三自由度齿轮传动系统的非线性振动及混沌控制

【作者】 刘晓宁；

【导师】 王三民；

【作者基本信息】 西北工业大学 ， 机械电子工程， 2003， 硕士

【摘要】 本文针对三自由度间隙非线性齿轮传动系统发生的混沌现象，采用增量谐波平衡法深入研究了齿轮传动系统的非线性振动特性，采用混沌控制方法中的连续变量反馈方法，对齿轮传动系统中的混沌运动有效的加以抑制。 在建立三自由度齿轮间隙非线性动力学模型的基础上，利用增量谐波平衡法获得了受到参数激励和外部谐波激励的三自由度齿轮传动系统模型的周期响应，包括稳定和不稳定的周期轨道，并利用Floquet理论研究其稳定性、分岔类型，对系统的参数变化进行分析，研究了系统通向混沌的倍周期分岔道路和拟周期分岔道路，绘制了系统周期解分岔图。 对现有的混沌控制方法的优缺点进行了比较，利用混沌控制理论中的连续变量反馈控制方法，实现了系统混沌吸引子内部的不稳定周期轨道的稳定化，对齿轮传动系统进行了有效的混沌控制，并对连续变量反馈方法的结果进行了分析，包括噪声的影响和方法的改进。更多还原

【Abstract】 This dissertation mainly studies the non-linear dynamics and chaotic motions of 3-d.o.f geared rotor-bearing system with piecewise linear clearance. The periodic motions of such model are investigated by the incremental harmonic balance(IHB) method. On this basis, using continuous feedback chaos control method, the chaotic motions are effectively suppressed in this system.The IHB method is used to obtain periodic motions of a 3-d.o.f non-linear model of a geared rotor system subjected to parametric and external harmonic excitations. The stability of the periodic motions is investigated by the Floquet theory, the bifurcation behavior is traced. Parametric studies are performed to understand the effect of system parameters such as excitation frequency and bearing damping ratio on the nonlinear dynamic behaviors. In addition to the familiar period doubling bifurcation scenario leading to chaos, a quasiperiodic route to chaos is also observed which occurs through an initial Hopf bifurcation.The current chaos control methods are compared, the stabilization of unstable periodic orbits of this chaotic system is achieved by continuous feedback control method, the specially designed external oscillator which used as target motion orbit in continuous feedback control method is obtained directly from IHB method. Also, the effect of noise and improvements on the control method are studied.更多还原