Influences of Girder Parameters on the Maglev Vehicle-Guideway Coupled Vibration
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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.
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.
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Key words:
- maglev train /
- vehicle-girder coupled /
- vibration /
- girder /
- parameters
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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 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 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 kp 5 000 N 360 kd 50 R/Ω 0.55 kc 40 z0/mm 8 μ0/(H·m−1) 4π × 10−7 m1/kg 650 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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