Bemerkungen zur Lösung des dreidimensionalen Wirbelstromproblems in Kreiszylindern endlicher Länge

Filtz, M.; Nethe, A.

doi:10.1007/bf01573692

Cited by 8 publications

(4 citation statements)

References 4 publications

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“…The complex eigenvalue r 0 giving rise to the hyperbolic cosine term is due to the wedge and does not appear in the half-space solution. It was also taken into account by Flitz & Nethe (1993) where a problem of eddy current induction in a finite length cylinder was studied. Note that from equations (4.5), (4.10) and the continuity of H y at x Zc, it is found that C ð2Þ 0 Z Kj coshðkcÞD 0 : ð4:11Þ…”

Section: (B ) Transverse Magnetic Potentialmentioning

confidence: 99%

Eddy current coil interaction with a right-angled conductive wedge

Theodoulidis

Bowler

2005

Proc. R. Soc. A.

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The time-harmonic electromagnetic field in an electrically conductive right-angled wedge due to an inductive excitation by circular coil in air has been calculated. Using a formulation in Cartesian coordinates, the problem domain is truncated in a dimension whose axis is normal to a wedge face, and an approximate series solution found using elementary functions satisfying Maxwell's equations in the quasi-static limit. The coil impedance variation with position and frequency is calculated and compared with measurements made on a coil near the edge of a large aluminium block which approximates the effect of a conductive quarter-space. The comparison between theory and experiment shows very close agreement.

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Section: (B ) Transverse Magnetic Potentialmentioning

confidence: 99%

Eddy current coil interaction with a right-angled conductive wedge

Theodoulidis

Bowler

2005

Proc. R. Soc. A.

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“…However, the successful implementation of TREE for the model of end effects depends on the solution of relevant eigenvalue equations, which are transcendental, and complex roots should be determined. Conventionally, the Newton-Raphson algorithm [10][11][12][13] or contour integral based on the Cauchy's theorem [14][15][16][17] are applied to solve the eigenvalue equations. A novel method based on the Sturm-Liouville theory and Galerkin approach has been proposed recently [18][19][20], which greatly simplifies the process of locating the complex eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

Impedance Variation in a Coaxial Coil Encircling a Metal Tube Adapter

Luo,

Yang

2023

Sensors

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The impedance change in an induction coil surrounding a metal tube adapter is investigated using the truncated region eigenfunction expansion (TREE) method. The conventional TREE method is inapplicable to this problem as a consequence of the numerical overflow of the eigenfunctions of the air–metal multi-subdomain regions. The difficulty is surmounted by a normalization procedure for the numerical eigenfunctions obtained from the 1D finite element method (FEM). An efficient algorithm is devised by the Clenshaw–Curtis quadrature rule for integrals involving the numerical eigenfunctions. The numerical results of the TREE and FEM simulation coincide very well in all cases, and the efficiency of the proposed method is also confirmed.

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“…In the solving process, the second order vector potentials (SOVPs) are applied to simplify the calculations. This technique remarkably expands the range of the analytical models and is necessary for the solution of a 3D boundary value problem (BVP) [8][9][10][11][12][13]. In Section 3, a novel approach for the complex eigenvalue computation, based on the 1D finite-element method (FEM), is proposed for the solving procedure.…”

Section: Introductionmentioning

confidence: 99%

An analytical model of an eddy‐current coil near the edge of a conductive plate

Yang

Luo

Kyrgiazoglou

et al. 2022

IET Electric Power Appl

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Truncated region eigenfunction expansion (TREE) method is applied to the analysis of impedance change of a coil in the vicinity of the edge of a metal plate. The analysis is carried out with the second order vector potentials (SOVPs) and provided for both cylindrical and rectangular coils. By full discretisation of the eigenvalues, double series solutions are obtained for the field and coil impedance variations. To simplify the solving procedure further, a novel approach for the determination of eigenvalues is proposed by means of the 1D finite element method (FEM), which is easy to implement and works well for the plate of non-magnetic material. Numerical results for the impedance variations of cylindrical and rectangular coils are compared with those of 3D FEM simulation, by which the efficiency and accuracy of the authors' method are confirmed, and the former is much faster and more memory efficient.

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Bemerkungen zur Lösung des dreidimensionalen Wirbelstromproblems in Kreiszylindern endlicher Länge

Cited by 8 publications

References 4 publications

Eddy current coil interaction with a right-angled conductive wedge

Eddy current coil interaction with a right-angled conductive wedge

Impedance Variation in a Coaxial Coil Encircling a Metal Tube Adapter

An analytical model of an eddy‐current coil near the edge of a conductive plate

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