基于OGY的含间隙单级齿轮系统混沌运动控制  

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

作　　者：田亚平[1] 徐璐[1] 宋佩颉 褚衍东[2] TIAN Yaping;XU Lu;SONG Peijie;CHU Yandong(School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;Key Laboratory of System Dynamics and Reliability of Rail Transport Equipment of Gansu Province,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070 [2]兰州交通大学,甘肃省轨道交通装备系统动力学与可靠性重点实验室,兰州730070

出　　处：《振动与冲击》2020年第14期17-21,35,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(11262009,11462012);高等学校博士学科点专项科研基金(20136204110001);兰州市人才创新创业项目(2015-RC-3)。

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,用伪不动点法(PNF)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。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 a chaotic attractor was stabilized by the improved OGY chaotic control principle. The OGY control for a smooth dynamic system was transformed into that for a non-smooth multi-dimensional dynamic system by the finite difference method instead of the Jacobi matrix under non-smooth point. And the Poincaré-newton-floquet(PNF) method was used to search the unstable periodic pseudo-fixed points in chaotic regions. 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 the chaotic attractor were analyzed by combined use of the Poincaré mapping. The simulation results show that the improved OGY control method is also effective for the chaos control of multi-dimensional non-smooth gear systems. When the multi-period orbit is 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 

分 类 号：TH132.425[机械工程—机械制造及自动化] O322[理学—一般力学与力学基础]