A four degrees-of-freedom model for a misaligned electrical rotor

●Angular eccentricity is investigated in the three-dimensional space.●Air-gap length of an eccentric rotor is systematically derived.●Dynamic equations of the rotor system with four dofs are established.●Electromagnetic force and torque are analytically obtained.●Effects of various parameters on vibration are systematically discussed.

The eccentricity is one of the most common trouble sources in the rotor of electrical machine. This paper aims to investigate the vibration characteristics of an inclined rotor with both the static displacement eccentricity and the static angle eccentricity in the three-dimensional space. The air-gap length of an eccentric rotor is derived and the electromagnetic excitation which consists of the unbalanced magnetic pull (UMP) and the electromagnetic torque is obtained. The gyroscopic effect is taken into consideration and dynamic equations of the rotor system with four degrees of freedom are established. The static displacement eccentricity, static angle eccentricity, coexistence of static displacement and angle eccentricity, rotor location, unbalanced mass eccentricity and the rotating frequency are investigated for their effects on the dynamic responses in both the time domain and the frequency domain, respectively. Simulation results illustrate that both the static displacement eccentricity and the static angle eccentricity can lead to the increase in amplitudes of the dynamic displacement response and the angle response. The displacement and angle parameters are interactive in both the time domain and the frequency domain. The frequency components contained in the dynamic responses are related to multiples of the supply frequency and the rotating frequency. High integer multiples of rotating frequency are found when amplitudes of dynamic responses increase.