Abstract:

Aiming at researching the bifurcation and chaos characteristics of planetary reverse system with time-varying rotating speeds and torques, a nonlinear rotating vibration model was found. The differential equation of the system was salved with the Runge-Kutta numerical integration method, the bifurcation, phase plane and Poincare mapping were draughted to analyze the changing course, due to the outer inspiration. Additionally, the judgment of the system chaos state was made out by maximum Lyapunov exponent with the theory of chaotic time series. The results show that: in long stage of rotating speed, the system reaction will keep in single period motion with certain torque, but bifurcation, amplitude jump and state mutation occured at harmonic frequency, and jumped into chaos from single period motion at last. But the torque will restrain the trend to chaos, and the high enough torque will push the system from chaos back to single period motion.

Key words: planetary reverse system, nonlinear dynamics, bifurcation, chaos identification

摘要：

为分析行星换向机构在动态外部激励即转速和扭矩作用下的分岔及混沌特性,建立了该行星系统的非线性扭转振动模型。采用变步长4-5阶Runge-Kutta算法对动力学方程进行数值求解,根据仿真结果绘制了系统分岔图,并结合典型工况下的相图和庞加莱截面图,得到系统响应随外部激励的变化历程。另外,借助混沌时间序列分析理论,计算最大Lyapunov指数,对系统是否处于混沌状态进行判定。结果表明:在一定的扭矩作用下,随着转速的增大,系统在较长范围内维持单周期运动状态,但在共振频域附近因啮合冲击的出现而产生频繁的分岔行为、振幅跳跃及状态突变,且期间出现了倍周期、拟周期等状态以及状态之间的交替现象,并最终由周期状态突变为混沌状态;与此相反,扭矩的增大对系统随转速增大而进入混沌状态的趋势有一定的抑制作用,且扭矩增大至一定程度时可使系统由混沌状态退化为单周期运动状态。

关键词: 行星换向机构, 非线性动力学, 分岔, 混沌识别