Spatial Tooth Profile Design of Triple-circular-arc Harmonic Gears and Finite Element Simulation of Torsional Stiffness

Xing Jingzhong; Chen Liang; Chen Xiaoxia; Yao Yunpeng

doi:10.16578/j.issn.1004.2539.2023.09.006

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Spatial Tooth Profile Design of Triple-circular-arc Harmonic Gears and Finite Element Simulation of Torsional Stiffness

Design· Calculation | 更新时间：2023-09-18

- Spatial Tooth Profile Design of Triple-circular-arc Harmonic Gears and Finite Element Simulation of Torsional Stiffness
- Journal of Mechanical Transmission Vol. 47, Issue 9, Pages: 37-43(2023)
- 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.1004.2539.2023.09.006
  CLC：
- Published：15 September 2023，
  
  Received：23 June 2022，
  
  Revised：31 July 2022，
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邢静忠,陈亮,陈晓霞等.三圆弧谐波齿轮空间齿廓设计与扭转刚度的有限元仿真[J].机械传动,2023,47(09):37-43.

Xing Jingzhong,Chen Liang,Chen Xiaoxia,et al.Spatial Tooth Profile Design of Triple-circular-arc Harmonic Gears and Finite Element Simulation of Torsional Stiffness[J].Journal of Mechanical Transmission,2023,47(09):37-43.
邢静忠,陈亮,陈晓霞等.三圆弧谐波齿轮空间齿廓设计与扭转刚度的有限元仿真[J].机械传动,2023,47(09):37-43. DOI： 10.16578/j.issn.1004.2539.2023.09.006.

Xing Jingzhong,Chen Liang,Chen Xiaoxia,et al.Spatial Tooth Profile Design of Triple-circular-arc Harmonic Gears and Finite Element Simulation of Torsional Stiffness[J].Journal of Mechanical Transmission,2023,47(09):37-43. DOI： 10.16578/j.issn.1004.2539.2023.09.006.

摘要

为评价齿廓方案的负载传动性能，提升负载传动能力，建立有限元分析（Finite Element Analysis，FEA）仿真模型，揭示了输出端扭转刚度与负载啮合特性的关系。构造三圆弧柔轮齿廓，调整柔轮齿廓的径向变位系数，使柔轮齿廓啮合运动的外包络重叠量最小化，并基于外包络用包络法设计了三圆弧平面齿廓刚轮；在多个横截面内构造径向变位的三圆弧柔轮齿廓，在有限元环境下轴向放样生成柔轮空间齿廓，建立了包含平面齿廓刚轮、空间齿廓柔轮和波发生器外圈的有限元仿真模型；固定刚轮，对柔轮杯底法兰施加不同幅值和转向的负载转矩，仿真计算了啮合力分布与扭转刚度滞回曲线；通过建立啮合齿数与刚度特性的关系，揭示了扭转刚度特性与齿面啮合特性之间的关系。仿真结果表明，啮合齿数与扭转刚度成正相关；使用可测量的扭转刚度迟滞曲线，可以估算啮合齿数等不可测量的啮合特性。

Abstract

In order to improve the transmission capability by exploring the relationship between torsional stiffness on output shaft and load meshing characteristics

a simulation model of finite element analysis (FEA) is built to evaluate the performance of tooth profile under transmission loading. A triple-circular-arc tooth profile of flexspline is constructed

and the radial modification of the tooth profile is adjusted to minimize the outer envelope overlap of meshing motion of the tooth profiles. Then

a triple-circular-arc planar tooth profile of circular splines is designed with the envelop method according to the outer envelope. A triple-circular-arc tooth profile of flexspline with tradial modification is constructed in several cross sections

and the spatial tooth profiles of flexsplines are generated by axial lofting in finite element environment. A finite element simulation model including circular spline with planar tooth profile

cup-shaped flexspline with spatial tooth profile and outer ring of wave generators is established. Transmission torques of different amplitudes in two rotational directions are applied on the flange plate at the bottom of the flexspline engaged with a fixed circular spline

and the meshing force distribution and torsional stiffness hysteresis curves are simulated. The number of meshing teeth in different meshing states can be estimated with the relationship between torsional stiffness and meshing characteristics of tooth profiles. The simulation results show that the number of meshing teeth is positively correlated with the torsional stiffness. Using the measureable hysteresis curve of torsional stiffness

the immeasurable meshing characteristics such as the number of meshing teeth can be estimated.

关键词

三圆弧齿廓空间齿廓啮合特性有限元仿真扭转刚度

Keywords

Triple-circular-arc tooth profileSpatial tooth profileMeshing characteristicsFinite element simulationTorsional stiffness

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