Influence of pole and slot number combinations on cogging torque in permanent magnet machines with static and rotating eccentricities

With aid of finite element and analytical methods, this paper investigates the influence of static/rotating eccentricities on the cogging torque of permanent magnet machines having various pole/slot number combinations (2p/N_s), including fractional-slot topologies, such as 2p=N_s±1, 2p=N_s±2 and 2p/N_s=8/12, as well as an integer-slot machine 2p/N_s=4/12. It is found that the influence of eccentricity reduces significantly with the number of structure cyclic symmetry, which is equal to the greatest common divisor of slot and pole numbers. Hence, the eccentricity shows the largest influence in machines having 2p=N_s±1, relatively large influence in machines having 2p=N_s±2, but very small influence in the other machines. As for machines having 2p=N_s±1 and 2p=N_s±2, the static and rotating eccentricities result in (2p)th and (N_s)th order cogging torque components, respectively. Both static and rotating eccentricities produce similar cogging torque magnitude. The experimental results validate the FE and analytical investigation.