Mutual Inductance and Force Exerted Between Thick Coils

Ravaud, Romain; Lemarquand, Guy; Lemarquand, V.; Babić, Slobodan; Akyel, C.

doi:10.2528/pier10012806

Cited by 72 publications

(37 citation statements)

References 22 publications

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“…We confirmed already obtained formulas of the magnetic force between inclined circular loops derived by the Biot-Savart law and by the approach of the mutual inductance. In order to use the new formula, whose final expressions are given per (16) or per (17), (18), (19) and (20), one needs to provide the radius of the primary and secondary coils, the position of the center of the secondary coil (the primary coil is assumed to be centered at origin), and the plane equation with all unit vectors in which the secondary coil is located. With these parameters, the problem is completely defined.…”

Section: Resultsmentioning

confidence: 99%

“…The vast majority of this attention has been given to the purely coaxial geometries [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. More recently the focus has been shifted to calculation of the mutual inductance and magnetic force between circular coils with lateral and angular misalignments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

Babić

Akyel

2012

IEEE Trans. Magn.

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Abstract-This paper presents a new general formula for calculating the magnetic force between inclined circular loops placed in any desired position. This formula has been derived from the Lorentz force equation. All mathematical procedures are completely described to define the coil positions that lead to a relatively easy method for calculating the magnetic force between inclined circular loops in any desired position. The presented method is easy to understand, numerically suitable and easily applicable for engineers and physicists. The obtained formula is given in its simplest form from the already existing formulas for calculating the magnetic force between inclined circular loops. We validated the new formula through a series of examples, which are presented here.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

Babić

Akyel

2012

IEEE Trans. Magn.

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“…Thus, an accurate evaluation of the interaction force is required. Many contributions to the interaction force calculation with coaxial or parallel axes based on the analytical or semi-analytical, and the filament method have been performed [1][2][3][4][5][6][7][8][9][10]. The magnetic force can be obtained by using series which converge slowly.…”

Section: Introductionmentioning

confidence: 99%

Magnetic Force Calculation Between Circular Coils of Rectangular Cross Section With Parallel Axes for Superconducting Magnet

Babić

Akyel²,

Ren³

et al. 2012

PIER B

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Abstract-The electromagnetic force between two misaligned coils (coils with parallel axes) with uniform current density distribution and rectangular cross section based on the derived semi-analytical expressions was presented. Using the semi-analytical expressions for magnetic force between filamentary misalignment circular coils we calculate the propulsive and the transverse magnetic force. In order to verify the validity of the expressions, we use the filament method with Grover's formula to calculate the magnetic force for two coils with parallel axes. The results obtained by two methods are in a very good agreement. In this paper, the derivation of the semianalytical expressions and the calculation results of the magnetic force are introduced.

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“…Therefore, in the equations of mutual inductance between two rings, misalignments have to be taken into consideration. Many contributions have been made in the literature to the problem of mutual inductance calculation for coaxial circular coils [5][6][7][8][9][10][11]. These contributions have been based on the application of Maxwell's formula, Neumann's formula, and the Biot-Savart law.…”

Section: Introductionmentioning

confidence: 99%

Inductance Comparison of the Solenoidal Coil of Modular Toroidal Coils Using the Analytical and Finite Element Method

Pahlavani¹,

Shiri²,

Mohammadpour³

et al. 2010

PIER B

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Abstract-The modular toroidal coil (MTC) is composed of several solenoidal coils (SCs) connected in series and distributed in toroidal and symmetrical forms. In this paper, we present an accurate approach for calculation of the mutual and self-inductance between all the SCs of MTC with any arbitrary section. We use Biot-Savart's and Neumann's equations to calculate the self-and mutual inductance between two filamentary circular rings with inclined axes that lie in the same plane, respectively. Their centers are either displaced along the axis of one coil or displaced along one axis of the first coil and then displaced sideways. We use the extended three-point Gaussian algorithm to solve the numerical analysis of the integrations resulting from these equations. Additionally, we apply the filament method to calculate the inductance of the MTC coil. Moreover, the finite element method (FEM) is employed to obtain SC inductance. The results obtained using the FEM confirms the analytical and empirical results. Furthermore, the comparison of the behavior of SC inductance, when the dimensional parameters of the SC are changed, with the FEM results shows an error of less than 0.2%. In this approach, we clarify how the presented equations have to be used for different coil combinations in the filament treatment. Thus, the presented approach can be easily used to calculate the mutual and self-inductance of a MTC between any two MTC rings in three dimensions.Corresponding author: M. R. Alizadeh Pahlavani (Mr alizadehp@iust.ac.ir). 338Alizadeh Pahlavani and Mohammadpour

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Mutual Inductance and Force Exerted Between Thick Coils

Cited by 72 publications

References 22 publications

Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position

Magnetic Force Calculation Between Circular Coils of Rectangular Cross Section With Parallel Axes for Superconducting Magnet

Inductance Comparison of the Solenoidal Coil of Modular Toroidal Coils Using the Analytical and Finite Element Method

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