弹性轨道上磁浮车辆动力稳定性判断方法

分析了EMS型磁浮车辆的动力稳定性, 建立了简化的车轨耦合振动系统动力学模型, 推导了轨道各模态单独作用下系统的时变线性化动力学方程。通过对方程的化简, 得到系统状态矩阵和特征方程的相关系数, 根据系统渐进稳定条件下系数之间的关系, 推导了系统动力稳定应满足的基本条件, 并给出了快速判断动力稳定性的判据。当判据值大于1时, 系统稳定; 当判据值小于1时, 系统不稳定。研究结果表明: 当6种工况的速度分别为100、180、260、340、420、500km·h^-1, 抗弯刚度分别为4.83×1010、3.86×1010、3.38×1010、3.38×1010、3.86×1010、4.83×1010 N·m2, 轨道梁长度分别为24.8、22.4、20.4、20.4、22.4、24.8m时, 求得对应的稳定性判据值分别为1.639、0.624、2.339、0.870、3.252、0.571, 对应的Lyapunov特性指数分别为-3.580×10^-2、2.443×10^-1、-3.910×10^-2、1.515×10^-1、-5.471×10^-2、1.939×10^-1, 工况1、3、5的稳定性判据值大于1, 对应的Lyapunov特性指数小于0, 系统是稳定的, 工况2、4、6的稳定性判据值小于1, 对应的Lyapunov特性指数大于0, 系统是不稳定的, 2种判断结果一致, 因此, 提出的判据是有效的。而且稳定性判据解释了随着车辆速度增加而出现共振的原因, 揭示了车辆速度、车轨系统主要参数与磁浮车辆动力稳定性之间的关系, 避免了高维动力学微分方程求解的复杂性, 工程应用简便。

Judgment method of maglev vehicle dynamic stability on flexible track

The dynamic stability of EMS maglev vehicle was analyzed, a simplified dynamics model of vehicle-track coupling vibration system was set up, and the time-varying linear kinetics equations of the system were deduced based on each track mode separately.The state matrix and the correlation coefficients of characteristic equations for the system were produced by simplifying the equations.The basic conditions of the system on dynamic stability were derived from the proper relationship among the coefficients under the condition of asymptotically stable system, and the quick dynamic stability criterion was given.When the criterion value was greater than 1, the system was stable.When the criterion value was less than 1, the system was unstable.Research result indicates that when the speeds of 6kinds of working conditions are 100, 180, 260, 340, 420, 500km·h-1 respectively, the track bending stiffnesses are 4.83×1010, 3.86×1010, 3.38×1010, 3.38×1010, 3.86×1010, 4.83×1010 N·m2 respectively, and the track beam lengths are 24.8, 22.4, 20.4, 20.4, 22.4, 24.8mrespectively, the stability criterion values are1.639, 0.624, 2.339, 0.870, 3.252, 0.571 respectively, and the related Lyapunov characteristic exponents are-3.580×10-2, 2.443×10-1, -3.910×10-2, 1.515×10-1, -5.471×10-2, 1.939×10-1 respectively.Under conditions 1, 3, 5, the stability criterion values are greater than1, the related exponents are less than 0, so the system is stable.Under conditions 2, 4, 6, the stability criterion values are less than 1, the related exponents are greater than 0, so the system is unstable.The two judgment results are coincident, so the criterion is reliable.the stability criterion explains the reason of resonance caused by vehicle speed increase, reveals the relationship among maglev vehicle dynamic stability, vehicle speed and vehicle-track system main parameters, avoids the complexity to solve high-dimension dynamics differential equation, and is simpler and more convenient in engineering application.