摘 要

非圆齿轮分割器相比传统分度机构具有分度数大，结构紧凑，传动精确，效率高等优点，但在高速、重载的情况下能否继续满足其运转平稳的要求已成为影响其在实际生产运用范围的最重要的因素之一。再者，由于非圆齿轮分割器尚处于设计研究阶段,其设计与制造的理论依据并不完善成熟,对其动力学特性进行的理论研究少有涉及，因此开展这一方面的研究是十分必要的。

论文就非圆齿轮分割器的动态特性这一主题展开研究，就如下几个方面进行深入分析：

在考虑非圆齿轮分割器中各啮合齿轮的啮合刚度，行星轴的扭转刚度和支承轴承的支承刚度后，用集中质量法和牛顿第二定律建立了非圆齿轮分割器的整机动力学模型，整个系统共具有六个自由度。根据非圆行星齿轮节曲线的变化规律，采用节曲线分段近似的方法对非圆齿轮进行圆柱齿轮的等效转化，整个非圆齿轮啮合副可转化成三组不同的圆柱齿轮副的啮合过程的组合。在计算非圆齿轮转动惯量时，用三次样条插值和多项式拟合的数值方法近似求解出非圆齿轮节曲线在非圆部分的近似表达式，由此分析并计算出各零部件的转动惯量和刚度。根据多自由度系统振动理论，用MATLAB编程求解出整机的固有频率。

将非圆齿轮近似等效为圆柱齿轮附加偏心块的组合体形式，对分割器内各零部件的激振频率进行了分析。采用三维造型软件CREO建立非圆齿轮分割器的各零件三维实体模型，将模型导入至ANSYS有限元分析软件中,分别求解出分割器各零部件的固有频率和振型,将分析结果分别和整机固有频率与零件激励力频率进行比较分析，得出整个分割器系统的动态特性优良程度。

根据模态分析的结果，讨论分析得出主要零件的结构优化方案。主要是对圆柱行星齿轮进行齿数和模数的改进。在对齿轮轴进行齿数和模数上的改进之外，还削减了轴段部分的质量。在结构改进之后对每一个方案再次进行模态分析，对比优化前的固有模态，分析表明齿轮的啮合频率与整机固有频率差距进一步增大，齿轮轴的固有频率已不在整机固有频率的频率带之内。整体动态特性得到进一步加强，在理论上证明了方案的正确性。

关键词：非圆齿轮传动；动力学模型；固有频率；结构优化

Abstract

Compared to traditional indexing mechanism,divided number of non-circular gear splitter is larger.Besides,it has other advantages,such as compact structure,precise transmission,higher efficiency and so on.However,one of the most important factors which effect its application range is that whether this machine could work regularly if it would be in condition of high velocity and overloading.The theories of designing and manufacture for non-circular gear spitter which is in designing research stage is not mature and complete.Therefore, it is very necessary to study the dynamic characteristics of the system.

In this dissertation, the dynamic characteristics of the non- circular gear segment is presented further analysis, ,and the following aspects are analyzed:

First of all,in consideration of primary parts and bearing stiffness,this paper create the dynamic model of the entire system with lumped mass method and Newton's second law. The whole system has six degrees of freedom.According to the variation of pitch curve of Non-circular Planetary gear.Then, non circular gear is transformed equivalently to cylindrical gear with the pitch curve piecewise approximation.Therefore, the non circular gear meshing pair can be transformed into a combination of three groups of different cylindrical gear pair meshing process. According to cubic spline interpolation and polynomial fitting method , approximate expressions for the noncircular part of non circular gear pitch curve can be solved. Afterwads, the various components of the inertia and stiffness is calculated respectively. According to the theory of multi degree of freedom system vibration, the natural frequency of the whole machine is solved by MATLAB programming.

Secondly,the non circular gear is approximately equivalent to the combination of cylindrical gear with eccentric block, and the excitation frequency of each component is analyzed. excitation frequency of each part in the splitter are analyzed, using three-dimensional modeling software Creo establish 3D solid model of non-circular gear splitter. The model is imported into the ANSYS finite element analysis software, and then inherent frequency and vibration type of all parts of segmentation are solved respectively. The analysis results are compared with the natural frequency and the frequency of the excitation force, and the dynamic characteristics of the whole system are obtained.

According to the results of whole natural frequency of the whole of sysytem and parts, the optimization scheme for the structure of primary parts should be concluded. Improvement of tooth number and modulus of cylindrical planetary gear.As for gear shaft, the number of teeth on the gear shaft and the number of modules can be improved, and cut the quality of the shaft section. The improvement of every scheme is again modal analysis after structure is optimized. compared with before the optimization modal analysis show that gear meshing frequency and the whole inherent frequency gap further increase, the natural frequency of the gear shaft is not in the natural frequency of the whole frequency band. The overall dynamic characteristics are further strengthened, and the correctness of the scheme is proved in theory.

Key Words: non-circular gear transmission; dynamic model; natural frequency; optimization for structure

目录

摘要 3

Abstract 4

1 绪论 1

1.1 课题研究背景目的及意义 1

1.2 国内外发展现状及分析 2

1.2.1 分度机构国内外发展现状 2

1.2.2 非圆齿轮国内外发展现状 2

1.2.3 非圆齿轮动力学国内外发展现状 3

1.3 机械系统动力学问题的研究内容 4

1.4 非圆齿轮分割器的工作原理 5

1.5 以往研究的不足及本文的研究内容 5

1.6 本章小结 6

2 系统动力学模型的建立 8

2.1 引言 8

2.2 非圆齿轮分割器的动力学分析过程 9

2.3 非圆齿轮分割器的动力学模型的建立 10

2.3.1 非圆齿轮等效简化为圆柱齿轮 10

2.3.2 非圆齿轮分割器物理模型的建立 11

2.3.3 各个组件相互作用的弹性变形 12

2.3.4 非圆齿轮分割器的动力学微分方程 12

2.4 本章小结 14

3 非圆齿轮分割器动力学模型的求解 15

3.1 引言 15

3.2 固有频率和模态向量求解方法 15

3.3 MATLAB软件概述 17

3.3.1 MATLAB功能特点概述 17

3.3.2 MATLAB程序求解过程 18

3.4 系统主要质量的计算 19

3.4.1 非圆齿轮转动惯量的计算 19

3.4.2 普通圆柱齿轮的转动惯量的计算 20

3.4.3 行星架的转动惯量计算 21

3.5 等效圆柱齿轮的计算 21

3.5.1 非圆齿轮等效分析过程 21

3.5.2 非圆齿轮的等效计算 22

3.6 系统主要刚度的计算 23

3.5.3 轴承刚度计算 23

3.5.4 行星轴的扭转刚度计算 24

3.5.5 齿轮的啮合刚度计算 25

3.7 非圆齿轮分割器的整机固有频率计算 26

3.8 本章小结 27

4 有限元模态分析 29

4.1 有限元分析简介 29

4.1.1 有限元法简介 29

4.1.2 有限元法的特点 30

4.1.3 ANSYS简介 30

4.1.4 ANSYS分析步骤 30

4.2 模态分析概念及过程 31

4.2.1 模态分析的基本概念 31

4.2.2 模态分析的主要步骤 31

4.3 非圆齿轮分割器激振频率分析 32

4.3.1 由非圆齿轮结构不对称引起的激振频率 32

4.3.2 齿轮啮合频率 33

4.3.3 行星齿轮的转速 33

4.3.4 行星架激振频率 34

4.4 建立几何模型 34