Study on stability and bifurcation of electromagnet-track beam coupling system for EMS maglev vehicle
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ORIGINAL PAPER
Study on stability and bifurcation of electromagnet-track beam coupling system for EMS maglev vehicle Xiaohao Chen
. Weihua Ma
. Shihui Luo
Received: 20 October 2019 / Accepted: 25 August 2020 Ó Springer Nature B.V. 2020
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. X. Chen W. Ma (&) S. Luo Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu, People’s Republic of China e-mail: [email protected] X. Chen e-mail: [email protected]
Keywords Maglev vehicle Stability analysis Hopf bifurcation Bautin bifurcation Limit cycle
1 Introduction EMS (electromagnetic suspension) maglev vehicles rely on electromagnetic levitation to avoid mechanical contact in traditional wheel-rail trains, thus enjoying the advantages of being smooth and comfortable, with low noise, small turning radius and strong climbing ability [6, 14]. It also has broad application and development prospects in the intercity highway and low-speed urban traffic system. With electromagnet suspended under the track beam by electromagnetic attraction, the stable levitation of the vehicle is realized by the active control of the electromagnetic coil current [21]. However, the variation of the electromagnetic force acting simultaneously on the flexible track beam will cause the vibration, which then changes the size of the air gap between the electromagnet and the track, thus in turn affecting the variation of the electromagnetic force, thereby forming the electromagnet-track beam coupled vibration system. If the parameters of the vehicle system do not match the track beam system, coupled self-excited vibrations may occur between the electromagnet and the track beam, affecting the stable levitation of the vehicle. The EMS maglev transportation system often
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