摘 要

本文借助软件MATLAB针对以质量-弹簧-带模型为理论基础搭建的摩擦自激振动试验台进行了数值仿真模拟。介绍并总结了现有的几种经典的摩擦理论模型。结合试验台，采用库伦摩擦模型，Stribeck摩擦模型，LuGre摩擦模型等构建了相应的自激系统和数学模型，并进行MATLAB数值仿真，分析了摩擦自激振动系统在不同参数下的振动特性。所得结果对于研究摩擦自激振动机理具有一定的参考意义。

论文主要研究了以摩擦自激振动试验台和Stribeck摩擦模型为基础构建的自激系统，用MATLAB数值仿真方法分析得到了摩擦自激振动系统在不同速度，不同刚度，不同加载以及不同摩擦系数下的振动特性。

研究结果表明：Stribeck摩擦模型相对适用性较强，仿真结果表明，减小加载和动静摩擦系数差值以及增加刚度，系统中的粘滞阶段会减小，系统会由不稳定逐渐变为稳定。提高速度，能消除宏观现象上的自激振动。

关键词：摩擦自激振动 摩擦模型 MATLAB仿真

Abstract

In this thesis, a numerical simulation is carried out on the friction self - excited vibration test bed based on the mass - spring - belt model. I introduced and summarized several existing classical models of friction theory. The corresponding self - excited system and mathematical models are constructed by using the Coulomb friction model, the Stribeck friction model and the LuGre friction model. The vibration characteristics of the self - excited vibration system under different parameters are analyzed by MATLAB numerical simulation. The results are of some reference significance for studying the mechanism of friction self - excited vibration.

In this thesis, the self-excited system based on the friction self-excited vibration test bed and the Stribeck friction model are mainly studied. The friction self-excited vibration system is analyzed by MATLAB numerical simulation method under different speed, different stiffness, different loading and different friction coefficient Of the vibration characteristics.

The results show that the Stribeck friction model has a strong applicability. And the simulation results show that ,when reduced the difference of the loading and the dynamic ,and increased static friction coefficient ,the viscous phase of the system will decrease and the system can also become unstable .Improving the speed is a good way to eliminate the macroscopic phenomenon of self-excited vibration.

Key Words：frictional self-excited vibrating；friction model；MATLAB simulation

目 录

第1章 绪论 1

1.1 课题来源 1

1.2 研究现状 1

1.3 存在问题及发展趋势 2

第2章 摩擦自激振动试验台 4

第3章 摩擦模型 6

3.1 库伦摩擦模型 6

3.2 Stribeck摩擦模型 6

3.3 LuGre摩擦模型 8

3.4 摩擦模型分析与总结 9

第4章 数值仿真 10

4.1 基于库伦模型的自激系统数值仿真 10

4.2 基于负阻尼模型的自激系统数值仿真 13

4.3 基于LuGre模型的自激系统数值仿真 15

4.4 基于Stribeck模型的自激系统数值仿真 17

4.4.1不同速度的振动特性 18

4.4.2 不同刚度的振动特性 20

4.4.3 不同加载的振动特性 22

4.4.4 不同摩擦系数的振动特性 23

第5章 试验台搭建理论分析 27

5.1 基于库伦模型的质量块-弹簧理论分析 27

5.2 基于Stribeck模型的质量块-弹簧理论分析 28

5.3理论方案及总结 29

第6章 总结 30

参考文献......................................................................................................................................31

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附录D..........................................................................................................................................35