Lateral motion stability of high-temperature superconducting maglev systems derived from a nonlinear guidance force hysteretic model

High-temperature superconducting (HTS) maglev, owning to the capability of passive stabilization, is potentially promising for high-speed transportation. The guidance force of bulk HTS materials above a permanent magnetic guideway has a nonlinear response due to the hysteresis effect. As a kind of rail transit, when the vehicle runs along the track, the curve and other disturbances will cause vibrations to the vehicle system. These physical factors will pose dynamic loads on the components, reducing structural reliability as well as affecting the ride comfort. The lateral motion, as an important part of the vehicle system dynamics, needs to be studied in the pursuit of HTS maglev realization. In this paper, we first measured the guidance forces of HTS bulks under different motion conditions, and analyzed the relationship between the lateral displacement, the movement velocity and the guidance force. Then, a mathematical model was built based on these experimental data. The key feature of this mathematical model is that it can describe the hysteresis characteristic of the guidance force. Based on this model, we investigated the lateral motion stability of the HTS levitation system, and found three singular points, one stable focus point, and two unstable saddle points. Lastly, a phase portrait was proposed to indicate the safe working region of the HTS maglev vehicle where the vehicle can automatically return to its equilibrium position. These experimental and simulation results are important to clarify the lateral motion stability under external disturbance or shock, and provide a reference basis for the design of levitation systems.