Travelling-wave problem in electrical machines

Abstract

SynopsisThe problem discussed relates to the calculation of electromagnetic travelling fields in electrical machines. The idealised structure considered comprises a number of laminar regions of infinite extent in the plane of lamination and of arbitrary thickness. Some or all of these regions may be conducting and/or ferromagnetic with constant permeability. The travelling field is produced by an applied current sheet at the interface between two layers, distributed sinusoidally along the plane of lamination and flowing normally to the direction of motion. A convenient reformulation of existing theory is suggested which simplifies calculation. The normal limitations imposed by the amount of algebraic manipulation involved are removed by the use of a transfer matrix. This provides the facility to introduce numerical values directly into the matrix formulation.List of symbols B =• magnetic-flux density, T / = frequency, Hz F r = force/m 2 in z direction, N/m 2 F L = levitation force, N/m 2 F, -force/m 2 tangential to surface, N/m 2 J' = line-current density, A/m J x = current density in x direction, A/m 2 k = 2TT/A P = power/m 2 , W/m 2 s n = slip in region n S n = thickness of region n, m x, y, z -Cartesian co-ordinates A = wavelength of applied field, m p n = resistivity of region n, Qm permeability of region n -angular velocity of field in region ñ -denotes conjugate part

Tubular Linear Induction Machine as a Fast Actuator: Analysis and Design Criteria

“…A number of analytical models of TLIM when fed by a current sheet are derived under the hypothesis of indefinite axial length of the machine and in steady operating conditions [3,8,9]. A quasi-analytical model is used here to approximate the finite length of the stator by considering a finite axial extension of the primary currents windings and an indefinite length of the primary core [33][34][35].…”

“…Introducing in the Maxwell equations the vector potential with the Coulomb gauge, for field equation of an isotropic medium moving with velocity [8] we can write: where µ and σ respectively indicate the permeability and the conductivity of the medium. In the following analysis we assume that the permeability of the iron is constant.…”

“…A step forward can be performed by means of analytical methods which provide simple closed formulas for a quick evaluation of the distribution of magnetic flux density and induced currents as a function of the machine's dimensions and of the slip [8,9].…”

New Scientific Contribution on the 2-D Subdomain Technique in Cartesian Coordinates: Taking into Account of Iron Parts

“…This approach, developed by Mishkin (1953) [36], was first applied to squirrel-cage induction machine in Cartesian coordinates with three-layers (i.e., stator slotting, air-gap, and rotor slotting). It was used and enhanced by many authors, viz., * simplification of the electromagnetic theory [37]; * extended with an infinite number of layers [38]; * converted into equivalent circuits and terminal impedance [39]; * included the curvature effect with the magnetizing current [40]; * incorporated spatial harmonics in the multi-layers theory by considering isotropic and anisotropic (e.g., laminated, composite, and toothed) regions [41,42]; * introduced the nonlinear B(H) curve in homogenous layers by an iterative procedure [43,44]; * taking account of the effect of slot openings [45], i.e., the multi-layers model is combined with the subdomain technique for slotted structures by assuming infinitely permeable tooth tips; * included the current penetration effect in conductive layers [43,46]. The analytical solution for the electromagnetic field in conductive layers is then defined by Bessel functions.…”

Induction motor analyses including non-sinusoidal excitation

“…The purpose of this study is to provide a general analysis for the field problem in induction machines, based on the solution of Barton [26], Freeman [37,38], Freeman and Smith [40] and Greig and Freeman [45]. The analysis establishes a general approach capable of describing any arbitrary electric or magnetic loading, as well as a general method for calculating the machine currents and equivalent impedances.…”