Radial Force Reconstruction in Permanent Magnet Synchronous Machines Using Air Gap Flux Density Measurements

While most acoustic models of electrical machines are validated by external measurements, empirical determination of tooth forces within the air gap of electrical machines is usually not able to be carried out directly without interfering with the machine's structure. In this manuscript, a measurement method is presented using coils on a Flexible Printed Circuit (FPC), that does influence neither the machine's electromagnetic nor mechanical behavior. The method is based on the numerical integration of the induced voltages in the coils, and it is examined, concerning its ability to reconstruct radial forces. The results show an adequate agreement with simulation in no-load operation and the method's capacity to reconstruct the force ripple created by the current ripple due to the inverter switching. Having shown the capabilities, we suggest the method can be used to reconstruct tangential and axial forces as well as investigate manufacturing effects such as rotor eccentricity quantitatively.