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The purpose of this paper is to analyse the accuracy of the thrust force of a linear actuator computed with different finite elements models.

A series of 2D and 3D models corresponding to different levels of approximation of the original problem are considered. A reliable error estimator based on dual magnetostatic formulations is used.

A 3D model does not necessarily ensure more accurate results than a 2D model. Because of limitations on the number of mesh elements, the discretisation error in 3D can be of the same order of magnitude as the error introduced by the 2D approximation.

The results emphasise the need to consider errors arising from different simplifications with respect to one another, in order to avoid improvements of the model increasing the complexity but not improving the accuracy of the results.

Two complementary 3D finite element formulations, with either the magnetic field or the magnetic vector potential as unknowns, are developed to deal with the modeling of eddy currents in electrical steel laminations. The magnetic flux through the flux gates of the conducting region is imposed via the boundary terms of the weak formulations, in a natural way thanks to the use of edge finite elements. The two formulations are applied to a simple 1D eddy current problem with analytical solution. As a practical 3D application example, a T‐joint region of an electrical steel lamination is considered.

A finite element analysis of a permanent magnet transverse flux linear actuator is presented. In this application where we need a small model (for optimisation purposes) as well as a high accuracy on the computed force, we propose to combine several models with different levels of size and complexity, in order to progressively elaborate an accurate, but nevertheless tractable, model of the system.

To understand the behavior of the magnetization processes in ferromagnetic materials in function of temperature, a temperature-dependent hysteresis model is necessary. This study aims to investigate how temperature can be accounted for in the energy-based hysteresis model, via an appropriate parameter identification and interpolation procedure.

The hysteresis model used for simulating the material response is energy-consistent and relies on thermodynamic principles. The material parameters have been identified by unidirectional alternating measurements, and the model has been tested for both simple and complex excitation waveforms. Measurements and simulations have been performed on a soft ferrite toroidal sample characterized in a wide temperature range.

The analysis shows that the model is able to represent accurately arbitrary excitation waveforms in function of temperature. The identification method used to determine the model parameters has proven its robustness: starting from simple excitation waveforms, the complex ones can be simulated precisely.

As parameters vary depending on temperature, a new parameter variation law in function of temperature has been proposed.

A complete static hysteresis model able to take the temperature into account is now available. The identification is quite simple and requires very few measurements at different temperatures.

The results suggest that it is possible to predict magnetization curves within the measured range, starting from a reduced set of measured data.

Finite element (FE) models are considered for the penetration of magnetic flux in type-II superconductor films. A shell transformation allows boundary conditions to be applied at infinity with no truncation approximation. This paper aims to determine the accuracy and efficiency of shell transformation techniques in such non-linear eddy current problems.

A three-dimensional H – ϕ formulation is considered, where the reaction field is calculated in the presence of a uniform applied field. The shell transformation is used in the far-field region, and the uniform applied field is introduced through surface terms, so as to avoid infinite energy terms. The resulting field distributions are compared against known solutions for different geometries (thin disks and thin strips in the critical state, square thin films). The influence of the shape, size and mesh quality of the far-field regions are discussed.

The formulation is shown to provide accurate results for a number of film geometries and shell transformation shapes. The size of the far-field region has to be chosen in such a way to properly capture the asymptotic decay of the fields, and a practical procedure to determine this size is provided.

The importance of the size of the far-field region in a shell transformation and its proximity to the conducting domains are both highlighted. This paper also provides a numerical way to apply a constant magnetic field in a given region, while the source, on which only the far-field behaviour of the applied field depends, is excluded from the model.

The purpose of this paper is to calculate the electromagnetic torque at a radius of an integration contour for which an optimal value is determined.

To analyze electrical machine dynamics, the electromagnetic torque should be precisely determined. This paper presents a method for calculating the torque, where the radius of the integration contour is variable and estimated from the field distribution.

The electromagnetic torque of the three‐phase AC motor model proposed in TEAM Problem No. 30 is estimated using the proposed method. The obtained results are compared to solutions obtained analytically.

This paper examines the application of the presented method to determine the electromagnetic torque in three‐phase AC motors.

The purpose of this paper is to investigate the lateral forces during the fall of a magnet in a conducting pipe, when the direction of magnetization of the magnet is fixed. If the direction of magnetization is not parallel to the axis of the pipe, lateral forces occur and a decentration of the magnet happens.

The problem is studied numerically, with a T − h 3D FE formulation well‐suited for the problem. Computational results are compared with experimental results.

The physical model is given and the main force coefficients analyzed. The lateral forces and the decentration phenomenon are studied as a function of the main parameters (thickness and radius of the pipe).

The direction of magnetization is a key parameter to analyze the dynamics of a magnet motion inside a conducting pipe, when the radii of the pipe and the magnet are not so close. This analysis with a fixed direction of magnetization allows one to quantify the lateral forces and the decentration, and is a first step to understand the complete motion which includes the rotation which can be linked to the decentration.

An enhanced version of a mixed field‐based formulation for magnetostatics previously developed by the authors is presented and its features are discussed. The formulation minimises the residual of the constitutive equation, and exactly imposes Maxwell’s equations with Lagrange multipliers. Finite elements satisfying the physical continuity properties for both the magnetic and the magnetic induction fields are used in the numerical approximation. The possibility of decoupling the formulation in two separate sets of equations is discussed. A preconditioned iterative method to solve the final algebraic linear system is presented. Finally, a very natural refinement indicator is defined to guide an adaptive mesh refinement procedure.

The aim of the paper is to provide a simple and reliable hysteresis model for prediction of magnetization curves of a resistance spot welding transformer (RSWT) core, operating in a wide range of flux densities and excitation frequencies.

The hysteresis model considered in the paper is the T(x) description advanced by J. Takács. Three options to extend the model to the dynamic magnetization conditions are considered. The excitation conditions differ from those prescribed by international standards.

The quasi‐static Takács model combined with a fractional viscosity equation similar to that proposed by S.E. Zirka outperforms other considered options. The effect of eddy currents may be considered as a disturbance factor to the frequency‐independent quasi‐static hysteresis loop.

The combined approach yields in most cases a satisfactory agreement between theory and experiment. For highest frequency considered in the paper (1 kHz) excessive “heels” were observed in the modelled loops. This artifact may be reduced by the introduction of a more complicated relationship for the viscous term. Future work shall be devoted to this issue.

The combined Takács‐Zirka model is a useful tool for prediction of magnetization curves of a RSWT core in a wide range of flux densities and excitation frequencies.

The usefulness of the Takács description has been verified in a practical application. The model is able to predict magnetization curves under non‐standard excitation conditions.

The high calculation effort for accurate material loss simulation prevents its observation in most magnetic devices. This paper aims at reducing this effort for time periodic applications and so for the steady state of such devices.

The vectorized Jiles-Atherton hysteresis model is chosen for the accurate material losses calculation. It is transformed in the frequency domain and coupled with a harmonic balanced finite element solver. The beneficial Jacobian matrix of the material model in the frequency domain is assembled based on Fourier transforms of the Jacobian matrix in the time domain. A three-phase transformer is simulated to verify this method and to examine the multi-harmonic coupling.

A fast method to calculate the linearization of non-trivial material models in the frequency domain is shown. The inter-harmonic coupling is moderate, and so, a separated harmonic balanced solver is favored. The additional calculation effort compared to a saturation material model without losses is low. The overall calculation time is much lower than a time-dependent simulation.

A moderate working point is chosen, so highly saturated materials may lead to a worse coupling. A single material model is evaluated. Researchers are encouraged to evaluate the suggested method on different material models. Frequency domain approaches should be in favor for all kinds of periodic steady-state applications.

Because of the reduced calculation effort, the simulation of accurate material losses becomes reasonable. This leads to a more accurate development of magnetic devices.

This paper proposes a new efficient method to calculate complex material models like the Jiles-Atherton hysteresis and their Jacobian matrices in the frequency domain.