2-D quasi-static fourier series solution for a single coil of a linear induction motor

Abdelqader, Majd; Morelli, Jordan; Pałka, Ryszard; Woronowicz, Konrad

doi:10.1109/cefc.2016.7815923

Cited by 2 publications

(7 citation statements)

References 2 publications

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“…The source demonstrated in Figure 1 is a single coil of a LIM where the back iron and primary iron are modeled with infinite permeability; however, the derivation presented is for a general source in 2-D. Assuming a time harmonic excitation, Maxwell's field equations combined with Ohm's law can be expressed concisely by using the magnetic vector potential formalism (Nasar and Boldea, 1976;Yamamura, 1979;Abdelqader et al, 2016, Abdelqader et al, 2017) by a single partial differential equation:…”

Section: Vector Potential Solution In Fourier Seriesmentioning

confidence: 99%

“…A simplified two-dimensional (2-D) model, as shown in Figure 1, is considered, where an excitation source resides in the airgap, as presented by Abdelqader et al (2016), which contains preliminary results of the analysis further presented and completed here. The source demonstrated in Figure 1 is a single coil of a LIM where the back iron and primary iron are modeled with infinite permeability; however, the derivation presented is for a general source in 2-D.…”

Section: Vector Potential Solution In Fourier Seriesmentioning

confidence: 99%

“…Assuming a time harmonic excitation, Maxwell’s field equations combined with Ohm’s law can be expressed concisely by using the magnetic vector potential formalism (Nasar and Boldea, 1976; Yamamura, 1979; Abdelqader et al , 2016, Abdelqader et al , 2017) by a single partial differential equation: where A is the z -component of the magnetic vector potential, ω is the angular frequency of the harmonic fields, μ and σ are the permeability and conductivity of the medium, respectively, and v is the relative horizontal ( x -direction) velocity of the medium with respect to the lab frame.…”

Section: Vector Potential Solution In Fourier Seriesmentioning

confidence: 99%

“…The validity of the analytical solution is established by comparing the analytical current density [equation (12)] to FEA simulations, as shown in Figure 2 and as presented by Abdelqader et al (2016). The source in this example is the single coil pictured in Figure 1, where A p for each wire is given by A wire = – Iμ 0 /4 π ln( r 2 ), where I is the current in the wire and r is the distance to the wire.…”

Section: Current Densitymentioning

confidence: 99%

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2-D quasi-static Fourier series solution for a linear induction motor

Woronowicz

Abdelqader

Pałka

et al. 2018

COMPEL

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Purpose This paper aims to present a method for calculating electromagnetic fields, eddy currents and forces for a quasi-static two-dimensional (2-D) model of linear induction motors (LIMs) where the primary side is modeled as a collection of individual coils. Design/methodology/approach An analytical solution using Fourier series is derived for a general source with current excitations residing in an airgap and moving relative to a conducting plate and back iron. Ideal magnetic material with infinite permeability is used to model the primary iron above the primary source and the back iron below the conducting plate. Findings The analytical solution is compared to a commercial 2-D finite element analysis (FEA) simulation for validation and then compared to a 2-D FEA model with a more detailed geometry of the LIM. The analytical model accurately predicts LIM thrust even though the geometry of the primary core is simplified as an infinitely long flat slab. 2-D frequency FEA can be used successfully to predict in motion LIM performance. Originality/value The analytical solution presented here models the primary excitations as individual discrete coils instead of current sheets, which all existing models are based on. The discrete coils approach provides a more intuitive and realistic model of the LIM.

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Section: Vector Potential Solution In Fourier Seriesmentioning

confidence: 99%

Section: Vector Potential Solution In Fourier Seriesmentioning

confidence: 99%

Section: Vector Potential Solution In Fourier Seriesmentioning

confidence: 99%

Section: Current Densitymentioning

confidence: 99%

See 2 more Smart Citations

2-D quasi-static Fourier series solution for a linear induction motor

Woronowicz

Abdelqader

Pałka

et al. 2018

COMPEL

Self Cite

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“…Field analysis-based models with closed-form solutions are the most appealing from the authors' point of view because they allow to accurately model most LIM characteristics while reducing the computational complexity compared to numerical solutions (f.e.m.-based). To the best of the authors' knowledge, the vast majority of field analysis-based models with closed-form solutions found in the literature use Fourier series decomposition methods to solve the governing differential equations [7], [14], [15]. One of the main hypotheses of such an approach is the assumption of a constant air gap along the entire domain (i.e.…”

Section: Introductionmentioning

confidence: 99%

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

Rametti,

Pierrejean,

Hodder

et al. 2024

IEEE Trans. Transp. Electrific.

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Literature on linear induction motors (LIMs) has proposed several approaches to model the behavior of such devices for different applications. In terms of accuracy and fidelity, field analysis-based models are the most relevant. Closedform or numerical solutions can be derived, based on the complexity of the model and the underlying hypotheses. In terms of simplicity, equivalent circuit-based models are the most effective, since they can be easily integrated into optimization frameworks. To the best of the authors' knowledge, the literature has not yet provided a computationally efficient LIM analytical model that considers the main characteristics of this type of motor altogether (i.e. finite motor length, magnetomotive force (mmf) space harmonics, slot effect, edge effect, and tail effect) and that is numerically and experimentally validated, especially at high speed (i.e. v ≃ 100 m s −1 ). Within this context, this paper proposes a field analysis-based pseudo-three-dimensional model of LIMs that explicitly takes into account the above-mentioned effects. The derived closed-form solution makes the model computationally more effective than traditional f.e.m. models and, therefore, suitable to be coupled with optimization frameworks for optimal LIM design. The performance and accuracy of the proposed model are assessed through numerical simulations and experimental measurements, carried out by means of a dedicated test bench.

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2-D quasi-static fourier series solution for a single coil of a linear induction motor

Cited by 2 publications

References 2 publications

2-D quasi-static Fourier series solution for a linear induction motor

2-D quasi-static Fourier series solution for a linear induction motor

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

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