摘 要

与传统减速传动装置相比，谐波减速器具有更大的传动比、更高的承载和传动精度、更小的体积和重量等优势，因而在各类高精尖领域，谐波减速器成为传动装置中的首选。本文根据谐波减速机的工况，确定谐波减速机的尺寸与型号，决定谐波减速机传动比，据此确定二齿差谐波减速机的齿数。基于MATLAB软件，根据谐波传动的共轭啮合关系，列出谐波减速机齿廓共轭啮合方程，求解刚柔轮共轭啮合区域；进而根据共轭区域通过坐标变换求出齿廓坐标数值解,从而得到谐波减速机轮齿齿廓，并基于SolidWorks软件建立谐波减速机刚轮、柔轮、波发生器三维实体模型。将三维实体模型导入ANSYS Workbench有限元分析软件中，对谐波减速机的装配过程与啮合过程进行了变形分析与应力分析，重点分析了柔轮与波发生器、柔轮与刚轮之间的接触情况，并比较柔轮变形理论值与有限元仿真结果，衡量文中数学模型简化的合理性。本文还分析了柔轮的频率特性。最后，对本文所应用的谐波传动技术进行了环保性与经济性的评估。

研究结果表明：本文数学模型的误差在合理范围之内，本文所设计的谐波减速机基本能够满足工作要求，但仍有进一步改善结构优化受力情况的空间。

关键词：谐波传动；有限元；仿真建模；MATLAB

Abstract

Compared with the traditional reduction gearbox, the harmonic reducer has the advantages of larger transmission ratio, higher bearing and transmission accuracy, smaller volume and weight, so the harmonic reducer becomes the first choice in the transmission of the most sophisticated field. According to the working condition of the harmonic reducer, this paper designed the size and model of the harmonic reducer, then the gear ratio of the harmonic reducer, and the number of teeth of the two-tooth difference type harmonic drive. Based on the MATLAB software, according to the conjugate meshing relationship of harmonic drive, the conjugate meshing equation of the harmonic reducer had been formed, and the conjugate meshing region of the rigid gear and flexible gear had been solved out. Then the coordinate value of the tooth profile of the conjugate region is obtained by coordinate transformation. Solution, so as to obtain the tooth profile of the harmonic reducer, and input into SolidWorks software to establish three-dimensional solid model of rigid gear, flexible gear and wave generator of the harmonic reducer. The 3D solid model was introduced into the ANSYS Workbench finite element analysis software. The deformation analysis and stress analysis of the assembly process and meshing process of the harmonic reducer were carried out. The analysis of the contact status between the flexible gear and the wave generator, between the flexible gear and the rigid gear was carried out. and compare the theoretical value of the deformation of the flexible gear with the finite element simulation results, to measure the rationality of the simplified mathematical model. This paper also analyzes the frequency characteristics of the flexible gear. Finally, the harmonic drive technology applied in this paper is evaluated for environmental protection and economy.

The research results show that the error of the mathematical model in this paper is within a reasonable range. The harmonic reducer designed in this paper can basically meet the working requirements, but there is still room to further improve the structural optimization of the force.

Key words: harmonic drive; finite element; simulation and modeling; MATLAB

目录

第1章 绪论 1

1.1 应用方向与前景 1

1.2 国内外研究概述 1

1.3 本课题的意义 3

第2章 谐波传动过程中柔轮的变形及其共轭啮合 4

2.1谐波传动柔轮变形模型的简化与假设 4

2.2谐波减速机各构件坐标系的建立及其坐标变换关系 6

2.3柔轮及其齿廓的初步设计 8

第3章 求谐波减速机齿廓的数值解以及谐波减速机实体模型的建立 12

3.1改进运动学原理介绍 12

3.2编写MATLAB程序求解刚柔轮齿共轭啮合区域 13

3.3求刚轮齿廓数值解 18

3.4建立谐波减速机主要零件的实体模型 21

第4章 谐波减速机的有限元分析 23

4.1谐波减速机装配过程有限元分析 23

4.2谐波减速机啮合过程有限元分析 33

4.3柔轮频率特性的分析 42

第5章 结论以及环保与经济性分析 45

5.1研究过程与结果总结 45

5.2环保与经济性评估 45

参考文献 47

致谢 48

第1章 绪论

1.1 应用方向与前景

减速器是机械传动中的核心部件，它在机械结构中常占有较大的重量与体积。但随着工业技术的飞快发展，在诸多需要使用精密机械的部门，如航空航天、医疗器械、机械臂等领域，传统的传动装置难以满足这些工作环境下对结构紧凑、能够在密闭条件下工作、具有稳定的传动性能等要求，因而在这些高度精密的领域中，谐波减速器成为传动装置中的首选。与传统减速传动装置相比，谐波减速器具有更大的传动比、更高的承载和传动精度、更小的体积和重量等优势^[1]。

在工业机器人领域，谐波减速器是重要的零部件。据统计，谐波减速器的成本占机器人总成本的30%以上。日本的Harmonic Drive公司占据了我国谐波减速器市场约大部分的份额。我国正处于工业机器人进步的时期，但谐波减速器自给率的低下，制约了我国工业的发展^[2]。因此，在现阶段研究优化谐波减速器的设计，对提升我国自主知识产权有着重要的意义。