外部动态激励作用下齿轮系统非线性动力学特性  

Non-Linear Dynamics of Spur Gear Pair under External Periodic Excitation

作　　者：李应刚[1,2] 陈天宁[1,2] 王小鹏[1,2] 于坤鹏[1,2] 周汉[1,2] 张哲[1,2] 

机构地区：[1]西安交通大学机械工程学院,西安710049 [2]西安交通大学机械结构强度与振动国家重点实验室,西安710049

出　　处：《西安交通大学学报》2014年第1期101-105,共5页Journal of Xi'an Jiaotong University

基　　金：国家科技重大专项资助项目(2012ZX04012-032);长江学者和创新团队发展计划资助项目(IRT1172)

摘　　要：为了研究外部动态激励作用下齿轮系统非线性动力学特性,建立了考虑周期时变刚度、齿侧间隙、黏弹性阻尼和外部动态激励的单自由度直齿轮副系统动力学模型。针对外部动态激励作用下的周期时变刚度、齿侧间隙、激励幅值和阻尼比对齿轮副系统动力学特性的影响,采用增量谐波平衡法来求解齿轮副系统的稳态周期响应,并采用四阶变步长Runge-Kutta数值方法进行了验证。研究结果表明,增量谐波平衡法求解结果与数值仿真结果吻合得较好,齿轮系统在外部动态激励作用下会引起参数共振、多值解和幅值跳跃等非线性动力学行为,增大激励幅值和阻尼比等参数,能够有效控制齿轮系统的非线性振动响应。Under external periodic excitation, the dynamic model of a single-degree-of-freedom spur gear pair with periodic time-varying stiffness, backlash and viscous damping is established. The incremental harmonic balance method （IHBM） is applied to analyze the dynamic responses of the gear pair system. A comparison with Runge-Kutta integration results shows the accuracy and authority of IHBM. The effects of the periodic time-varying stiffness, backlash, excitation amplitude and viscous damping ratio on the dynamic characteristics of gear pair system are investigated. It indicates that the time-varying factors and backlash under periodic excitation usually lead to parametric resonance, multi-valued properties and amplitude jump phenomena. The enhanced excitation amplitude and the damping ratio facilitate controlling the nonlinear vibration.

关 键 词：齿轮系统 外部动态激励 增量谐波平衡法 非线性动力学 

分 类 号：O121.8[理学—数学] G558[理学—基础数学]