In this article, the electromagnetic force and vibration characteristics of 10-pole 12-slot and 14-pole 12-slot permanent magnet synchronous motors (PMSMs) are examined considering the tooth modulation effect. In contrast to the conventional electromagnetic force analysis process which considers only the radial force of the lowest spatial harmonic order, the radial and tangential forces include low and high spatial harmonic orders which can be modulated with a lower spatial harmonic order, are analyzed. Then, a structural finite-element (FE) model is developed, and vibration analysis is performed by applying a modulated force and moment. In the analysis, the amplitude and phase of the modulated radial force, tangential force, and moment are considered. The vibration analysis result shows that the 10-pole 12-slot PMSM is disadvantageous with respect to vibration when compared to the 14-pole 12-slot PMSM owing to the large modulated force. Also, it is confirmed that the effect of modulated tangential force and moment cannot be neglected, and the phase difference between modulated radial, tangential force and moment is also an important factor in vibration. Finally, the two motors are fabricated, and the validity of the FE analysis results is verified using the test results.
