Dynamic analysis of a BLDC motor with mechanical and electromagnetic interaction due to air gap variation

In this study, the dynamic behaviors of a BLDC motor are analyzed, when the motor undergoes mechanical and electromagnetic interaction due to an air gap variation between the stator and rotor. When considering the air gap variation caused by the translational motion of the rotor relative to the stator, the kinetic and potential energies, Rayleigh dissipation function, and the magnetic coenergy are expressed in terms of the rotor displacements and stator currents. With these energies and function, new equations of motion are derived using Lagrange’s equation. The equations for the proposed model are nonlinear equations in which the displacements and currents are coupled. The time responses for the displacements and currents are computed for the proposed and previous models. Furthermore, the effects of rotor eccentricity are also investigated. It is found that, when the air gap varies with time, the time responses for the proposed and previous models have small differences in the stator currents, electromagnetic torques, and rotating speeds. However, the time responses have large differences in the rotor displacements. Therefore, this paper claims that the proposed model describes the dynamic behaviors of the motor more accurately than the previous model. It is also shown that rotor eccentricity increases the stator current period and the electromagnetic torque, while it decreases the rotating speed of the rotor.