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Study on stability and bifurcation of electromagnet-track beam coupling system for EMS maglev vehicle

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Abstract

The stability and bifurcation behavior of the electromagnet-track beam coupling system of the electromagnetic suspension maglev vehicle are studied by the theoretical and numerical analyses. The stability domain of three key dynamics parameters of the track beam as well as the Lyapunov coefficient at the degenerated equilibrium point is calculated. The topological structure of the solution to the coupling system near the Bautin bifurcation point is determined. The results show that in the engineering practice, the intermediate frequency should be avoided in the natural frequency of the track beam; when a low frequency is taken, it should be reduced as much as possible; when a high frequency is taken, it should be increased as much as possible and the damping ratio should also be increased, so that the system can remain stable while a lighter-weight track beam is used, thereby reducing the engineering costs. Besides, when the parameters are near the Bautin bifurcation point, the system will have complex dynamics behaviors. Within a certain parameter range, multiple stable and unstable limit cycles exist simultaneously, so that the system tends to have different stable solutions under different initial disturbances.

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Acknowledgements

This study was funded by the National Natural Science Foundation of China (Grant Number 51875483), the National Key R&D Program of China (Grant Number 2016YFB1200601-A03) and Independent Topics of National Key Laboratories (Grant Number 2020TPL-T04).

Funding

This study was funded by the National Natural Science Foundation of China (Grant Number 51875483).

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Authors and Affiliations

  1. Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu, People’s Republic of China

    Xiaohao Chen, Weihua Ma & Shihui Luo

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  1. Xiaohao Chen
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  2. Weihua Ma
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  3. Shihui Luo
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Correspondence to Weihua Ma.

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Appendix: Parameters of electromagnet-track beam coupling system in Sect. 4

Appendix: Parameters of electromagnet-track beam coupling system in Sect. 4

Parameter

Description

Value

m

Mass of electromagnet

550 kg

g

Gravity acceleration

9.8 m/s2

\( \mu_{0} \)

Permeability in vacuum

\( 4\pi \times 10^{ - 7} \;{\text{T}}\;{\text{m/A}} \)

N

Coil turns of electromagnet core

800

A

Area of the magnetic pole of the electromagnet

0.014 m2

\( \delta_{0} \)

Rated levitation gap

8 mm

i 0

Stable levitation current

11.07 A

k P

Gap feedback coefficient

3500

k D

Velocity feedback coefficient

300

k e

Current feedback coefficient

25

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Chen, X., Ma, W. & Luo, S. Study on stability and bifurcation of electromagnet-track beam coupling system for EMS maglev vehicle. Nonlinear Dyn 101, 2181–2193 (2020). https://doi.org/10.1007/s11071-020-05917-8

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