摘要：根据齿轮齿面的形成过程建立齿轮齿面的数学模型，得到齿轮齿面方程及其法向矢量；基于交错轴螺旋齿轮啮合原理建立滚插加工的运动坐标系，确定滚插刀与工件的运动关系，并以曲面共轭原理为基础，求得齿轮齿面的共轭曲面方程；选择平面作为滚插刀的前刀面并建立坐标系，获得前刀面的数学方程；最后借助曲面与平面求交理论与改进的欧拉法，得到了滚插刀的切削刃方程。

关键词：滚插刀；曲面共轭原理；曲面与平面求交；欧拉法

中图分类号：TG721；TH111文献标志码：A DOI：10.3969/j.issn.1000-7008.2021.08.012

Study on Design Theory of Gear Skiving

Zhang Heng，Xin Jiayi，Wang Shiying，Lv Ming

Abstract:According to the formation process of the gear tooth surface，the mathematical model of the gear tooth surface is established，and the gear tooth surface equation and its normal vector are obtained.Based on the meshing principle of the space crossaxis helical gear，the motion coordinate system of the gear skiving processing is established，the movement relationship between the gear skiving cutter and the workpiece is determined.Based on the principle of surface conjugation to obtain the conjugate surface equation of the gear tooth surface，a plane as the rake surface of the gear skiving cutter and establish a coordinate system to obtain the mathematical equation of the rake surface is selected.By using the surface and plane intersection theory and improved Euler method，the cutting edge equation of the gear skiving cutter is obtained.

Keywords:gear skiving；surface conjugation principle；intersection principle of surface and plane；explicit method