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The Quarterly Journal of Mechanics and Applied Mathematics 1954 7(4):472-487; doi:10.1093/qjmam/7.4.472
© 1954 by Oxford University Press
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THEORY OF THE SQUIRREL-CAGE INDUCTION MACHINE DERIVED DIRECTLY FROM MAXWELL'S FIELD EQUATIONS

E. MISHKIN

( Israel Institute of Technology Haifa )

The current-vector locus found experimentally deviates substantially, in form, from the classical circle because the ordinary theory, wrongly, assumes a constant leakage inductance. The squirrel-cage's preponderant skin effect causes the leakage inductance to vary with the slip.

Due to the alternating teeth and sloth, the teeth zones of the stator and rotor exhibit different mean permeabilities in the radial and peripheral directions. A machine model is chosen which substitutes the teeth zones by an anisotropio magnetic mass with equivalent permeabilities. This model, while sacrificing the finer details of construction, yields, through direct integration of Maxwell's field equations, a unified analytical solution of the machine's overall performance at variable slip. The stator current and torque are calculated as functions of the slip and compared with those obtained by the classical method.

Formulae derived for the stator current at no-load and infinite slip prove to be very simple and suitable for the designer.


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