Permanent magnet (PM) induced vibration is one of the major concerns for PM motors. This work aims at the identification and suppression of the vibration source from magnetic field distortions caused by magnet/slot combination, uneven-magnetization, and magnet shifting. Modulation method is employed to predict the relationships between parameters and unbalanced magnetic force (UMF) and cogging torque (CT). Motivated by the magnetic field periodicity and structure especially air-gap symmetry, a new concept of equivalent magnet (EM) wherein one or more real magnets are defined as an imaginary one is introduced to help predict the unexpected force harmonics normally lower than magnet number, and rotation-frequency is used to present unified interpretation on magnetic force regarding the three distortions. The results imply that the relationships are determined by magnet/EM/slot combination including their greatest common divisor (GCD). Compared with CT, the UMF is more sensitive to the uneven-magnetization and magnet shifting. Like ideal motors, if the GCD is greater than unity, the UMF is eliminated, but the CT is not simply via altering the combination. The results also show that magnetic forces for the same EM/slot combinations share similar behaviors regardless of specific magnetic field details. The results can be utilized to suppress undesirable force, or inspect magnetization and installation status by monitoring force frequency and its amplitude, or gain vibration suppression by magnet's selective assembly. The modulation method, EM concept, and main findings are successfully verified by the finite element method (FEM) and comparison with the existing results in the literature. Main contribution of this work is the unified explanation on the relationships between the three distortions and unique force behaviors, especially the prediction on those unexpected harmonic forces.

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