基于OGY的含间隙单级齿轮系统混沌运动控制

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (14) : 17-21.

论文

田亚平1，徐璐1，宋佩颉1，褚衍东2

作者信息 +

Chaos control of a single-stage spur gear system with backlash based on the OGY method

TIAN Yaping1，XU Lu1，SONG Peijie1，CHU Yandong2

Author information +

文章历史 +

摘要

针对含齿侧间隙和轴承支承间隙的单级齿轮系统在部分参数区域内的混沌运动，用改进的OGY混沌控制原理实现了混沌吸引子内部不稳定周期轨道的稳定化。通过有限差分法替代非光滑点Jacobi矩阵实现光滑系统的OGY控制向非光滑多维系统转变，用PNF法搜索混沌区域内不稳定周期伪不动点，根据动力学方程和变分形式，求解改进OGY算法中的Jacobi矩阵和敏感度列向量，结合Poincaré映射截面解析了混沌吸引子向多周期轨道转迁时的轨道间隔及迁移特性。仿真结果表明改进后的OGY控制法对高维非光滑齿轮系统混沌控制同样有效；多周期轨道持续控制时随目标周期轨道增加控制难度增大，所需参数摄动量相应增加。

Abstract

For the chaotic motion of a single-stage gear system with tooth backlash and bearing clearance in some parameter region, the unstable periodic orbit of chaotic attractor was stabilized by improved OGY chaotic control principle. The OGY control for a smooth dynamic system was transformed to a non-smooth multi-dimensional dynamic system by the finite difference method instead of the Jacobi matrix under non-smooth point. And PNF method is used to search the pseudo-fixed points of unstable periodic in chaotic region. The Jacobi matrix and sensitivity column vectors in the improved OGY algorithm were solved according to the dynamic equation and variation form, the periodic orbital interval and transfer characteristics of chaotic attractor were analyzed combined with Poincaré mapping. The simulation results show that the improved OGY control method is also effective for chaos control of multi-dimensional non-smooth gear systems. When the multi-period orbit was continuously controlled, the difficulty of chaos control increases with the increase of the target periodic orbit, and the required parameter perturbation increases correspondingly.

关键词

单级齿轮传动 / 混沌吸引子 / OGY控制 / 不稳定周期轨道 / 齿侧间隙

Key words

single-stage spur gear system

/ chaotic attractors / unstable periodic orbit / OGY chaotic control method / gear backlash

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导出引用

田亚平1，徐璐1，宋佩颉1，褚衍东2. 基于OGY的含间隙单级齿轮系统混沌运动控制[J]. 振动与冲击, 2020, 39(14): 17-21

TIAN Yaping1，XU Lu1，SONG Peijie1，CHU Yandong2. Chaos control of a single-stage spur gear system with backlash based on the OGY method[J]. Journal of Vibration and Shock, 2020, 39(14): 17-21

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