Nonlinear resonance behavior for HTS pinning maglev system with electromagnetic compensation based on multi-scale method and experimental analysis

In high-speed applications, high-temperature superconducting (HTS) magnetic levitation (maglev) trains face the problem of levitation force attenuation caused by eddy current losses in HTS bulks. The representative solution relies on the electromagnetic compensation subsystem (EMCS), but the interaction between the EMCS and permanent magnet guideway (PMG) exhibits nonlinear behaviors. The relationship is further superimposed with the hysteresis characteristics of HTS bulks, resulting in more complex nonlinear low-frequency vibrations. Due to the weak stiffness of the HTS maglev systems, sensitive spectra are easily excited when subjected to external disturbances, leading to resonance and endangering the safety and stability of train operation. In view of this, this paper focuses on exploring the nonlinear resonance behavior of the HTS-EMCS hybrid system. Firstly, the vertical dynamic equation of the hybrid system is constructed based on experimental results. Secondly, the analytical solutions of nonlinear equations are solved using the multi-scale method. Next, the nonlinear behavior of the system under different resonance conditions is analyzed through spectrum and phase trajectory analysis. Finally, vibration tests are conducted under different resonance forms to verify the conclusions. The study elucidates the nonlinear resonance laws of HTS-EMCS, and the results indicate that EMCS can effectively improve the damping and natural frequency of the original system. This helps to enhance system stability and avoid low-frequency resonance. This research provides a reference for the design, analysis, and application of HTS maglev equipped with the EMCS.