环面齿轮离散模型,为后期的复杂曲面插值重构提供了基础。

The tooth surface of the stationary internal toroidal gear that is the key parts of the toroidal drive is a complex space curved surface. In order to realize the complex surface of the NC processing and using the finite element method for the contact analysis, whether obtaining the accurate entity model of the stationary internal toroidal gear or not is the key to resolving the problem. In this paper aiming at the stationary internal toroidal gear digital modeling problems, according to the mathematical model of the stationary internal toroidal gear, the grid division method of the helical tooth surface is given, the method of the stationary internal toroidal gear discrete modeling based on the numerical method is put forward. The method adopts cutting planes to scatter the stationary internal toroidal gear model into data point cloud, so as to get the stationary internal toroidal gear discrete model as the basis for later complex curved surface interpolation reconstruction.