求解弧面分度凸轮廓面数控加工刀具轨迹通用方程

Unified Expression of Tool Path Equation Based on NC Machining Globoidal Indexing Cam Surface

对弧面分度凸轮轮廓曲面进行数控加工编程前需确定刀具轨迹方程。针对不同滚子形状及凸轮轴线与从动盘轴线成任意角度的情况,基于微分几何原理,应用包络面理论建立统一数学模型的弧面凸轮廓面方程。在此基础上进一步推导出数控加工刀具轨迹方程的通用解析表达式。此结果可作为数控加工弧面分度凸轮廓面编程时的数学模型,也可应用于弧面凸轮加工过程的仿真、加工误差分析和廓面修形等方面。

The tool path equation must be determined before the NC machining program for the contour surface of globoidal indexing cam is programmed.In view of the difference of the shape of the rollers and the angle between the axis of globoidal cam and the axis of the follower plate,the profile equation of globoidal cam is established by using envelope theory based on the principle of differential geometry.On this basis,the general analytic expression for the tool path equation of NC machining is further derived.This result can not only be used as a mathematical model for the programming of the NC machining globoidal cam profile,but also can be applied to the simulation for the machining process of the globoidal cam,the analysis of the machining error and the profile modification.