E.E. Kriezis

Eddy currents: theory and applications

The theory and applications of eddy currents induced in conducting materials by time-varying magnetic fields are reviewed. The mathematical methods employed in solving the relevant problems are presented. Both analytical and numerical methods are described. Applications based on effects arising from eddy currents are discussed in detail. These applications are to magnetic levitation, electromagnetic launching, hyperthermia treatment of cancer, and nondestructive testing. >

Impedance evaluation of rectangular coils for eddy current testing of planar media

As for any other eddy current probe coil, the analysis of rectangular ones plays a vital role towards understanding their characteristics and performance. In this paper, closed-form expressions are provided both for the impedance of rectangular coils of rectangular cross-section located above a conducting half-space and for the eddy current density induced therein. The formulation is general and can be easily used for any coil shape.

Analytical and numerical solution of the eddy-current problem in spherical coordinates based on the second-order vector potential formulation

The three-dimensional (3-D) eddy-current problem, described in spherical coordinates, is studied both analytically and numerically. Since the vector field equation is not separable in the spherical coordinate system, the second-order vector potential (SOVP) formulation is used to treat the problem by reducing it to the solution of the scalar field equation. While the analytical solution is expressed in terms of known orthogonal expansions, the numerical solution utilizes the finite difference method. Examples of engineering applications are provided, concerning computation of eddy-current distribution in a conducting sphere by a filamentary excitation of arbitrary shape.

Analytical solutions in eddy current testing of layered metals with continuous conductivity profiles

In this paper exact analytical expressions for the impedance of a cylindrical air-core coil above a layered metal structure whose conductivity varies continuously with depth are presented. Although the model is general, attention is focused on three conductivity profiles: the linear, the quadratic and the exponential. The derived expressions for the impedance change for each profile could provide a useful tool for the solution of the inverse problem: that of determining the conductivity from variable frequency measurements of the impedance. Furthermore, the obtained final formulas contain elegant mathematical functions and show a substantially higher computational efficiency with respect to existing methods. >

Eddy current distribution due to a rectangular current frame moving above a conducting slab

ContentsThe purpose of this work is the determination of the eddy current distribution within a conducting slab, when a rectangulr current frame is moving above this slab. The frame is placed parallel to the slab and the velocity of the slab is constant. The field also is determined in the regions outside the slab. Using the expressions of the field it can be calculated the forces acting on the frame. By applying 3-D Fourier transforms general expressions are derived either for the induced current density inside the slab or for the magnetic flux density outside the slab.ÜbersichtDer Zweck dieser Arbeit ist die Bestimmung der Wirbelstromdichte innerhalb einer leitenden Platte, wenn sich ein viereckiger Stromrahmen über die Platte bewegt. Der Stromrahmen liegt parallel zu der Plattenoberfläche und die Geschwindigkeit des Rahmens ist konstant. Das Feld wird auch in den Regionen außerhalb der Platte bestimmt. Die Verwendung der feldbeschreibenden Formelausdrücke crlaubt die Berechnung der Kräfte auf den Rahmen. Durch Anwendung der 3-D Fourier-Transformation erhält man Ausdrücke sowohl für die induzierte Wirbelstromdichte innerhalb der Platte als auch für die Feldgrößen außerhalb der Platte.

Field calculation in single- and multilayer coaxial cylindrical shells of infinite length by using a coupled T- Omega and boundary element method

A method is presented for the calculation of the electromagnetic field in systems of single-layer or multilayer coaxial cylindrical shells of infinite length excited by an oscillating current source arbitrarily oriented inside the first shell. The electric vector potential T and the magnetic scalar potential Omega are used for the evaluation of the quantities of the problem. The Helmholtz equations for T and Omega are transformed into integral equations by the use of the Greens function method. Applying the boundary element method, three systems of simultaneous equations have to be solved to give the sought field quantity. >

Low-Frequency Electromagnetic Shielding in a System of Two Coaxial Cylindrical Shells

In this work, the problem of shielding is examined for a system of two coaxial cylindrical shells, when the excitation is a current filament placed parallel to the axis of the cylinders either inside or outside them. For the calculation of the current density within the conducting material of the shells and the magnetic flux density in the different regions of the system, the diffusion equation for the magnetic vector potential is used. The incident field of the filament has a harmonic time variation, but the method can be applied to any time variation of the excitation by using a Laplace or Fourier transform.

A generalized nondiagonally anisotropic perfectly matched layer for wide-angle absorption in finite element electromagnetic scattering analysis

A generalization of the concept of the anisotropic perfectly matched layer is proposed in this paper. The new PML has a nondiagonal symmetric tensor anisotropy. Through the investigation of its properties, it is proven that by an appropriate choice of its parameters, the PML can serve as a wide-angle, reflectionless absorbing layer for electromagnetic scattering analysis. In other words, it can efficiently absorb waves of grazing incidence. Hence, this kind of PML is suitable for the analysis of electrically large structures, since it can be placed close to the scatterer and in a conformal way. The efficiency of the generalized PML is investigated via an analytical approach and a finite element implementation with higher order Whitney elements.

3D eddy current computation with edge elements in terms of the electric intensity

A finite element formulation for the solution of 3D eddy current problems in terms of the electric intensity E is presented. A weak formulation, based on a Galerkin weighted residual procedure, is presented and edge elements, that impose only tangential continuity across element interfaces of the approximated field, are employed for the discretization of the problem with the finite element method. The reliability and validity of the suggested method is verified by its application to the calculation of the 3D eddy current distribution in two conducting systems.

Coil impedance due to a sphere of arbitrary radial conductivity and permeability profiles

This paper presents analytical expressions for coil impedance due to a spherical workpiece consisting of concentric spherical shells. The expressions are used to simulate the nondestructive inspection of a sphere having arbitrary radial conductivity and magnetic permeability profiles by a circular coil of rectangular cross section. The simulation replaces continuous profiles with piecewise constant profiles. The paper compares the results to published experimental measurements and the results of other analytical solutions.