正交面齿轮最小内半径分析

Analysis of the Minimum Inner Radius of Orthogonal Face Gear

面齿轮传动相对于圆柱齿轮传动,其传动的性能好、重量轻、承载能力高,具有良好的经济和技术效益,但面齿轮在内半径处会发生根切现象,限制了面齿轮的应用推广。为了得到精确求解面齿轮最小内半径理论方法,根据正交面齿轮插齿加工过程和齿轮啮合原理,推导出了正交面齿轮的工作齿面方程、过渡曲面方程及根切界限线的曲线方程。通过对根切界限线曲线方程的求解和分析,得出不产生根切的关键点坐标位置,进而得到正交面齿轮最小内半径计算公式。在MATLAB软件中对工作齿面方程、过渡曲面方程及根切界限线方程进行参数离散化,并进行可视化生成和仿真分析,验证本文所述精确求解面齿轮最小内半径理论方法的正确性。

Compared with cylindrical gear transmission,face gear transmission has good transmission performance,light weight and high load capacity,with good economic and technical benefits.However,the inner radius of face gear will have undercut phenomenon,application and popularization of restricted face gear.In order to get the theory of accurately solve minimum inner radius of face gear.This article according to the gear shaper machining process of the orthonormal face gear and the theory of gearing derived the working tooth surface equation and the transition surface equation of the orthogonal face gear,and the curve equation of undercut boundary line.Through the solution and analysis of curve equations of undercutting boundary line,get the key point coordinate position of no undercutting,and then get the calculation formula for minimum inner radius of orthogonal face gear.In the MATLAB software on working tooth surface equations,transition surface equation and undercut boundary line equation to carry out parameter discretization,and carry out visual generation and simulation analysis,Verify the correctness of the theory method for accurately solve minimum inner radius of face gear described in this paper.