Induction Machine with Anisotropic Multilayer Rotor Modelling the Electromagnetic and the Electrodynamic States of a Symmetrical Machine with Deep Bar Cage in Solid Iron Rotor Core

Abstract

Eddy current phenomena in the deep bar cage situated in the slots of the solid iron rotor complicate immensely the analysis of transients of such symmetrical polyphase induction machines. When the end effects in the rotor including the influence of end rings are neglected, one obtains two dimensional electromagnetic field distributions. In this case the copper bars and the solid iron teeth can be substituted accurately with an anisotropic two-layer continuous secondary structure having different electromagnetic constants (permeability, conductivity) in the tangential, radial and axial direction1. The successive layers in the multilayer machine model are: isotropic air gap, the first magnetically anisotropic rotor layer substituting the slot openings and tooth-top space, the second anisotropic layer substituting the deep bars with adjacent solid iron teeth and the isotropic solid iron layer under the slots. The sinusoidal1y distributed symmetrical m1-phase winding was assumed in the stator with p pole pairs, ξ1w1 effective number of turns per phase winding and an ideal sheeted magnetic nonsatureted core. The orthogonal transformation of the stator phase current in a two phase current I 1(t) expressed in new frames attached to the rotor, enables the solution of the electromagnetic field in the rotor, excited by the primary equivalent current sheet fixed relative to the rotor body \({{a}_{1}}(x,t) = - 2\sqrt {{\frac{{{{m}_{1}}}}{2}}} \frac{{{{w}_{1}}{{\xi }_{1}}}}{{\bar{p}{{\tau }_{p}}}}{{I}_{1}}(t)\sin (\frac{\pi }{{{{\tau }_{p}}}}x)\).