Investigation of electromagnetic noise on pole and slot number combinations with possible fractional-slot concentrated windings

The aim of this paper is to investigate the pole (2p) and slot (Q <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</inf> ) number combinations with concentrated windings to yield a minimum electromagnetic noise resulting from vibration mode order and torque variation. Preferentially, a novel method of finding possible pole and slot number combination is provided based on the new factor, i.e., C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cw</inf> called key winding factor. In addition, the relationship between pole/slot number combination and the electromagnetic noise behaviors is established. The major finding can be summarized as follows: 1) Possible pole and slot number combinations are simply determined by whether C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cw</inf> is the natural number (i.e., 1, 2, 3…) or not. 2) The vibration mode order is determined by the greatest common divisor (GCD) of pole and slot numbers with all teeth wound. 3) Unbalanced magnetic force (UMF) can occur in not only 2p = Q <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</inf> ± 1 but also other combinations. 4) The peak to peak cogging torque is greatly influenced by the least common multiple (LCM) of pole and slot numbers. 5) The electromagnetic torque ripple can be reduced by high C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cw</inf> . The proposed analysis is implemented on 10-pole/9-slot, 10-pole/12-slot, and 10-pole/15-slot motors and validated with both analytical and finite element (FE) results.