螺旋锥齿轮齿面接触分析改进算法研究  

Research on improved tooth contact analysis algorithm of spiral bevel gears

作　　者：唐进元[1] 卢延峰[1] 周超[1] 

机构地区：[1]中南大学现代复杂装备设计与极端制造教育部重点实验室,机电工程学院,长沙410083

出　　处：《航空动力学报》2009年第1期189-195,共7页Journal of Aerospace Power

基　　金：国家自然基金科学(50875263);国家重点基础研究发展计划(973计划)(2005CB724100)

摘　　要：针对现有齿面接触分析(TCA)的不足,提出了螺旋锥齿轮齿面接触分析的改进算法.基于空间曲面啮合原理、Enler-Rodrigues公式以及接触区几何形状的等量关系对齿面接触分析算法进行了改进,通过方程变换,减少了求解接触点位置的非线性方程组维数,由啮合方程求得到初值选取计算公式,使初始值求解有规律可循.以一对弧齿锥齿轮为例,对算法进行了对比分析与验证,结果表明:改进的齿面接触分析算法可减少求解非线性方程组时初值选取的繁复性与增强非线性方程组迭代求解的稳定性;并利用几何等量关系求解接触区几何参数,能避免求解复杂的齿面相对曲率等二阶几何参数.According to the deficiency of tooth contact analysis analysis, an improved tooth contact analysis algorithm was proposed. Based on the spatial surface engagement theory, the Enler-Rodrigues formula and the equivalent relationship between the contacted areas shapes, the tooth contact analysis algorithm was proved. Through the equation transformation, the dimensions of the nonlinear equations for the contact points＇ position were decreased. The initial value was obtained regularly by the meshing equations. Taking a pair of spiral bevel gears as an example, the algorithm was proved. The results show that the complexity of initial values is decreased, the stability of the solution for nonlinear equations is enhanced, and the complex calculation of relative curvatures of the tooth surface is avoided by using the geometrical educational relationships between the geometrical parameters.

关 键 词：齿面接触分析(TCA) 螺旋锥齿轮 改进的TCA算法 非线性方程 

分 类 号：TH132.4[机械工程—机械制造及自动化]