Mutual inductance of arbitrary‐shaped coils using shape functions

Ishida, Koichi; Itaya, Toshiya; Tanaka, Akio; Takehira, Nobuo

doi:10.1049/iet-smt.2018.5642

Cited by 5 publications

(5 citation statements)

References 13 publications

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“…The analysis will begin with the magnetic induction component B z of a rectangular filament of centre (0, 0, ζ 1 ) and sides 2a and 2b [60][61][62].…”

Section: Integral Solutions For Mutual Inductance Of Rectangular and ...mentioning

confidence: 99%

“…The analysis will begin with the magnetic induction component B z of a rectangular filament of centre (0, 0, ζ 1 ) and sides 2 a and 2 b [60–62].

\begin{align*}{B}_{z}(x,y,z)=\frac{{\mu }_{0}I}{2{\pi }^{2}}{\int }_{-\infty }^{\infty }{\int }_{\infty }^{\infty }{\left({\alpha }^{2}+{\beta }^{2}\right)}^{1/2}{e}^{-{\left({\alpha }^{2}+{\beta }^{2}\right)}^{1/2}\vert z-{\zeta }_{1}\vert }\\ \cdot \frac{\sin (\alpha a)\sin (\beta b)\cos (\alpha x)\cos (\beta y)}{\alpha \beta }d\alpha d\beta \end{align*}

where I is the current flowing through the filament.…”

Section: Integral Solutions For Mutual Inductance Of Rectangular and ...mentioning

confidence: 99%

See 1 more Smart Citation

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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“…The analysis will begin with the magnetic induction component B z of a rectangular filament of centre (0, 0, ζ 1 ) and sides 2a and 2b [60][61][62].…”

Section: Integral Solutions For Mutual Inductance Of Rectangular and ...mentioning

confidence: 99%

“…The analysis will begin with the magnetic induction component B z of a rectangular filament of centre (0, 0, ζ 1 ) and sides 2 a and 2 b [60–62].

\begin{align*}{B}_{z}(x,y,z)=\frac{{\mu }_{0}I}{2{\pi }^{2}}{\int }_{-\infty }^{\infty }{\int }_{\infty }^{\infty }{\left({\alpha }^{2}+{\beta }^{2}\right)}^{1/2}{e}^{-{\left({\alpha }^{2}+{\beta }^{2}\right)}^{1/2}\vert z-{\zeta }_{1}\vert }\\ \cdot \frac{\sin (\alpha a)\sin (\beta b)\cos (\alpha x)\cos (\beta y)}{\alpha \beta }d\alpha d\beta \end{align*}

where I is the current flowing through the filament.…”

Section: Integral Solutions For Mutual Inductance Of Rectangular and ...mentioning

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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“…However, this method is still difficult for considering special structures such as a circular coil, thick circular coil, and thin disk coil. This drawback can be easily improved by using the semi-analytic methods developed in [22,23].…”

Section: Conductor System Modellingmentioning

confidence: 99%

“…where u i is a basis vector of magnetizations; n i is the normal vector of the element Γ i and l k is the vector unit of the current direction in the conductor k. Let us note that the mutual inductance terms m ik can be calculated by the well-known semi-analytic formulas in [7][8][9]22,23]. Whereas, the terms m f ik , m q ik are computed with a standard numerical integration.…”

Section: Final System Of Equationsmentioning

confidence: 99%

3-D Integral Formulation for Thin Electromagnetic Shells Coupled with an External Circuit

Duc

Meunier

2020

Applied Sciences

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The aim of this article is to present a hybrid integral formulation for modelling structures made by conductors and thin electromagnetic shell models. Based on the principle of shell elements, the proposed method provides a solution to various problems without meshing the air regions, and at the same time helps to take care of the skin effect. By integrating the system of circuit equations, the method presented in this paper can also model the conductor structures. In addition, the equations describing the interaction between the conductors and the thin shell are also developed. Finally, the formulation is validated via an axisymmetric finite element method and the obtained results are compared with those implemented from another shell formulation.

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“…The algorithm in Matlab enabling the effective determination of the parameters r 0 , h 0 was presented in [ 39 ] and subsequently used to detect defects with a filamentary coil [ 40 ]. The mathematical model for the system consisting of two coils was developed in [ 41 , 42 , 43 , 44 , 45 , 46 ]. In [ 47 ], it was proved that the change in the frequency and the change of the conductivity of the plate do not affect the change of the equivalent parameters.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the Properties of Eddy Current Sensors Based on Their Equivalent Parameters

Dziczkowski

Tytko

2023

Sensors

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This paper presents a practical way of using the method of evaluating the metrological properties of eddy current sensors. The idea of the proposed approach consists of employing a mathematical model of an ideal filamentary coil to determine equivalent parameters of the sensor and sensitivity coefficients of tested physical quantities. These parameters were determined on the basis of the measured value of the real sensor’s impedance. The measurements were carried out with an air-core sensor and an I-core sensor while they were positioned at different distances from the surface of tested copper and bronze plates. An analysis of the influence of the coil’s position in relation to the I core on the equivalent parameters was also carried out, and the interpretation of the results obtained for various sensor configurations was presented in a graphical form. When equivalent parameters and sensitivity coefficients of examined physical quantities are known, it is possible to compare even very different sensors with the employment of one measure. The proposed approach makes it possible to make a significant simplification of the mechanisms of calibration of conductometers and defectoscopes, computer simulation of eddy current tests, creating the scale of a measuring device, and designing sensors.

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Mutual inductance of arbitrary‐shaped coils using shape functions

Cited by 5 publications

References 13 publications

Mutual inductance calculation for rectangular and circular coils with parallel axes

Mutual inductance calculation for rectangular and circular coils with parallel axes

3-D Integral Formulation for Thin Electromagnetic Shells Coupled with an External Circuit

Evaluation of the Properties of Eddy Current Sensors Based on Their Equivalent Parameters

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