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

Abstract

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.

Current mode performance of a traction linear induction motor driven from the voltage converter

“…where A is the z-component of the magnetic vector potential, J is the impressed current source density (z-component), ω is the angular frequency of the harmonic field, µ and σ are the permeability and conductivity of the medium respectively, and v is the relative horizontal (x-direction) velocity of the medium. Given the source's excitation field in the air-gap, an analytic solution for equation (2) can be obtained, following the formalism given in [3,4]. In some formulations for thin conducting plates, the magnetic field due to eddy-currents can be neglected, what leads to the simplification of the problem.…”

Linear Induction Motors in Transportation Systems

“…The Fourier series method was applied in [61,62] for the LIM evaluations. Instead of simplifying the primary excitation to a form of current sheets, the authors modeled the primary excitations as discrete coils.…”

“…The Fourier series method was applied in [61,62] for the LIM evaluat simplifying the primary excitation to a form of current sheets, the autho primary excitations as discrete coils. The discrete coils approach leads to a and realistic model of the LIM and allows for the representation of spatial ing from a discrete current distribution.…”

“…Two satisfy the analytical solution for the entire LIM by referring to a vector p ism only. The validation of results obtained in [61] and [62] was perform The approach presented in [61] is similar to the algorithm given in [63,64], where Fourier transform and a mixture of magnetic scalar and vector potential formalism were used. However, the solution presented in [61] makes use of the Fourier series instead of transform and of vector potential formalism without the need of scalar potential to achieve the desired results.…”

“…The analytical approach presented in [62] is similar to the work first presented in [32] and [61], where models of the LIM with current sheet finite primary excitations were presented using Fourier transforms and series methods, respectively. Two papers, [61,62], satisfy the analytical solution for the entire LIM by referring to a vector potential formalism only. The validation of results obtained in [61] and [62] was performed by means of FEA, described in the next chapter.…”