Design Tradeoff Between Cogging Torque and Torque Ripple in Fractional Slot Surface-Mounted Permanent Magnet Machines

Abstract

In designing the fractional slot surface-mounted permanent magnet (SPM) machines for servo and direct-drive applications, the cogging torque and on-load torque ripple are both major design considerations. Nevertheless, since the torque ripple depends on load conditions, the optimal tooth-tip design for the smallest cogging torque may not be the same for the smallest torque ripple as well. Usually cogging torque will reduce with slot opening width (b 0 ) [1] as shown in Fig.1(a). However, the variations of torque ripple are more complicated. With the help of frozen permeability method [2], the on-load torque can be seen as composed by PM torque (T PM ), reluctance torque (T r ) and on-load cogging torque (T cog ), which all contribute to torque ripple, Fig.1(b). The variation of these components against different b 0 under full-load are shown in Figs.1(c) and (d). It can be seen that the average torque for T r will not be zero even in SPM machines due to cross-coupling saturation. With the reducing of b 0 , the leakage flux will increase, which reduces the average torque and makes the fluctuations of T cog even increase under full-load condition. However, under half-load condition, the variation of torque components against b 0 is totally different, Figs.1(e) and (f). It reveals that the cross-coupling effect under half-load becomes unobvious while T cog reduces when b 0 is small.