桥梁参数对磁浮系统车-桥耦合稳定性的影响

周丹峰; 朱鹏翔; 屈鸣鹤; 王连春; 李杰

doi:10.3969/j.issn.0258-2724.20240381

桥梁参数对磁浮系统车-桥耦合稳定性的影响

doi: 10.3969/j.issn.0258-2724.20240381

国防科技大学智能科学学院，湖南长沙 410073

基金项目: 国家自然科学基金项目（52332011）

详细信息

作者简介:
周丹峰（1982—），男，副研究员，博士，研究方向为磁悬浮控制和电磁发射技术，E-mail：zhoudanfeng@nudt.edu.cn

通讯作者:
王连春（1984—），男，讲师，博士，研究方向为磁悬浮控制，E-mail：spring_512@163.com

中图分类号: TP273
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- HTML全文浏览量: 16
- PDF下载量: 7
- 被引次数: 0
出版历程
- 收稿日期: 2024-08-01
- 录用日期: 2025-05-12
- 修回日期: 2025-04-20
- 网络出版日期: 2025-05-17

Influences of Girder Parameters on the Maglev Vehicle-Guideway Coupled Vibration

College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China

摘要

摘要:
为解决磁浮交通车-桥耦合自激振动问题并指导磁浮桥梁的设计，基于模态分析法建立桥梁的数学模型，研究桥梁的参数对磁浮列车车-桥耦合稳定性的影响. 首先，以磁浮工程某外伸型高架桥梁为例，用模态分析法建立弹性支撑结构的桥梁数学模型，探讨支墩位置对桥梁模态频率的影响；其次，结合磁浮列车悬浮控制系统的模型构建车-桥耦合系统模型，通过分析其开环频率特性研究自激振动发生的原因；最后，探讨桥梁的一阶模态频率、跨径、阻尼比、线密度等参数对车-桥耦合稳定性的影响. 研究表明：桥梁一阶模态频率接近或高于悬浮临界频率易导致闭环不稳定，故一阶模态频率高于10 Hz的轻质梁易引发车-桥耦合自激振动；大跨径梁的模态频率和模态增益更低，稳定性优于小跨度梁；桥梁的阻尼比、线密度越小，不稳定的频率范围越宽；相比两端支撑梁，在桥梁长度和截面固定情况下外伸梁的一阶模态频率随跨径减小呈先增后减的趋势，其最高频率可高出53.9%，故更容易进入不稳定频率范围，因此在磁浮工程中应尽量避免使用这类短跨外伸梁.
- 磁浮列车 /
- 车桥耦合 /
- 振动 /
- 桥梁 /
- 参数
Abstract:
To solve the vehicle-girder coupled self-excited vibration problem of the maglev transit, and to provide a reference for girder design, the influences of the parameters of the girder on the stability of the vehicle-girder coupled system is investigated based on the mathematical model established though modal analysis method. First, taking an extended elevated girder in a maglev project as an example, its mathematical model with flexible supports is established using the modal analysis method, and the effect of the pier position on the modal frequencies is studied. Second, combing the levitation control model of the maglev train, the maglev vehicle-girder coupled model is established. Then, the effects of the girder parameters, including the first order mode frequency, the span length, the damping ratio, and the liner density, etc., on the stability of the vehicle-girder coupled system are discussed. Results show that, when the first order mode frequency of the girder is close to or higher than the critical frequency of the levitation controller, the closed loop system may be instable, hence light girder, whose first order mode frequency is above 10 Hz, is likely to induce vehicle-girder coupled vibration; longer span girders are with lower mode frequencies and lower mode gains, and are more stable than short span girders; the smaller the damping and linear density of the girder, the wider unstable frequency range will be; for the girders with the same length and the cross-section, the mode frequency of the extended girder is higher than the terminal-supported girder, and in an extreme case the formal is 53.9% higher than the latter, which is more easier to lie in the unstable frequency range, hence the short span extended girder should be avoided in maglev projects.
- maglev train /
- vehicle-girder coupled /
- vibration /
- girder /
- parameters

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图 1 CMS-04中低速磁浮列车通过高架桥梁

Figure 1. The CMS-04 medium-low speed maglev train passing through an elevated girder

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图 2 CMS-04磁浮列车通过图1所示桥梁时的悬浮间隙和电磁铁加速度

Figure 2. The suspension gap and acceleration of the electromagnet when the CMS-04 maglev train is passing the girder shown in Fig. 1

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图 3 非对称外伸梁的简化结构示意

Figure 3. Simplified structure of the asymmetrical extended girder

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图 4 外伸梁的前三阶模态振型

Figure 4. The first three order mode shapes of the extended girder

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图 5 唐山线道岔梁车-岔耦合振动时的悬浮间隙功率谱

Figure 5. The power spectrum of the levitation gap when the maglev vehicle-turnout coupled vibration occurred.

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图 6 桥梁的频率响应曲线

Figure 6. Frequency responses of the girder

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图 7 悬浮系统的频率响应特性

Figure 7. Frequency responses of the levitation control system

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图 8 车轨耦合系统的开环频率特性

Figure 8. Frequency response of the open-loop system of the maglev vehicle-girder coupled system

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图 9 车轨耦合系统的悬浮间隙曲线

Figure 9. Suspension gap of the vehicle-girder coupled system

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图 10 桥梁一阶模态频率和跨径的关系

Figure 10. First order mode frequency of the girder vs. girder span

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图 11 桥梁一阶模态增益同跨径的关系

Figure 11. First order mode gain of the girder with respect to span length

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图 12 箱梁的截面结构示意

Figure 12. Cross-section of the box girder

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图 13 箱梁的一阶模态频率和跨径的关系

Figure 13. First order mode frequency of the box girder with respect to span length

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图 14 桥梁的不稳定频率范围和桥梁阻尼比的关系

Figure 14. Unstable frequency range of the girder vs. damping ratio of the girder

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图 15 桥梁的不稳定频率范围同桥梁线密度的关系

Figure 15. Unstable frequency range of the girder vs. linear density of the girder

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表 1 不同跨径下外伸梁的前三阶模态频率

Table 1. The first three order mode frequencies of the girder with different span lengths Hz

跨径/m	弹性支撑			简支支撑
跨径/m	一阶	二阶	三阶	一阶	二阶	三阶
10.0	16.05	23.23	54.10	16.98	38.54	106.22
11.0	16.55	26.00	51.22	17.45	44.56	93.50
12.0	14.86	33.96	48.67	15.95	55.81	96.44
12.5	13.92	38.10	49.09	14.99	56.89	114.08
13.0	13.02	39.68	52.96	13.94	54.86	118.95
14.0	11.40	37.84	62.92	12.07	48.29	108.58
14.5	10.75	36.56	64.57	11.42	45.67	102.91

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表 2 悬浮系统的主要参数

Table 2. Parameters of the suspension control system

参数	数值	参数	数值
A/m²	0.018 48	k_p	5 000
N	360	k_d	50
R/Ω	0.55	k_c	40
z₀/mm	8	μ₀/（H·m⁻¹）	4π × 10⁻⁷
m₁/kg	650

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表 3 唐山试验线几种典型的桥梁一阶模态频率

Table 3. First order mode frequencies of several typical girders in the Tangshan maglev test line

编号	跨径/m	一阶模态频率/Hz	梁类型
L1_1	12.5*	13.8	外伸混凝土箱梁
L1_3	14.5	11.0	简支混凝土箱梁
L1_6	18.0	9.0	简支混凝土箱梁
L1_8	18.0	9.1	简支混凝土箱梁
L2_29	24.0	6.8	简支混凝土箱梁
L2_30	24.0	7.0	简支混凝土箱梁
注：*表示L1_1梁全长为14.5 m，支墩间距为12.5 m.

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