Vibration Synthesis of Permanent Magnet Synchronous Machines Considering Simply Supported Constraints and Tooth Modulations

The analytical methods (AMs) are of value in predicting the electromagnetic vibrations of permanent magnet synchronous machines (PMSMs). In conventional AMs, the stator system is normally equivalent to a circular ring or a cylindrical shell, while the effects of the end covers and stator teeth are ignored, sacrificing the accuracy. Given the shortcomings of existing AMs, an improved model for the vibration synthesis of PMSMs is proposed in this article, which considers the constraint effect of the end covers and the modulation effect of the stator teeth. The vibration response of a single-layer cylindrical shell with simply supported (SS) constraints at both ends is derived under the excitation of radial force waves, based on which the total mass is modified to enhance the vibration prediction accuracy of the double-layer SS stator system. The radial electromagnetic force on the air-gap is transmitted to the stator yokes via a force transmission model. Based on the proposed AM, the electromagnetic vibrations of three PMSMs with different geometric parameters and slot/pole number combinations are predicted, and the results are verified by the finite element method. Finally, a 24-slot/4-pole PMSM prototype is manufactured and tested for the experimental verification.