Research on vehicle-rail coupling vibration at turnout and suppression method of medium and low speed maglev vehicle

HOU Longgang; LIANG Shulin; CHI Maoru

doi:10.13890/j.issn.1000-128X.2022.05.008

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Research on vehicle-rail coupling vibration at turnout and suppression method of medium and low speed maglev vehicle

Railway Rolling Stock | Updated：2024-08-02

- Research on vehicle-rail coupling vibration at turnout and suppression method of medium and low speed maglev vehicle
- role： Corresponding author , First author , 通讯作者 , 第一作者 ,
  
  Affiliation：
  State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031，China
  
  Email： 2086386952@qq.com
  
  Introduction：侯龙刚（1996—），男，硕士研究生，主要研究方向为车辆系统动力学；E-mail: 2086386952@qq.com
  
  No information about the author is available
  HOU Longgang
  ,
  role：
  
  Affiliation：
  State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031，China
  
  Email：
  
  No information about the author is available
  LIANG Shulin
  ,
  role：
  
  Affiliation：
  State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031，China
  
  Email：
  
  No information about the author is available
  CHI Maoru
  ,
- Electric drive for locomotives Issue 5, Pages: 49-55(2022)
- Affiliations：
  
  State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031，China
- Author bio：
- Funds：
- DOI：10.13890/j.issn.1000-128X.2022.05.008
  CLC： U237
- Published：10 September 2022，
  
  Received：27 May 2021，
  
  Revised：26 August 2022，
- Accepted：
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HOU Longgang, LIANG Shulin, CHI Maoru. Research on vehicle-rail coupling vibration at turnout and suppression method of medium and low speed maglev vehicle. [J]. Electric drive for locomotives (5):49-55(2022)
DOI：

HOU Longgang, LIANG Shulin, CHI Maoru. Research on vehicle-rail coupling vibration at turnout and suppression method of medium and low speed maglev vehicle. [J]. Electric drive for locomotives (5):49-55(2022) DOI： 10.13890/j.issn.1000-128X.2022.05.008.

Abstract

In the medium and low speed maglev vehicle-rail coupling system, the turnout is an important part of the line change of the maglev vehicle, and its main beam mostly adopts the web or box-shaped steel beam structure with relatively low modal frequency and damping. When the maglev vehicle passes the turnout at a certain speed, it is easy to couple vibration with it, which affects the running stability and driving safety of the vehicle. For this reason, this paper took Changsha medium and low speed maglev vehicle as a prototype, established a maglev vehicle-turnout beam coupling system model, and analyzed the vibration response of the maglev vehicle-turnout beam coupling system by studying the magnetic-rail interaction relationship and vibration control method of the coupling system. In addition, a tuned mass damper (TMD) based on dynamic vibration absorption was proposed, and its effectiveness in suppressing the vibration response of a maglev vehicle-turnout beam coupling system was demonstrated. The research results show that the feedback coefficient of the control system can change the magnetic-rail interaction relationship of the coupled system to different degrees, and the gap feedback coefficient and the velocity feedback coefficient have obvious effects. The speed of the vehicle has a significant effect on the vibration response of the vehicle body and the active beam of the turnout, the medium and low speed maglev vehicles are more sensitive to the speed within 40 km/h when passing through the steel beam of the variable cross-section switch. During the operation of the maglev vehicle, the lower modes of the turnout beam are more easily excited, which is the key factor that causes the resonance of the maglev vehicle-turnout coupling system. The principle of tuning the mass damper device is to adjust the vibration frequency of the TMD device to the vicinity of the vibration coupling frequency of the main structure of the switch beam by increasing or decreasing the weight of the device, and to change the resonance characteristics of the switch beam by means of dynamic vibration absorption, so as to achieve the effect of suppressing the coupled vibration of the turnout beam. The comparative analysis in this paper shows that TMD controller has obvious effect on improving the stability of maglev vehicle-turnout coupling system, it is an effective coupled vibration control measure.

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Keywords

medium and low speed maglev vehicle; coupling vibration; variable section turnout beam; TMD control; suspension stability; urban rail transit

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0 引言

随着城市化进程的不断深化，城市人口流动量也逐年增加，城市轨道交通迎来了新的挑战和机遇。如何解决城市交通拥堵、噪声和环保问题，并满足城市大运量、高效率的交通需求已经成了城市发展需要解决的问题。中低速磁浮交通以其噪声低、振动小、低碳环保、安全可靠、选线灵活和爬坡能力强等优点在城市轨道交通系统中越来越受关注^[

1-2]。

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在磁浮轨道交通不断发展的同时，其特有的车轨耦合振动现象也成为了各国研究者关注的问题。德国TR04磁浮列车在试验过程中在钢梁桥上悬浮时出现了耦合振动的现象，而在区间轨道梁上则无此现象。在上海磁浮示范线的磁浮列车调试过程中，也出现了车辆与钢轨的自激振动现象^[

3-4]。文献[5]将列车简化为移动载荷模型，分析了列车过桥时的振动形态和调谐质量阻尼器（tuned mass damper，TMD）控制特点，为桥梁振动控制的进一步研究提供了参考依据；文献[6]从非线性特性的角度研究了静止悬浮条件下磁浮车轨耦合系统的振动特性，分析了轨道参数和控制参数对系统振动的影响；文献[7]基于Simpack和Ansys联合仿真，探讨了“中低速磁浮列车-低置梁系统”垂向耦合振动和不同参数下的垂向动力响应；文献[8]分析了多力元模拟悬浮电磁铁线圈悬浮力的准确性，并对不同波长轨道高低不平顺激励下的磁浮车辆动态特性进行了研究。但是上述文献并没有对车辆通过道岔的磁轨作用关系和悬浮稳定性控制得出相应的结论，本文将通过建立车岔耦合动力学模型，分析磁轨相互作用关系和车岔耦合振动响应，了解车岔耦合振动产生原理和影响规律，并提出一种基于动力吸振的TMD装置，分析其结构和振动控制效果。

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1 建模与悬浮控制方法

1.1 中低速磁浮车辆和道岔建模

为了研究中低速磁浮车辆车岔耦合振动动力学问题，本文以长沙磁浮线中低速磁浮列车为原型^[

9-10]，运用Simpack软件建立了如图1所示的中低速磁浮车辆动力学模型。模型考虑了车辆结构、悬浮架和悬挂元件的非线性，车辆和道岔建模主要动力学参数如表1所示。

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图1 中低速磁悬浮车辆动力学模型

Fig. 1 Dynamic model of medium and low speed maglev vehicle

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表1 车辆动力学基本参数

Table 1 Basic parameters of vehicle dynamics

参数名称	参数值
车体质量 $M_{C}$ /kg	20 870
二系空簧刚度 $K_{S}$ /( $N \cdot m^{- 1}$ )	0.8×10⁵
二系空簧阻尼 $C_{S}$ /( $N \cdot s \cdot m^{- 1}$ )	800
悬浮架质量m/kg	500
道岔梁截面惯性矩I/m²	0.166
道岔主动梁弹性模量E/Pa	2.10×10¹¹
净截面积A/ m²	0.135
道岔质量 $m_{b}$ /t	20
一阶垂弯频率f/Hz	25
结构阻尼比 $ς$	0.01
密度 $ρ$ /( $k g \cdot m^{- 3}$ )	7.8×10³
长度l/m	19

Download: CSV

Download: Table Images

道岔作为连接车辆换线运行的过渡结构，在磁浮车辆系统应用广泛，其结构和状态对车辆安全性和运行品质影响巨大^[

11]。中低速磁浮道岔主要由垛梁、跨中有垂向支承的双跨连续钢性主动梁、两段从动梁和安装于梁上翼缘的F轨组成。主梁和两段从动梁都有1个固定于地面的转动中心，为三段定心式结构，如图2所示。

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图2 中低速磁浮道岔结构

Fig. 2 Structure of medium and low speed maglev turnout

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本文使用欧拉-伯努利梁理论对中低速磁浮道岔梁进行建模^[

12]。采用模态叠加法，道岔梁挠度

u (x, t)

可以表示为

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u (x, t) = \sum_{n = 1}^{N} [q_{n} (t) ϕ_{n} (x)]

(1)

式中： $q_{n} (t)$ 为广义坐标； $ϕ_{n} (x)$ 为振型函数。

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Euler-Bernoulli梁的固有频率 $p_{n}$ 为

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p_{n} = \frac{{(n π)}^{2}}{l^{2}} \sqrt[]{\frac{E I}{ρ A}} (n = 1,2, 3, \dots)

(2)

式中： $E I$ 为道岔梁的抗弯刚度；A为轨道截面积； $ρ$ 为轨道的密度。

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振型函数 $Z (n, x)$ 为

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Z (n, x) = \sqrt[]{\frac{2}{ρ A l}} s i n \frac{n π x}{l}

(3)

因此，道岔结构动力学方程由第一类拉格朗日方程可表示为

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M_{n} {\ddot{q}}_{n} + C_{n} {\dot{q}}_{n} + K_{n} q_{n} = ϕ_{n}^{T} P (x, t)

(4)

式中： $M_{n}$ 为模态质量； $C_{n}$ 为模态阻尼； $K_{n}$ 为模态刚度； $P (x, t)$ 为作用在道岔梁上的电磁悬浮力合力。

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由道岔主动梁模型参数和有限元计算可得，前三阶模态频率和道岔主动梁振型如表2所示。

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表2 道岔主动梁振型和模态

Table 2 Mode shapes and modes of turnout main beam

阶次	振型	频率/Hz
1	一阶垂向弯曲	25.0
2	二阶垂向弯曲	100.1
3	三阶垂向弯曲	225.3

Download: CSV

Download: Table Images

1.2 悬浮控制方法与耦合模型

中低速磁浮列车各控制点在结构设计上要尽可能实现解耦，因此对整车悬浮控制的研究，可简化为对单电磁铁在垂直方向上一个自由度的悬浮控制问题^[

13]，其物理模型如图3所示。

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图3 单电磁铁悬浮物理模型

Fig. 3 Suspension physical model of single electromagnet

m—悬浮电磁铁质量； $ϕ$ —磁通量； $f_{d}$ —外界干扰力；c(t)—额定悬浮间隙；i(t)—电磁铁线圈输入控制电流； $N$ —线圈匝数。

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由上述单电磁铁悬浮物理模型，可推导出磁铁悬浮系统垂向动力学方程如下：

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力学方程：

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m \frac{d^{2} z (t)}{d t^{2}} = m g + f_{d} (t) - F (i, c)

(5)

电压方程：

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u (t) = R i (t) + \frac{μ_{0} N^{2} A}{2 c (t)} \cdot \frac{d i (t)}{d t} - \frac{μ_{0} N^{2} A i (t)}{2 [c {(t)]}^{2}} \cdot \frac{d c (t)}{d t}

(6)

边界条件：

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m g = F (i_{0}, c_{0}) = \frac{μ_{0} N^{2} A}{4} {(\frac{i_{0}}{c_{0}})}^{2}

(7)

磁悬浮车辆控制算法可以通过传感器信号实时计算控制电流，但由于存在电感的原因，传递到悬浮电磁铁上的电流有滞后现象，造成控制延迟。实践证明，这种电流滞后是造成悬浮系统不稳定的原因之一^[

14]。因此，本文采用电流内环和前级控制外环2个子系统共同作用的双环PID悬浮控制器模型（如图4所示）研究控制过程参数对耦合振动的影响。其中，间隙反馈系数为

K_{p}

，速度反馈系数为

K_{v}

，加速度反馈系数为

K_{a}

，分别取

K_{p}

=6 000、

K_{v}

=20和

K_{a}

=0.5。系统中的控制器电流环可使电磁铁电流快速跟踪控制电压，补偿电感造成的系统延迟；前级控制子系统可直接采集间隙传感器和加速度传感器信号，速度信号则由加速度信号积分获得，然后经过算法控制悬浮电磁力，保证车辆悬浮系统稳定性。

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图4 双环PID悬浮控制器原理

Fig. 4 Principle of double loop PID suspension controller

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“车辆-道岔”弹性梁单铁悬浮系统耦合模型如图5所示。该耦合系统由磁浮车辆、柔性道岔梁和悬浮控制系统组成。考虑到道岔支座对振动的影响，模型将道岔梁视为自由边界的欧拉梁，支座对梁的支撑作用通过外力施加。在仿真计算中，首先计算车辆与道岔梁在悬浮控制力的作用下的时程动态响应，再以此结果计算新的悬浮控制力，循环迭代。

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图5 “车辆-道岔”耦合模型

Fig. 5 Vehicle-turnout coupling model

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2 车岔耦合悬浮稳定性分析

2.1 磁轨相互作用关系研究

电磁悬浮力作用于磁浮车辆与轨道梁之间，基于动力吸振的TMD车岔耦合振动控制装置，其变化是在悬浮系统有源闭环主动控制作用下，由悬浮间隙和线圈电流共同作用的结果^[

15]。控制系统各反馈参数和车辆运行环境对耦合振动影响显著，因此有必要分析悬浮间隙、速度和加速度反馈系数对磁轨关系的影响，进行系统参数优化。

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间隙反馈系数 $K_{p}$ 、速度反馈系数 $K_{v}$ 和加速度反馈系数 $K_{a}$ 可等效于悬浮系统的刚度、阻尼和质量，在悬浮平衡系统施加一阶跃激扰，系统不同反馈系数下悬浮间隙变化如图6所示。

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(a) 间隙反馈系数

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(b) 速度反馈系数

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图6 不同反馈系数下悬浮系统间隙变化

Fig. 6 Variation of suspension system clearance under different feedback coefficients

由图6可知，系统悬浮间隙变化随间隙反馈系数的增大而减小，间隙反馈系数越大，悬浮间隙稳态下变化量越小；悬浮系统间隙变化收敛时间随速度反馈系数的增大而变短，体现了速度反馈系数的阻尼特性；而加速度反馈系数对悬浮间隙变化影响不明显。

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2.2 车岔耦合振动稳态响应

车岔耦合振动稳态响应反映了在正常运行工况下车辆的基本动力学特性，本节主要考虑当车辆直向通过轻型道岔双跨连续主动钢梁时，车速、道岔质量和刚度的变化对磁浮车辆与主动梁的振动响应的影响。仿真结果展示如图7~图11所示。从时域结果可以看出，车辆以不同速度经过道岔时，均对道岔主动梁产生了冲击；道岔主动梁第1跨跨中的垂向变形最为显著，并且跨中变形量大于其余部分；道岔主动梁第2跨跨中的横向变形最为明显，并且第2跨横向变形量总体要大于第1跨；在时程图中，道岔第1跨和第2跨的变形总是反向的，这是两跨弹性梁的一般属性。从频域图可以看出，道岔主动梁振动频率中含有25 Hz左右的主频，这与道岔主动梁一阶弯曲模态相近，是本文车岔耦合振动控制中主要关注的模态。从图11可以看出，当车速小于

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图7 道岔主动梁跨中垂向加速度

Fig. 7 Vertical acceleration of middle span of turnout main beam

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图8 主动梁动力响应及振动频谱

Fig. 8 Dynamic response and vibration spectrum of main beam

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图9 道岔主动梁垂向变形最值

Fig. 9 Maximum vertical deformation of turnout main beam

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图10 道岔主动梁横向变形最值

Fig. 10 Maximum transverse deformation of turnout main beam

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图11 车体加速度最大值

Fig. 11 Maximum acceleration of car body

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40 km/h时车体加速度随车速增大而明显下降，车速大于40 km/h时，车体加速度变化较小，这表明中低速磁浮车辆通过变截面道岔钢梁时对40 km/h以下的速度更为敏感，因此车辆过岔时应高于此速度运行。

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2.3 基于调谐质量的车岔耦合振动控制

由于中低速磁浮道岔采用钢梁结构，相对于区间轨道梁，其自重小，结构自振频率和阻尼较低，车辆过岔时容易发生耦合振动^[

16]。根据稳定性理论可知，防止磁浮车辆与道岔耦合的方法有2种：方法一是通过改变道岔结构频率来避开耦合振动区间，方法二是通过提高系统阻尼来抑制耦合振动。方法一主要是通过改变道岔梁的结构刚度和质量实现的，然而改变道岔结构只会将车岔耦合振动区间移至其他频段，无法从根源上抑制这种耦合，当车辆或者控制系统参数发生改变时，耦合振动可能又会出现，并且改变道岔结构参数在线路建设完成后不易实现。因此，提高系统阻尼，在道岔梁结构中加装阻尼器是一种有效且具有工程实施性的耦合振动控制方法。本文提出了一种基于动力吸振原理的调谐质量阻尼器（TMD）控制方法，以实现其在车岔耦合振动中的吸振要求，提高车辆过岔悬浮稳定性。

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TMD主要由质量装置、弹簧与阻尼系统组成。质量装置由箱体、配重块和锁紧装置组成，弹簧阻尼器由钢弹簧和液压阻尼器组成。质量装置通过各方向对称的8个弹簧阻尼器悬挂于道岔主钢梁上，如图12所示。通过改变液力阻尼器的阻尼系数可调整吸振装置的吸振能力。该装置原理是将其振动频率调整至主结构耦合振动频率附近，通过动力吸振改变主结构共振特性，达到主结构减振的效果。装置频率的调整通过增减质量装置配重块来实现。

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图12 调谐质量阻尼器装置

Fig. 12 Tuned mass damper device

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根据TMD的工作原理可知，要让吸振装置发挥主结构减振效果，动力吸振器的固有频率应该根据道岔耦合振动的频率来设置。从上文可知，最有可能产生车岔耦合振动的频率是25 Hz的道岔主动梁一阶垂弯频率，故本文将调谐质量动力吸振器固有频率设置为25 Hz。吸振装置关键参数为动力吸振器刚度、阻尼和质量，并且当质量和耦合振动频率确定时，根据振动理论吸振器的等效刚度也将确定。因此，在该吸振装置设计中，独立参数为动力吸振器质量参数和阻尼参数。

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通过数值分析，TMD关键参数对车岔耦合振动的控制效果影响规律如图13、图14所示。本文以磁浮车辆悬浮控制稳定域的大小作为车辆稳定性的评判指标。从图13和图14可以看出，随着调谐质量的动力吸振装置质量的增加，悬浮车辆控制系统稳定域逐渐增大，系统表现出更好的鲁棒性；而随其阻尼特性的提高，控制系统稳定域在阻尼比为0.1时有小幅的增大，之后随着阻尼特性的提高，系统稳定域逐渐缩小，系统鲁棒性也变差。

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图13 TMD质量和系统稳定域的关系

Fig. 13 Relationship between TMD mass and system stability region

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图14 TMD阻尼和系统稳定域的关系

Fig. 14 Relationship between TMD damping and system stability region

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基于上述调谐质量的动力吸振阻尼器参数对控制效果的影响规律，确定吸振装置基本参数如表3所示。对比在阶跃激励下有无TMD阻尼器控制的磁悬浮车岔耦合振动的动态响应，仿真计算结果如图15和表4所示。

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表3 TMD装置主要参数

Table 3 Main parameters of TMD device

参数名称	参数值	参数名称	参数值
质量/kg	1 300	固有频率/ Hz	25
刚度/( $M N \cdot m^{- 1}$ )	32.1	阻尼/( $k N \cdot s \cdot m^{- 1}$ )	40.9

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Download: Table Images

(a) 悬浮架和车体位移（无TMD控制）

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(b) 悬浮架和车体位移（有TMD控制）

Download: Full-size image | High-res image | Low-res image

Download: Full-size image | High-res image | Low-res image

(d) 道岔梁跨中振动位移和加速度最大值（有TMD控制）

Download: Full-size image | High-res image | Low-res image

图15 有无TMD装置控制下耦合系统振动位移和加速度对比

Fig. 15 Comparison of vibration displacement and acceleration of coupling system with/withou TMD device

表 4 TMD装置控制效果对比

Table 4 Comparison of control effect of TMD device

参数名称		控制状态
参数名称		无措施	TMD阻尼器
道岔梁跨中	加速度最大值/g	6.910	0.021
道岔梁跨中	振动位移/mm	3.680	0.023
振动位移	车体位移/mm	1.13	0.68
振动位移	悬浮架位移/mm	2.85	0.22

Download: CSV

Download: Table Images

由图15和表4可知，当道岔主动梁安装TMD阻尼器时，道岔主动梁跨中加速度、振动位移、车体和悬浮架振动位移相比于无阻尼器控制下的各项指标都有更好的收敛性，并且振动幅值更小。该装置对磁浮车岔耦合振动控制效果明显，是一种有效的耦合振动控制方式。

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3 结论

本文针对磁悬浮车辆在道岔钢梁上产生的车岔耦合振动现象，建立了“磁浮车辆-道岔”耦合动力学模型，阐述了磁浮车辆振动控制研究方法，分析了车岔耦合磁轨相互作用关系和振动响应，最后提出了基于动力吸振的TMD振动控制装置，研究了其对振动的控制效果，研究发现：①悬浮控制系统间隙反馈系数和速度反馈系数的增大可以改善悬浮系统趋于稳定状态的速度和误差，体现出更好的鲁棒性，而加速度反馈信号对悬浮系统影响不明显。②中低速磁浮车辆以不同速度经过变截面道岔梁时，道岔梁第1跨跨中垂向变形最为显著，第2跨跨中横向变形最为明显；在时程上，道岔梁第1跨和第2跨变形总是反向的；另外，车体横向加速度和垂向加速度对40 km/h以下的车速更为敏感，故车辆过岔时应高于此速度运行；从频域图可以看出，道岔主动梁25 Hz的一阶垂向弯曲模态是引起车岔耦合振动的主要原因。③在安装对应模态TMD控制器的车岔耦合系统中，计算验证了该装置抑制系统耦合振动的有效性，为后续车岔系统耦合振动控制研究提供了一种方法。

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参考文献

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ZHANG Zhi, ZONG Lingxiao, REN Zhonghua. Design of medium and low speed small maglev system and its application[J]. Electric Drive for Locomotives, 2020(6): 75-79. [Baidu Scholar]

赵春发, 翟婉明. 磁浮车辆/轨道系统动力学(Ⅱ)——建模与仿真[J]. 机械工程学报, 2005, 41(8): 163-175. [Baidu Scholar]

ZHAO Chunfa, ZHAI Wanming. Dynamics of maglev vehicle/guideway systems(Ⅱ)-modeling and simulation[J]. Chinese Journal of Mechanical Engineering, 2005, 41(8): 163-175. [Baidu Scholar]

赵春发. 磁悬浮车辆系统动力学研究[D]. 成都: 西南交通大学, 2002. [Baidu Scholar]

ZHAO Chunfa. Maglev vehicle system dynamics[D]. Chengdu: Southwest Jiaotong University, 2002. [Baidu Scholar]

肖守讷, 沈安林, 阳光武. 中低速磁悬浮车体的结构特点及其分析[J/OL]. 中国科技论文, 2010, 5(10): 803-806 [2022-01-25]. https://d.wanfangdata.com.cn/periodical/zgkjlwzx201010011. [Baidu Scholar]

XIAO Shoune, SHEN Anlin, YANG Guangwu. Structure feature and analysis of the middle low speed magnetic levitation train carbody[J/OL]. China Sciencepaper, 2010, 5(10): 803-806 [2022-01-25]. https://d.wanfangdata.com.cn/periodical/zgkjlwzx201010011. [Baidu Scholar]

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XIAO Xinbiao, SHEN Huoming. Vibration and the TMD control of bridges under moving loads[J]. Journal of Vibration and Shock, 2005, 24(2): 58-61. [Baidu Scholar]

施晓红, 龙志强. 磁悬浮车轨耦合控制系统的非线性振动特性分析[J]. 铁道学报, 2009, 31(4): 38-42. [Baidu Scholar]

SHI Xiaohong, LONG Zhiqiang. Nonlinear vibration analysis of the maglev guideway-vehicle coupling control system[J]. Journal of the China Railway Society, 2009, 31(4): 38-42. [Baidu Scholar]

李小珍, 耿杰, 王党雄, 等. 中低速磁浮列车-低置梁系统竖向耦合振动研究[J]. 工程力学, 2017, 34(12): 210-218. [Baidu Scholar]

LI Xiaozhen, GENG Jie, WANG Dangxiong, et al. Study on vertical coupling vibration of low-medium speed maglev train and at-ground-structure system[J]. Engineering Mechanics, 2017, 34(12): 210-218. [Baidu Scholar]

魏高恒, 陈晓昊, 罗世辉, 等. 轨道高低不平顺对磁浮车辆动力学性能的影响[J]. 机车电传动, 2019(4): 56-60. [Baidu Scholar]

WEI Gaoheng, CHEN Xiaohao, LUO Shihui, et al. Influence of track vertical irregularity on dynamic performance of maglev vehicles[J]. Electric Drive for Locomotives, 2019(4): 56-60. [Baidu Scholar]

马卫华, 罗世辉, 张敏, 等. 中低速磁浮车辆研究综述[J]. 交通运输工程学报, 2021, 21(1): 199-216. [Baidu Scholar]

MA Weihua, LUO Shihui, ZHANG Min, et al. Research review on medium and low speed maglev vehicle[J]. Journal of Traffic and Transportation Engineering, 2021, 21(1): 199-216. [Baidu Scholar]

李小珍, 金鑫, 王党雄, 等. 长沙中低速磁浮运营线列车-桥梁系统耦合振动试验研究[J]. 振动与冲击, 2019, 38(13): 57-63. [Baidu Scholar]

LI Xiaozhen, JIN Xin, WANG Dangxiong, et al. Tests for coupled vibration of a train-bridge system on Changsha low-medium speed maglev line[J]. Journal of Vibration and Shock, 2019, 38(13): 57-63. [Baidu Scholar]

李国豪. 桥梁结构稳定与振动[M]. 北京: 中国铁道出版社, 1992: 287-344. [Baidu Scholar]

LI Guohao. Bridge structure stability and vibration[M]. Beijing: China Railway Publishing House, 1992: 287-344. [Baidu Scholar]

耿杰. 中低速磁浮简支轨道梁关键设计参数的理论与试验研究[D]. 成都: 西南交通大学, 2018. [Baidu Scholar]

GENG Jie. Theoretical and experimental research on key design parameters of medium and low speed maglev simply supported track beams[D]. Chengdu: Southwest Jiaotong University, 2018. [Baidu Scholar]

梁鑫, 罗世辉, 马卫华, 等. 磁浮列车单铁悬浮车桥耦合振动分析[J]. 交通运输工程学报, 2012, 12(2): 32-37. [Baidu Scholar]

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XIONG Gaoxiang, LIU Feng, LIU Shaoke. Adaptive PID control of hybrid suspension system[J]. Electric Drive for Locomotives, 2014(4): 33-36. [Baidu Scholar]

梁潇, 陈峰, 傅庆湘. 160 km/h中速磁浮交通系统的关键技术问题[J]. 城市轨道交通研究, 2019, 22(9): 21-26. [Baidu Scholar]

LIANG Xiao, CHEN Feng, FU Qingxiang. Key technical issues on 160 km/h medium-speed maglev transit system[J]. Urban Mass Transit, 2019, 22(9): 21-26. [Baidu Scholar]

韩霄翰, 李忠继, 池茂儒. 轨道梁结构对中低速磁浮车轨耦合振动的影响[J]. 铁道机车车辆, 2019, 39(5): 36-42. [Baidu Scholar]

HAN Xiaohan, LI Zhongji, CHI Maoru. Influence of track beam structure on the mid-low maglev vehicle-rail coupling vibration[J]. Railway Locomotive & Car, 2019, 39(5): 36-42. [Baidu Scholar]

摘要

在中低速磁浮车轨耦合系统中，道岔作为磁浮车辆运行换线的重要组成部分，其主梁多采用模态频率和阻尼相对较低的辐板或箱型钢梁结构。当磁浮车辆以一定速度通过道岔时，易与道岔发生耦合振动，影响车辆的运行平稳性和行车安全。为此，文章以长沙中低速磁浮车辆为原型，建立了“磁浮车辆-道岔梁”耦合系统模型，通过研究耦合系统的磁轨相互作用关系和振动控制方法，分析了“磁浮车辆-道岔梁”耦合系统的振动响应和影响因素，提出了一种基于动力吸振的调谐质量阻尼器（tuned mass damper，TMD），并论证了其对“磁浮车辆-道岔梁”耦合系统振动响应抑制的有效性。研究结果表明，控制系统反馈系数可不同程度地改变耦合系统的磁轨相互作用关系，其中间隙反馈系数和速度反馈系数影响作用明显；同时，车速对车体和道岔主动梁振动响应影响显著，尤其是当中低速磁浮车辆以40 km/h以下的速度通过变截面道岔钢梁时。在磁浮车辆运行过程中，道岔梁的低阶模态更容易被激发，是导致“磁浮车辆-道岔”耦合系统发生共振的关键因素。调谐质量阻尼器装置的原理是通过增减装置配重块质量，将TMD装置振动频率调整至道岔梁主结构振动耦合频率附近，利用动力吸振的方式改变道岔梁的共振特性，进而达到抑制道岔梁耦合振动的效果。文章通过对比分析表明，TMD控制器对改善“磁浮车辆-道岔”耦合系统稳定性效果明显，是一种有效的耦合振动控制措施。

Abstract

In the medium and low speed maglev vehicle-rail coupling system

the turnout is an important part of the line change of the maglev vehicle

and its main beam mostly adopts the web or box-shaped steel beam structure with relatively low modal frequency and damping. When the maglev vehicle passes the turnout at a certain speed

it is easy to couple vibration with it

which affects the running stability and driving safety of the vehicle. For this reason

this paper took Changsha medium and low speed maglev vehicle as a prototype

established a maglev vehicle-turnout beam coupling system model

and analyzed the vibration response of the maglev vehicle-turnout beam coupling system by studying the magnetic-rail interaction relationship and vibration control method of the coupling system. In addition

a tuned mass damper (TMD) based on dynamic vibration absorption was proposed

and its effectiveness in suppressing the vibration response of a maglev vehicle-turnout beam coupling system was demonstrated. The research results show that the feedback coefficient of the control system can change the magnetic-rail interaction relationship of the coupled system to different degrees

and the gap feedback coefficient and the velocity feedback coefficient have obvious effects. The speed of the vehicle has a significant effect on the vibration response of the vehicle body and the active beam of the turnout

the medium and low speed maglev vehicles are more sensitive to the speed within 40 km/h when passing through the steel beam of the variable cross-section switch. During the operation of the maglev vehicle

the lower modes of the turnout beam are more easily excited

which is the key factor that causes the resonance of the maglev vehicle-turnout coupling system. The principle of tuning the mass damper device is to adjust the vibration frequency of the TMD device to the vicinity of the vibration coupling frequency of the main structure of the switch beam by increasing or decreasing the weight of the device

and to change the resonance characteristics of the switch beam by means of dynamic vibration absorption

so as to achieve the effect of suppressing the coupled vibration of the turnout beam. The comparative analysis in this paper shows that TMD controller has obvious effect on improving the stability of maglev vehicle-turnout coupling system

it is an effective coupled vibration control measure.

关键词

中低速磁浮耦合振动变截面道岔梁TMD控制悬浮稳定性城市轨道交通

Keywords

medium and low speed maglev vehiclecoupling vibrationvariable section turnout beamTMD controlsuspension stabilityurban rail transit

references

章致, 宗凌潇, 任忠华. 中低速小型磁浮系统设计及其应用研究[J]. 机车电传动, 2020(6): 75-79.

ZHANG Zhi, ZONG Lingxiao, REN Zhonghua. Design of medium and low speed small maglev system and its application[J]. Electric Drive for Locomotives, 2020(6): 75-79.

赵春发, 翟婉明. 磁浮车辆/轨道系统动力学(Ⅱ)——建模与仿真[J]. 机械工程学报, 2005, 41(8): 163-175.

ZHAO Chunfa, ZHAI Wanming. Dynamics of maglev vehicle/guideway systems(Ⅱ)- modeling and simulation[J]. Chinese Journal of Mechanical Engineering, 2005, 41(8): 163-175.

赵春发. 磁悬浮车辆系统动力学研究[D]. 成都: 西南交通大学, 2002.

ZHAO Chunfa. Maglev vehicle system dynamics[D]. Chengdu: Southwest Jiaotong University, 2002.

肖守讷, 沈安林, 阳光武. 中低速磁悬浮车体的结构特点及其分析[J/OL]. 中国科技论文, 2010, 5(10): 803-806 [2022-01-25]. https://d.wanfangdata.com.cn/periodical/zgkjlwzx201010011https://d.wanfangdata.com.cn/periodical/zgkjlwzx201010011.

肖新标, 沈火明. 移动荷载作用下的桥梁振动及其TMD控制[J]. 振动与冲击, 2005, 24(2): 58-61.

XIAO Xinbiao, SHEN Huoming. Vibration and the TMD control of bridges under moving loads[J]. Journal of Vibration and Shock, 2005, 24(2): 58-61.

施晓红, 龙志强. 磁悬浮车轨耦合控制系统的非线性振动特性分析[J]. 铁道学报, 2009, 31(4): 38-42.

SHI Xiaohong, LONG Zhiqiang. Nonlinear vibration analysis of the maglev guideway-vehicle coupling control system[J]. Journal of the China Railway Society, 2009, 31(4): 38-42.

李小珍, 耿杰, 王党雄, 等. 中低速磁浮列车-低置梁系统竖向耦合振动研究[J]. 工程力学, 2017, 34(12): 210-218.

LI Xiaozhen, GENG Jie, WANG Dangxiong, et al. Study on vertical coupling vibration of low-medium speed maglev train and at-ground-structure system[J]. Engineering Mechanics, 2017, 34(12): 210-218.

魏高恒, 陈晓昊, 罗世辉, 等. 轨道高低不平顺对磁浮车辆动力学性能的影响[J]. 机车电传动, 2019(4): 56-60.

WEI Gaoheng, CHEN Xiaohao, LUO Shihui, et al. Influence of track vertical irregularity on dynamic performance of maglev vehicles[J]. Electric Drive for Locomotives, 2019(4): 56-60.

马卫华, 罗世辉, 张敏, 等. 中低速磁浮车辆研究综述[J]. 交通运输工程学报, 2021, 21(1): 199-216.

MA Weihua, LUO Shihui, ZHANG Min, et al. Research review on medium and low speed maglev vehicle[J]. Journal of Traffic and Transportation Engineering, 2021, 21(1): 199-216.

李小珍, 金鑫, 王党雄, 等. 长沙中低速磁浮运营线列车-桥梁系统耦合振动试验研究[J]. 振动与冲击, 2019, 38(13): 57-63.

LI Xiaozhen, JIN Xin, WANG Dangxiong, et al. Tests for coupled vibration of a train-bridge system on Changsha low-medium speed maglev line[J]. Journal of Vibration and Shock, 2019, 38(13): 57-63.

李国豪. 桥梁结构稳定与振动[M]. 北京: 中国铁道出版社, 1992: 287-344.

LI Guohao. Bridge structure stability and vibration[M]. Beijing: China Railway Publishing House, 1992: 287-344.

耿杰. 中低速磁浮简支轨道梁关键设计参数的理论与试验研究[D]. 成都: 西南交通大学, 2018.

GENG Jie. Theoretical and experimental research on key design parameters of medium and low speed maglev simply supported track beams[D]. Chengdu: Southwest Jiaotong University, 2018.

梁鑫, 罗世辉, 马卫华, 等. 磁浮列车单铁悬浮车桥耦合振动分析[J]. 交通运输工程学报, 2012, 12(2): 32-37.

熊高翔, 刘峰, 刘少克. 混合悬浮系统的自适应PID控制研究[J]. 机车电传动, 2014(4): 33-36.

XIONG Gaoxiang, LIU Feng, LIU Shaoke. Adaptive PID control of hybrid suspension system[J]. Electric Drive for Locomotives, 2014(4): 33-36.

梁潇, 陈峰, 傅庆湘. 160 km/h中速磁浮交通系统的关键技术问题[J]. 城市轨道交通研究, 2019, 22(9): 21-26.

LIANG Xiao, CHEN Feng, FU Qingxiang. Key technical issues on 160 km/h medium-speed maglev transit system[J]. Urban Mass Transit, 2019, 22(9): 21-26.

韩霄翰, 李忠继, 池茂儒. 轨道梁结构对中低速磁浮车轨耦合振动的影响[J]. 铁道机车车辆, 2019, 39(5): 36-42.

HAN Xiaohan, LI Zhongji, CHI Maoru. Influence of track beam structure on the mid-low maglev vehicle-rail coupling vibration[J]. Railway Locomotive & Car, 2019, 39(5): 36-42.

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