Inductance and force calculations of circular coils with parallel axes shielded by a cuboid of high permeability

et al. 2019

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A detailed analysis is presented for the inductance calculations of rectangular coils with parallel end faces, with the coils of parallel sides as the special case. Integral solutions are given by the theory of second-order scalar potential. The authors further provide the series solutions for the inductance, which are based on the truncated region eigenfunction expansion method. These series are quite concise and accurate, and with higher computational efficiency by comparison with the integrals. The integral and series solutions are also obtained for the planar rectangular coils. The numerical results of both methods are compared with those of the experimental data, and the proposed methods prove to be accurate and efficient enough for practical applications.

Section: Experiments For Mutual and Self-inductance Of Rectangular Comentioning

confidence: 99%

Section: Experiments For Mutual and Self-inductance Of Rectangular Comentioning

confidence: 99%

“…For this BVP, we can refer to [23, 24], and establish the ansatz for the scalar potential V ( x , y , z ):

\begin{matrix} right leftthickmathspace.5em \\ V (x, y, z) & = I_{1} {false\sum}_{m, n = 1}^{normal∞} A_{m n} \sin (][, λ_{m} ()(, l_{x} - x)) \\ \cdot \sin [λ_{n} (l_{y} - y)] {normale}^{- λ_{m n} (z - ζ_{1})} for z > ζ_{1} \end{matrix}

and

\begin{matrix} 1em4pt \\ V ()(, x, y, z) = - I_{1} \sum_{m, n = 1}^{\infty} A_{m n} \sin [λ_{m} (l_{x} - x)] \\ \cdot \sin (][, λ_{n} ()(, l_{y} - y)) e^{- λ_{m n} ()(, ζ_{1} - z)} for z < ζ_{1} \end{matrix},

where the eigenvalues are

\begin{matrix} 1em4pt \\ λ_{m} = \frac{m π}{2 l_{x}}, λ_{n} = \frac{n π}{2 l_{y}}, λ_{m n} = \sqrt{λ_{m}^{2} + λ_{n}^{2}}, \\ m, n = 1, 2, 3, . . . \end{matrix} .

It is apparent that the PMB conditions on the truncating walls can be satisfied with the eigenfunctions of x and y of (24a), (24b), to...…”

Section: Series Expressions Of Mutual and Self‐inductance For Rectamentioning

confidence: 99%

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Integral and series solutions for inductance of rectangular coils with parallel end faces

Zhou

Chen

et al. 2019

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“…Still, little efforts have been devoted to the determination of the formulas for the mutual inductance between Bitter coils, not necessarily coaxial. However, the infinite integrals of Bessel functions should be evaluated numerically; this may decrease the computational efficiency of inductance calculations [13][14][15]. Under this circumstance, solving the integrals analytically is the most natural way to overcome this shortcoming.…”

Section: Introductionmentioning

confidence: 99%

Inductance calculations for non‐coaxial Bitter coils with rectangular cross‐section using inverse Mellin transform

2019

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Recently, the mutual inductance between Bitter coils with rectangular cross-section has been calculated through Bessel function approach or figured out with analytical and semi-analytical formulas. In this study, using the inverse Mellin transform, relevant Bessel integrals will be continued analytically to the complex plane, and then by virtue of contour deformation and residue theorem, they can be expanded to the series containing the hypergeometric functions. In addition, the results obtained by this method are compared with those by finite element method software. Also, the presented approach shows great advantages of high accuracy and very short computational time.

“…In [17], based on TREE method, iron-core coil systems without shielding cases are analysed in detail by introducing a kind of source function. Besides, considering the fact that the coils are supposed to be placed in shielding cases of high permeability, [18][19][20] deduced formulas of air-core coils with magnetic screens.…”

Section: Introductionmentioning

confidence: 99%

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

Zhu

Chen

et al. 2019

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Coaxial iron-core coil system shielded by a magnetic screen is a complex model for analytical calculation, because a complicated boundary value problem must be tackled for obtaining inductances of the coils in this situation. Truncated region eigenfunction expansion method is a suitable way to work out such a problem containing complex boundary conditions. Three different models are taken into consideration in this study. Starting with coil system shielded by two infinitely large plates, the basic steps of the proposed method are introduced carefully. Then the relevant techniques and conclusions are applied to the iron-core coils shielded by a fully enclosed cylindrical screen of high permeability and a lidless one. The effectiveness of the proposed method is verified by comparing with finite element method software and experiments. From relevant data, it is evident that the proposed method is much faster and can be easily used for forecast and evaluation of new schemes in device design process.