The effect of asymmetry on torque in permanent magnet motors

Electronically controlled permanent magnet motors are increasing in popularity due to high efficiency and power density. The noise and vibration issues in permanent magnet motors have not been studied extensively. This paper presents a general purpose method to understand the sources of torque pulsation in permanent magnet motors. This method is based on the analysis of the traveling wave components of the radial and tangential air gap flux. These flux densities are obtained from time domain finite element solutions which are then analyzed to find the time and frequency Fourier components. The harmonic components in the cogging torque can then be attributed to specific air gap flux harmonics. A surface mounted brushless DC motor is used as a case study to analyze the effect of rotor asymmetry on torque pulsation. Several guidelines relating to the finite element modeling of the machine are given concerning grid generation and the inclusion of external circuit connections. The effect of magnet imbalance, static rotor eccentricity, dynamic eccentricity, and combined static and dynamic eccentricity are investigated. Load cases are also studied. These results are then related to the expected frequency components in the torque ripple. The authors conclude the paper with overall comments on the modeling and a discussion of the suitability of these motors for low vibration applications.