不同重合度非圆齿轮设计及弯曲应力分析

doi:10.3901/JME.2022.19.206

摘要/Abstract

摘要： 非圆齿轮传动具有广泛的应用场景。针对非圆齿轮传动，采用齿轮啮合原理和材料力学等原理及方法，提出了大重合度非圆齿轮设计方法。探讨了非圆齿轮传动原理和节曲线构建方法，计算了其节曲线曲率半径和重合度方程。建立了不同重合度非圆齿轮轮齿时变啮合刚度与载荷分配率计算模型，推导了不同重合度非圆齿轮齿根弯曲应力方程。探讨了不同结构参数下非圆齿轮副重合度、时变啮合刚度、时变载荷分配率及齿根弯曲应力变化规律，确定了轮齿所受最大载荷位置。开展了不同重合度非圆齿轮齿根弯曲应力仿真分析和实验测量，与理论计算结果进行了对比分析，最大误差分别约为4.8%和5.9%，验证了理论方法的合理性与正确性，为大重合度非圆齿轮传动的工程应用奠定了基础。

关键词: 设计, 非圆齿轮, 重合度, 时变啮合刚度, 载荷分配率, 弯曲应力

Abstract: Non-circular gear transmission has a wide range of application scenarios. For the non-circular gear transmission, based on the principle and method of gear engagement and material mechanics, the design method of non-circular gear with high contact ratio is proposed. The principle of non-circular gear transmission and the construction method of pitch curve are discussed. The curvature radius of pitch curve and contact ratio of non-circular gear pair are calculated. The calculation models of time-varying meshing stiffness and load sharing ratio of non-circular gears with different contact ratio are established, and the bending stress equation of tooth root of non-circular gears with different contact ratio is derived. The variation rules of contact ratio, time-varying meshing stiffness, time-varying load sharing ratio and tooth root bending stress of non-circular gear pair under different structural parameters are discussed, and the maximum load position of the gear tooth is determined. The simulation analysis and experimental measurement of tooth root bending stress of non-circular gear with different contact ratio are carried out, and the results are compared with the theoretical calculation results. The maximum errors are about 4.8% and 5.9% respectively, which verified the rationality and correctness of the theoretical method and laid a foundation for the engineering application of non-circular gear transmission with high contact ratio.

Key words: design, non-circular gear, contact ratio, time-varying meshing stiffness, load sharing ratio, bending stress

中图分类号:

TH114

喻永权, 林超, 胡亚楠. 不同重合度非圆齿轮设计及弯曲应力分析[J]. 机械工程学报, 2022, 58(19): 206-220.

YU Yongquan, LIN Chao, HU Yanan. Design and Bending Stress Analysis of Non-circular Gears with Different Contact Ratio[J]. Journal of Mechanical Engineering, 2022, 58(19): 206-220.

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