Research on reverse design method of small-modulus offset face gears based on modified surface optimization

采用修形曲面优化的小模数偏置面齿轮逆向设计

¹ Shaanxi Key Laboratory of Gear Transmission, Northwestern Polytechnical University, Xi'an 710072, China
² Guangdong Globalsino Outdoor Sports Equipment Limited, Qingyuan 511520, China

Received: 27 August 2024

Abstract

Aiming at the problem of high-precision reconstruction of the tooth face of small-modulus offset face gears, a reverse design method based on three-coordinate measurement and optimization of modified surfaces is proposed. Initially, a coordinate system of tooth face conjugate expansion is established, and the theoretical tooth face radial vector equation and normal vector equation of the small-modulus offset face gear are derived; subsequently, the measurement coordinate system and measurement path are designed and planned, and the tooth face data of the sample gear are obtained by the high-precision coordinate measuring machine; thereafter, a comprehensive modified surface design method for the small-modulus face gear is given, and precise optimal modification parameters that closely approximate the tooth surface of the sample gear are solved through optimization iterations, enabling the reverse design of smooth tooth surface. Finally, comparative analysis and meshing experiments were conducted for the sample gear, the reverse-designed gear and other conventionally designed gears. The results show that the error in the range of working tooth surface between the optimized reverse-designed tooth surface and the original sample gear tooth surface is less than 2 μm, and the contact patterns are highly consistent, which is significantly better than that of the tooth surface designed by other methods, confirming the practicality and effectiveness of the proposed reverse-design method.

摘要

针对小模数偏置面齿轮齿面的高精度重构问题, 提出了一种基于三坐标测量和修形曲面优化的逆向设计方法。建立了齿面共轭展成坐标系, 推导出小模数偏置面齿轮理论齿面径矢方程和法矢方程; 设计规划了测量坐标系和测量路径, 通过高精度三坐标测量仪获得了样品齿轮的齿面数据; 给出了小模数面齿轮综合修形曲面设计方法, 并通过优化迭代精确求解出能够逼近样品齿轮齿面的最佳修形参数, 实现光滑齿面的逆向设计; 进行了样品齿轮、逆向设计齿轮和其他常规设计齿轮的对比分析和啮合实验。结果表明: 经过修形曲面优化的逆向设计齿面与原样品齿轮齿面之间在工作齿面范围的误差小于2 μm, 接触印痕高度一致, 且明显优于采用其他2种方式设计的齿面性能, 证实了该逆向设计方法的实用性和有效性。