Time⁃varying meshing stiffness calculation of straight bevel gears based on energy equivalence

Siyu CHEN; Rulong TAN; Xiaodong GUO; Weiqing ZHANG; Ruizhi SHU

doi:10.13224/j.cnki.jasp.20210095

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Time⁃varying meshing stiffness calculation of straight bevel gears based on energy equivalence

Power Transimission | 更新时间：2025-04-07

- Time⁃varying meshing stiffness calculation of straight bevel gears based on energy equivalence
- Journal of Aerospace Power Vol. 37, Issue 2, Pages: 320-329(2022)
- 作者机构：
  
  重庆理工大学机械工程学院，重庆 400054
- 作者简介：
- 基金信息：
- DOI：10.13224/j.cnki.jasp.20210095
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Siyu CHEN, Rulong TAN, Xiaodong GUO, et al. Time⁃varying meshing stiffness calculation of straight bevel gears based on energy equivalence[J]. Journal of Aerospace Power, 2022, 37(2): 320-329.
DOI：

Siyu CHEN, Rulong TAN, Xiaodong GUO, et al. Time⁃varying meshing stiffness calculation of straight bevel gears based on energy equivalence[J]. Journal of Aerospace Power, 2022, 37(2): 320-329. DOI： 10.13224/j.cnki.jasp.20210095.

摘要

针对直齿圆锥齿轮啮合刚度的计算问题，从微元思想出发，将变截面齿廓划分为若干等截面微段齿段，基于能量等效建立微段齿段啮合刚度计算模型，并利用积分方法获得单齿啮合刚度。此外，基于力平衡和变形协调条件进一步提出了齿轮时变啮合刚度计算模型，同时根据几何关系导出了相应传动误差计算式。利用有限元分析对解析计算模型进行了验证，并分析了误差来源。结果表明：利用该模型不仅能够将直齿锥齿轮啮合刚度计算精度保证在2%以内，还达到了快速求解的目的。

Abstract

As one of the most important dynamic excitation sources of gear system，gear time⁃varying meshing stiffness is a key parameter of gear system dynamics model. In view of the problem of calculating the meshing stiffness of straight bevel gears，the variable section tooth profile was divided into several micro⁃section tooth segments with equal section based on the idea of micro⁃element. The calculation model of meshing stiffness of micro⁃section tooth segments was established based on energy equivalent，and the single tooth meshing stiffness was obtained by using integral method. In addition，based on force balance and deformation coordination conditions，a computational model of gear time⁃varying meshing stiffness was proposed，and the corresponding formula of transmission error was derived according to geometric relations.The finite element analysis was used to verify the calculation method and analyze the error source. The results showed that the calculation accuracy of meshing stiffness of straight bevel gears can be guaranteed within 2% by using this model，and the purpose of quick solution can be achieved.

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references

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