Bifurcation analysis and parameter matching in maglev vehicle-guideway coupling systems

Abstract

This paper aims to investigate the bifurcation characteristics and parameter matching properties of the maglev vehicle-guideway coupling system(VGCS). Firstly, a nonlinear dynamic model of the VGCS is established. Based on this model, the stability regions of the VGCS in the track parameter plane and the control parameter plane are calculated using codimension-1 and codimension-2 bifurcation theories. And the influence of different system parameter variations on the stability regions is further studied. Then, the impact of magnetic saturation effect on Hopf bifurcation and limit cycle(LC) bifurcation is discussed. Under the influence of magnetic saturation, the VGCS exhibits a larger stability boundary, and its critical state is prone to manifest as stable. The periodic motion near the critical state and the evolution characteristics of LCs are studied, and the influence of bifurcation parameter changes on the critical state is presented. The results indicate that the VGCS will converge to LCs of different amplitudes under different disturbances. Finally, the effectiveness of the stability region calculation method is validated on a single electromagnet levitation platform.

Keywords

Maglev vehicle-guideway coupling system Hopf bifurcation stable domain limit cycle

Get full access to this article

View all access options for this article.

References

Chen

Luo

, et al. (2020) A vehicle–track beam matching index in EMS maglev transportation system. Archive of Applied Mechanics 90: 773–787.

Chen

, et al. (2023) Experimental study on vertical vehicle-rail-bridge coupling of medium and low speed maglev train based on track beam with different stiffness. Journal of Vibration and Control 29(17–18): 4129–4142.

Cheng

Y-C

Hsu

C-T

(2012) Hunting stability and derailment analysis of a car model of a railway vehicle system. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 226(2): 187–202.

Feng

Zhao

, et al. (2023) Effect of levitation gap feedback time delay on the EMS maglev vehicle system dynamic response. Nonlinear Dynamics 111(8): 7137–7156.

Govaerts

(2000) Numerical bifurcation analysis for ODEs. Journal of computational and applied mathematics 125(1–2): 57–68.

Guo

Chen

, et al. (2022) Coupling vibration analysis of high-speed maglev train-viaduct systems with control loop failure. Journal of Central South University 29(8): 2771–2790.

Guo

Shi

Zeng

(2023) Bifurcation and stability analysis of a high-speed rail vehicle with active yaw dampers. Journal of Vibration and Control 30(15–16): 2023.

Luo

(2021) Coupled dynamic analysis of low and medium speed maglev vehicle-bridge interaction using SIMPACK. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 235(3): 377–389.

Kamel

Kandil

El-Ganaini

, et al. (2014) Active vibration control of a nonlinear magnetic levitation system via Nonlinear Saturation Controller (NSC). Nonlinear Dynamics 77: 605–619.

10.

Kuznetsov

(1998) Elements of Applied Bifurcation Theory. Springer.

11.

Lee

S-Y

Cheng

Y-C

(2005) Hunting stability analysis of high-speed railway vehicle trucks on tangent tracks. Journal of Sound and Vibration 282(3–5): 881–898.

12.

Lee

Kim

Lee

(2006) Review of Maglev train technologies. IEEE Transactions on Magnetics 42(7): 1917–1925.

13.

Jie

Zhou

, et al. (2014) The active control of maglev stationary self-excited vibration with a virtual energy harvester. IEEE Transactions on Industrial Electronics 62(5): 2942–2951.

14.

Wang

Shen

(2019) Research on control method of Maglev vehicle-guideway coupling vibration system based on particle swarm optimization algorithm. Journal of Vibration and Control 25(16): 2237–2245.

15.

Schmid

Schneider

Dignath

, et al. (2020) Static and dynamic modeling of the electromagnets of the maglev vehicle transrapid. IEEE Transactions on Magnetics 57(2): 1–15.

16.

Shi

Wei

Zhao

(2007) Analysis of dynamic response of the high-speed EMS maglev vehicle/guideway coupling system with random irregularity. Vehicle System Dynamics 45(12): 1077–1095.

17.

Sun

Qiang

, et al. (2019) Hopf bifurcation analysis of maglev vehicle–guideway interaction vibration system and stability control based on fuzzy adaptive theory. Computers in Industry 108: 197–209.

18.

Sun

, et al. (2023) Dynamic analysis and vibration control for a maglev vehicle-guideway coupling system with experimental verification. Mechanical Systems and Signal Processing 188: 109954.

19.

Wang

Zhang

(2008) Sup-resonant response of a nonautonomous maglev system with delayed acceleration feedback control. IEEE Transactions on Magnetics 44(10): 2338–2350.

20.

Wang

Zhong

Shen

(2015) Analysis and experimental study on the MAGLEV vehicle-guideway interaction based on the full-state feedback theory. Journal of Vibration and Control 21(2): 408–416.

21.

Wiggins

(1990) Introduction to Applied Nonlinear Dynamical Systems and Chaos. New York: Springer.

22.

Zeng

X-H

Gao

D-G

, et al. (2021) Dynamic stability of an electromagnetic suspension maglev vehicle under steady aerodynamic load. Applied Mathematical Modelling 97: 483–500.

23.

Y-L

Wang

Z-L

G-Q

, et al. (2019) High-speed running maglev trains interacting with elastic transitional viaducts. Engineering Structures 183: 562–578.

24.

Yan

(2008) Development and application of the Maglev transportation system. IEEE Transactions on Applied Superconductivity 18(2): 92–99.

25.

Zhang

Dai

(2016) Bifurcation analysis of high-speed railway wheel-set. Nonlinear Dynamics 83: 1511–1528.

26.

Zhang

Huang

Zhang

(2009) Stability and Hopf bifurcation of the maglev system with delayed position and speed feedback control. Nonlinear Dynamics 57(1): 197–207.

27.

Zhang

Campbell

Huang

(2011) Nonlinear analysis of a maglev system with time-delayed feedback control. Physica D: Nonlinear Phenomena 240(21): 1761–1770.