高阶变性椭圆锥齿轮传动模式设计与分析

Design and Analysis of Transmission Mode for High-order Deformed Elliptic Bevel Gears

高阶变性椭圆锥齿轮是球面大端节曲线为高阶椭圆或变性椭圆的非圆锥齿轮。针对目前非圆锥齿轮的设计与分析方法较繁复的问题,根据齿轮空间啮合原理,提出一种仿真加工获得高阶变性椭圆锥齿轮齿形的方法。模拟加工刀具与高阶变性椭圆锥齿轮的节曲线作纯滚动的齿形生成过程,推导出齿形形成过程中的运动参数,并对其节曲线、齿顶曲线及齿根曲线进行设计。重点分析高阶椭圆锥齿轮与变性椭圆锥齿轮齿廓的传动模式及其运动学特性,建立以高阶变性椭圆为基础的椭圆锥齿轮族的仿真模型,统一各种椭圆锥齿轮的传动模式及其设计过程,获得高阶变性椭圆锥齿轮齿廓在传动过程中的运动变化规律及齿轮副匹配模式的通式。通过试验验证该仿真加工获得高阶变性椭圆锥齿轮齿形的方法的正确性。此齿形获得方法可推广应用到任意球面节曲线形状及任意轴间夹角的非圆锥齿轮,从而实现非圆锥齿轮的通用参数化设计。

High-order deformed elliptic bevel gear is a noncircular bevel gear,whose spherical pitch curve of big end is high-order or deformed ellipse.According to the space mesh theory,a processing method of this gear is proposed.Based on the pure rolling motion of pitch curves between the high-order deformed elliptic bevel gear and virtual cutting tool,parameter of tooth profile can be analyzed and the curves of pitch,addendum and dedendum of gears also can be designed.The transmission mode and the kinematics characteristics of tooth profile of the high-order deformed elliptic bevel gear are analyzed emphatically.The simulation model of elliptic bevel gears based on high-order deformed ellipse is built.A common transmission mode and design method,the movement regularity of tooth profile and the general match pattern formula of different elliptic bevel gears are obtained.This method is verified by experiments and can be applied to any non-bevel gear with spherical pitch curve.Finally the universal parametric design of noncircular bevel gear is provided.