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This paper aims to introduce an alternative for modeling levitation forces between NdFeB magnets and bulks of high-temperature superconductors (HTS). The presented approach should be evaluated through two different formulations and compared with experimental results.

The T-A and H-ϕ formulations are among the most efficient approaches for modeling superconducting materials. COMSOL Multiphysics was used to apply them to magnetic levitation models and predict the forces involved.The permanent magnet movement is modeled by combining moving meshes and magnetic field identity pairs in both 2D and 3D studies.

It is shown that it is possible to use the homogenization technique for the T-A formulation in 3D models combined with mixed formulation boundaries and moving meshes to simulate the whole device’s geometry.

The case studies are limited to the formulations’ implementation and a brief assessment regarding degrees of freedom. The intent is to make the simulation straightforward rather than establish a benchmark.

The H-ϕ formulation considers the HTS bulk domain as isotropic, whereas the T-A formulation homogenization approach treats it as anisotropic. The originality of the paper lies in contrasting these different modeling approaches while incorporating the external magnetic field movement by means of the Lagrangian–Eulerian method.

Semi-active suspension systems with electromagnetic dampers allow energy regeneration and the required control strategies are easier to implement than the active suspensions are. This paper aims to address the application of a tubular linear permanent magnet synchronous machine for a semi-active suspension system.

Classical rules of mechanics and electromagnetics were applied to describe a dynamic model combining vibration and electrical machines theories. A multifaceted MATLAB®/Simulink model was implemented to incorporate equations and simulate global performance. Experimental tests on an actual prototype were carried out to investigate displacement transmissibility of the passive case. In addition, simulation results were shown for the dissipative semi-active case.

The application of the developed model suggests convergent results. For the passive case, numerical and experimental outcomes validate the parameters and confirm system function and proposed methodology. MATLAB®/Simulink results for the semi-active case are consistent, showing an improvement on the displacement transmissibility. These agree with the initial conceptual thoughts.

The use of linear electromagnetic devices in suspension systems is not a novel idea. However, most published papers on this subject outline active solutions, neglect semi-active ones and focus on experimental studies. However, here a dynamic mechanical-electromagnetic coupled model for a semi-active suspension system is reported. This is in conjunction with a linear electromagnetic damper.

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