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Article
Publication date: 7 September 2012

Andrzej Demenko and Jan. K. Sykulski

The purpose of this paper is to emphasise the analogies between variational and network formulations using geometrical forms, with the purpose of developing alternative…

Abstract

Purpose

The purpose of this paper is to emphasise the analogies between variational and network formulations using geometrical forms, with the purpose of developing alternative but otherwise equivalent derivations of the finite element (FE) method.

Design/methodology/approach

FE equations for electromagnetic fields are examined, in particular nodal elements using scalar potential formulation and edge elements for vector potential formulation.

Findings

It is shown how the equations usually obtained via variational approach may be more conveniently derived using integral methods, employing a geometrical description of the interpolating functions of edge and facet elements. Moreover, the resultant equations describe the equivalent multi‐branch circuit models.

Originality/value

The approach proposed in the paper explores the analogy of the FE formulation to loop or nodal magnetic or electric networks and has been shown to be very beneficial in teaching, especially to students well familiar with circuit methods. The presented methods are also helpful when formulating classical network models. Finally, for the first time, the geometrical forms of edge and facet element functions have been demonstrated.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 31 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 11 July 2008

Andrzej Demenko

This paper seeks to develop 3D finite element methods for the electromagnetic field calculation in electrical machines and to present the discrete methods of winding description.

Abstract

Purpose

This paper seeks to develop 3D finite element methods for the electromagnetic field calculation in electrical machines and to present the discrete methods of winding description.

Design/methodology/approach

The 3D finite element models of electrical machine windings are considered. Attention is paid to the windings with stranded conductors. The finite element equations are considered as the equations of magnetic networks. The formulation of matrix that transforms winding currents into the field sources is discussed. This matrix is also used in the calculations of flux linkages. In the proposed method, the winding loops are replaced by a set of plane loops. The field sources are defined by the numbers of these loops around the element edges and loops associated with element facets.

Findings

The presented description is the 3D finite element representation of MMF description used in the classical models of electrical machines. The advantage of the proposed approach is that the source description can be successfully applied in the FE method using single scalar potential. In addition, the presented approach guarantees a good convergence of ICCG procedure of solving edge element equations for ungauged formulation using magnetic vector potential.

Originality/value

The applied analogies between the finite element formulation and the equivalent magnetic network models help to formulate an efficient method of field source description. The developed method allows one to apply single magnetic scalar potential in the 3D finite element analysis of electrical machines.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 27 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 March 2002

Andrzej Demenko, Lech Nowak, Wojciech Pietrowski and Dorota Stachowiak

The paper presents a method for the 3D edge element analysis of saturation effects in the classical rotating electrical machines of cylindrical structure. The edge element

Abstract

The paper presents a method for the 3D edge element analysis of saturation effects in the classical rotating electrical machines of cylindrical structure. The edge element (EE) method using vector magnetic potential has been applied. Special attention is paid to the saturation effects in permanent magnet motors. In order to solve the non‐linear EE equations the authors propose to apply the modified Newton algorithm with block relaxation solver and Cholesky decomposition procedure for block matrices. The convergence of the algorithm is analysed. The influence of core non‐linearity on the values of electromagnetic torque and armature inductances is considered. The results for 3D and 2D models are compared.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 21 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 27 January 2022

Matthias Kowalski, Martin Hanke and Christian Kreischer

Resolving eddy currents in three dimensions with finite elements, especially in geometrically complex structures, is very time consuming. Notable additional efforts will…

Abstract

Purpose

Resolving eddy currents in three dimensions with finite elements, especially in geometrically complex structures, is very time consuming. Notable additional efforts will be required, if these eddy currents are influenced by magnetic fields arising from larger parts or range over widespread regions. The purpose of this article is to present a new sub-modelling simulation technique, based on the finite-element approach. This method offers remarkable advantages for solving this type of problems.

Design/methodology/approach

A novel sub-modeling technique is developed for the finite-element method addressing this problem by dividing the process into two steps: firstly, a simulation of a “source”-model is carried out providing magnetic field distributions within the entire domain neglecting local eddy current effects and without modeling it in full detailed geometry. A subsequent “sub”-model comprises only the region of interest in higher resolution and is solved while being constrained with boundary conditions derived from the previous source-model. An implementation in ANSYS Mechanical is carried out with the objective to validate finite-element simulation against measurement results.

Findings

The proposed simulation technique performs robustly and time efficiently. Applying this method to an end-region of a turbogenerator allows comparisons with test data of this region for validation purposes. The comparison between measured and simulated radial flux densities shows good correspondence.

Originality/value

This work is novel in many aspects: a new technique for three-dimensional (3D) finite-element method using edge-elements is introduced. To the best of the authors’ knowledge, for the first time, these 3D sub-models are compared against measurement results of an electric machine with net currents. Leveraged from this work, detailed analyses of eddy current phenomena under influences of external magnetic fields can be investigated in higher detail within shorter calculation times.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 July 2006

Andrzej Demenko and Jan Sykulski

The aim of this paper is to develop network models of an electromagnetic field containing both eddy and displacement currents. The proposed network models provide good…

Abstract

Purpose

The aim of this paper is to develop network models of an electromagnetic field containing both eddy and displacement currents. The proposed network models provide good physical insight, help understanding of complicated electromagnetic phenomena and aid explanation of methods of analysis of electromagnetic systems.

Design/methodology/approach

The models consist of magnetic and electric networks coupled via sources. The analogy between the finite element method and the loop and nodal formulations of electric circuits is emphasised. The models include networks containing branches associated with element edges (edge networks) or facets (facet networks).

Findings

Methods of determining mmf sources of magnetic networks from loop and branch currents in electric circuits, as well as emf sources in electric networks on the basis of the rate of change of loop and branch fluxes in electric networks, have been carefully considered. The models are general and allow creation of networks of electromagnetic systems containing non‐homogenous materials and multiply‐connected conducting regions.

Originality/value

The presented analogies between the finite element formulation and the equivalent network models not only facilitate understanding of the methods of field analysis but also help to formulate efficient computational algorithms.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 August 1999

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element methods (FEMs) applied to the analysis of ceramics and glass materials. The bibliography at the end of the…

2146

Abstract

This paper gives a bibliographical review of the finite element methods (FEMs) applied to the analysis of ceramics and glass materials. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1977‐1998. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, ferrites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.

Details

Engineering Computations, vol. 16 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 2001

M. Kaltenbacher, S. Reitzinger, M. Schinnerl, J. Schöberl and H. Landes

The focus of this paper is on the efficient numerical computation of 3D electromagnetic field problems by using the finite element (FE) and multigrid (MG) methods. The…

Abstract

The focus of this paper is on the efficient numerical computation of 3D electromagnetic field problems by using the finite element (FE) and multigrid (MG) methods. The magnetic vector potential is used as the field variable and the discretization is performed by Lagrange (nodal) as well as Ne´de´lec (edge) finite elements. The resulting system of equations is solved by applying a preconditioned conjugate gradient (PCG) method with an adapted algebraic multigrid (AMG) as well as an appropriate geometric MG preconditioner.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 20 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 December 2005

Christian Vollaire, François Musy and Ronan Perrussel

Propose post processing methods for the edge finite element (FE) method on a tetrahedral mesh. They make it possible to deduce vector values on the vertices from scalar…

Abstract

Purpose

Propose post processing methods for the edge finite element (FE) method on a tetrahedral mesh. They make it possible to deduce vector values on the vertices from scalar values defined on the edges of the tetrahedra.

Design/methodology/approach

The new proposed techniques are based on a least squares formulation leading to a sparse matrix system to be solved. They are compared in terms of accuracy and CPU time on a FEs formulation for open boundary – frequency domain problems.

Findings

A significant improvement of vector values accuracy on the vertices of the tetrahedra is obtained compared to a classical approach with a very small additional computation time.

Originality/value

This work presents techniques: to obtain the values at the initial nodes of the mesh and not inside the tetrahedra; and to take into account the discontinuity to the interface between two media of different electromagnetic properties.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 24 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 March 2001

A. Demenko, L. Nowak and W. Pietrowski

The end‐turn leakage inductances of the armature winding of the permanent magnet motor have been calculated. In order to describe the magnetic field distribution the edge

Abstract

The end‐turn leakage inductances of the armature winding of the permanent magnet motor have been calculated. In order to describe the magnetic field distribution the edge element method using vector magnetic potential has been applied. First, the formulae that describe the total self‐inductance and total mutual conductance for phase windings are presented. Three‐dimensional and two‐dimensional formulations are considered. The end‐turn leakage inductances have been obtained by comparing the results of these formulations. The symmetrical components transformation has been applied, and the self inductances and mutual inductances have been transformed into the zero‐sequence and positive‐sequence inductances. The calculations have been performed for different dimensions of the coil‐end region. The influence of the position of the boundary surfaces on the results has been investigated.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 20 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 December 2004

Dorota Stachowiak

This paper demonstrates how the 3D edge element method can be applied to the analysis of permanent magnet motors. The edge element method using the vector magnetic…

Abstract

This paper demonstrates how the 3D edge element method can be applied to the analysis of permanent magnet motors. The edge element method using the vector magnetic potential has been used. Special attention has been paid to the analysis of systems with inhomogeneously magnetized permanent magnets. The magnets are not skewed and are mounted on a cylindrical laminated rotor. Calculations have been performed for different magnet widths and different distribution of the magnetization vector. Brushless motors with radially and inhomogeneously magnetized magnets have been compared.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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