外啮合标准齿轮齿廓曲线齿根部分的形状及其数学描述

The Shape and Mathematical Description or Root or Tooth outline in Standard External Gear

本文通过对外啮合标准渐开线齿轮的佳合和范成切齿过程的分析，提出了齿轮齿廓曲线上渐开线部分与非渐开线部分的划分依据，并给出了具体的范围；阐述了非渐开线部分的形成原理；给出了齿轮齿廓曲线非渐开线部分显式的极坐标方程；从而解决了外啮合标准齿轮齿廓合根部分形状的数学描述问题。

In this paper,the basis dividing involute part and non-involute part of tooth outline in gear, as well as concrete range,is presented through analysis of the engagement of standard external involute gear and the process of shaping gear.farther,the shaping principle of noninvolu te part of expouned, and along with it,the(explicit) equation in the form of polar coordinates on non-involute part of tooth outline of gear is given, and the mathematical description of the shape of root of tooth outline in standard external gear is solved.