Abstract
The modeling of superconducting magnetic bearings (SMBs) is of great significance for predicting and optimizing their levitation performance before construction. Although much effort has been made in this area, there still remains some space for improvements. Thus the goal of this work is to report a flexible, fast and trustworthy H-formulation finite element model. First the methodology for modeling and calibrating both bulk-type and stack-type SMBs is summarized. Then its effectiveness for simulating SMBs in 2D, 2D axisymmetric and 3D is evaluated by comparison with measurements. In particular, original solutions to overcome several obstacles are given: clarification of the calibration procedure for stack-type and bulk-type SMBs, details on the experimental protocol to obtain reproducible measurements, validation of the 2D model for a stack-type SMB modeling the tapes’ real thickness, implementation of a 2D axisymmetric SMB model, implementation of a 3D SMB model, and extensive validation of the models by comparison with experimental results for field cooling and zero field cooling, for both vertical and lateral movements. The accuracy of the model being having proven, it now has a strong potential for speeding up the development of numerous applications including maglev vehicles, magnetic launchers, flywheel energy storage systems, motor bearings and cosmic microwave background polarimeters.
Highlights
The relative movement between a permanent magnet (PM) and a high temperature superconductor (HTS) can induce supercurrents in the HTS
Repulsive depending on the arrangement and on the operating conditions. It can even provide passive stable levitation. This unique feature motivated the development of superconducting magnetic bearings (SMBs) [1,2,3,4]
The PM assembly is an arrangement of any number of PMs and ferromagnetic pieces surrounded by air
Summary
The relative movement between a permanent magnet (PM) and a high temperature superconductor (HTS) can induce supercurrents in the HTS. This is probably an evolution of the code reported in [54] for the 3D simulation of a cylindrical HTS bulk over a PM guideway In those articles, the field of the moving PM, obtained analytically, was applied as a timedependent Dirichlet boundary condition on the outer boundary of a model including only the HTS domain and a thin air domain. Key advancements with respect to previous models include: clarification of the calibration procedure for stack-type and bulk-type SMBs, details on the experimental protocol to obtain reproducible measurements, validation of the 2D model for a stack-type SMB considering the tapes real thickness, implementation of a 2D axisymmetric SMB model, implementation of a 3D SMB model, and extensive validation of the models by comparison with experimental results for field cooling and zero field cooling, for both vertical and lateral movements. The test cases reported here have been selected to serve as benchmarks, with the aim to help focus the effort of the numerical modeling community towards the most relevant approaches [65]
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