Analysis of Inductance Calculation of Coaxial Circular Coils With Rectangular Cross Section Using Inverse Hyperbolic Functions

Liang, Sizhuang; Fang, Youtong

doi:10.1109/tasc.2015.2427353

Cited by 12 publications

(28 citation statements)

References 10 publications

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“…Using the method in [2] to analytically solve (2) (see the work in [2] for details), we can obtain

\begin{matrix} right leftthickmathspace.5em \\ G_{a b c d} (R_{1}, R_{2}, R_{3}, R_{4}, Z_{1}, Z_{2}, Z_{3}, Z_{4}, φ) \\ = F_{a b c d} (r, R, z, Z, φ) |_{r = R_{1}}^{{(r = R_{2})}_{a}} |_{R = R_{3}}^{{(R = R_{4})}_{b}} |_{z = Z_{1}}^{{(z = Z_{2})}_{c}} |_{Z = Z_{3}}^{{(Z = Z_{4})}_{d}} . \end{matrix}

For example, when abcd = 1100, we have

\begin{matrix} right leftthickmathspace.5em \\ G_{1100} (R_{1}, R_{2}, R_{3}, R_{4}, Z_{1}, Z_{2}, Z_{3}, Z_{4}, φ) \\ = F_{1100} (r, R, z, Z, φ) |_{r = R_{1}}^{r = R_{2}} |_{R = R_{3}}^{R = R_{4}} |_{z = Z_{1}} | \end{matrix}

…”

Section: Calculation Methodsmentioning

confidence: 99%

“…The model in this paper is generally the same as that in [2]. Coil 1 radially extends from R 1 to R 2 , and it axially extends from Z 1 to Z 2 .…”

Section: Description Of Modelmentioning

confidence: 99%

“…A lot of research has been carried out on calculating the inductance of coaxial circular coils, including filamentary coils, thin‐wall solenoids, disk coils, and coils with rectangular cross‐section. Župan et al [1] came up with a method using logarithmic functions to calculate the inductance of coaxial circular coils with rectangular cross‐section, and the method was further improved by Liang and Fang [2] using inverse hyperbolic functions. Although the method is accurate, it is not applicable to filamentary coils, thin‐wall solenoids, and disk coils.…”

Section: Introductionmentioning

confidence: 99%

“…This paper presents an all‐encompassing method to calculate the mutual and self‐inductance of coaxial circular filamentary coils, thin‐wall solenoids, disk coils, and coils with rectangular cross‐section in air. The method is actually an extension of the method in [2], and is an alternative to the methods in [3–8].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of inductance calculation of coaxial circular filamentary coils, thin‐wall solenoids, and disk coils using inverse hyperbolic functions

Liang

2016

IET Science, Measurement & Technology

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“…Using the method in [2] to analytically solve (2) (see the work in [2] for details), we can obtain

\begin{matrix} right leftthickmathspace.5em \\ G_{a b c d} (R_{1}, R_{2}, R_{3}, R_{4}, Z_{1}, Z_{2}, Z_{3}, Z_{4}, φ) \\ = F_{a b c d} (r, R, z, Z, φ) |_{r = R_{1}}^{{(r = R_{2})}_{a}} |_{R = R_{3}}^{{(R = R_{4})}_{b}} |_{z = Z_{1}}^{{(z = Z_{2})}_{c}} |_{Z = Z_{3}}^{{(Z = Z_{4})}_{d}} . \end{matrix}

For example, when abcd = 1100, we have

\begin{matrix} right leftthickmathspace.5em \\ G_{1100} (R_{1}, R_{2}, R_{3}, R_{4}, Z_{1}, Z_{2}, Z_{3}, Z_{4}, φ) \\ = F_{1100} (r, R, z, Z, φ) |_{r = R_{1}}^{r = R_{2}} |_{R = R_{3}}^{R = R_{4}} |_{z = Z_{1}} | \end{matrix}

…”

Section: Calculation Methodsmentioning

confidence: 99%

“…The model in this paper is generally the same as that in [2]. Coil 1 radially extends from R 1 to R 2 , and it axially extends from Z 1 to Z 2 .…”

Section: Description Of Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of inductance calculation of coaxial circular filamentary coils, thin‐wall solenoids, and disk coils using inverse hyperbolic functions

Liang

2016

IET Science, Measurement & Technology

Self Cite

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“…Recently, analytic calculations experienced a come-back in several publications related to superconducting shim coil [1] or related to mutual inductance and force calculation for circular coils with rectangular cross-section [2]- [4]. Mostly, the integral method is used in combination with geometry optimisation problems in coil and winding design areas.…”

Section: Introductionmentioning

confidence: 99%

Rapid 3-D Magnetic Integral Field Computation of Current-Carrying Finite Arc Segments With Rectangular Cross Section

2020

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The computation of three-dimensional (3-D) magnetic fields is a demanding task in the analysis of electrical machines and other electromagnetic devices. In this context, integral field calculation provides a smooth solution, high precision and resolution, "on-demand"calculation, and an origin-based formulation of the magnetic field and the magnetic vector potential. However, conventional elliptic methods lead to huge parallelizable computing efforts and significant errors. In this paper, a 3-D generic current-carrying arc segment with rectangular cross-section is studied. A new analytic formulation is proposed to speed up the computation of magnetic fields and reduce the error by more than three orders of magnitude. In addition, the proposed magnetic vector potential expression has similar accuracy as numerical integration. In fact, a significant reduction of the error level has been showcased clearly with respect to existing approaches. The present work is promising for improving the design methodology and optimization of large superconducting dipole magnets or arched end-winding geometries of large electrical machines.

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Analytical magnetic field and eddy currents computation in a conductive rod wound by a cylindrical coil of finite length

Sari

Ouazir

2022

2022 2nd International Conference on Advanced Electrical Engineering (ICAEE)

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Analysis of Inductance Calculation of Coaxial Circular Coils With Rectangular Cross Section Using Inverse Hyperbolic Functions

Cited by 12 publications

References 10 publications

Analysis of inductance calculation of coaxial circular filamentary coils, thin‐wall solenoids, and disk coils using inverse hyperbolic functions

Analysis of inductance calculation of coaxial circular filamentary coils, thin‐wall solenoids, and disk coils using inverse hyperbolic functions

Rapid 3-D Magnetic Integral Field Computation of Current-Carrying Finite Arc Segments With Rectangular Cross Section

Analytical magnetic field and eddy currents computation in a conductive rod wound by a cylindrical coil of finite length

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