Mathematical rotordynamic model for lateral vibration analysis of induction motors with dynamic eccentricities regarding start-up

The paper shows a mathematical rotordynamic model for lateral vibration analysis of induction motors with dynamic eccentricities regarding start-up. With this mathematical model, different kinds of dynamic eccentricities—mass eccentricity, magnetic eccentricity and bent rotor deflection—can be analyzed. Beside the mechanical influences—e.g. the rotor mass, rotor shaft stiffness, oil film coefficients of the sleeve bearings, structural stiffness of the sleeve bearing housings and end shields—also electromagnetic influence—e.g. the electromagnetic field and magnetic eccentricity—can be analyzed for the start-up. The paper is based on the well-known theory of accelerated resonance passing and is an enhancement of the theory for induction motors, considering also electromagnetism during start-up. Based on this rotordynamic model, the absolute displacements of the shaft centre, the shaft journals and the sleeve bearing housings can be analyzed as well as the relative displacements between the shaft journals and the sleeve bearing housings. Additionally, also the vibration velocities at the sleeve bearing housings can be derived. The aim of the paper is not to replace a detailed finite-element-model by a simplified analytical model, but to show the mathematical coherences between rotordyamics and electromagnetics for a start-up of an induction motor, considering different dynamic eccentricities.