Fourier-Based Vibration Model of Electrical Machines Considering Nonideal Orthogonality Between Electromagnetic Forces and Structural Modes

This article proposes a Fourier-based model of vibration synthesis, improving both precision and speed. For the first time, the nonideal orthogonality between electromagnetic (EM) forces and structural modes is theoretically proposed and modeled by spatial harmonics. Different from the discrete vectors used in the previous literature, the proposed method achieves a one-dimension continuous model of EM forces and modes. On the basis, the vectors of modes and forces on tooth surfaces are decomposed by fast Fourier transform, so that the vibration response is synthesized based on Fourier coefficients. Furthermore, the proposed model is applied to a 12-slot/10-pole interior permanent-magnet machine. The spatial harmonics of mode vectors are elaborated to identify the key orders of EM forces before the vibration response is completed. Then, the proposed model is compared with the coupled-field finite element analysis (FEA). The advantages are verified in terms of computational accuracy, speed, and sensitivity to mesh quality. Finally, the feasibility of the proposed model is verified by both coupled-field FEA and experiment.