A Simplified Electromagnetic Theory of the Induction Motor , Using the Concept of Wave Impedance

SUMMARY Electromagnetic field theory is applied to the analysis of performance of an induction-motor rotor when it is exposed to a rotating magnetic field of constant amplitude. An idealized model of the rotor is taken and the analysis is simplified by the application of the concept of wave impedance. The model rotor is capable of simulating the effects of tooth-top and zigzag leakage fluxes, but end effects are neglected. The equations of performance thus obtained are shown to be identical with those obtained by the conventional theory when the latter includes skin effect. The model motor used by Mishkin {Quarterly Journal of Mechanics and Applied Mathematics, 1954, 7, p. 472) is shown to give results widely different from those obtained in practice, since it neglects the zigzag leakage fluxes. The analogy between the tangential force acting on the rotor and radiation pressure is indicated, and it is shown that a change of variable familiar in microwave theory leads to the theory of the variable-speed induction motor developed by Williams and Laithwaite [ LIST OF PRINCIPAL SYMBOLS a = Depth of tooth-top region of rotor. b = Depth of rotor bars. b s = Width of rotor bars. B m = Maximum magnetic flux density. d = Width of opening between tops of teeth on rotor. E z = Electric field strength in equivalent uniform rotor. f x = Force per unit volume on equivalent uniform rotor. F = Force per unit area of rotor surface. H x , H y — Magnetic field components in equivalent uniform rotor. J z = Current density in equivalent uniform rotor. p s = Slot pitch. R = Rotor-bar resistance. s = Slip. X Q = Equivalent standstill rotor-bar reactance. x, y — Rectangular coordinates. Z 01 , Z o2 = Wave impedances in tooth-top and rotor-bar regions respectively. a = Skin effect parameter: a" 1 = skin depth. fi = Phase-change coefficient of flux wave. Y\>Y2 = Propagation coefficients looking into rotor through tooth-top and rotor-bar regions respectively. [x 0 = Absolute permeability of free space. fx r — Relative permeability. fju x , fjL y , (x x , fjL y = Absolute permeabilities of equivalent uniform anisotropic media. (1) INTRODUCTION The induction motor, like all other electrical devices, must obey the laws of electricity and magnetism as formulated in Maxwell's equations of the electromagnetic field. However, a practical induction motor is …