2-D quasi-static solution of a coil in relative motion to a conducting plate

Abstract

Purpose The aim of this paper is to present a method for calculating the electromagnetic fields, forces and current density distribution using Fourier series for a two-dimensional quasi steady state model consisting of a conducting uniform plate moving relative to an arbitrary current source with time harmonic excitation. Design/methodology/approach The presented solution is valid for an arbitrary source. A specific source is chosen consisting of a single coil made up of two-time harmonic current filaments. The solutions are derived and presented in a form that allows its expansion to include an arbitrary number of spatially shifted coils conducting arbitrary harmonic currents. Findings The analytical solution is compared to simulations produced using commercial finite element analysis software, ANSYS Maxwell2D and COMSOL, and is found to be in good agreement. The analytical solution provides a direct method to analyze the spatial harmonics in the system and can be computationally significantly faster especially at high relative speeds between the primary source and conducting plate. Originality/value The presented Fourier series solution is applied to simple 2-D model of a single coil with AC current excitation moving relative to a conducting plate. An analytical solution and analysis of this system has not been presented before, to the authors’ knowledge, using Fourier series or any other method.

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

“…Due to its finite nature, resulting in end-effect, the FEA electromagnetic transient solver is mostly applied to carry out computational tasks. However, it has been shown [3] that if applied properly, the frequency domain solver FEA simulation can not only validate and cross-check the analytical model of the LIM but also establish the validity and applicability of the FEA frequency domain solver solution as a preferred replacement for the time consuming electromagnetic transient FEA calculations. Fig.…”

“…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.…”

“…Figure 5a shows a steady-state 2D calculation model of a discretely distributed coil with AC current excitation at an arbitrary frequency, moving over and in parallel to a conducting plate with an arbitrary speed [61], and Figure 5b shows the extension of this model. demonstrated by comparing experimental results with measurement, a d izing inductance correction factor predicts the LIM performance much bet…”

“…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.…”