Research on Correction Algorithms of Tooth Profile Error of Cycloidal Bevel Gear Formate Gear

Zhiyong Wang; Xiaolong Liu; Xin Liu; Yu Zhang

doi:10.16578/j.issn.1004.2539.2020.09.004

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Research on Correction Algorithms of Tooth Profile Error of Cycloidal Bevel Gear Formate Gear

Theory·Reserach | 更新时间：2022-11-02

- Research on Correction Algorithms of Tooth Profile Error of Cycloidal Bevel Gear Formate Gear
- Journal of Mechanical Transmission Vol. 44, Issue 9, Pages: 21-26(2020)
- 作者机构：
  
  1.中南林业科技大学机电工程学院，湖南长沙 410004
  2.长沙哈量凯帅精密机械有限公司技术中心，湖南长沙 410100
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2020.09.004
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王志永,刘晓龙,刘鑫等.摆线齿锥齿轮成形法大轮齿形误差修正算法的研究[J].机械传动,2020,44(09):21-26.

Wang Zhiyong,Liu Xiaolong,Liu Xin,et al.Research on Correction Algorithms of Tooth Profile Error of Cycloidal Bevel Gear Formate Gear[J].Journal of Mechanical Transmission,2020,44(09):21-26.
王志永,刘晓龙,刘鑫等.摆线齿锥齿轮成形法大轮齿形误差修正算法的研究[J].机械传动,2020,44(09):21-26. DOI： 10.16578/j.issn.1004.2539.2020.09.004.

Wang Zhiyong,Liu Xiaolong,Liu Xin,et al.Research on Correction Algorithms of Tooth Profile Error of Cycloidal Bevel Gear Formate Gear[J].Journal of Mechanical Transmission,2020,44(09):21-26. DOI： 10.16578/j.issn.1004.2539.2020.09.004.

摘要

针对奥利康（Oerlikon）制摆线齿锥齿轮成形法大轮齿形误差修正问题，使用矢量运算法建立了大轮齿面几何模型，对齿面进行离散化处理，计算了齿面各离散点的坐标及法矢；基于齿形误差修正原理，由实际齿面与理论齿面之间的齿形误差和反调参数敏感系数矩阵，建立了齿形误差修正方程组，使用吉洪诺夫（Tikhonov）正则化和L曲线优化算法求解线性方程组，得到机床调整参数的修正量；使用Fortran语言开发了齿面坐标计算及齿形误差反调修正软件。通过实验，验证了齿形误差反调修正算法的正确性，实验工件的齿形误差最大值由37.5 μm减小到5.2 μm。

Abstract

Aming at the problem of correction algorithms of tooth profile errors of Oerlikon cycloidal bevel formate gear， by using the vector operation method， the geometric model of the tooth surface of gear is established. The method of tooth surface discretization is provided， and the coordinates and normal vectors of the discrete points on the tooth surface are calculated. Based on the principle of tooth profile error correction， the tooth profile error correction equation group is established based on the tooth profile error and inverse parameter sensitivity coefficient matrix between the actual tooth surface and the theoretical tooth surface. By using the Tikhonov regularization and L curve optimization algorithm， the linear equation group is solved， the correction value of the adjustment parameter of the machine tool is obtained. The software for tooth surface coordinate calculation and tooth profile error correction is developed by using Fortran. The correctness of the correction algorithm is verified by experiments and the maximum tooth profile error of the experimental workpiece is reduced from 37.5 μm to 5.2 μm.

关键词

摆线齿锥齿轮机床调整参数齿形误差修正几何建模

Keywords

Cycloidal bevel gearMachine tool adjustment parameterTooth profile error correctionGeometric modeling

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