正交面齿轮传动的两类界线

赵亚平; 娄海青

doi:10.11990/jheu.202210027

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正交面齿轮传动的两类界线

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- 正交面齿轮传动的两类界线
- Two types of boundary line of orthogonal face gear drives
- 哈尔滨工程大学学报 2024年45卷第4期页码：764-770
- 作者机构：
  
  东北大学机械工程与自动化学院, 辽宁沈阳 110004
- 作者简介：
  
  [ "赵亚平, 男, 教授, 博士生导师" ]
- 基金信息：
  
  国家自然科学基金项目(52075083);武汉科技大学冶金装备及其控制教育部重点实验室开放基金项目(MECOF2022B04);武汉科技大学冶金装备及其控制教育部重点实验室开放基金项目(MECOF2023B01)
- DOI：10.11990/jheu.202210027
  中图分类号： TH132.41
- 收稿：2022-10-20，
  
  网络首发：2024-03-08，
  
  纸质出版：2024-04-05
- 稿件说明：
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赵亚平, 娄海青. 正交面齿轮传动的两类界线[J]. 哈尔滨工程大学学报, 2024,45(4):764-770.

Yaping ZHAO, Haiqing LOU. Two types of boundary line of orthogonal face gear drives[J]. Journal of Harbin Engineering University, 2024, 45(4): 764-770.
赵亚平, 娄海青. 正交面齿轮传动的两类界线[J]. 哈尔滨工程大学学报, 2024,45(4):764-770. DOI： 10.11990/jheu.202210027.

Yaping ZHAO, Haiqing LOU. Two types of boundary line of orthogonal face gear drives[J]. Journal of Harbin Engineering University, 2024, 45(4): 764-770. DOI： 10.11990/jheu.202210027.

摘要

为了建立系统的正交面齿轮传动啮合界线与曲率干涉界线理论

本文通过求解非线方程组获得了两类界线的数值解。证明了啮合界线在小轮齿面上是渐开线; 其共轭线也是渐开线。发现干涉界线一般有2条

近齿面干涉界线存在于面齿轮内端附近

大致沿齿高走向。近齿面干涉界点存在平凡解

是干涉界线和啮合界线共轭线的交点

位于传动副瞬时相对转动轴上。基于近齿面干涉界线

建立了面齿轮无根切内径公式

通过数值迭代可以获得内径准确值; 还导出了无根切内径估算公式

便于设计中应用。

Abstract

In order to establish the theory of two kinds of limit line is set forth for the orthogonal face gear drive. By solving the nonlinear equations

the numerical solutions of the limit lines are obtained. It is proved that both the meshing limit line and its conjugate line are all involute. Generally

the interference limit line has two branches

and one branch near the gear exists approximately at its inner end

roughly along the tooth height and slightly aslant. The interference limit point has a trivial solution

and the related limit point is the intersecting point of the limit line and the conjugate line of meshing limit line. The trivial limit point is on the instantaneous axis of the relative rotation of the gear pair. By means of the theory proposed

a method based numerical iteration to compute the exact inner radius is proposed for the face gear without undercutting. Meanwhile an approximate formula to estimate the non-undercutting inner radius is put forward for convenient design.

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references

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