Modeling saturation of main magnetic circuit of cage induction motors in presence of eccentricity

Nowadays, diagnostics and monitoring of rotor eccentricity in induction cage motors is based on Fourier spectrum of stator currents. To predict precisely the current spectrum an adequate mathematical model should be used. In this paper the authors presented an improved model of induction cage motor accounting for saturation of the magnetic circuit due to the main MMF harmonic in presence of eccentricity. The crucial point of this improvement is to determine non-linear inductances of motor windings under such conditions. In this paper it is done by introducing an equivalent magnetizing current, which determines a state of machine magnetic circuit. It allows to predict qualitatively (by, physical considerations) the co-energy function and finally, to create machine equations by Lagrange formalism. In order to find data for a such model, magnetic field distribution has to be found from field model of a machine. In this paper the authors created a model for a real induction motor being tested in the field by authors. Field distribution in magnetic circuit of this machine is found by FEM and basing on it the co-energy is calculated as a function of the equivalent magnetic current and parameters determining eccentricity. Resulting equations with all necessary non-linear functions for this real motor are presented.