椭圆齿轮传动系统参数设计对啮合特性影响的研究

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湖南理工学院硕士学位论文摘要

摘要

齿轮广泛运用在机械装备中，具有稳定、精确等传动特性，是目前最重要的零部件之

一。但传统的齿轮只能传递等速比运动，为满足新型、复杂的特定传动函数要求，椭圆齿

轮应运而生。和传统齿轮相比，其不仅将角速度恒定的运动传递为具有一定规律的变速运

动，还具有传递运动稳定、紧密的构造、能满足特殊的传动函数等优势。伴随椭圆齿轮的

应用愈加广泛及在传动中的独特性质，研究椭圆齿轮的设计参数对其传动特性的影响，及

分析在承受载荷的情况下椭圆齿轮齿面啮合性质具有重要意义。

本文采用 1 阶椭圆齿轮作为研究分析对象，通过理论和有限元仿真工具相互论证的分

析方法，对于椭圆齿轮在实际工作中的独有传动特性、齿面啮合特性、齿轮的疲劳寿命等

几个方面展开系统的研究，主要的研究内容包括：

1.提出一种准确、高效的椭圆齿轮建模方法，通过仿真模拟滚齿刀在齿坯表面进行滚齿

加工，来构建椭圆齿轮滚齿刀加工的数学模型。采用 MATLAB 与 CAD 相结合的方式提取

椭圆齿轮的齿廓包络线。

2.对椭圆齿轮的设计参数进行探讨，分析了设计参数对椭圆齿轮加工过程中出现齿根

切除现象的影响。齿轮长半轴与滚齿刀齿形角越大，越不容易发生齿根切除现象；齿轮偏

心率与滚齿刀安装位置越小，越不容易发生齿根切除现象。此外，椭圆齿轮的传动特性，

例如齿轮系统的传动比、从动轮的转角变化速度、变化加速度、齿轮不同轮齿啮合过程中

压力角和重合度会随偏心率的变大出现增加的趋势。并且齿轮不同轮齿的齿廓角不同，会

随着齿轮排号顺序出现周期性的规律。以及随着齿轮的负载转矩加大，椭圆齿轮传动系统

受到的扭矩波动也会变剧烈。

3.利用 Recur Dyn 构建椭圆齿轮传动系统啮合接触的有限元仿真模型，分析了齿轮中端

面是椭圆齿轮啮合过程中的重要区域。并划分轮齿编号及沿齿高方向的不同区域，分析出

齿轮在啮合过程中等效应力最大的区域。

4.通过疲劳分析，得出齿轮啮合过程中的疲劳危险点，论证了上文的理论。最后，分析

出在不同承载和摩擦系数的条件下，椭圆齿轮的疲劳寿命的变化趋势。

关键词：椭圆齿轮；参数设计；固有特性；啮合特性；疲劳寿命

湖南理工学院硕士学位论文 Abstract

Abstract

Gears are widely used in machinery and equipment，it has stable and accurate transmission

characteristics, and it's one of the most important component. But the traditional gear can only

transfer the same speed ratio motion, in order to meet the requirements of new and complex

transmission function, elliptical gear came into being. Compared with the traditional gear, elliptical

gear not only transfers the motion with constant angular velocity into the variable motion with

certain regularity, but also has the advantages of stable transfer motion, compact structure and also

can meet the special transmission function. With the application of elliptical gear more and more

widely and the unique properties in transmission, it is important to study the influence of design

parameters of elliptical gear on its transmission characteristics, and it's also important to analysis

the meshing properties of elliptic gear tooth surface under load.

The research object of this paper is the first order elliptical gear, and the research methods in

this paper are theoretical research and finite element simulation. The transmission characteristics,

meshing characteristics and fatigue life of elliptical gear in practice were studied, the main research

contents are as follows:

1. An accurate and efficient elliptic gear modeling method was proposed. The mathematical

model of elliptic gear hobbing was constructed by simulating hobbing on the surface of the blank.

And the profile envelope of elliptical gear was extracted by combining MATLAB and CAD.

2. The design parameters of elliptic gear were discussed and the influence of design

parameters on the root excision phenomenon in the process of elliptic gear machining was analyzed.

The research showed that the larger the tooth Angle between the long shaft of gear and the hobbing

cutter, the more difficult to remove the tooth root; the smaller the gear eccentricity and hob

installation position, the more difficult to remove the tooth root. In addition, transmission

characteristics of elliptical gears, such as the transmission ratio of the gear system, the change speed

of the rotation angle of the driven wheel, the change acceleration, the pressure angle and the contact

degree of different gear teeth during the engagement process will increase with the increase of the

eccentricity. And the tooth profile angle of different gear teeth is different, the gear alignment

sequence will appear periodic rule. As the load torque of the gear increases, the torque fluctuation

of the elliptical gear transmission system will become severe.

3. The finite element simulation model of meshing contact of elliptical gear transmission

system was constructed by Recur Dyn, the results showed that middle face of gear face is an

湖南理工学院硕士学位论文目录

摘要......................................................................................................................... I

Abstract ..................................................................................................................... II

目录...................................................................................................................... IV

第 1 章绪论 ........................................................................................................ 1

1.1 研究背景及意义 ............................................................................................................... 1

1.2 椭圆齿轮国内外研究现状 ............................................................................................... 3

1.2.1 椭圆齿轮设计研究现状 ........................................................................................ 3

1.2.2 椭圆齿轮制造研究现状 ........................................................................................ 4

1.2.3 椭圆齿轮啮合特性研究现状 ................................................................................ 6

1.3 研究目的、研究内容及技术路线 ................................................................................... 7

1.3.1 研究目的 ................................................................................................................ 7

1.3.2 研究内容 ................................................................................................................ 7

1.3.3 技术路线 ................................................................................................................ 8

第 2 章椭圆齿轮滚齿仿真加工过程的研究 ........................................................ 9

2.1 滚齿加工原理 ................................................................................................................... 9

2.2 椭圆齿轮齿廓形成原理 ................................................................................................... 9

2.3 椭圆齿轮滚齿加工过程及数学模型 ............................................................................... 9

2.3.1 数学模型 ................................................................................................................ 9

2.3.2 简化数学模型 ...................................................................................................... 10

2.4 椭圆齿轮滚齿加工运动模型 ......................................................................................... 12

2.4.1 节曲线仿真 .......................................................................................................... 12

2.4.2 滚齿刀端面数学模型 .......................................................................................... 14

2.5 椭圆齿轮滚齿加工齿廓成形仿真 ................................................................................. 15

2.6 本章小结 ......................................................................................................................... 16

第 3 章椭圆齿轮的参数设计和固有特性分析 ..................................................17

3.1 设计参数对椭圆齿轮根切的影响 ................................................................................. 17

3.1.1 椭圆齿轮的根切机理 .......................................................................................... 17

3.1.2 椭圆齿轮根切极限函数 ...................................................................................... 18

3.1.3 参数设计对椭圆齿轮根切的影响趋势 .............................................................. 18

3.2 椭圆齿轮的固有特性分析 ............................................................................................. 21

湖南理工学院硕士学位论文 Abstract

3.2.1 椭圆齿轮传动系统的设计 .................................................................................. 21

3.2.2 传动比 .................................................................................................................. 22

3.2.3 压力角 .................................................................................................................. 23

3.2.4 重合度 .................................................................................................................. 25

3.2.5 齿廓角 .................................................................................................................. 26

3.2.6 负载波动性 .......................................................................................................... 27

3.3 本章小结 ......................................................................................................................... 30

第 4 章椭圆齿轮的啮合特性分析 ......................................................................31

4.1 椭圆齿轮啮合仿真的准备工作 ..................................................................................... 31

4.1.1 椭圆齿轮的三维建模 .......................................................................................... 31

4.1.2 软件 Recur Dyn 的介绍 ...................................................................................... 32

4.2 椭圆齿轮刚性分析 ......................................................................................................... 33

4.3 椭圆齿轮动态啮合分析 ................................................................................................. 34

4.4 椭圆齿轮在齿高方向的动态啮合特性分析 ................................................................. 36

4.5 椭圆齿轮在不同方向的动态啮合特性分析 ................................................................. 39

4.6 本章小结 ......................................................................................................................... 40

第 5 章椭圆齿轮疲劳寿命分析 ..........................................................................41

5.1 名义应力法 ..................................................................................................................... 41

5.2 线性损伤累积理论 ......................................................................................................... 41

5.3 椭圆齿轮疲劳寿命分析 ................................................................................................. 42

5.3.1 椭圆齿轮材料的 S-N 曲线 ................................................................................. 42

5.3.2 椭圆齿轮疲劳寿命仿真分析 .............................................................................. 43

5.4 运行参数对椭圆齿轮疲劳寿命的影响 ......................................................................... 44

5.4.1 不同负载对椭圆齿轮疲劳寿命的影响 .............................................................. 44

5.4.2 不同表面粗糙度对椭圆齿轮疲劳寿命的影响 .................................................. 45

5.5 本章小结 ......................................................................................................................... 46

第 6 章结语 ......................................................................................................47

6.1 结论 ................................................................................................................................. 47

6.2 展望 ................................................................................................................................. 47

参考文献 ..................................................................................................................49

攻读硕士学位期间主要研究成果 ..........................................................................54

致谢.......................................................................................................................55

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