Nonlinear dynamics of 3D superconducting maglevs with six degrees of freedom: dependence on magnetization strategy and disturbance type

Abstract

Based on the heat diffusion equation, Maxwell’s equations, and translational and rotational dynamic equations, we establish and theoretically validate an electromagnetic-thermal-mechanical coupling model to analyze the levitation performance during normal operation and the nonlinear dynamic behavior under disturbance for 3D maglev systems composed of a six-degree-of-freedom bulk superconductor (SC) and a Halbach-type guideway of permanent magnets (PMs) with different magnetization strategies and different types of disturbances, as well as the change rules of magnetic force and torque during translational or rotational cycle movement. In order to ensure the system security, we propose a generalized electromagnetic restoring force model to theoretically analyze the stability of the SC moving along the directions of various degrees of freedom. The results show that after being disturbed, the SC vibrates along the direction of each degree of freedom, and the vibration center, i.e. equilibrium position, will drift along each vibration direction. With time increasing, the equilibrium position will appear periodically on both sides of the working position. Compared to zero-field cooling magnetization, field cooling magnetization enables the SC to trap more flux in its interior to alleviate the drift phenomenon and reduce the energy loss. This advantage can be further enhanced by adding an extra step of preloading treatment. For the lateral motion, the system has one stable focus point and two unstable saddle points. Whether the system at these saddle points is stable depends on the direction of disturbance-induced velocity. For the rotational motion, the system has only one stable focus point, which means that regardless of the type of disturbance, the SC will finally come back to its stable equilibrium position. Besides, the stability is related to the axis around which the SC rotates, and rotating around the longitudinal axis is more likely to generate larger magnetic force, torque and local temperature rise. Either field cooling magnetization or preloading treatment can effectively improve system stability.