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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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).
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This study was funded by the National Natural Science Foundation of China (Grant Number 51875483).
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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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DOI: https://doi.org/10.1007/s11071-020-05917-8