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An appropriate equivalent model is the key to the effective analysis of the system and structure in which permanent magnet takes part. At present, there are several equivalent models for calculating the interacting magnetic force between permanent magnets including magnetizing current, magnetic charge and magnetic dipole–dipole model. How to choose the most appropriate and efficient model still needs further discussion.

This paper chooses cuboid, cylindrical and spherical permanent magnets as calculating objects to investigate the detailed calculation procedures based on three equivalent models, magnetizing current, magnetic charge and magnetic dipole–dipole model. By comparing the accuracies of those models with experiment measurement, the applicability of three equivalent models for describing permanent magnets with different shapes is analyzed.

Similar calculation accuracies of the equivalent magnetizing current model and magnetic charge model are verified by comparison between simulation and experiment results. However, the magnetic dipole–dipole model can only accurately calculate for spherical magnet instead of other nonellipsoid magnets, because dipole model cannot describe the specific characteristics of magnet's shape, only sphere can be treated as the topological form of a dipole, namely a filled dot.

This work provides reference basis for choosing a proper model to calculate magnetic force in the design of electromechanical structures with permanent magnets. The applicability of different equivalent models describing permanent magnets with different shapes is discussed and the equivalence between the models is also analyzed.

The purpose of this paper is to solve generic magnetostatic problems by BEM, by studying how to use a boundary integral equation (BIE) with the double layer charge as unknown derived from the scalar potential.

Since the double layer charge produces only the potential gap without disturbing the normal magnetic flux density, the field is accurately formulated even by one BIE with one unknown. Once the double layer charge is determined, Biot‐Savart's law gives easily the magnetic flux density.

The BIE using double layer charge is capable of treating robustly geometrical singularities at edges and corners. It is also capable of solving the problems with extremely high magnetic permeability.

The proposed BIE contains only the double layer charge while the conventional equations derived from the scalar potential contain the single and double layer charges as unknowns. In the multiply connected problems, the excitation potential in the material is derived from the magnetomotive force to represent the circulating fields due to multiply connected exciting currents.

The application of the equivalent source methods for the numerical calculation of the total magnetic force acting upon a permanent magnet is proposed. These methods are formulated in terms of the external field, which allows the complete avoidance of the numerical inaccuracies affecting force computation due to the singularity of the self‐field of the magnet on its edges. It is shown, with the help of some 2D and 3D test cases, that the proposed formulae provide reliable and stable results, even when the FEM mesh is not refined. Such results have also been compared with those derived from more traditional methods, such as the surface integration of the Maxwell’s stress tensor and the virtual work method, exhibiting better precision and lower computational costs.

The purpose of this paper is to deal with the investigation of no-load operation of tubular linear permanent magnet synchronous machines (T-LPMSMs). It is aimed at the prediction of the phase flux linkages, the back-EMF and the cogging force using a position varying magnetic equivalent circuit (MEC).

This study is based on the elaboration and the resolution of the position varying MEC, and the utilization of its results for the prediction of the phase flux linkages, the back-EMF and the cogging force, considering a general topology of T-LPMSMs. Then, a case study is treated with a position varying MEC-based investigation of its no-load features. These are validated by a 2-D finite element analysis (FEA).

It has been found that the developed position varying MEC can be regarded as an accurate tool that requires a low CPU-time.

Beyond the FEA validation, this work should be extended to an experimental one. Moreover, the position varying MEC validity should be extended to load operation in order to enable the prediction of the force production capability.

The developed position varying MEC could be suitably used for the pre-design of T-LPMSMs. These are currently given an increasing attention in many applications, such as wave energy conversion and free-piston engines.

The paper proposes a position varying MEC for the prediction of the features of T-LPMSMs.

The paper seeks to solve nonlinear magnetostatic field problems with the integral equation method and different indirect formulations.

To avoid large cancellation errors in cases where the demagnetizing field is high a difference field concept is used. This requires the computation of sources of the scalar potential of the excitation field.

A new formulation to compute these sources is presented. The improved computational accuracy is demonstrated with numerical examples.

The paper develops a novel formulation for the computation of sources of scalar excitation potential.

This paper aims to suggest the use of air or iron intervals between axially magnetized rings to increase the forces and stiffness of permanent magnet passive magnetic bearings (PMBs). The paper calculates the stiffness of such bearings through an analytical method and optimizes the dimensions of the magnets for achieving maximum stiffness.

For determining the magnetic fields distribution, forces and stiffness of the bearings, a 2D analytical method is used, based on the subdomain method. For the sake of generalization, all of the parameters are normalized and optimized for maximum normalized stiffness per magnet volume ratio.

The optimum sizes of the magnets as well as the optimum dimensions of the air or iron intervals are calculated in this paper. The optimum sizes of the magnets are around the air gap length and it is very difficult to realize them. Using iron intervals can improve the stiffness to the extremely high values in practical dimensions of the magnets.

This paper presents a novel configuration for improving the performance of PMBs with alternately axially magnetized rings.

To show for magnetostatic problems, how the numerically expensive post‐processing with the integral equation method (IEM) can be accelerated with the fast multipole method (FMM) and how this approach can be used to generate post‐processing data that allow for drawing streamlines.

In general, post‐processing with the IEM requires computation of the induced field due to solution variables, the field of permanent magnets and of free currents. For each of the three parts an approach to apply the FMM. With these approaches, large numbers of evaluation points can be used which are needed when streamlines are to be drawn. It is shown that this requires specially tailored meshes.

Post‐processing time can be largely reduced by applying the FMM. Additional memory requirements are acceptable even for high numbers of evaluation points. In order to obtain streamline breaks at material discontinuities, flat volume elements can be used.

The presented application of the FMM is applicable only to static problems.

Application of the FMM during post‐processing allows for a large number of evaluation points which are often required to visualize electromagnetic fields. This approach in combination with specially tailored meshes allows for drawing of streamlines.

The FMM is used not only to solve the field problem, but also for post‐processing which requires using the FMM to compute induced magnetic fields as well as the field due to permanent magnets and free currents. This leads to a speedup which allows for a large number of evaluation points which can be used, e.g. for high‐precision drawing of streamlines.

Two magnetostatic applications are reported, related to the magnetic field around the aluminium electrolysis cells. The first exhibits the magnetic field created by the current carrying parts in the cell neighbourhood, by taking into account the influence of the magnetic bodies. The second is referring to a magnetostatic shield with double walls, designated to protect the electronic data acquisition equipment when is used in this environment. As introduction, some features are presented and discussed for three models used in the field calculation of magnetically polarised bodies and the algorithm of iterative calculation in spaces with sparse magnetic bodies.

A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived equations are expressed in a general form so that any magnetic source can be utilized. The model assumes the length of the conductive plate is large and the thickness of the plate is thin but not negligible. The paper aims to discuss these issues.

The conducting and non-conducting regions are formulated in terms of decoupled magnetic vector potential components. In order to accurately compute the eddy current fields and forces the source field only needs to be applied on the surface of the conducting plate. The primary focus is on reducing the eddy current computational time.

The accuracy of the presented approach is verified by utilizing a magnetic rotor that has both a rotational and translational motion. The proposed method is computationally efficient and its accuracy is validated using the finite element method.

The conducting plate thickness is assumed to be thin (but not negligible), and this enables the field interaction through the edge of the plate to be neglected. The lateral force is not calculated in the proposed approach.

The calculation procedure presented is computationally fast and therefore this can enable the 3-D eddy current forces to be computed in near real-time.

This paper presents a fully 3-D analytic based eddy current formlation for computing the eddy current fields and forces in a conducting plate of finite thickness and finite width. The modeling approach is shown to be computationally accurate and relatively fast.

The paper aims to describe the coupling of magnetostatic finite formulation of electromagnetic field with two integral methods.

The first hybrid scheme is based on Green's function applied to magnetization source while the other one is based on a magnetic scalar potential boundary element method. A comparison of the two techniques is performed on a benchmark case with analytical solution, on a 2D multiply‐connected problem and on an industrial case where measurements are available.

The proposed hybrid approaches have proved to be effective techniques to solve open boundary non‐linear magnetostatic problems. Similar convergence speed with respect to the number of unknowns is found for both schemes

The paper shows the effectiveness of hybrid schemes applied to the finite formulation, assessing their performances on various test cases.