Inductance calculations for coaxial iron‐core coils shielded by cylindrical screens of high permeability

Zhu, Yuanzhe; Chen, Baichao; Luo, Yao; Zhu, Runhang

doi:10.1049/iet-epa.2018.5667

Cited by 9 publications

(4 citation statements)

References 21 publications

(25 reference statements)

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“…What poses a real challenge is the determination of complex eigenvalues when the region under consideration consists of several sub-regions (containing conductive material or air). Such a situation occurs when modeling disks [ 8 , 9 , 10 , 11 ], tubes [ 12 , 13 , 14 , 15 , 16 ], rods [ 17 , 18 ], materials with a defect [ 19 , 20 , 21 , 22 , 23 , 24 ], and wherever there are edges [ 25 , 26 , 27 , 28 , 29 ] or discontinuities [ 30 , 31 , 32 ] ( Figure 1 ). Determination of the eigenvalues then boils down to finding complex roots of the appropriate complex function.…”

Section: Introductionmentioning

confidence: 99%

Computation of Eigenvalues and Eigenfunctions in the Solution of Eddy Current Problems

Theodoulidis

Skarlatos

Tytko

2023

Sensors

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The solution of the eigenvalue problem in bounded domains with planar and cylindrical stratification is a necessary preliminary task for the construction of modal solutions to canonical problems with discontinuities. The computation of the complex eigenvalue spectrum must be very accurate since losing or misplacing one of the thereto linked modes will have an important impact on the field solution. The approach followed in a number of previous works is to construct the corresponding transcendental equation and locate its roots in the complex plane using the Newton–Raphson method or Cauchy-integral-based techniques. Nevertheless, this approach is cumbersome, and its numerical stability decreases dramatically with the number of layers. An alternative, approach consists in the numerical evaluation of the matrix eigenvalues for the weak formulation for the respective 1D Sturm–Liouville problem using linear algebra tools. An arbitrary number of layers can thus be easily and robustly treated, with continuous material gradients being a limiting case. Although this approach is often used in high frequency studies involving wave propagation, this is the first time that has been used for the induction problem arising in an eddy current inspection situation. The developed method is implemented in Matlab and is used to deal with the following problems: magnetic material with a hole, a magnetic cylinder, and a magnetic ring. In all the conducted tests, the results are obtained in a very short time, without missing a single eigenvalue.

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Section: Introductionmentioning

confidence: 99%

Computation of Eigenvalues and Eigenfunctions in the Solution of Eddy Current Problems

Theodoulidis

Skarlatos

Tytko

2023

Sensors

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“…We have employed two methods to solve the problem. The classical integral method, expressing the accurate solution by 2D integrals, is applied in Section 2; a novel approach, namely the truncated region eigenfunction expansion (TREE) method [12,[41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58], is used in Section 3, to enhance the efficacy of our formulas. By artificial boundaries introduced to truncate the solution domain, the continuous eigenvalues will be discretised and a series solution can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Mutual inductance calculation for rectangular and circular coils with parallel axes

Yu,

Chen,

Luo

et al. 2023

IET Electric Power Appl

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Simple and practical methods have been provided for the mutual inductance between rectangular and circular coils with parallel axes. The 2D Integral solution is given for the coils without the axial overlap. To improve the efficacy of the proposed approach for the partial or full axial overlap, the series solution derived by the truncated region eigenfunction expansion (TREE) is provided. Both integral and TREE expressions show very high accuracy through comparison with the finite element method simulation and experiment results. Numerical comparisons reveal that the TREE solution is the most efficient while keeping sufficient accuracy, and it is also applicable to all sorts of coil positions.

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“…Tytko and Dziczkowski, in [ 22 , 23 , 24 ], modeled the I-cored and E-cored coils in the presence of the layered medium with a hole, and they verified their work using a Comsol-based finite element model. Zhu et al, in [ 25 ], analyzed an I-cored coil screened with a thin sheet of material with infinite permeability.…”

Section: Introductionmentioning

confidence: 99%

Model of Magnetically Shielded Ferrite-Cored Eddy Current Sensor

Vasić

Rep

Špikić

et al. 2022

Sensors

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Computationally fast electromagnetic models of eddy current sensors are required in model-based measurements, machine interpretation approaches or in the sensor design phase. If a sensor geometry allows it, the analytical approach to the modeling has significant advantages in comparison to numerical methods, most notably less demanding implementation and faster computation. In this paper, we studied an eddy current sensor consisting of a transmitter coil with a finitely long I ferrite core, which was screened with a finitely thick magnetic shield. The sensor was placed above a conductive and magnetic half-layer. We used vector magnetic potential formulation of the problem with a truncated region eigenfunction expansion, and obtained expressions for the transmitter coil impedance and magnetic potential in all subdomains. The modeling results are in excellent agreement with the results using the finite element method. The model was also compared with the impedance measurement in the frequency range from 5 kHz to 100 kHz and the agreement is within 3% for the resistance change due to the presence of the half-layer and 1% for the inductance change. The presented model can be used for measurement of properties of metallic objects, sensor lift-off or nonconductive coating thickness.

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Inductance calculations for coaxial iron‐core coils shielded by cylindrical screens of high permeability

Cited by 9 publications

References 21 publications

Computation of Eigenvalues and Eigenfunctions in the Solution of Eddy Current Problems

Computation of Eigenvalues and Eigenfunctions in the Solution of Eddy Current Problems

Mutual inductance calculation for rectangular and circular coils with parallel axes

Model of Magnetically Shielded Ferrite-Cored Eddy Current Sensor

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