Nonlinear Eddy Current Problems Research Articles

Parallel field computation based on coupling of differential and integral methods

This paper deals with the coupling of a parallelized differential (FEM) and a parallelized integral approach (BEM) under control of a master process within the framework of a preconditioned iterative solver. Applying a domain decomposition scheme splits the problem into separate FEM and BEM parts preserving the typical advantages of both methods. Therefore an independent parallelization with respect to the special properties of both methods is possible. The limitations that arise on sequential computers when performing 3D transient analysis of nonlinear eddy current problems especially with motion can be overcome with this approach. The parallel implementations are discussed with focus on a strategy that keeps substantial parts of the parallelization separated from the numerical algorithm. The numerical modeling of an electromagnetic valve is presented as an example.

A multi-step method for 3-D nonlinear transient eddy current problems

A new method for solving the 3-D nonlinear transient eddy current problem is presented in this paper. The original finite element governing equations are separated into two parts: algebraic and differential equations. Multi-step algorithm, which is used only for the variables in conducting area, is adopted to analyze the first order differential equations. The investigating results reveal that this method avoids the oscillation occurred in single-step method and has higher precision with less computational effort.

A new method for periodic solutions of nonlinear eddy current problems

A new algorithm for the computation of steady-state conditions of electric machines is presented. It is based on a large time increment method used in mechanics. It is applied to the electromagnetic field computation in a generator. Compared with the step by step algorithm, the CPU time is greatly reduced.

Field and temperature calculations in transverse flux inductive heating devices heating nonparamagnetic materials using surface impedance formulations for nonlinear eddy-current problems

This paper presents the calculation of both the field and temperature distribution in thin moving nonparamagnetic sheets in transverse flux inductive heating devices (TFIH). The surface impedance formulation for nonlinear materials is extended to this thin plate problem. The temperature distribution is obtained by solving Fourier's thermal conduction equation. In this nonlinear coupled electromagneto-thermal problem the temperature dependencies of the B/H curve, the conductivity and the thermal conductivity are fully considered.

Use of transmission-line modelling method in FEM for solution of nonlinear eddy-current problems

Classical numerical algorithms such as Runge–Kutta and trapezoidal methods are the most generally accepted techniques for the FEM solution of the nonlinear eddy-current problem in the time domain. To account for the nonlinearity, a new linear system is solved at each time step, which is not favourable with regard to the computation costs. The authors deal with a new solution method which is based on the transmission-line modelling (TLM) technique used for electric circuit analysis. The underlying idea is the analogy that exists between a finite element matrix and the node-admittance matrix of an equivalent network. An iterative scheme emerges in which the nonlinearity appears as a source term on the right-hand side of the linear system so that the stiffness matrix remains unchanged at all iterations. In that manner, substantial reduction in computation time is obtained. As an example, a nonlinear eddy-current problem is treated, and a comparison with the classical Crank–Nicholson technique shows the efficiency of the method.

A predictor-corrector scheme for open boundary problems

In this paper an iterative finite-element procedure is described for the solution of nonlinear time-varying eddy current problems in open boundaries, A fictitious boundary delimiting a bounded domain is introduced. At each discrete time, two algebraic systems are set up and solved for the predictor and corrector solutions. Both these systems are solved iteratively by assuming a first guess for the Dirichlet condition on the fictitious boundary and improving it by making use of the free-space Green's function until convergence takes place. A great reduction of computing time is obtained with respect to the solution with a Newton-Raphson solver.

Complex representation in nonlinear time harmonic eddy current problems

Several possibilities are presented to deal with nonlinearity in ferromagnetic media in the case of time harmonic excitation in steady state, without losing simplicity in describing the potentials by means of complex peak values. The main idea is to introduce a fictitious time independent and inhomogeneous material to take into account the nonlinear relationship between the field quantities. Four methods are shown and investigated on a 3D time harmonic eddy current problem, using the T,/spl Phi/-/spl Phi/ finite element formulation. The vector potential is represented by means of edge elements and the scalar potential by nodal elements. The results obtained are compared with transient computation.

Analysis of transient nonlinear eddy current fields by space-time finite element method

A suitable functional in the form of a convolution of the magnetic vector potential in the space-time domain for transient nonlinear eddy current problem has been derived. Appropriate element equations have thus been derived following the usual finite element variational procedure. The space-time finite element method has then been used to compute the transient nonlinear electromagnetic field in a practical transformer. Numerical illustrations have indicated that the computed results are good agreement with the tested ones.

Calculation of the induced currents and forces for a hybrid magnetic levitation system

This paper presents the calculation of the induced currents and forces for a 3D nonlinear eddy current field problem with ferromagnetic moving conductors. The A/spl I.oarr/, V-A/spl I.oarr/ formulation is used in combination with four different gauging methods to stabilize the solution process. To consider nonrectangular shapes of geometries tetrahedral elements were employed. The computation procedure is applied to a hybrid magnetic levitation system of a contactless and frictionless conveyance system.

Analysis of 3D nonlinear eddy current problem using the field variables H and E directly

The 3D nonlinear eddy current fields in the steel plates of TEAM Problem 21 are analyzed by using H and E directly as state variables respectively. The boundary conditions of the eddy current region are provided by means of the surface impedance method based on two magnetic scalar potentials. The calculated values of eddy current losses are compared with the measured values, and the results indicate the presented methods are valid. Furthermore, the dual-complementary phenomena between the lower and upper bounds of the eddy current losses and reactive powers are numerically shown when H-oriented formulae and E-oriented formulae are separately used. For the nonlinearity of permeability of the steel plate, an equivalent permeability /spl mu//sub c/, and the finite element technique of frequency domain are employed to solve directly the governing equations by using the Newton-Raphson algorithm.

Nonlinear periodic eddy currents in single and multiconductor systems

The application of the finite element method to the calculation of nonlinear periodic eddy current problems is discussed. Special attention is paid to the case when specific conditions on the current or voltage of several conductors have to be fulfilled. An efficient iterative procedure has been developed to satisfy these conditions in 2D problems solved by a single component magnetic vector potential with the nonlinearity taken into account. The total current condition can be fulfilled in 3D with a noniterative scheme, but voltage conditions still require a multistep approach. Additionally, a possibility of accelerating the time stepping algorithm in reaching steady state is presented for a 3D eddy current problem involving a single conductor.

Modelling of three-dimensional nonlinear eddy current problems with conductors in motion by an integral formulation

An integral formulation for the analysis of electromagnetic fields distribution in systems with bodies in motion is presented. This formulation is based on the subdivision of conductive and ferromagnetic regions in elementary volumes in which a uniform distribution of current density J and magnetization M is assumed. By integrating in every volume Ohm's law in term of the magnetic vector potential produced by the conduction and magnetization currents we obtain an equivalent electric network whose lumped parameters vary during every time step interval as the moving parts of the system change their positions. The proposed model has been tested by comparison with analytical solutions.

A nonlinear eddy current integral formulation in terms of a two-component current density vector potential

This paper presents an iterative procedure based on an integral formulation for nonlinear eddy current problems. Its main advantages are the possibility of assuring the convergence of the numerical scheme (Picard-Banach), the need of discretizing only the conducting domain (and, if different, the ferromagnetic domain) and, finally, the necessity of forming and inverting the matrices only once (a typical feature of the Picard-Banach procedure). Some numerical results are also reported to validate the numerical implementation.

Hybrid FE-BE method for EMC problems in power cable systems

The simulation of EMC problems in underground power cable systems is characterized by solving an open nonlinear eddy current problem, to which the hybrid FE-BE method is applied in this paper. The significance of this approach is the combination of the advantages of the FEM and the BEM. The influence of a thin ferromagnetic plate on the nonlinear iteration convergence is discussed. Furthermore, the shielding effects of the ferromagnetic plates are numerically investigated.

Analysis of a transient nonlinear 3-D eddy current problem with differential and integral methods

The paper compares the features of integral and differential formulations for the solution of of transient eddy current problems in nonlinear media. The integral method used reduces the nonlinear eddy current problem to the analysis of an equivalent network. Two dual edge element differential formulations are also used. Their field estimates automatically verify Faraday's and Ampere's laws and furnish the distribution of the constitutive error in the solution domain, which provides a useful tool for the refinement of the discretization. The methods are applied to analyze a massive magnetic circuit characterized by the presence of soft and hard magnetic materials with narrow gaps.

On the convergence of the iterative A-BEM formulation for 2-D nonlinear eddy currents

In this paper the convergence of the iterative BEM formulation for the 2-D nonlinear eddy current problems, in which both location and time dependency of permeability are considered, is investigated. An adaptively damped iteration method with incremental loading technique and adaptive starting is proposed, by which a good convergence of the iterative BEM formulation can be ensured. >

The fixed point method approach to nonlinear open boundary eddy current problems under TM field excitation

Eddy currents induced in a ferromagnetic slab of arbitrary cross section placed in an alternating transverse magnetic (TM) field are analyzed. A hybrid method is used, based on the Galerkin formulation of the finite element method (FEM) coupled with the method of separation of variables. The quasilinearisation is performed on the basis of the Brouwer's fixed point theorem. A numerical example is presented for a conductor of rectangular cross section. Plots of the eddy current power losses against the excitation frequency are shown.

NUMERICAL INTEGRATIONS IN THE BEM FORMULATION WITH E AND H FOR 3‐D EDDY CURRENTS

The computation of 3‐D eddy current problems is an important topic both in theoretical and engineering areas. Based on Green's theorem, Kost theoretically developed a BEM formulation for general 3‐D nonlinear eddy current problems. The parallel implementation of this formulation in the linear case has been made on a massively parallel supercomputer, where a constant triangular element was used.

Numerical procedures for the solution of nonlinear electromagnetic problems

A typical nonlinear three-dimensional eddy current problem is analyzed using dual finite element formulations in terms of the two-component vector potential. Each of the two formulations enforces one of the Maxwell equations exactly. In this way, the numerical error is concentrated in the constitutive equations, allowing for an estimation of local and global errors. The authors assess how the performances of the methods are affected by choice of the gauge, substructuring of the problem. and choice of the iterative algorithm for the treatment of the nonlinearity. In agreement with previous results, it was found that the choice of the tree does affect the properties of the systems of equations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Periodic solutions of nonlinear eddy current problems in three-dimensional geometries

The collocation and the Galerkin methods are used for the finite-element computation of T-periodic nonlinear eddy currents in three-dimensional geometry. The periodic solutions are computed by using two static methods and are compared with the solution obtained by the brute-force method. The algorithms are very simple. It is found that they require a CPU time much smaller than that required by the brute-force method if the system is lightly damped, and it is also shown that they are robust only if the norm-reducing procedure is used. Furthermore, the Galerkin method provides a satisfactory solution even with few harmonics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>