Nonlinear dynamics characteristics of maglev vehicle under track random irregularities
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摘要: 基于柔性轨道研究了随机不平顺下磁浮车辆的动力学特性, 在将轨道受力分解为分段链式结构的基础上, 提出了一种磁浮车辆垂向悬浮稳定性分析方法, 定义了不同悬浮力作用于各自悬浮点时柔性轨道的振动固有频率和模态矩阵; 建立了轨道分段链式结构的离散形式和轨道结构的运动方程, 采用虚拟激励法将轨道不平顺产生的随机激励转化为系统输入激励, 并将轨道随机高低不平顺作为振动激励源进行车轨振动控制; 在不同反馈控制参数下采用电压反馈双环PID控制器数值仿真车辆的悬浮状态, 并分析了轨道随机不平顺激励下反馈控制参数对磁浮系统稳定性的影响。研究结果表明: 当磁浮车辆速度为50~80 km·h-1, 位移反馈参数、速度反馈参数和电流反馈参数分别为140 000、50、500时, 车辆可以从起始间隙16 mm快速定位到平衡位置间隙9 mm, 在2.2 s时即可稳定悬浮, 系统的超调量和稳态误差分别为1.50和0.13 mm, 且系统振动频率趋近于0;当位移反馈参数、速度反馈参数和电流反馈参数分别为15 000、50、400时, 磁浮车辆在轨道随机不平顺作用下的悬浮稳定性变差, 系统在9 s左右逐渐趋于稳定, 但仍旧在平衡位置上下浮动, 且系统振动频率和振动幅值分别为7 Hz和0.5 mm; 当磁浮车辆的速度超出50~80 km·h-1时, 第1组反馈控制参数不再适用, 磁浮系统在1.7 s左右发散, 车辆失稳, 表明在不同车辆速度和反馈控制参数的作用下, 轨道随机不平顺能显著影响磁浮车辆的悬浮稳定性。Abstract: The dynamics characteristics of maglev vehicle caused by the random irregularity were studied based on the flexible track. Based on decomposing the track force into a segmented chain structure, an analysis method for the vertical suspension stability of maglev vehicle was proposed. The vibration natural frequencies and modal matrices of flexible track were defined when different suspension forces acted on their respective suspension points. The discrete form of track segmented chain structure and the motion equation of track structure were established. The random excitation generated by the track irregularity was transformed to the system input excitation by the virtual excitation method, and the vibrations of vehicle and track were controlled by taking the random unevenness irregularity of track as the vibration excitation source. The double-loop PID controller with the voltage feedback was used to numerically simulate the vehicle suspension state under different feedback control parameters, and the influences of feedback control parameters on the maglev system stability under the random track irregularity excitation were analyzed. Research result shows that when the maglev vehicle speed is 50-80 km·h-1 and the displacement feedback parameter, speed feedback parameter and current feedback parameter are 140 000, 50 and 500, respectively, the vehicle can quickly locate from the initial gap of 16 mm to the equilibrium position (9 mm), and can achieve a stable suspension at 2.2 s. The overshoot and steady-state error of system are-1.50 and 0.13 mm, respectively, and the vibration frequency approaches zero. When the displacement feedback parameter, speed feedback parameter and current feedback parameter are 15 000, 50 and 400, respectively, the maglev vehicle suspension stability becomes worse under the action of track random irregularity. The system tends to be stable gradually around 9 s, but it still floats up and down at the equilibrium position, and the vibration frequency and amplitude of system are 7 Hz and 0.5 mm, respectively. When the maglev vehicle speed exceeds 50-80 km·h-1, the first set of feedback control parameters are no longer applicable. The maglev system diverges around 1.7 s, and the train is unstable, indicating that under the actions of different vehicle speeds and feedback control parameters, the track random irregularity can significantly affect the suspension stability of maglev vehicle.
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图 4 不同反馈控制参数下悬浮间隙曲线
Figure 4. Suspension gap curves under different feedback control parameters
图 5 不同反馈控制参数下控制电流曲线
Figure 5. Control current curves under different feedback control parameters
图 6 不恰当反馈控制参数下悬浮间隙发散曲线
Figure 6. Suspension gap divergence curve under unsuitable feedback control parameters
图 7 不恰当反馈控制参数下控制电流发散曲线
Figure 7. Control current divergent curve under unsuitable feedback control parameters
表 1 车轨耦合系统物理参数
Table 1. Physical parameters of vehicle track coupling system
物理参数 参数值 车体质量/t 25 悬浮架质量/kg 750 每延米轨道质量/kg 8 937.755 线圈匝数 700 目标气隙/m 0.009 电磁铁面积/m2 0.024 真空磁导率/ (H·m-1) 4π×10-7 线圈电阻/Ω 1.2 稳定电流/A 19.5 漏磁率 0 
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