齿轮-轴承系统非线性混沌控制参数摄动与轨道偏差分析  

Nonlinear chaos control parametric perturbation and orbital deviation of a gear-bearing system

作　　者：林何 王三民[2] RATSCH Matthias 胥光申[1] LIN He;WANG Sanmin;RATSCH Matthias;XU Guangshen(School of Mechanical and Electrical Engineering,Xi’an Polytechnic University,Xi’an 710048,China;School of Mechanical Engineering,Northwestern Polytechnic University,Xi’an 710072,China;School of Engineering,Reutlingen University,Reutlingen 72762,Germany)

机构地区：[1]西安工程大学机电工程学院,西安710048 [2]西北工业大学机电学院,西安710072 [3]Reutlingen University School of Engineering,Reutlingen 72762

出　　处：《振动与冲击》2020年第15期250-256,265,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(51805402);陕西省自然科学基础研究计划项目(2019JQ-851);陕西省教育厅科研计划项目(18JK0351)。

摘　　要：针对齿轮-轴承系统混沌响应减振控制问题,建立了含多间隙的系统非线性振动模型,模型中考虑了齿侧间隙、轴承径向间隙等非线性激励因素。通过系统状态模型与变分转换求解了Jacobi矩阵与敏感度矢量,结合微分流形理论和OGY(Ott-Grebogi-Yorke)控制法对混沌吸引子高周期轨道控制不稳定维数变异情形改进控制条件;采用Newton-Raphson数值法搜寻到混沌吸引子内部镶嵌的P8和P10等不稳定周期轨道不动点,发现二者Jacobi矩阵特征值谱中均存在模为1的临界复共轭特征根,目标周期轨道表现非双曲性。以轴承预载荷为名义控制参数,对P1、P2、P4、P8和P10等周期的多阶段控制表明状态迁移点附近存在短暂混沌瞬态振荡,高周期轨道控制精度下降、轨道偏差增高,控制稳定后参数摄动按受控周期轨道状态规律演化。Aiming at chaotic vibration control problems of a gear-bearing system, its nonlinear dynamic model with multi-clearance was established considering nonlinear excitation factors including backlash, bearing radial clearance, etc. The system state model and variational transformation were used to solve Jacobi matrix and sensitivity vector. Then combining the differential manifold theory and Ott-Grebogi-Yorke(OGY) chaos control method, the control condition for the unstable dimension variation of high period orbit control of chaotic attractor was improved. Newton Raphson numerical method was used to search fixed points of unstable periodic orbits, such as, P8 and P10 embedded in chaotic attractor, and find that there are critical complex conjugate eigenvalues of module 1 in eigenvalue spectra of both their Jacobi matrices, and the target’s periodic orbits are non-hyperbolic. The multi-stage control of periods P1, P2, P4, P8 and P10 with bearing preload as the nominal control parameter showed that there is short-term chaotic transient oscillation near the state transfer point;the control accuracy of high cycle orbit decreases, the orbit deviation increases;the parametric perturbation evolves according to the controlled cycle orbit state law after the control is stable.

关 键 词：混沌控制 JACOBI矩阵 非双曲性 参数摄动 轨道偏差 

分 类 号：TH131.1[机械工程—机械制造及自动化]