Analytical Modeling and Finite-Element Computation of Radial Vibration Force in Fractional-Slot Permanent-Magnet Brushless Machines

An analytical model has been developed for analyzing the radial vibration force in fractional-slot permanent-magnet machines. It is compared extensively by finite-element analyses and used to investigate the influence of the following: 1) stator slotting; 2) tangential field component; 3) radius in the air gap for computation; 4) load condition, etc. The major findings include the following: 1) even on an open circuit, the low harmonic component (e.g., the second for a 10-pole/12-slot machine) of the radial force exists due to the slotting effect, although the amplitude is relatively low, while the slotless analytical model cannot predict this phenomenon; 2) on a load, the slotless analytical model is accurate enough for the radial force analysis since the low-order harmonic component of the radial force is mainly due to the interaction between the magnet field and the armature-reaction field and is largely determined by the combination of the pole and slot numbers; 3) it is much more reliable to calculate the radial force in the middle of the air gap rather than close to the stator bore; and 4) the simple formula accounting only for the radial field component in the middle of the air gap is accurate enough for the radial force calculation.