Modeling and dynamic analysis of vibratory rotor motion in‎ induction machines with three degrees of freedom

Bearings are one of the most important components of an electric machine that are continuously exposed to the electromagnetic and mechanical forces. Vibration caused by various mechanical and electrical faults can impose an irregular rotor-motion in the machine air-gap. In this paper, with the augmented modeling of the electromagnetic and mechanical equations of an induction machine, the dynamics of rotor movement in the air gap are introduced. For this purpose, using the principle of the energy conservation and the Lagrangian theorem, the electromagnetic forces and torques generated from the electromagnetic field of an induction machine are applied by in the mechanical equations of the rotor with three degrees of freedom. Then, the instantaneous position of the rotor in the air-gap and the electromagnetic redial forces on bearing surfaces are identified based on the electrical and mechanical parameters. The numerical analysis is backed up with the experimental results as well in order to validate the accuracy of the proposed model.‎