Electromagnetic-thermal behaviors of bulk superconductor with cuboid slot under moving magnetic field

Abstract

We established a 3D coupled model to study the electromagnetic-thermal behaviors of a levitation system containing a bulk high-temperature superconductor (HTS) with a cuboid slot under the nonuniform magnetic field due to the movement of a permanent magnet (PM), analysing the influences of the geometrical parameters of the slot and inclination angle on the electromagnetic-thermal behaviors, giving the dynamic distribution of the global electromagnetic force density in the HTS. The results show that the longer the length of the slot, the smaller the levitation force, and the greater the loss. As its length takes up 7/10 of the HTS diameter, the loss is 4 times that of the HTS without damage. Due to the homodromous induced current appearing near the slot, the maximum guidance force increases with the length. The levitation force decreases with the increase of the slot depth. Its curve near the maximum becomes blunt and the loss increases significantly. As the depth is 3/5-4/5 of the HTS height, the loss is 300-400 times of that without damage. The guidance force and loss increase with the depth. As the inclination angle rises, the levitation and guidance force both drop. At 30 • , their maximums decrease by 70 % and 90 %, respectively. The lateral stability of the system thus becomes poorer, indicating the inclination angle is one of the important factors for instability. As the PM moves vertically, the guidance force density symmetrically distributes near the both wide sides of the slot. Its side faces with the wide sides will bear the shear force, resulting in that the slot has the tendency to tear along these faces. As the PM reciprocates laterally, the slot is subjected to the lateral shear force, proportional to the displacement.

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

“…In order to numerically solve the problem, a discretization method that previously used in [14][15][16] is adopted here. Based on Galerkin method and Green formula, the weak form of equation ( 7) be expressed as [14] ˆΩ…”

“…where W is the weight function of H. Supposing the computational domain Ω is divided by N tetrahedral elements, the equation of any node in each element can be obtained by means of the tetrahedron-element interpolation function. With the help of equation ( 13), the equations of all nodes in element i are assembled together to obtain a matrix form [15]…”

“…Based on different models and tools such as critical state models, frozen and diamagnetic image methods, and dipole-dipole interaction, a large number of theoretical works have studied the levitation force and the static stability by changing the system parameters, such as, on the one hand, the dimensions, critical current density, working position and cooling process of the SC and, on the other hand, the magnetization, number, size and arrangement of the PMs in the guideway [4][5][6][7][8][9]. Furthermore, finite element models using various formulations, such as A − V formulation for the magnetic potential vector and electric scalar potential, T − ω formulation for the current potential vector and scalar magnetic potential, and H formulation for the magnetic field, have been proposed to analyze the levitation and guidance forces including their relaxation behavior in two-dimensional (2D) or even 3D maglevs, taking into account the effect of thermally activated flux motion [10][11][12][13][14][15][16].…”

Effects of interior angle and inclination angle of slot defect on electromagnetic-stress behaviours of superconducting swing system

“…The HTS they used was fabricated from a non-uniform functional gradient material. In the literature [16], the electromagnetic-thermal behaviours of an HTS with a cuboid slot were studied during the horizontal or vertical movement of a permanent magnet (PM). And the influence of the variation of the length and depth of the slot on the electromagnetic-thermal behaviours was discussed.…”

“…As mentioned above, the 2D model is still the main established model. However, the inherent disadvantages of the 2D model itself limit the dimensionality of the object and the accuracy of the calculation [16]. With the upgrading of some commercial software, the use of 3D models is gradually increasing [12,17].…”