Analysis of induced EMF waveforms and torque ripple in a brushless permanent magnet machine

Permanent magnet machines with trapezoidal back EMF waveform have been the subject of several papers in the past. The simplicity in control and the absence of an absolute position sensor makes this type of motor very attractive. Idealized analysis of such a machine is simple and will result in trapezoidal or square wave back EMF waveforms depending on the assumptions made. In the case of an idealized quasi-square wave current excitation, a ripple-free torque will be obtained. The actual back EMF waveform of these machines depends on the flux density and the conductor distributions. This in turn is a function of the magnet magnetization and the stator tooth and slot structure. In applications where a fairly smooth torque is needed, these machines are made with either the stator slots or the rotor magnets skewed by one slot. This paper deals with the analysis of the back EMF waveform and of the torque ripple waveform of such a machine when the stator slots or rotor magnets are skewed by one slot. The analysis takes into consideration the actual stator conductor distribution and the effect of magnet magnetization on the back EMF waveform. An empirical formula is developed for the magnet flux density distribution which could be used for various magnetization conditions of the magnet. Experimental results are included to confirm the analytical results.