Analytical model of an ironless axial flux permanent magnet machine for electromagnetic force calculation and vibration analysis

Vibration is a challenging issue during the design process of electric machines. In this article, an analytical model of an ironless axial flux permanent magnet machine (AFPM) is proposed for electromagnetic force calculation. And the vibration of the machine is analyzed combined with the electromagnetic force and modal shape. Firstly, the causes of the machine vibration are analyzed based on a 12-slot/10-pole AFPM machine configured with a middle ironless stator and double-sided rotor. Then, an analytical model with the end effect considered for air gap magnetic flux density is presented and compared to the finite element analysis (FEA). The electromagnetic force is calculated based on the air gap flux density. The final analytical calculation results of air gap flux density and electromagnetic force both match the FEA ones well. After that, a three-dimensional simulation model is built and modal shape analysis of the entire machine system is studied. Finally, the validity of the vibration spectrum simulation results is verified through experiments, proving the effectiveness of the presented AFPM machine vibration mechanism and the electromagnetic force analytical model.