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Double‐sided permanent magnet linear synchronous machine with 120° phase belt toroidal windings (120°‐TWDSPMLSM) suffers from large detent force due to the end effect and slot effect. Many existing methods can reduce the detent force of the 120°‐TWDSPMLSM effectively. But they also minimize the back electromotive force (back‐EMF) and thrust simultaneously. To alleviate this problem, this paper adopts a method of combining slot‐shift structure with rearranging the 120° phase belt toroidal windings (120°‐TW) to suppress the detent force and improve the back‐EMF and thrust of the 120°‐TWDSPMLSM simultaneously. First, the slots on the two sides of the primary part are stagger by an optimal distance to reduce the detent force. The models of the detent force, including the end force and cogging force, is established theoretically, and then verified by finite‐element analysis (FA). Then, the 120°‐TW are rearranged to improve the back‐EMF and average thrust. And the electromagnetic characteristics of the 120°‐TWDSPMLSM under different shifted distances are analyzed and compared in detail. Finally, the result shows that the detent force of optimized machine is 70.19% lower than that of the original machine, and the thrust fluctuation reduces 19.21%. Besides, the back‐EMF of optimized machine is 6.84% lower than that of the original machine, but 31.86 higher than the machine with shifting slots and without rearranging the 120°‐TW. Therefore, the optimal method in this paper is available in the detent force reduction and thrust improvement of the 120°‐DSPMLSM.

The three-phase permanent magnet synchronous motor (three-phase PMSM) has gained much popularity in many applications due to its various advantages. In addition, due to the good fault tolerance, simple inverter circuit structure and high torque density, the six-phase PMSM has better prospects than three-phase PMSM in biomedical devices, electric vehicles and other fields with high reliability requirements. In this study, a six-phase axial-flux PMSM inherently without cogging torque is proposed to improve torque density, which equips the 60° phase-belt toroidal winding (60°TW) and slotless stator core. Based on the same effective volume, permanent magnet material, power grade and the other major motor parameters, two six-phase PMSMs with 30° phase-belt toroidal winding (30°TW) and 60°TW are designed, respectively. The armature reaction field, air gap magnetic density, back-electromotive force, output torque, loss characteristic and torque-speed characteristic are compared by using three-dimensional (3D) finite-element models in detail. Finally, the experimental test is carried out using the prototype of three-phase PMSM with 120° phase-belt toroidal winding. The experimental results indirectly verify the feasibility of 60° phase-belt toroidal winding and correctness of 3D FEM. The 3D FEM analysis results are presented to show that torque density of the proposed six-phase PMSM with 60°TW is improved in comparison to the six-phase PMSM with 30°TW. Index Terms—60° phase-belt toroidal winding, axial flux, six-phase permanent magnet synchronous motor, torque density.

The method which combines objective weights model with subjective weights model is usually used to weigh the factors to overcome the impacts of decision-makers in the multi-attribute group decision making. Due to the incomplete decision-making information, the weights given by each expert are regarded as the uncertain grey value according to the grey system theory and a combined weights algorithm based on grey relational analysis is proposed. According to the experts' comparison judgment matrix, the weight decision matrix is gained, and the positive and the negative ideal reference sequences are constructed. Then the grey relational grade between the positive ideal reference sequence and the weight sequence of each expert and that between the negative ideal reference sequence and the weight sequence of each expert are calculated. Subsequently, the expert weights are acquired through an optimal function that maximizes the subjective decision preference of each expert. And the weights that have subjective and objective information are acquired by integrating the expert weights with the weight decision matrix. Finally, with the help of simulation example, the rationality and feasibility of the proposed method are proved.