Design trade-off between cogging torque and torque ripple in fractional slot surface-mounted permanent magnet machines

Summary form only given. 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 (b₀) [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 b₀ 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 b₀, 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 b₀ 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 b₀ is small. Therefore, a trade-off exists in designing the tooth-tips for SPM machines . By way of example, if a SPM machine mainly works under idle (no-load) and low load conditions, the closed slot opening can be adopted since it will result in low open-circuit cogging torque as well as relative low torque ripple under low load conditions . A prototype machine with 12-slot/8-pole has been designed, analyzed and tested according to this application as shown in Figs .2(a) a- d (b) . Since the predicted cogging torque is extremely small, the experimental error may cover the real data . However, the amplitude of measured result still proves the tiny cogging torque . Meanwhile, the measured on-load torque validates the small torque ripples for low load regions .