Self-excited vibration of maglev vehicle track coupling based on flexible suspension module
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摘要:
针对车辆悬浮状态下出现的车-轨高频耦合振动问题，本文在考虑悬浮模块及轨道结构柔性特征的基础上，系统研究了耦合自激振动的形成机理与抑制方法；基于Euler-Lagrange法建立了表征电磁铁及F轨柔性特征的刚柔耦合多自由度系统动力学模型，利用多模态特征值法分析了控制参数及结构参数对于耦合系统稳定性的影响规律；进一步提出了基于周期性能量平衡的自激振动能量分析方法，探讨了临界失稳状态下各个参数的贡献大小，从能量输入、耗散与转移的角度揭示了悬浮模块与F轨的耦合自激振动机理。仿真结果表明：自激振动可由电磁铁的主导模态引起，也可由F轨的主导模态引起；结构参数上可通过适当减小电磁铁长度、降低F轨支撑刚度及增大F轨跨距，来提升闭环系统的稳定性；由电磁铁柔性模态主导的自激振动对其一阶弯曲模态参数及悬浮传感器在电磁铁上的安装位置较为敏感，通过引入模态阻尼补偿控制或优化传感器布置，可实现特定频段内耦合振动的有效抑制，具有一定的工程指导意义。
Abstract:In response to the high-frequency coupled vibration between the vehicle and track occurring during vehicle suspension, the formation mechanism and suppression methods of coupled self-excited vibration were systematically studied, taking into account the flexible characteristics of the suspension module and track structure. A rigid-flexible coupled multi-degree of freedom system dynamics model characterizing the flexible characteristics of the electromagnet and the F-rail was established based on the Euler-Lagrange method. The influence law of control parameters and structural parameters on the stability of the coupled system was analysed using multimodal eigenvalue method. Furthermore, a self-excited vibration energy analysis method based on periodic energy balance was developed to explore the contribution of each parameter under critical instability conditions. The coupled self-excited vibration mechanism of the suspension module and the F-rail was revealed from the perspective of energy input, dissipation, and transfer. Simulation results show that the self-excited vibration may be caused by either the dominant mode of the electromagnet or that of the F-rail. In terms of structural parameters, the stability of the closed-loop system can be improved by appropriately reducing the electromagnet length, decreasing the support stiffness of the F-rail, and increasing the span of the F-rail. Self-excited vibration dominated by the flexible mode of the electromagnet is highly sensitive to its first-order bending mode parameters and the installation position of the suspension sensor on the electromagnet. By introducing modal damping compensation control or optimizing the sensor arrangement, the coupled vibration in a specific frequency band can be effectively suppressed, which has certain significance in engineering guidance.
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图 5 车辆静浮时电磁铁加速度响应
Figure 5. Electromagnet acceleration response when the vehicle is stationary
图 6 车辆运行时电磁铁加速度响应
Figure 6. Electromagnetic acceleration response during vehicle operation
图 10 多自由度的柔性悬浮模块-轨道结构等效动力学模型
Figure 10. Equivalent dynamic model of the multi-degree-of-freedom flexible suspension module-track structure
图 12 电磁铁与轨道的柔性模态位移曲线
Figure 12. Flexible modal displacement curves of electromagnet and track
图 13 以弹性模态主导的特征根实部随kp的变化趋势
Figure 13. Variation trend of real part of eigenvalue dominated by elastic mode with kp
图 14 以弹性模态主导的特征根实部随kd的变化趋势
Figure 14. Variation trend of real part of eigenvalue dominated by elastic mode with kd
图 15 以弹性模态主导的特征根实部随电磁铁长度的变化趋势
Figure 15. Variation trend of real part of eigenvalue dominated by elastic mode with electromagnet length
图 16 以弹性模态主导的特征根实部随F轨支撑刚度的变化趋势
Figure 16. Variation trend of real part of eigenvalue dominated by elastic mode with F-rail support stiffness
图 17 以弹性模态主导的特征根实部随F轨跨距的变化趋势
Figure 17. Variation trend of real part of eigenvalue dominated by elastic mode with span of F-rail
图 18 能量平衡法与特征值法结果对比
Figure 18. Results comparison of energy balance method and eigenvalue method
图 19 各个自由度对应的耦合自激力分量做功
Figure 19. Work done by the coupled self-excited force components corresponding to each degree of freedom
图 20 控制参数项、相对速度项及位移项做功
Figure 20. Work done by the control parameter, relative velocity, and displacement terms
图 21 不同传感器位置对应振动抑制效果
Figure 21. Vibration suppression effect corresponding to different sensor positions
图 22 基于PPF的闭环耦合系统控制结构
Figure 22. Control structure of closed-loop coupled system based on PPF
表 1 仿真参数
Table 1. Simulation parameters
参数 数值 比例项 6 500 积分项 3 500 阻尼项 32 补偿器阻尼比 0.03 补偿器固有频率/(rad·s-1) 55.9 补偿器增益 20 
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