Levitation Stability and Hopf Bifurcation of EMS Maglev Trains

Hu, Jinglu; Ma, Wei; Chen, Xiaohao; Luo, Shan

doi:10.1155/2020/2936838

Cited by 10 publications

(6 citation statements)

References 18 publications

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“…In the previous formula, X 0 � x 0 y 0 􏼂 􏼃 T 􏼐 􏼑 and ΔX � Δx Δy 􏼂 􏼃 T 􏼐 􏼑. Substituting equation (12) into equation (11), using Taylor expansion and ignoring the higher-order small quantities in it, we get…”

Section: Vehicle-rail Coupling Modelmentioning

confidence: 99%

“…At present, the suspension control model of the maglev train mostly adopts the single electromagnet suspension system model, and the linearized model is applied to the classical control theory-PID or PD controller for control. In the suspension control of the maglev train, it is divided into voltage [12,13] and current [14][15][16][17][18] as the control target.…”

Section: Introductionmentioning

confidence: 99%

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Vertical Dynamic Response of the 2-DOF Maglev System considering Suspension Nonlinearity

Lin

et al. 2022

Mathematical Problems in Engineering

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In order to study the dynamic characteristics of the nonlinear system of the maglev train, a vibration model of the two-degree-of-freedom nonlinear suspension system of the maglev train is established in this paper. Based on the linearized model of the suspension control module, the suspension system is controlled by the state feedback method. Compared with the results of the Runge–Kutta method, the accuracy of the settlement results is verified. This paper analyzes the influence of system parameters and feedback control parameters on the system. The results show that the linear stiffness mainly affects the left-right migration of the resonance peak and the difference between the maximum and minimum of the resonance region of the suspension frame; the nonlinear stiffness mainly affects the slope of the resonance region of the car body and the suspension frame; displacement feedback control parameters can reduce the amplitude of the system, velocity feedback control parameters can make the state change of the suspension frame more smoothly, and acceleration feedback control parameters make the car body and the suspension frame have a strong coupling effect. According to the Hurwitz criterion of Hopf bifurcation, this paper deduces the conditions that the control parameters should satisfy when the equilibrium point is stable, and the instability produces periodic vibration under PID control. Through numerical simulation, it is found that the system has complex dynamic behavior, the results show that the system works under some conditions, and there are multiple stable and unstable limit cycles simultaneously. Therefore, the system will appear alternately between multiperiod and chaotic motion, which will affect the stability of the system.

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Section: Vehicle-rail Coupling Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vertical Dynamic Response of the 2-DOF Maglev System considering Suspension Nonlinearity

Lin

et al. 2022

Mathematical Problems in Engineering

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“…2,14 To determine the dynamic stability of a maglev system, Zhou et al 15 used the Lyapunov characteristic index, and some researchers used the Hopf bifurcation. 16–18…”

Section: Introductionmentioning

confidence: 99%

“…2,14 To determine the dynamic stability of a maglev system, Zhou et al 15 used the Lyapunov characteristic index, and some researchers used the Hopf bifurcation. [16][17][18] German Transrapid maglevs, Japanese L0 maglevs and the first commercial high-speed maglev based on the German Transrapid technology in Shanghai have shown that the speed of future guideway vehicles can reach 600 km/h or higher. Therefore, there is an urgent requirement for the development of more capable braking methods.…”

Section: Introductionmentioning

confidence: 99%

A small-distributed aerodynamic brake prototype and its effects on the vertical dynamics of high-speed electromagnetic suspension maglevs

Weng

Tian

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part F:

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Aerodynamic brake is a clean and environmentally friendly braking mode, which does not use mechanical friction as a braking force. This paper describes the development of a small-distributed aerodynamic brake prototype, including its structure, working principle, ground test, and test results. A computational fluid dynamics (CFD) method is developed to obtain the aerodynamic forces of the prototype, and the simulation results are validated by performing a wind tunnel test. On the basis of the CFD simulation, the panel opening process and braking process are modelled to analyse the vertical dynamic characteristics of a high-speed electromagnetic suspension maglev with aerodynamic brakes. In addition, a vehicle, guideway, and levitation controller are modelled. Finally, a three-car system dynamic model is solved to obtain the influences of the opening time, initial braking position, and feedback gains. The aerodynamic forces of the first car show the most significant changes when the braking panels are opened. The increase in the longitudinal force is 15461.16N, and the vertical force varies from a lift force of 35342.98N to a downforce of 40721.35N. The maximum guideway deflection decreases as the opening time increases. The difference between the deflections obtained at opening times of 0.064 s and 0.6 s is 1.2 mm. Furthermore, vertical accelerations decrease as the opening time increases. The condition in which the vehicle brakes when the first car enters the object guideway has the largest influence on the deflection of the guideway. To ensure levitation stability influenced by the vertical change of the first car, a high feedback gain for the levitation clearance change is required. However, the levitation stability with aerodynamic brakes is weakly affected by the feedback gains for the observed velocity and acceleration of the system.

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“…Due to the merits of wide speed range, low noise and low maintenance cost, the maglev train is a very competitive green ground transportation tool [2,3]. Based on the levitation principle, the maglev technologies can be divided into four forms: permanent magnetic suspension (PMS) [4,5], electromagnetic suspension (EMS) [6,7], electrodynamic suspension (EDS) [8,9] and flux pining suspension (FPS) [10,11]. Among them, the electrodynamic suspension is further divided into permanent magnet electrodynamic suspension (PM EDS) and superconducting electrodynamic suspension (SC EDS).…”

Section: Introductionmentioning

confidence: 99%

Design and Analysis of Guidance Function of Permanent Magnet Electrodynamic Suspension

et al. 2022

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Inspired by the guidance principle in the electromagnetic levitation system, a new permanent magnet electrodynamic suspension (PM EDS) structure with ferromagnetic guidance track is proposed and analyzed in this paper. Considering the lack of effective guidance ability for the PM EDS system, we adopted the ferromagnetic guidance track as being mounted under the conductor plate. The guidance principle is studied and the implementation of the guidance function is also introduced, and the finite element method (FEM) is employed and its accuracy is confirmed via the PM EDS high-speed rotating experimental platform fabricated in our laboratory. The influence of longitudinal speed on the guidance force is taken into account, which shows that the guidance performance is enhanced more obviously at low speeds. Moreover, the influence of the guidance track parameters on the guidance performance is also analyzed, including the geometric parameters, section shape, installation position and material. The equivalent small-scale PM EDS system experimental prototype is carried out to validate the effectiveness of the ferromagnetic guidance. The proposed ferromagnetic guidance structure is demonstrated to improve the guidance performance of the PM EDS system effectively, which will offer a technical reference for the practical engineering application of the PM EDS system.

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Levitation Stability and Hopf Bifurcation of EMS Maglev Trains

Cited by 10 publications

References 18 publications

Vertical Dynamic Response of the 2-DOF Maglev System considering Suspension Nonlinearity

Vertical Dynamic Response of the 2-DOF Maglev System considering Suspension Nonlinearity

A small-distributed aerodynamic brake prototype and its effects on the vertical dynamics of high-speed electromagnetic suspension maglevs

Design and Analysis of Guidance Function of Permanent Magnet Electrodynamic Suspension

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