Numerical simulations of the mutual effect among the superconducting constituents in a levitation system with translational symmetry

Abstract

By the introduction of a generalized magnetic vector potential, which contains the contributions of both the magnetic and electric parts, and the use of the Ampere's law within the quasistatic approximation as the state equation, the partial differential equations for governing the electromagnetic properties of superconductors as well as the surrounding coolant were established and numerically discretized by resorting to the finite-element technique and finite-difference scheme, respectively, in the spatial and temporal domain. In conjunction with an analytic method to calculate the magnetic field generated by permanent magnet, we compiled a numerical tool for performing an intricate study of the mutual effect among the superconducting constituents in a superconducting levitation system with translational symmetry. Taking a superconducting unit with three constituents inside as a practice, we simulated the electromagnetic responses of this unit while moving in the nonuniform magnetic field generated by permanent magnet guideway and, identified the influences of the mutual effect on the levitation force as well as on the distributions of the magnetic flux density, the supercurrent density, and the levitation force density by comparing to an envisaged reference, one constituent was simulated with all the rest absent to remove the mutual effect. The insights attained by the present study, mostly being inaccessible from the experiments, are aimed to provide useful implications for the design of a superconducting levitation system for the transit and analogous purposes, which usually employ multiple superconductors to achieve the desired capability.

Superconducting magnetic bearings simulation using an H-formulation finite element model

“…A summary of the formulation used by independent groups to model SMBs with homemade FE codes and free/nonfree FE softwares is proposed in Table I. TABLE I SMB FINITE ELEMENT MODELS 2-D 2-D axi 3-D A˗V Homemade Hofmann et al [24] Dias et al [25][26][27] Ma et al [28][29][30] Sugiura et al [31] Takeda et al [32] Chun et al [33] Ruiz-Alonso et al [34] Wang et al [35] Sotelo et al [36] Ueda et al [38] Software -Li et al [37] Hauser [39] T˗Ω Homemade Zheng et al [40] Zhang et al [41] Gou et al [42] Uesaka et al [43,44] Tsuchimoto et al [45] Tsuda et al [46][47][48] Ma et al [49,50] Pratap et al [ Sass et al [53] Quéval et al [54] *this work* Patel et al [55] *this work* Patel et al [55] Quéval et al [54] *this work* All these models have their own features and limitations. Focusing on the H-formulation, important efforts have been made to simulate SMBs using homemade codes.…”

Levitation and guidance force efficiencies of bulk YBCO for different permanent magnetic guideways

“…Because of the studies in literature are mostly related to Halbach [18][19][20] and conventional PMG [20], there is no detailed study to investigate the efficiency of different PMGs and reduce the fabrication cost of Maglev systems. In the present study, firstly, magnetic flux distributions of the used PMGs were simulated before the experimental studies.…”

Structural effect of the permanent magnet guideway on the dynamic behavior of a levitated high temperature superconductor

“…The existing studies on the dynamic behavior of a HTS maglev can be classified into two categories, one being composed of a HTS and a permanent magnet [3,4], which has been studied extensively by experiment and simulation because of its simplified structure. The other one having HTSs levitated over a permanent magnet guideway (PMG) [5] is more complicated and researched less, owing to the its diverse forms of motion for its more degrees of freedom.…”