谐波齿轮柔轮中面曲线的几何特征拟合表达

邢静忠; 石立腾; 姚云鹏; 陈晓霞

doi:10.37188/OPE.20202807.1519

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谐波齿轮柔轮中面曲线的几何特征拟合表达

微纳技术与精密机械 | 更新时间：2020-08-13

- 谐波齿轮柔轮中面曲线的几何特征拟合表达
- Description of neutral line of harmonic drive flexspline with geometric property interpolation
- 光学精密工程 2020年28卷第7期页码：1519-1527
- 作者机构：
  
  天津工业大学机械工程学院, 天津 300387
- 作者简介：
  
  [ "邢静忠(1966-), 男, 甘肃平凉人, 博士, 教授, 1991年于兰州理工大学获得硕士学位, 2004年于中国科学院大学获得博士学位, 主要从事谐波齿轮减速器的结构分析和啮合性能仿真等方面的研究。E-mail:hsingjzh@tiangong.edu.cn" ]
  [ "石立腾(1992-), 男, 河南民权人, 硕士研究生, 2015年于河南机电高等专科学校(现河南工学院)获得专科学历, 主要从事谐波齿轮传动的研究。E-mail:shiliteng@163.com" ]
- 基金信息：
  
  天津市应用基础与前沿技术研究计划重点资助项目(18JCZDJC39000);天津市应用基础与前沿技术研究计划重点资助项目(19JCZDJC38700)
- DOI：10.37188/OPE.20202807.1519
  中图分类号： TH132.43
- 收稿日期：2019-12-02，
  
  修回日期：2020-02-05，
  
  录用日期：2020-2-5，
  
  纸质出版日期：2020-07-15
- 稿件说明：
移动端阅览
邢静忠, 石立腾, 姚云鹏, 等. 谐波齿轮柔轮中面曲线的几何特征拟合表达[J]. 光学精密工程, 2020,28(7):1519-1527.

Jing-zhong XING, Li-teng SHI, Yun-peng YAO, et al. Description of neutral line of harmonic drive flexspline with geometric property interpolation[J]. Optics and precision engineering, 2020, 28(7): 1519-1527.
邢静忠, 石立腾, 姚云鹏, 等. 谐波齿轮柔轮中面曲线的几何特征拟合表达[J]. 光学精密工程, 2020,28(7):1519-1527. DOI： 10.37188/OPE.20202807.1519.

Jing-zhong XING, Li-teng SHI, Yun-peng YAO, et al. Description of neutral line of harmonic drive flexspline with geometric property interpolation[J]. Optics and precision engineering, 2020, 28(7): 1519-1527. DOI： 10.37188/OPE.20202807.1519.

摘要

为了减少现有力学小变形假定下通过位移叠加表达导致的轮齿定位偏差，以长轴具有等曲率圆弧的凸轮波发生器为例，提出包角内利用凸轮等距线确定中面曲线，包角外利用两端斜率和曲率连续性条件，并考虑变形前后曲线的弧长增量等于周向力引起的伸长，构造以样条函数表达的柔轮中面曲线。在有限元环境中建立圆环与双偏心圆弧凸轮波发生器的接触模型，对位移叠加表达的柔轮中面曲线和本文的几何特征拟合的表达结果，利用有限元模型在小变形和大变形求解条件下进行数值验证。认为有限元模型在大变形求解条件下的非线性结果更符合实际，并以其为准则计算各方法的结果偏差。算例表明：现有基于小变形的理论解和有限元的小变形数值结果均与更贴合实际的大变形结果存在较大偏差。在30°包角模型中本文方法的极角偏差降低了约0.006°，极径偏差降低了约0.013 mm。本文方法在模型包角在25°~65°之间时更贴近实际，且易于实现，消除了几何大变形、接触非线性和中面伸长等因素对中面曲线表达的影响，为谐波齿轮齿廓设计提供更准确的轮齿定位。

Abstract

The existing neutral line expressed through displacement superposition under the small deformation assumption leads to a large positioning deviation of the flexspline teeth. By taking the double disk wave generator as an example

the neutral line in the wrap angle was determined using the CAM isometric line. The outside neutral line expressed using a spline function was constructed based on the continuous conditions

such as slope and curvature

at both ends

and the difference between the tension of the neutral line was equal to the elongation produced by the circumferential force. A Finite Element Method (FEM) model of the tooth ring in contact with a circular cam was developed to verify the geometric interpolation method and the neutral line expressed with radial and circumferential displacements numerically under small and large deformations

respectively. The differences between the verification examples were calculated using the large deformation results

which were considered more suitable for the actual conditions. The examples showed that both theoretical solutions and the FEM model based on small deformation had more significant differences with the more reasonable FEM results for the large deformation case. In the 30° wrap angle model

the pole angle of the proposed method decreased by approximately 0.006°

and the pole diameter decreased by approximately 0.013 mm. The method derived based on the geometric condition in this study was closer to actual conditions and easy to implement when the model envelope angle ranged between 25° and 65°. The proposed model eliminates the influence of large geometric deformation

contact nonlinearity

and neutral line elongation in providing more accurate gear tooth positioning for the tooth profile design of harmonic drives.

关键词

Keywords

references

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