Geometric Condition of Planar Engagement and Stress Analysis of Cup Bottom of Bell Shaped Harmonic Gear

Xing Jingzhong; Pang Manyi; Chen Xiaoxia; Yao Yunpeng

doi:10.16578/j.issn.1004.2539.2020.06.017

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Geometric Condition of Planar Engagement and Stress Analysis of Cup Bottom of Bell Shaped Harmonic Gear

Test·Analysis | 更新时间：2022-10-20

- Geometric Condition of Planar Engagement and Stress Analysis of Cup Bottom of Bell Shaped Harmonic Gear
- Journal of Mechanical Transmission Vol. 44, Issue 6, Pages: 96-102(2020)
- 作者机构：
  
  1.天津工业大学机械工程学院，天津 300387
  2.天津工业大学天津市现代机电装备技术重点实验室，天津 300387
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2020.06.017
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邢静忠,庞满意,陈晓霞等.钟形谐波齿轮平面啮合的几何条件及杯底应力分析[J].机械传动,2020,44(06):96-102.

Xing Jingzhong,Pang Manyi,Chen Xiaoxia,et al.Geometric Condition of Planar Engagement and Stress Analysis of Cup Bottom of Bell Shaped Harmonic Gear[J].Journal of Mechanical Transmission,2020,44(06):96-102.
邢静忠,庞满意,陈晓霞等.钟形谐波齿轮平面啮合的几何条件及杯底应力分析[J].机械传动,2020,44(06):96-102. DOI： 10.16578/j.issn.1004.2539.2020.06.017.

Xing Jingzhong,Pang Manyi,Chen Xiaoxia,et al.Geometric Condition of Planar Engagement and Stress Analysis of Cup Bottom of Bell Shaped Harmonic Gear[J].Journal of Mechanical Transmission,2020,44(06):96-102. DOI： 10.16578/j.issn.1004.2539.2020.06.017.

摘要

为实现齿轮齿圈的径向平面变形和齿廓间的平面啮合，依据圆柱壳理论的几何方程，提出钟形筒体与齿圈连接处的变形条件；建立参数化钟形柔轮壳体接触模型，迭代求解实现齿圈平面变形的钟形曲线的几何条件，即齿圈中面半径和钟形曲线半径比值与钟形曲线中心角的关系，并用五次样条曲线拟合表达。求解满足齿圈平面变形时筒体和杯底连接处的变形条件，并依据圆形薄板理论提出杯底变形及应力的计算方法。研究发现，从动轴半径大于0.65倍杯底半径时，钟形柔轮杯底应力随从动轴半径的增加呈指数级增大；但实现齿圈平面变形的钟形曲线几何条件与从动轴半径无关。

Abstract

In order to realize planar deformation of the tooth ring in radial direction which leads to planar line contact engagement between tooth profiles， according to the geometric equation of the cylindrical shell theory， the connection condition between the bell shaped shell and the tooth ring is proposed. A parametric bell shaped flexspline shell contact model is established. The geometric condition of the bell shaped curve which realizes planar deformation of the tooth ring is solved iteratively，that is，the relationship between the ratio of the radius of the tooth ring to the radius of the bell shaped curve and the central angle of the circular bell shaped curve. The result is fitted with a five-order spline curve expression. The connection condition between the bell shaped shell and the cup bottom is solved and according to the theory of circular thin plate，the calculation method of the deformation and stress of the cup bottom is proposed. The research found that the stress of the bell shaped flexspline cup bottom increases exponentially with the increase of the shaft radius when the shaft radius greater than 0.65 times of the cup bottom radius. However，the geometric conditions of the bell-shaped curve for the planar deformation of the tooth ring are independent of the shaft radius.

关键词

锥度变形有限元柱形壳体平面变形

Keywords

Taper deformationFinite elementCylindrical shellPlanar deformation

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