3-D Finite-Element Simulation of the Vertical Force Evolvement of a Bulk High-Tc Superconductor Subjected to Durative Vertical Fluctuation

The motivation of this paper is intended to investigate the evolving characteristics of the vertical force of a bulk high-Tc superconductor (HTSC) undergoing a durative vertical fluctuation above a permanent magnet guideway (PMG) with a 3-D finite-element model. To mathematically characterize the electromagnetic interaction of the HTSC/PMG system, the 3-D model was established by making recourse to a combination of current vector potential method and Helmholtz's theorem. The special properties of HTSC, including the anisotropic critical current density and nonlinear E-J relation, were taken into account by means of the elliptical model and power-law model respectively. The envisaged factors that may affect the vertical force of the HTSC in the case considered here, such as levitation height and amplitude of vertical fluctuation, were estimated by altering the specific shape of each factor. Numerical results demonstrate that, increasing the levitation height will result in a lower decay of the vertical force due to vertical fluctuation. In contrast, increasing the amplitude of the vertical fluctuation will deteriorate the vertical force decay. Fortunately, the levitation force decay tends to be suspended after a certain cycle of vertical fluctuation, which is in agreement with our previous experimental findings.