Sensitivity analysis and optimization design of hypoid gears’ contact pattern to misalignments

Abstract

Accurate evaluation of the misalignment sensitivity of hypoid gears is a significant foundation for analysis of its dynamics and for the calculation of machining parameters. A tooth contact analysis (TCA) methodology considering four kinds of misalignments is presented to calculate the contact pattern and transmission error. A sensitivity model of contact pattern to misalignments is established to investigate the effects of different alignment errors on meshing performance. By parameterizing the contact pattern, the influences of offset error, angular error, and the axial error of pinion and gear on the direction, shape, and position features of contact pattern are studied. Coefficients of four evaluation indexes to different misalignments are defined respectively, and the minimum sum of the weighted coefficients is utilized to establish a multi-objective comprehensive sensitivity model. Three curvatures of the pitch cone of the pinion are taken as the control variables, and a global selection space is then built within the reasonable range of those curvatures. An improved multi-population genetic algorithm (MPGA) is used to find the optimal set of curvatures to achieve the minimum synthetic sensitivity. TCA results indicate that the offset error and angular error have the greatest influence on the contact pattern. By adopting this methodology appropriately, the sensitivity of the contact pattern to misalignments can be reduced. The contributions of this paper can be summarized as: (1) an accurate parameterized measurement model of the contact pattern; (2) a comprehensive sensitivity model of the contact pattern to misalignments; (3) an optimization framework consisting of a calculation model of the machining parameters, a TCA model considering misalignments, and a misalignment sensitivity evaluation model.

目 的

准双曲面齿轮副在实际装配过程中不可避免地存在安装误差。 本文旨在建立考虑多种安装误差的准双曲面齿轮啮合模型, 对齿轮副啮合印痕特征 (齿面分布位置、 大小和方向) 进行参数化建模, 精确评价印痕对安装误差的敏感性, 以及研究降低接触性能对安装误差的敏感度的方法, 为准双曲面齿轮副的加工和安装提供理论依据。

创新点

• 1. 对准双曲面齿轮齿面接触印痕进行精确的参数化建模;

• 2. 建立考虑轴交角误差、 偏置距误差以及大小轮轴向误差的齿轮副啮合分析模型;

• 3. 建立准双曲面齿轮副安装误差敏感度综合评价模型;

• 4. 通过优化齿轮加工参数, 在齿轮副设计环节实现齿轮副安装误差敏感度的降低。

方 法

• 1. -

• 2. 对准双曲面齿轮副安装误差和齿面接触印痕进行参数化建模, 推导出表示接触印痕大小、 方向和齿面分布位置的解析表达式 (公式 (1) ~ (3)); 2. 建立考虑4 种安装误差的准双曲面齿轮副啮合分析模型 (公式 (4) ~ (11)), 得到不同安装误差对啮合印痕的影响 (图5~7);

• 3. 建立准双曲面齿轮副安装误差综合敏感度优化模型 (公式 (15)), 并基于改进的多种群遗传算法 (图14) 实现齿轮副安装误差敏感性的降低 (图8)。

结 论

• 1. 四种安装误差对准双曲面齿轮啮合质量的影响程度不同; 其中轴交角误差的影响最大, 其次是偏置距误差, 而大小轮的轴向安装误差的影响最小, 因此安装齿轮副必须注重轴交角及偏置距的安装精度。

• 2. 通过降低齿轮副安装误差综合敏感度, 可在一定程度上降低系统对装配误差的敏感性; 在齿轮副设计环节加入安装误差敏感度分析, 优化机床加工参数, 对装配后的啮合质量控制具有积极意义。

• 3. 考虑安装误差的轮齿接触分析模型能够得到不同安装误差对啮合印痕及传动误差的影响规律, 是一种对失配状态下的准双曲面齿轮副进行无载啮合分析的有效工具。