Analytical Modeling for Unbalanced Magnetic Force Suppression in FSCW PMSMs With Slot–Pole Combination of <i>Ns</i> = 2 <i>pr</i> ± 1

Fractional slot concentrated winding (FSCW) permanent magnet synchronous motors (PMSMs) with slot-pole combination of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub>=2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub>±1 exhibit significant unbalanced magnetic force (UMF). In this article, an analytical model incorporating the modulation effect of auxiliary slot is proposed for suppressing UMF while maintaining electromagnetic torque. The effectiveness of the proposed analytical model is validated through static UMF and electromagnetic torque measurement experiments. Firstly, airgap flux density is established, which accounts for the modulation effect of both stator and auxiliary slots. Using the phase difference of first order electromagnetic force waves (EFWs) as the objective function, the solution for the position of auxiliary slot in FSCW PMSMs with slot-pole combination of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub>=2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub>±1 is obtained. Secondly, a quantitative analysis of the UMF and electromagnetic torque in an 8-pole 9-slot FSCW PMSM is performed. By considering the influence of auxiliary slot width on the initial phase of the first order EFWs, the optimal position and structural parameters of the auxiliary slot in 8-pole 9-slot FSCW PMSM are determined. Compared to traditional prototype, the optimized prototype based on the proposed analytical model achieves an 18% reduction in UMF with only a 2% decrease in electromagnetic torque. Finally, the effectiveness of the proposed analytical model in suppressing UMF and maintaining electromagnetic torque is confirmed through static UMF and electromagnetic torque measurement experiments. Additionally, the UMF measurement introduced in this article provides a comparative measurement framework for evaluating the UMF generated by electromagnetic asymmetric in motor with different slot-pole combinations.