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.

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.

This paper presents a new design for a superconducting linear motor (SLM). This SLM uses stacks of second-generation (2G) superconducting tapes, which are responsible for replacing yttrium barium copper oxide 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 the 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.

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.

The second-generation (2G) YBCO wire has been used for several applications, such as electric power transmission and distribution cables, fault current limiters, MagLev vehicles, electric machines, high field magnets, superconducting magnetic energy storage, etc. The main advantages of 2G wires are: high critical current density values, large scale production, lower manufacturing cost than first generation, and superior performance under high magnetic fields. This work presents a preliminary study of superconducting magnetic bearings (SMB) using 2G wires as passive levitators. A superconducting block using stacked 2G wires was built to evaluate the behavior of coated conductors in the SMB application. The levitation and lateral force between the 2G block and a permanent magnet guideway was measured and compared with the results for an YBCO bulk with approximately the same dimensions. The results indicate that 2G wires have potential for applications with superconducting levitation, but its economic feasibility still depends on the coated conductors price decreasing.

The unique properties of high critical temperature superconductors (HTS) make possible the development of an effective and self-stable magnetic levitation (MagLev) transportation system. In this context, a full scale MagLev vehicle, named MagLev-Cobra, has been developed at the Laboratory for Applied Superconductivity (LASUP/UFRJ). The vehicle is borne by a linear superconducting magnetic bearing (LSMB). The most important design constraint of the levitation system is the force that appears due to the interaction between the HTS and the permanent magnetic (PM) rail, which composes the LSMB. Static and dynamic characteristics of this force must be studied. The static behavior was already reported in previous work. The dynamic operation of this kind of vehicle, which considers the entry and exit of passengers and vibration movements, may result in the decrease of the gap between the superconductor and the PM rail in LSMB. In order to emulate the vehicle operation and to study the gap variation with time, the superconductors are submitted to a series of vertical displacements performed with the help of an experimental test rig. These movements are controlled by a time-variant reference force that reproduces the vehicle dynamic. In the present work, the results obtained for the dynamic gap behavior are presented. These measurements are essential to the commissioning process of a superconducting MagLev full scale vehicle.