Analysis of the magnetic force and the torque in a brushless DC motor

As permanent-magnet motors and generators produce torque, vibration occurs through the small air gap due to the alternating magnetic forces created by the rotating permanent magnets and the current switching of the coils. The magnetic force can be calculated from the flux density by finite element methods and the Maxwell stress tensor in cylindrical coordinates. The transition of the magnetic force with the rotation of rotor and the commutation of current, was analyzed by assuming the quasi static magnetic field. The cogging and the commutating torques were also investigated by integrating the magnetic shear force in a small air-gap. In addition, the characteristics of these forces and torques were also investigated by multi-dimensional spectral analysis, so that this paper makes it possible to predict the frequency spectrum of magnetic force and the torque in a brushless do motor.