摘要齿轮传动系统是各类机械系统和机械装备的主要传动系统，齿轮系统振动特性直接影响机械系统和机械装备的性能和工作可靠性。由于齿面摩擦、齿侧间隙及时变啮合刚度等因素的存在，导致齿轮传动系统成为一个复杂的强非线性动力学系统。43655

本文主要研究在考虑摩擦和时变刚度时，轮齿间隙等对齿轮系统动力学响应的影响，建立包含摩擦、时变刚度和齿侧间隙的单对齿轮系统振动模型，推导综合考虑时变刚度、齿侧间隙、传递误差等非线性因素的振动微分方程。运用四阶Runge-Kutta方法计算系统在无冲击、单边冲击和双边冲击状态下，系统参数、载荷参数对系统振幅及稳定性的影响。利用数值仿真的方法得到系统的幅频响应曲线和时间历程曲线。数值仿真表明：考虑时变刚度、齿面摩擦、齿侧间隙等非线性因素时齿轮系统具有复杂的振动特性。随着摩擦因数、间隙幅值的增大，系统提前进入混沌运动状态。

毕业论文关键词：摩擦；间隙；非线性；齿轮系统

Abstract Gear transmission system is the main driving system of chanical system and mechanical equipment, acteristic of gear system directly affect the performance and working reliability of the mechanical system and mechanical equipment. Because of the teeth surface friction、backlash and time-varying mesh stiffness and other factors existing, gear transmission system becomes a complex nonlinear dynamic system.

The chief objective is to study the effect of backlash on nonlinear dynamic response of spur gear pair system with consideration of friction and time-varying stiffness,creat single on gear vibration model which includes the establishment of friction, time-varying stiffness and backlash。Time-varying stiffness and tooth bacldash vibration model is set up and the vibration differential equations are deduced via comprehensively taking time—varying stiffness，tooth backlash and dynamic transmission error nonlinear factor into consideration．Non-impact，single-impact and double-impact arenumerically simulated by fourth-order Runge-Kutta method．The effects of system parameters and load parameters on the system of the ampfitude and vibration stabifitv are calculated.The simulation results show that：gear system exhibits complex vibration behaviors in considering time-varying stiffness、gear tooth friction and tooth backlash non-1inear factors．With the increase of friction coefficient and time—varying backlash，the system enters into chaotic motion state。.

Keywords: Friction；Clearance；Non—linear；Gear system

目  录

第一章  绪论 1

1.1 研究背景及意义 1

1.2 齿轮系统的非线性动力学研究现状及发展 1

1.3 本文的主要内容 3

第二章  齿轮传动系统动力学的基本内容 5

2.1 齿轮传动系统的动态激励 5

2.1.1 齿轮传动系统的外部激励 6

2.1.2 齿轮传动系统的刚度激励 6

2.1.3 齿轮传动系统的误差激励 7

2.1.4  齿轮传动系统的啮合冲击激励 8

2.2 齿轮传动系统动态特性 8

第三章  直齿轮系统非线性动力学模型 10

3.1 建立直齿轮系统动力学模型 10

3.1.1 非线性动力学模型及其方程的建立 10