齿轮-轴承系统非线性振动混沌吸引子周期轨道控制

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摘要

考虑轴承支撑齿轮传动系统建立了含多间隙的系统非线性动力学模型，模型中考虑了时变啮合刚度和综合传动误差等因素。基于OGY混沌控制改进策略对高维非双曲齿轮系统实施了多周期混沌控制，采用Newton-Raphson迭代法搜寻了P1、P2、P4和P8等多组不稳定周期轨道（UPO, Unstable periodic orbits）不动点，求解了各UPO解对应的Jacobi矩阵特征值和局部参数敏感度矢量，结合Poincaré截面等工具解析了混沌吸引子向P10周期轨道转换时的轨道间隔及迁移特性。在2000周期步下对混沌吸引子实施了P1、P2、P4、P8和P10等多种周期组合式控制，结果表明在状态转换阶段，尤其30周期步内控制参数摄动量发生激增，此后恢复稳定且保持与目标控制轨道相同周期的状态演化；多周期轨道持续控制时周期状态越高，控制难度越大，所需参数摄动量相应增加。研究结果在理论上有助于齿轮系统混沌响应减振控制。

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	林何1
	屈文宽1
	MATTHIAS Rtsch2
	王三民3

关键词 ：混沌吸引子, 混沌控制, 不稳定周期轨道, Jacobi矩阵, 组合式控制

Abstract：Nonlinear dynamical model of a gear-bearing system with multiple clearances is built, time-varying meshing stiffness and general transmission error are involved too. Several periodic orbit controls for high-dimensional non hyperbolic gear system is performed based on a proposed improved OGY chaos control strategy, the saddle points of unstable periodic trajectories of P1, P2, P4 and P8 (UPO) are obtained by applying Newton-Raphson iteration algorithm, and the eigenvalues of Jacobi matrix as well as local parameter sensitivity vectors with respect to UPO are investigated, the trajectory interval and transition behaviors of chaotic attractors onto P10 periodic orbit are analyzed by employing Poincaré section as well. The chaotic attractor is performed by combinatorial control with multiple states in terms of P1, P2, P4, P8 and P10 under 2000 periodic steps, the results show that excitation parameter increases significantly during transition period, especially within 30 periods, parameter excitation keeps the same period state as target periodic orbits when trajectory goes stable; more difficulty occurs while higher integrated periodic trajectories controlled, meanwhile, parameter perturbations increase accordingly. The investigations will theoretically contribute to eliminate and control the chaotic vibrations of gear system.

Key words： Chaotic attractors chaos control UPO Jacobi matrix combination control

收稿日期: 2018-11-21 出版日期: 2020-06-28

引用本文:

林何1，屈文宽1，MATTHIAS Rtsch2，王三民3. 齿轮-轴承系统非线性振动混沌吸引子周期轨道控制[J]. 振动与冲击, 2020, 39(13): 1-6.
LIN He1, QU Wenkuan1, MATTHIAS Rtsch2, WANG Sanmin3. Periodic orbit control of nonlinear vibration chaotic attractors of a gear-bearing system. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(13): 1-6.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I13/1

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