齿轮轮齿接触分析的分解算法

Decomposition methodology for gear tooth contact analysis

提出了齿轮轮齿接触分析算法——分解算法。传统的轮齿接触分析方法求啮合点时需要求解含5个非线性方程的方程组,求解性差;齿面接触和边缘接触的数学模型不同,需要分别进行求解,求解过程复杂。轮齿接触分析算法——分解算法,提出了瞬时共轭啮合线的概念,可有效分离传动误差,得到啮合点、瞬时接触线,求啮合点时非线性方程的个数由5个减少为2个。分解算法建立的数学模型也适用于边缘接触分析,算法简单、有效、适应性强。以一对弧齿锥齿轮为例,对比分析了传统方法和分解算法,结果表明:齿面部分的印痕是一致的,传动误差幅值相差0.3″;边缘接触部分的印痕存在少许差异。

A methodology for gear tooth contact analysis was proposed. The convention- al approach of tooth contact analysis was used to solve a system of five nonlinear equations for each contact point, but the numerical stability of the algorithm was weak. In addition, the mathematical models for tooth surface contact and edge contact were not the same; there- fore, different systems of five nonlinear equations were required for different mathematical models, causing complex computing process and too many parameters involved therein. This decomposition methodology defined and utilized a concept called instantaneous conjugate con- tact curve. By constructing instantaneous conjugate contact curve, the transmission errors can be separated effectively and then the contact point and instantaneous contact curve can be loeated effortlessly. The number of nonlinear equations for searching contact point was re- duced from 5 to 2. This mathematic model was also applied to edge contact analysis. So the decomposition methodology was simple, effective and adaptable. At the end, the decomposi-tion methodology was applied to a pair of spiral bevel gears to demonstrate its effectiveness compared with the conventional method. For tooth surfaces contact, contact patterns were identically calculated by the two methods, and the relative difference for the magnitude of transmission errors was about 0.3＂. In the case of edges contact, there were relatively few differences for patterns.