直纹面面齿轮共轭小齿轮的滚齿加工研究

彭先龙; 吴易凯; 胡锡文; 徐磊; 刘忠亮

doi:10.7652/xjtuxb202407015

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直纹面面齿轮共轭小齿轮的滚齿加工研究

—————————————————————— | 更新时间：2025-07-28

- 直纹面面齿轮共轭小齿轮的滚齿加工研究
- Hobbing of Pinions Conjugate with Ruled Surface Face Gears
- 西安交通大学学报 2024年58卷第7期页码：160-169
- 作者机构：
  
  1. 西安科技大学机械工程学院,西安,710054
  2. 中国核电工程有限公司,北京,100840
- 作者简介：
  
  : 2023-12-24。作者简介: 彭先龙(1982-),男,副教授,硕士生导师。基金项目: 陕西省自然科学基础研究计划资助项目(2020JM-521)
- 基金信息：
  
  : 2023-12-24。作者简介: 彭先龙(1982-),男,副教授,硕士生导师。基金项目: 陕西省自然科学基础研究计划资助项目(2020JM-521)
- DOI：10.7652/xjtuxb202407015
  中图分类号： TH132.4
- 网络首发：2024-07-10，
  
  纸质出版：2024
- 稿件说明：
移动端阅览
彭先龙, 吴易凯, 胡锡文, 等. 直纹面面齿轮共轭小齿轮的滚齿加工研究[J]. 西安交通大学学报, 2024,58(7):160-169.

PENG Xianlong, WU Yikai, HU Xiwen, et al. Hobbing of Pinions Conjugate with Ruled Surface Face Gears[J]. 2024, 58(7): 160-169.
彭先龙, 吴易凯, 胡锡文, 等. 直纹面面齿轮共轭小齿轮的滚齿加工研究[J]. 西安交通大学学报, 2024,58(7):160-169. DOI： 10.7652/xjtuxb202407015.

PENG Xianlong, WU Yikai, HU Xiwen, et al. Hobbing of Pinions Conjugate with Ruled Surface Face Gears[J]. 2024, 58(7): 160-169. DOI： 10.7652/xjtuxb202407015.

摘要

针对直纹面面齿轮与圆柱齿轮不满足共轭关系而限制其在小传动比应用场合的情况

提出与直纹面面齿轮共轭的小齿轮及其滚齿加工方法。首先建立了直纹面面齿轮及其共轭小齿轮的齿面方程

获得共轭小齿轮相比圆柱齿轮的齿面偏差形貌; 随后推导了阿基米德齿轮滚刀的齿面方程

并根据滚齿加工运动坐标系和啮合原理建立了圆柱齿轮的数学模型; 在滚齿加工圆柱齿轮的运动基础上

通过增加滚刀的径向移动和工件的附加转动使滚刀切削刃逼近共轭齿面

附加运动由泰勒多项式表示

通过建立敏感矩阵方程并采用奇异值分解法迭代求解方程获得附加数控运动多项式系数

最后获得数控加工齿面; 为评价直纹面面齿轮副的传动性能

进行了齿面承载接触分析

并与传统面齿轮-圆柱齿轮副进行了对比。研究结果表明:相同参数下

直纹面面齿轮副与传统面齿轮副的承载性能基本相同

完全能够代替传统面齿轮副传动; 数值算例和仿真加工对该方法的验证表明

其数值算例误差不超过1 μm

仿真结果误差不超过6 μm

证明了该方法的可行性和准确性。

Abstract

To address ruled surface face gears' limited application in small transmission ratios resulting from the lack of conjugacy with cylindrical gears

pinions conjugate with ruled surface face gears and outlines a corresponding hobbing method is proposed. Firstly

the equations of ruled surface face gears and the conjugate pinion are established

and the deviation morphology between a conjugate pinion and a cylindrical gear is obtained. Subsequently

the equation of Archimedes worm hob is derived

and a mathematical model of the cylindrical gear is developed according to the motion coordinate systems used in hobbing and meshing principles. Based on the motions of cylindrical gear hobbing

the hob's cutting edge approximates the conjugate surface through radial movement of the hob and additional rotation of the workpiece

expressed using Taylor polynomials. A sensitivity matrix equation is established

the singular value decomposition method is used to iteratively solve the equation to obtain the polynomial coefficients

and finally

the machining tooth surface is obtained. To evaluate the transmission performance of ruled surface face gear pairs

load tooth contact analysis is conducted

with a comparison made with conventional face gear pairs and cylindrical gear pairs. The research results reveal that with the same parameters

the load performance of the ruled surface face gear pairs aligns closely with that of the conventional face gear pairs

which indicates the potential for the former to fully replace the latter. Finally

the method is validated through numerical examples and simulation processing

with a numerical example error of less than 1 μm

and a simulation result error of less than 6 μm. This underscores the feasibility and accuracy of this method.

关键词

Keywords

references

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