Influence Analysis of Vibration Control Parameters for High-Speed Maglev Train-Bridge Coupling
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摘要:
磁浮列车悬浮系统控制参数取值不当可能导致车-桥系统异常振动. 因此，明确悬浮系统控制参数与磁浮车-桥系统动力响应之间的关系十分重要. 首先，建立包含比例-微分控制的5节编组磁浮列车动力学模型和20跨简支梁桥有限元模型；其次，与实测结果进行对比验证所建立模型的正确性；最后，计算车速430 km/h时不同控制参数下列车和桥梁的动力响应. 结果表明：增大比例系数会使悬浮和导向系统刚度增大，增大微分系数会使悬浮和导向系统阻尼增大；车体竖向加速度随比例和微分系数的增大而增大，车体横向加速度随比例系数的增大而增大；悬浮间隙和桥梁竖向加速度均随比例系数的增大而减小，随微分系数的增大而增大；导向间隙随微分系数的增大而减小，比例系数对导向间隙的影响较小；桥梁横向加速度随比例系数的增大而减小，随微分系数的增大而增大；桥梁竖向加速度主要受电磁力中悬浮电磁铁长度特征频率1倍～12倍频的影响，桥梁横向加速度主要受导向磁极长度特征频率及其2倍频和导向电磁铁长度特征频率2倍频及4倍频的影响；为减小车-桥系统动力响应，综合建议竖向比例和微分系数的取值范围分别为3000～4000和10～25，横向比例和微分系数的取值范围分别为4000～5000和10～25.
Abstract:Improper control parameters of the suspension system of maglev trains may lead to abnormal vibration of the train-bridge system. Therefore, it is important to clarify the relationship between the control parameters of the suspension system and the dynamic response of the maglev train-bridge system. Firstly, the dynamic model of a 5-car maglev train with proportional-differential control, as well as the finite element model of a 20-span simply supported beam bridge was established. Secondly, the correctness of the models was verified by comparing them with the measured results. Finally, the dynamic responses of the train and bridge under different control parameters at 430 km/h were calculated. The results show that increasing the proportional coefficient will increase the stiffness of the suspension and guidance system, and increasing the differential coefficient will increase the damping of the suspension and guidance system. The vertical acceleration of the car body increases with the increase in the proportional and differential coefficients, and the lateral acceleration of the car body increases with the increase in the proportional coefficient. The suspension gap and the vertical acceleration of the bridge decrease with the increase in the proportional coefficient, and they increase with the increase in the differential coefficient. The guidance gap decreases with the increase in the differential coefficient, and the proportional coefficient has little effect on the guidance gap. The lateral acceleration of the bridge decreases with the increase in the proportional coefficient and increases with the increase in the differential coefficient. The vertical acceleration of the bridge is mainly affected by a characteristic frequency of 1–12 times of the length of the suspended electromagnet in the electromagnetic force, and the lateral acceleration of the bridge is mainly affected by the characteristic frequency and frequency of 2 times of the length of the guidance pole, as well as the characteristic frequency of 2 times and 4 times of the length of the guidance electromagnet. In order to reduce the dynamic response of the train-bridge system, it is suggested that the values of vertical proportional and differential coefficients should be 3 000–4 000 and 10–25, respectively, and the values of lateral proportional and differential coefficients should be 4 000–5 000 and 10–25, respectively.
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图 5 不同控制参数下车体竖向加速度最大值
Figure 5. Maximum values of vertical acceleration of car body under different control parameters
图 6 不同控制参数下悬浮电磁力最大值
Figure 6. Maximum values of suspended electromagnetic force under different control parameters
图 7 不同控制参数下悬浮电磁力幅值谱
Figure 7. Amplitude spectrum of suspended electromagnetic force under different control parameters
图 8 不同控制参数下中间悬浮磁极间隙变化量
Figure 8. Variation of intermediate suspended pole gap under different control parameters
图 9 不同控制参数下悬浮间隙时程曲线及其幅值谱（KD1=25）
Figure 9. Suspension gap time history curve and amplitude spectrum under different control parameters （KD1 = 25）
图 10 不同控制参数下主梁跨中竖向加速度最大值
Figure 10. Maximum values of vertical acceleration at midspan of girder under different control parameters
图 11 不同KD1下主梁跨中竖向加速度幅值谱（KP1=6000）
Figure 11. Amplitude spectrum of vertical acceleration at midspan of girder under different KD1 （KP1 = 6 000）
图 12 不同控制参数下车体横向加速度最大值
Figure 12. Maximum values of lateral acceleration of car body under different control parameters
图 13 不同控制参数下导向电磁力最大值
Figure 13. Maximum values of guidance electromagnetic force under different control parameters
图 14 不同控制参数下导向电磁力幅值谱
Figure 14. Amplitude spectrum of guidance electromagnetic force under control parameters
图 15 不同控制参数下中间导向磁极间隙变化量
Figure 15. Variation of intermediate guidance pole gap under different control parameters
图 16 不同控制参数下主梁跨中横向加速度最大值
Figure 16. Maximum values of lateral acceleration at midspan of girder under different control parameters
图 17 不同KD2下主梁跨中横向加速度幅值谱（KP2=6000）
Figure 17. Amplitude spectrum of lateral acceleration at midspan of girder under different KD2 （KP2 = 6 000）
表 1 车辆模型参数
Table 1. Parameters of train model
参数 数值 车体质量/（× 104 kg） 3.90 车体侧滚质量惯性矩/（× 104 kg•m2） 6.46 车体摇头质量惯性矩/（× 104 kg•m2） 1.75 车体点头质量惯性矩/（× 104 kg•m2） 1.76 一系/二系弹簧竖向刚度/（×106 N•m−1） 20/2 一系/二系弹簧竖向阻尼/（×103 N•s•m−1） 5/5 一系/二系弹簧横向刚度/（×106 N•m−1） 28/2 一系/二系弹簧横向阻尼/（×102 N•s•m−1） 5/20 空气弹簧刚度竖向/（× 106 N•m−1） 1.90 
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表 2 桥梁模型参数
Table 2. Parameters of bridge model
参数 数值 主梁/钢轨/桥墩密度/（kg•m−3） 2551/7850/2500 主梁/钢轨/桥墩弹性模量/GPa 44.5/206.0/30.0 主梁/钢轨/桥墩泊松比 0.2/0.3/0.2
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