Improved algorithm for time-varying meshing stiffness of helical gears considering axial force component and its influencing factors

MAO Hancheng; DING Yuanwei; LI Xuwei; ZHANG Bingqian

doi:10.16578/j.issn.1004.2539.2026.03.011

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Improved algorithm for time-varying meshing stiffness of helical gears considering axial force component and its influencing factors

Dynamic Performance and Mesh Characteristics | 更新时间：2026-05-27

- Improved algorithm for time-varying meshing stiffness of helical gears considering axial force component and its influencing factors
- Journal of Mechanical Transmission Vol. 50, Issue 3, Pages: 89-97(2026)
- 作者机构：
  
  黑龙江科技大学机械工程学院，哈尔滨 150022
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2026.03.011
  CLC： TH132.413
- Received：11 March 2025，
  
  Published：15 March 2026
- 稿件说明：
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毛汉成，丁元伟，李旭伟，等. 考虑轴向分力的斜齿轮时变啮合刚度改进算法及影响因素研究［J］. 机械传动，2026，50（3）：89-97.

MAO Hancheng，DING Yuanwei，LI Xuwei，et al. Improved algorithm for time-varying meshing stiffness of helical gears considering axial force component and its influencing factors［J］. Journal of Mechanical Transmission，2026，50（3）：89-97.
毛汉成，丁元伟，李旭伟，等. 考虑轴向分力的斜齿轮时变啮合刚度改进算法及影响因素研究［J］. 机械传动，2026，50（3）：89-97. DOI： 10.16578/j.issn.1004.2539.2026.03.011.

MAO Hancheng，DING Yuanwei，LI Xuwei，et al. Improved algorithm for time-varying meshing stiffness of helical gears considering axial force component and its influencing factors［J］. Journal of Mechanical Transmission，2026，50（3）：89-97. DOI： 10.16578/j.issn.1004.2539.2026.03.011.

摘要

目的

针对斜齿轮时变啮合刚度精确求解问题，提出基于轴向力及切片思想的斜齿轮啮合刚度计算方法。

方法

将每一薄片齿轮简化为变截面悬臂梁，通过受力分析加入新的轴向弯曲势能，并对现有基于势能法的斜齿轮啮合刚度计算方法做了进一步修正，提出一种刚度改进算法；通过与有限元法、切片法对比分析，验证了该改进算法的可行性；在此算法基础上，研究了螺旋角、压力角、齿数、齿宽等参数对啮合刚度的影响。

结果

结果表明，传统势能法只适用于螺旋角较小的斜齿轮，而改进算法适用于任意斜齿轮；增大螺旋角，可使齿轮传动愈加平稳；压力角对时变啮合刚度均值影响较小；齿宽对时变啮合刚度均值影响较大，近似成线性关系；中心距一定时，齿数变化对时变啮合刚度均值影响较小，齿数较多时，啮合刚度波动值较小；当轴向重合度接近整数时，啮合刚度波动值最小。

Abstract

Objective

Aiming at the problem of finding an accurate time-varying mesh stiffness solution for helical gears

a helical gear mesh stiffness calculation method based on axial force and slicing was proposed.

Methods

Each lamellar gear was simplified as a variable-section cantilever beam

and a stiffness improved algorithm was proposed by adding a new axial bending potential energy through force analysis and further modifying the existing potential-energy-based method for calculating helical gear meshing stiffness. The feasibility of the improved algorithm was verified by comparing and analyzing with the finite element method and the slice method. On this basis

the effects of parameters such as helix angle

pressure angle

tooth number and tooth width on the meshing stiffness were investigated.

Results

The results show that the traditional potential energy method is only applicable to helical gears with small helix angles

while the improved algorithm applies to arbitrary helical gears. The smoother the gearing performance is at increasing the helix angle. The pressure angle has less effect on the mean value of time-varying meshing stiffness. The tooth width has a large influence

which is approximately linear. When the center distance is certain

the change of the number of teeth has a smaller influence on the mean value

and the fluctuation value of the meshing stiffness is smaller when the number of teeth is larger. The fluctuation value is the smallest when the axial overlap is close to an integer.

关键词

Keywords

references

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