摘要
针对含有时变啮合刚度的3自由度间隙非线性齿轮系统模型在其部分参数区间发生的混沌运动,提出一种多步混沌控制方法,借助该方法实现了系统混沌吸引子内部不稳定周期轨道的稳定化。建立3自由度齿轮系统的动力学模型,通过对其不稳定周期轨道结构的分析,观测到系统不稳定周期轨道的Jacobi矩阵存在位于单位圆上的复共轭特征值,以及周期轨道存在不稳定维数变异和稳定维数变异的现象,表明齿轮系统的非双曲性质。为了解决传统混沌控制方法不适用于非双曲系统的难题,分别以不稳定周期轨道的不稳定方向和稳定方向两种途径构造控制算法,通过连续的参数扰动将系统状态驱动到周期轨道点的局部稳定流形上。数值试验表明多步控制方法对于高维非双曲系统的长周期轨道控制是十分有效的。
Based on a three-degree-of-freedom nonlinear geared system with time-varying mesh stiffness and backlash, a multi-step chaos control method is presented to realize the stabilization of UPOs（Unstable period orbits） embedded in the chaotic attractor. Firstly, the nonlinear dynamics model of a gear pair system is established. By means of the analysis of the structure of system＇s UPOs, the existence of complex-conjugate eigenvalues on the unit circle along UPOs and unstable dimension or stable dimension variability of the UPOs indicate the nonhyperbolicity of the gear system. In order to resolv the difficulty that traditional chaos control method is not applicable to nonhyperbolic system, a multi-step method is set up in terms of the unstable and stable direction of UPOs respectively to drive the system state to lie on the local stable manifold of UPOs through continuous parametric perturbations. Numerical simulation proves the effectiveness of the control method for the UPOs even with long period in nonhyperbolic and high-dimensional system.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2006年第12期52-58,共7页
Journal of Mechanical Engineering
基金
国家自然科学基金(50075070)。
