A 3D Semi-analytical Calculation Method for a Slotless PMSM with End-wrapped FPCB Concentrated Winding

In this paper, an end-wrapped flexible printed circuit board (FPCB) concentrated winding radial-flux slotless PMSM is proposed. Unlike the traditional slotless motor whose ends are exposed outside the effective core, the winding ends of this motor are wrapped within the length of the effective core, which makes full use of the winding ends and effectively improves the utilization rate of the axial magnetic field, so that the torque density is increased by 14%. In order to fully consider the end leakage effect when calculating the electromagnetic performance, a novel threedimensional semi-analytical calculation method is proposed, which can accurately calculate the magnetic field distribution at each axial position of the motor and convert it into a function, so as to improve the calculation accuracy of the electromagnetic performance. Firstly, the correction functions of PM field and armature field are constructed respectively, and the 3D semianalytical magnetic field models considering the end leakage effect are established. Secondly, the 3D semi-analytical calculation methods of the electromagnetic performances including the back EMF, electromagnetic torque and inductance are established. Then, the correctness and accuracy of the proposed 3D semianalytical methods are verified by 3D finite element method. In addition, a prototype of end-wrapped FPCB concentrated winding is developed and the correctness of the proposed 3D semianalytical method are further verified by experiments.