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| A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears |
| Yao-bin Zhuo, Xue-yan Xiang, Xiao-jun Zhou, Hao-liang Lv, Guo-yang Teng |
| College of Engineering and Design, Lishui University, Lishui 323000, China; State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China |
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Abstract In this paper, we present a method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears, which includes three optimization objectives, three control parameters, and a complex-constrain genetic algorithm solving method. A new set of fundamental equations for pitch cone parameters of hypoid gear drives are established, as well as the relationships between pitch cone and curvature parameters. Based on this theory, three control parameters are selected to determine the pinion tooth surface. A hypoid gear drive is chosen for case studies. The results verify that the optimization methodology can achieve the expected optimization objectives and has good convergence. Correlations between optimization objectives and control parameters are discussed. Furthermore, a finite element model of a simplified hypoid gear drive system is established and its quasi-static meshing characteristics analyzed. The results again confirm the correctness of the optimization method. The effects of torque load on the contact pattern and transmission error are discussed. The results provide a theoretical reference for geometric calculations, quasi-static analysis, and optimal design of spiral bevel and hypoid gears.
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Received: 14 March 2016
Published: 03 May 2017
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一种螺旋锥齿轮齿面接触区和传动误差的全局优化方法
目的：传统的齿面接触分析技术存在调整参数繁多、控制目标不明确和不包含传动误差优化等缺陷。本文旨在提出一种齿面接触区和传动误差的全局优化设计方法，以得到满足齿轮传动性能要求的小轮产形轮节锥参数及机床调整参数。
创新点：1. 提出了新的确定各节锥参数之间几何关系的计算公式，并建立了节锥参数与曲率参数的相关公式；2. 提出以齿面接触区长半轴、接触线方向角和传动误差曲线交点纵坐标为优化目标，以齿面法曲率和短程挠率为控制参数，以复合形法约束处理的遗传算法为求解途径的齿面接触特性全局优化设计方法。
方法：1. 分析常见齿面接触区和传动误差曲线的缺陷及其原因（图1）；2. 提出全局优化目标（图2），进行节锥参数和曲率参数分析，从而确定控制参数（图3~6），建立优化方程并进行求解算法分析（图7和8），然后进行实例计算分析（图9和10）；3. 建立齿轮副传动系统有限元分析模型，验证优化方法的正确性（图11~13）。
结论：1.优化设计的实例分析表明，优化目标、控制参数和优化算法具有良好的匹配性；2. 通过优化目标与控制参数的相关性分析，得出了控制参数的影响特征；3. 通过有限元分析验证，优化设计结果达到了预期的齿轮传动性能指标。
关键词：
螺旋锥齿轮,
齿面接触,
传动误差,
优化设计,
遗传算法,
有限元分析
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