Eddy Current Phenomena Research Articles

Solution of a low-frequency coupled electromagnetic problem using the wavelet-Galerkin method

In this paper, we present an analysis of a two-dimensional electric circuit-electromagnetic field coupled problem using the wavelet-Galerkin method. For illustration, the bar-plate configuration, a basic model for analysing eddy current phenomenon in electrical apparatus, is chosen. Firstly, a brief description of wavelet theory and its application in computational electromagnetics is provided. Then, a description of the two-dimensional coupled problem formulation and its solution using the wavelet-Galerkin method is given. Finally, results obtained using simulation are presented.

와전류를 이용한 발열기의 개발

In this research, a heater using eddy current for generator is designed and some analysis is performed to validate the system. FEM (finite element method) is used for analysing eddy current phenomena at the various speed of rotor with permanent magnet. A real heater system is fabricated. Some experiment is also performed to validate the analysis result. Through the experiment, the FE analysis is validated and we found that the efficiency of developed heater is over 94%.

Modelling and position control of voltage forced electromechanical actuator

PurposeTo present modelling and control technique of an electromagnetic actuator.Design/methodology/approachA 3D modelling technique of voltage‐forced electromechanical actuator takes into account: motion, magnetic non‐linearity and eddy current phenomena. Control problem of closed loop system is described by coupled electro‐magneto‐mechanical equations and non‐linear PID controller equations.FindingsPresented methodology offers a powerful tool for analysis of control systems with distributed parameters models and may contribute to the improvement of the electromechanical performance of electrodynamic devices.Originality/valueAs original contribution a position feedback control using conventional PID controller is applied for iterative determining inverse dynamic problem, that is finding input voltage for a given position of an actuator.

Surface Charge Analysis in Eddy Current Problems

To estimate characteristics of electric machines that have conductors with complex form, it is effective to analyze the surface charge concerned with eddy current phenomena. However, the eddy current field is generally treated as quasi-static field in which the displacement current is neglected and the electric field is not defined in the non-conductive region in the calculating process. Therefore, when we adopt only the A-φ FE method as a field analysis method, it is difficult to directly calculate the surface charge at the interface between conductive and non-conductive regions. In this paper, with this background, we propose a novel analysis method of the surface charge based both on the A-φ formulation of 3D edge FE method and on the integral equation. This approach enables us to precisely calculate the surface charge. Some numerical results, which demonstrate the validity of the proposed method, are also presented, e. g., the surface charge analysis of linear induction motors for evaluating the relationships among the surface charge, eddy current, and conductor shape.

Micro coil modeling — benefit and implementation of a permeable layer

Rectangular micro coils which are used in a wide range of applications (e.g. medical or automotive area) are the main components of appropriate wireless transmission systems for frequencies up to 20MHz. As shown in previous works the self-inductance of micro coils has to be maximized to achieve a higher working distance. This can be done by the usage of a permeable layer underneath the micro coil.The existing model of the micro coil is extended by the use of the magnetic image method to include the inductance yield caused by the permeable layer. The underlying permeable layer or substrate is also modeled accurately to include eddy current phenomena and parasitic elements. To do this, the layer and the substrate respectively are divided into segments analog to the structure of the micro coil. Each segment is described by lumped elements. All elements are connected together to build up a network, which will be used to calculate the terminal impedance.The model and first results will be presented.

Simulation of motional eddy current phenomena in soft magnetic material

The finite element simulation of conductors moving in a magnetic field at elevated speeds, yields oscillatory solutions. To overcome the effect of the huge convection terms, the partial differential equation is stabilised by adding artificial diffusion. Accurate results are obtained by applying adaptive mesh refinement. A rotational magnetic brake with a solid ferromagnetic rotor is simulated.

Iron lamination efficient representation in power transformers

The paper presents a methodology enabling the accurate representation of iron losses in magnetic cores for a frequency range up to 10 kHz. The classical subdivision of iron losses into hysteresis and eddy current phenomena has been adopted. Hysteresis losses are calculated by means of a conveniently modified Preisach–Neel model representation while iron losses are taken into account through a Foster II equivalent circuit representation of the lamination. A final equivalent circuit of sufficient accuracy, combining both hysteresis and eddy current losses contributions is proposed. The model validity has been checked using an Epstein experimental set-up.

Three-dimensional finite element analysis of nondestructive testing of metallic tubular product

This paper presents the analysis of the remote field eddy current phenomenon for the nondestructive testing of metallic tubular products. A finite element code using linear tetrahedral edge elements is used for the analysis. The calculated results for different frequencies of exciting coil are evaluated. In the model without a hole in the pipe, the absolute value of the phase of the remote field depends on the frequency of the exciting coil. The phase varies around the hole and the phase difference compared with the case without hole also depends on the frequency. The calculated results and the developed code can be used for the design of the remote field nondestructive testing probe.

Evaluation of a 3-d bOunded Defect in the Wall of a Metal Tube At Eddy Current Frequencies: the Direct Problem

Effective eddy current nondestructive evaluation of metal tubes requires accurate modeling of the fields observed in known configurations in order to understand the behavior of such fields when a defect is present, to test inversion algorithms from synthetic data, and to appraise the output of these algorithms in real cases. Here we restrict ourselves to the interaction between a non-magnetic probe displaced along a straight part of the tube when a 3-D bounded defect is found nearby in the tube wall also assumed to be non-magnetic. Modeling of the anomalous fields at a given frequency and of the variations of impedance of the probe is carried out from an exact vector domain integral formulation of the eddy current phenomenon. This formulation results from the application of the Green's theorem to the wave equations and provides the sources induced in the defect volume, from which the variation of impedance follows by application of the reciprocity theorem. All depolarization effects in the flawed region are accounted for. This formulation is handled by a conjugate-gradient FFT-based Method of Moments. Difficulties met when carrying out the integrals involving the dyadic Green's function of the tubular structure are overcome by singularity extraction and the use of the nonlinear accelerating Shanks' transform. Results of numerical simulations for an axisymmetric probe and typical defects illustrate the effectiveness of the approach, while consequences of neglecting depolarization effects are discussed. These results are compared to those obtained by a localized nonlinear approximation and by the Born approximation, which have the advantage to bypass in part or altogether the calculation of the field inside the defect volume, and to experimental data acquired from calibration tubes.

Macroscopic fields in ferromagnetic laminations taking into account hysteresis and eddy current effects

In this paper the computation of the macroscopic fields inside thin ferromagnetic laminations is discussed. Emphasis is placed on the interplay of the hysteresis and eddy current phenomena. The solution of the problem is based on numerical discretization techniques, both in time and space. The variation in space is modeled with finite elements, either in one or two dimensions, while time-stepping techniques are used to represent the temporal variation. Throughout the paper hysteresis is modeled with Preisach type models, both static and rate-dependent. The method is applied to non-oriented silicon steels. It is shown that an excellent agreement is obtained between the measured and computed response, for strongly different material qualities. The topic of excess losses is addressed, and brought into relation with the rate-dependence of the hysteresis.

Efforts towards gaining a better understanding of the remote field eddy current phenomenon and expanding its applications

The paper begins with a brief summary of previous work done by the authors on gaining a better understanding of the remote field eddy current (RFEC) phenomenon and expanding the range of applications. It then introduces three new findings: (1) Modeling and experimental study of the RFEC phenomenon as observed from one side of both ferromagnetic and non-ferromagnetic plates. (2) Numerical prediction of possible existence of the RFEC phenomenon external to conducting tubes. (3) Numerical study of its possible application in underwater target detection problems.

An inverse analysis for crack identification in eddy current NDT of tubes

This paper presents an inverse analysis for crack identification in eddy current nondestructive testing of tubes. The finite element modeling of axisymmetric eddy current phenomena is based on the formulation of the energy functional with the magnetic vector potential. An optimization algorithm in the inverse process employs the objective function expressed in terms of the impedance change of a differential probe which consists of two coils. The proposed method is applied to a simple axisymmetric model with a crack made arbitrarily. >

Field Distribution and Evaluation of Eddy-Current Loss in Solid-Magnetic Cores Subjected to Time Varying Magnetic Fields

In the study of field distribution in solid magnetic cores subjected to a time-varying magnetic field, the field distribution inside the core is created by a magnetising winding that results in current flow within the material. These eddy currents, as they are called, depend on the geometry of the medium, on the electric and magnetic properties of the material and on the rapidity of alteration of the flux. It is obvious, therefore that the study of eddy current phenomena should centre round the determination of the field and current distribution in a conducting medium subjected to a time-varying field. The paper examines the field distribution for different boundary conditions. Based on these solutions formulae are derived for the evaluation of eddy current loss. The paper further examines the usefulness of the concept of Poynting vector for the evaluation of eddy current loss and thus offers an alternative method.

A diffraction tomographic algorithm for eddy current imaging from anomalous fields at fictitious imaginary frequencies

One key question when extending wave imaging algorithms to strongly attenuating environments like a damaged metallic structure where eddy currents are generated, is how to deal with evanescent waves. A similar question arises when super-resolution of a scatterer is aimed at by using the evanescent spectrum of its near-field. Here we focus on imaging a 2D anomaly within a metal half-space probed by a low-frequency electromagnetic source in air above, from the anomalous field the anomaly is associated with. Assuming the eddy current phenomenon to be cast in a wave framework, it is possible to devise a diffraction tomographic procedure that partially matches the skin-effect in the metal. From the same starting point, continuation of the time-harmonic anomalous data onto a set of fictitious imaginary frequencies leads to a diffraction tomographic procedure which works somewhat like in a nonattenuating embedding and which is not impaired by the same drastic approximations as the attenuation-matched approach. Simulations from synthetic fields calculated in the case of simple geometries illustrate the derivation. Ways to proceed with the continuation when probing an effectively unknown defect are discussed and a model-based approach is outlined.

Numerical analysis of field perturbation due to a crack in a conductor (abstract)

A wide range of nondestructive testing (NDT) applications to detect cracks and defects in conducting materials are based on eddy current effects. A study of electromagnetic fields and eddy currents that induced around defects is important to design and optimize eddy current probes. In order to determine the current density in the region that includes conducting material and field perturbation in the air, the solution of Maxwell’s equations is required. For most practical problems the geometry of the region is too difficult for analytical solution and numerical method must be used. Numerical analysis techniques such as the finite element method have been successfully developed for modeling eddy current NDT phenomena.1 We used the three-dimensional finite element formulation as a basis for calculation of the induced current density around the crack in a conductor. Space components perturbation both for current and flux densities is investigated. The influence of different crack sizes and excitation coil dimensions is studied. The computational results can be used for optimizing eddy current probe dimensions. Much information can be obtained to identify and quantify defects. Our future work will be devoted to this.

Exact first order finite element modeling for eddy current NDE

Abstract Numerical methods, including finite element analysis, have previously been applied to model eddy current phenomena. The purpose of this paper is to present a finite element formulation of eddy currents for axisymmetric geometries that is developed without centroid approximations, and to describe the agreement between experimental and calculated results for a coil-in-air. The boundary conditions required for using the code are developed, and practical options for application of the conditions are investigated.

Exact First Order Finite Element Modeling for Eddy Current NDE

Numerical methods, including finite element analysis, have previously been applied to model eddy current phenomena. The purpose of this paper is to present a finite element formulation of eddy currents for axisymmetric geometries that is developed without centroid approximations, and to describe the agreement between experimental and calculated results for a coil-in-air. The boundary conditions required for using the code are developed, and practical options for application of the conditions are investigated.

Comparing a one-dimensional skin effect equation with through transmission eddy current phenomena : British journal of non-destructive testing, Vol. 32, No. 2, pp. 71–75 (Feb. 1990)

Comparing a one-dimensional skin effect equation with through transmission eddy current phenomena : British journal of non-destructive testing, Vol. 32, No. 2, pp. 71–75 (Feb. 1990)

Comparing a one-dimensional skin effect equation with through transmission eddy current phenomena British journal of non-destructive testing, Vol. 32, No. 2, pp. 71–75 (Feb. 1990)

Comparing a one-dimensional skin effect equation with through transmission eddy current phenomena British journal of non-destructive testing, Vol. 32, No. 2, pp. 71–75 (Feb. 1990)

Optimization of Eddy-Current Probes for Detection of Garter Springs in Pressurized Heavy Water Reactors

One of the major safety concerns about pressurized heavy water reactors is the assurance requirement that the circular garter springs that surround pressure tubes remain at their specified locations. The eddy-current nondestructive method gives a timely warning when a significant displacement of garter springs occurs. The finite element method is used extensively to model eddy-current phenomena. Since a garter spring is an axisymmetric discontinuity, a two-dimensional finite element method is used to optimize eddy-current probe design parameters for the above application