Several techniques to model high temperature superconductors (HTSs) are used throughout the world. At the same time, the use of superconductors in transportation and magnetic bearings promises an increase in energy efficiency. However, the most widespread simulation technique in the literature, the H-formulation, has not yet been used to simulate superconducting levitation. The goal of this work is to present solutions for the challenges concerning the use of the H-formulation to predict the behavior of superconducting levitators built either with YBCO bulks or stacks of 2G wires. It is worth mentioning the originality of replacing bulks with HTS stacks in this application. In our simulation methodology, the movement between the HTS and the permanent magnet was avoided by restricting the simulation domain to the HTS itself, which can be done by applying appropriate boundary conditions and analytical expressions for the source field. Commercial finite element software was used for the sake of ease of implementation. Simulation results were compared with experimental data, showing good agreement. We conclude that the H-formulation is suitable for problems involving moving objects and is a good alternative to other approaches for simulating superconducting magnetic bearings.

A-V and H are two of the most widespread formulations applied in the literature to calculate current distribution in high-temperature superconductors (HTSs). Both formulations can successfully solve problems related to large-scale HTS applications, but the way to implement the calculations is different. In recent years, several authors have chosen the H formulation to solve problems related to HTS applications. This choice can probably be attributed to the easy implementation of the H formulation with the aid of commercial finite element method (FEM) software, producing precise results and performing fast calculations. In a previous work, we proposed the use of the H formulation to solve superconducting magnetic bearing (SMB) problems. However, most of the SMB simulations presented in the literature are solved using the A-V formulation implemented with the finite difference method (FDM). Which of these two techniques is more suitable for superconducting magnetic bearing applications? This paper aims to answer this question. In order to do so, an experimental rig was developed to test SMBs using YBCO bulks or stacks of coated conductors. The simulated levitation force results from the A-V formulation using FDM and from the H formulation using FEM were compared with the experimental data. In general, the calculation time and the results error obtained with both formulations are comparable. It is worth mentioning that the main contribution of this paper is to present improvements to reduce the A-V formulation computational time and details of how to implement it using FDM in any platform. For this reason, most of this work is about the A-V formulation, while the H formulation is just presented for comparison.

Considering the need for cost/performance prediction and optimization of superconducting maglev vehicles, we develop and validate here a 3D finite element model to simulate superconducting linear magnetic bearings. Then we reduce the 3D model to a 2D model in order to decrease the computing time. This allows us to perform in a reasonable time a stochastic optimization considering the superconductor properties and the vehicle operation. We look for the permanent magnet guideway geometry that minimizes the cost and maximizes the lateral force during a displacement sequence, with a constraint on the minimum levitation force. The displacement sequence reproduces a regular maglev vehicle operation with both vertical and lateral movements. For the sake of comparison, our reference is the SupraTrans prototype bearing. The results of the optimization suggest that the bearing cost could be substantially reduced, while keeping the same performances as the initial design. Alternatively, the performances could be significantly improved for the same original cost. I. INTRODUCTIONRecently, a full scale superconducting maglev vehicle, named MagLev-Cobra, was successfully demonstrated at the Federal University of Rio de Janeiro, Brazil [1,2]. In order to achieve the superconducting levitation, it uses a permanent magnet (PM) guideway and several cryostats containing YBCO superconducting bulks placed on the bottom of the vehicle. The interaction of the PM guideway static magnetic field with the superconductors produces stable levitation and lateral guidance forces. One issue of this technology is the cost, because of the large amount of rare earth PM used along the entire line. In this context, the optimization of the superconducting linear magnetic bearing (SLMB) focusing on the reduction of PM guideway material used, while maintaining the performances, motivates this work.Lately several models have been successfully developed by different research groups around the world to simulate superconducting magnetic bearings [3,4,5,6,7]. However, their use has been so far generally limited to parametric studies involving few hundred evaluations [8,9]. Indeed the problem is highly nonlinear and intrinsically time-dependent, leading to very large computing time in order to perform the numbers of simulations needed in a stochastic optimization process. This is the reason why, in [10,11], the shape of the PM guideway was optimized considering the superconductor as a perfect diamagnet. A SLMB model based on the critical state approximation was only used in a second step for verification.Besides, in previous works, only vertical motion was considered. But during the regular operation of a maglev vehicle, lateral displacements are to be expected, due to curves for example. This tends to modify the magnetization [12], and as a result to reduce the levitation force and alter the lateral force [13,14]. This should be taken into account during the optimization.We propose here to perform a stochastic optimization of the PM guideway geometry, takin...

This manuscript presents a new design for superconducting linear motor (SLM). This SLM uses stacks of second generation (2G) superconducting tapes, which are responsible for replacing YBCO bulks. The proposed SLM may operate as a synchronous motor or as a hysteresis motor, depending on the load force magnitude. A small scale linear machine prototype with 2G stacks was constructed and tested to investigate the proposed SLM topology. The stator traveling magnetic field wave was represented by several Nd-Fe-B permanent magnets. A relative movement was produced between the stator and the stack, and the force was measured along the displacement. This system was also simulated by finite element method, in order to calculate the induced currents in the stack and determine the electromagnetic force. The H-formulation was used to solve the problem and a power law relation was applied to take into account the intrinsically nonlinearity of the superconductor. The simulated and measured results were in accordance. Simulated results were extrapolated, proving to be an interesting tool to scale up the motor in future projects. The proposed motor presented an estimated force density of almost 500 N/kg, which is much higher than any linear motor.

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