An accurate modal analysis method for electric motors considering circumferential mode coupling

The vibration of the motor can shorten the lifespan and affect the comfort of the environment. Modal analysis is an important step in the vibration prediction and vibration control process. The nonuniform distribution of teeth can effectively reduce the cogging torque and back electromotive force harmonics of integer slot permanent magnet synchronous motors. Owing to the pronounced non-axisymmetric features of the teeth along the circumferential direction, notable circumferential mode coupling occurs in the vibration of these stators. Existing studies have not adequately addressed this phenomenon, thereby hindering the accurate prediction of modal characteristics for this kind of motors. This paper formulates a theoretical model for the free vibration of the motor stator using the first-order shear deformation theory. By integrating the Ritz method and a complete set of circumferential mode shape expansion functions, precise modal results that account for circumferential coupling can be achieved. The effectiveness and high precision of the proposed method have been demonstrated through the comparison with numerical methods and those obtained by existing studies. It is found that the stator structure with nonuniform distribution of teeth has obvious mode coupling, and the same order mode includes symmetric and asymmetric modes. Finally, the influence of structural parameters on mode coupling is studied and analyzed in detail.