Vibration Mode Number Calculation for PMSM by the Equivalent Concentrated Force and Moment

The vibration mode number (VMN) is the crucial parameter for the electromagnetic vibration in the permanent magnet synchronous machine (PMSM). This paper proposed a method using the equivalent concentrated force (ECF) and the equivalent concentrated moment (ECM) to calculate the VMN. First, the ECF and the ECM were analyzed based on the force-transformation model. Because the VMN is equal to the spatial cycle number (SCN) of the ECF or ECM harmonics over the entire machine, the SCN calculation of the ECF or ECM harmonics was proposed. Then, a 10-pole/12-slot PMSM was used to compare VMNs obtained by the proposed method and FEM. It was demonstrated that the calculated result generally agreed with the simulated result. Finally, the proposed method was validated by measuring the vibration of the 10-pole/12-slot PMSM. The results proved that the proposed method can calculate the VMN.