Magnetostatic Field Calculation Research Articles

3D non-linear anisotropic magnetostatic field computation in reactor

The general 3D vector potential FEM formulations of non‐linear anisotropic magnetostatic field have been derived by using the dyadic analysis in this paper. The Newton‐Raphson method and improved ICCG algorithm are used for the 3D non‐linear anisotropic magnetostatic field computation. The 3D magnetic field in a reactor, the inductance and the voltage‐current characteristic (V‐I curve) of the reactor are calculated. The harmonic components under 1.35 times rated voltage are analyzed by the calculated V‐I curve. The calculated results are quite satisfactory when compared with the measurement ones.

Micromagnetic computational standard problem (abstract)

Proposed solutions to a standard problem in micromagentics that were collected anonymously from a number of researchers using a variety of computational techniques are presented. This is the first time that a problem in micromagnetics has been attempted by a group. The sample problem is a 1 μm×2 μm rectangular element of Permalloy film, 20 nm thick. The material properties are specified by an exchange stiffness constant, A=1.3×10−11 J/m, a magnetization, M=8.0×105 A/m, and a uniaxial ansotropy constant, K=5.0×102 J/m3 with the easy axis directed parallel to the long edge of the sample. The requested calculations are hysteresis loops for fields directed one degree away from the long and short axes and magnetization configuration data for the remanent states. The results collected show a surprising lack of agreement. For fields applied nearly parallel to the long axis of the sample problem, calculated coercivities range from 2.4 to 33 mT, squareness values range from 0.23 to 1.00, and there is a variety of hysteresis loop shapes and mazgnetization patterns. Similar differences exist in the results for fields applied nearly parallel to the short axis of the sample. Differences in computational methods that give rise to the disparity in the results, e.g., grid geometry and size and magnetostatic field calculation methods, are highlighted.

Numerical procedures for the calculation and design of automotive alternators

Numerical procedures were developed for the calculation and design optimization of claw-pole alternators. Based on a three-dimensional (3D) magnetostatic field computation, the output performance, efficiency, local and global forces are computed and compared to measurements. The precalculation of a claw-pole alternator is presented based on the example of a prototype with additional permanent magnets.

Three-dimensional magnetostatic field calculation using integro-differential equation for scalar potential

An effective method for calculation of nonlinear three-dimensional magnetostatic fields is proposed. It is based on a numerical solution of the integro-differential equation for the total scalar potential. The main advantages of this method are that the problem has been formulated in terms of a scalar variable introduced only for regions filled with ferromagnetic materials and no artificial boundary conditions are required. The numerical algorithm which implements this method is described. Its application is illustrated with magnetostatic field calculation for C-magnets.

The calculation of magnetostatic fields from axisymmetric conductors

We describe a method for calculating the magnetostatic fields of an iron free system of axisymmetric conductors. It is based on a series expansion that has an extensive and useful convergence region. The method is compared to the standard zonal harmonic method of Garrett. The convergence regions and the rates of convergence of the two methods are compared. For conductors of rectangular cross section, an algorithm is described in detail that calculates the conductors' magnetic fields. The implementation of the algorithm is computationally efficient using recurrence relations throughout and involves no numerical integration.

Coupled vector-scalar potential method for 3D magnetostatic field computations using hexahedral finite elements

This paper introduces a three dimensional finite element (3D-FE) method based on a coupled vector-scalar potential formulation. The method is most suited for large-scale magnetostatic field applications containing mixed media (conductors-iron), due to substantial savings in computational storage and CPU time. The method allows one to calculate the magnetic field intensity in the current-carrying regions using a reduced curl-curl formulation based on a second order hexahedral type FE. The resulting reduced field intensity is used to develop forcing functions for a global magnetic scalar potential solution over the entire volume of the problem based on a first order hexahedral type FE. The analysis developed is applied to an illustrative shell-type transformer for verification purposes of the numerical results.

Axisymmetrical magnetostatic field computation by a hybrid finite element-series method

This paper deals with a hybrid FEM-SERIES formulation and solution for axisymmetrical linear and nonlinear magnetostatic problems with an open region. In the interior region, a conventional FEM is formulated, while a SERIES formulation is proposed in the exterior region. Several examples are given for illustration and the numerical results are compared with those obtained by finite element solutions.

Calculation of magnetostatic field around far side defects for nondestructive testing

This paper describes a series of benchmark experiments for studying the leakage flux pattern that is created above an annealed steel plate when a corrosion pit is present, using finite elements. Two different defect profiles have been chosen in order to demonstrate that it is possible to determine the shape of the corrosion pit from the calculated leakage flux pattern. >

Iterative procedure for 3D modelling of electromagnetic actuators

An iterative procedure for calculation of 3D magnetostatic field in nonhomogeneous, nonlinear, and anisotropic regions of electromagnetic actuators has been presented. In the proposed method, the 3D task has been substituted with a sequence of 2D problems, so it was possible to adapt the algorithm worked out to PC 486 computers. The decomposition of the problem consists in: (a) separation of magnetic vector potential components, (b) partition of the considered region with a number of surfaces with 2D discretization. >

Conservative methods in boundary-element calculations of static fields

Application of a conservative form of boundary condition to the boundary-element method in its indirect formulation is suggested. It has been shown that the use of these conditions not only increases the accuracy of the numerical solution but also becomes a matter of principle for the calculation of electrostatic and magnetostatic fields in piece-homogeneous media that include thin layers and shells.

An h-formulation for the computation of magnetostatic fields. Implementation by combining a finite element method and a boundary element method

A new formulation of magnetostatics is given: it uses the magnetic field h as variable and a penalty technique. For its discretization, a finite element method inside the magnetic materials is combined with a boundary integral method which describes the exterior domain. Numerical tests are presented. The value to be chosen for the penalty parameter and a criterion of validity of the computation are given.

Nonlinear 3D magnetostatic field calculation by the integral equation method with surface and volume magnetic charges

The authors present a mathematical model for the 3-D nonlinear magnetostatic field based on integral equations with fictitious surface and volume magnetic charges. The solution is performed by the extended boundary element method including surface elements and volume elements. Examples of calculation for both linear and nonlinear magnetic systems are presented. The method has been shown to be accurate and efficient. >

2スカラポテンシャルを用いた境界要素法にまる三次元静磁界解析法の改良

2スカラポテンシャルを用いた境界要素法にまる三次元静磁界解析法の改良

An incomplete gauge formulation for 3D nodal finite-element magnetostatics

A method for imposing the gauge condition on the 3-D magnetic vector potential magnetostatic field computation using nodal finite elements is presented. In this method, the gauge A.w=0 is applied in the part of the problem that is not situated in the neighborhood of the materials interfaces that are tangential to w. This results in a formulation which maintains the discontinuous properties of the magnetic induction tangential components, reduces the number of unknowns, and improves the system matrix conditioning. The proposed formulation is compared with the Coulomb-gauge and ungauged formulations, showing that it results in better precision and worse conditioning than the Coulomb-gauge and has the same precision with a better conditioning than the ungauged formulation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Three dimensional magnetostatic field calculation using equivalent magnetic charge method

The equivalent magnetic charge method for three-dimensional magnetostatic field calculation is described. This method saves computational time and makes the requirements of the computer memory capacity smaller. The accuracy of the calculation results in the air region is high. As an example, the calculation results on electromagnetic separators are presented. The method can be used to calculate the field of apparatuses excited by permanent magnets or by both magnets and currents. >

An eddy current constraint formulation for 3D electromagnetic field calculations

The use of Coulomb's gauge is sufficient for a unique solution in 3-D magnetostatic field calculations in terms of the magnetic vector potential. For the sinusoidal steady-state eddy current problem Coulomb's gauge is not sufficient. The combination of Coulomb's gauge and an eddy current constraint provides a simple way of guaranteeing uniqueness. A formulation for 3-D electromagnetic fields utilizing this constraint is proposed. Results comparing this formulation with other finite-element formulations and with experimental data are given. >

A combined vector potential-scalar potential method for FE computation of 3D magnetic fields in electrical devices with iron cores

A method of combined use of magnetic vector potential based finite-element (FE) formulations and magnetic scalar potential (MSP) based formulations for computation of three-dimensional magnetostatic fields is introduced. In this method, the curl-component of the magnetic field intensity is computed by a reduced magnetic vector potential. This field intensity forms the basis of a forcing function for a global magnetic scalar potential solution over the entire volume of the region. This method allows one to include iron portions sandwiched in between conductors within partitioned current-carrying subregions. The method is most suited to large-scale global-type 3D magnetostatic field computations in electrical devices, and in particular rotating electric machinery. >

Vector potential boundary element method for three dimensional magnetostatic

A three-dimensional magnetostatic field computation method is presented. It uses the vector potential formulation, which is valid for any topology in opposition to the scalar formulation needing special cuts that are not always obvious. Attention is given to the calculation of strongly singular integrals using the Cauchy principal value. Two examples show the accuracy of this method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Results on modeling magnetic hysteresis using the finite-element methoda)

We present results obtained with the two-dimensional finite-element method including hysteretic behavior in magnetostatic-field computation. This software is dedicated to simulation of longitudinal magnetic recording on thin-film media, and so a scalar model of hysteresis is enough to model the media. The model used is based on a polynomial approximation of the magnetization curves. The nonlinear system is solved using an iterative process (Gauss–Seidel). Underrelaxation and smoothing are necessary to ensure the convergence of the computation. Results on a simple infinite-pole head show the effect of the demagnetizing field on magnetization, the remanent magnetization when removing the field, and the transition written when reversing it.

Design of a LaB6 gun using EGN2 and INTMAG

Abstract In order to launch a high-density electron beam to be focused in the 5 T superconducting solenoid of the Frankfurt EBIS [R. Becker et al., Nucl. Instr. and Meth. B24 (1987) 838], an electron gun has been designed, with a 0.5 mm diameter LaB 6 cathode (FEI Comp., Beaverton, USA) in a 70 mm diameter electrode geometry. The emitting surface is placed in the axial fringing field of the solenoid, modified by an axial shielding disk and a bucking coil, to provide either immersed flow or Brillouin flow conditions for the focused beam. Since the cathode diameter is small as compared to the electrodes, a new feature of EGN2 [W.B. Herrmannsfeldt, SLAC-331 (1988)] had to be used in order to have a sufficient number of meshes along the emitting surface. By starting a field line in the large geometry, a curved Neumann boundary is found for a subdivided part of the gun, which represents the influence of the larger part. EGN2 writes the coordinates of this field line on a file, which can be used by POLYGON [R. Becker, Nucl. Instr. and Meth. B42 (1989) 162] (a boundary setup program for EGN2) to define a curved Neumann boundary. By this procedure, it becomes possible to get a reliable simulation of the emission properties of a small cathode in large gun electrodes. The magnetostatic field calculations have been performed with INTMAG [R. Becker, Nucl. Instr. and Meth. B42 (1989) 303], which is a new program of the boundary element method type. Due to the integration calculus, the results do not need smoothing or “Maxwellisation” for the use in EGN2, where the off-axis fields are evaluated by radial expansion. INTMAG provides an output file, which is suitably formatted to be read in by EGN2. The gun design is based on space-charge-limited emission, but no Pierce-type electrode has been provided in the vicinity of the cathode; instead a Wehnelt electrode on negative bias with respect to the cathode is used to create the correct Pierce-type equipotential in free space, ending on the cathode edge with the correct angle. This gives an additional adjustment tool, if the axial position of the gun is not perfect and it relaxes the radial tolerance requirements considerably.