PurposeThis paper comprehensively analyses the radial electromagnetic (EM) force by unit area and vibration characteristics in a permanent magnet synchronous motor (PMSM). This provides the possibility to verify the action law, causes, and influencing factors of vibration deformation and provides new ideas for vibration management.MethodsAnalytical and finite-element (FE) methods are utilized to deduce the spatial-temporal distribution of radial electromagnetic force and determine the force wave order with significant influence. Accordingly, the air-gap permeance is simplified as the superposition of constant and first-order variable permeance, and the air-gap flux density is regarded as spatial discretization and time continuity. After double equivalence, a theoretical analysis model is established, which is suitable for PMSM with the cogged stator, smooth rotor surface (CSSR) and smooth stator surface, and cogged rotor (SSCR). This model is utilized to analyze the vibration characteristics of the motor, including the deformation law.ResultsThe deformation law is in good agreement with FE analysis and experimental data, demonstrating the rationality of the hypothesis and the correctness of the theoretical analysis model.ConclusionsThe theoretical analysis model shows that the motor deformation is mainly attributed to the total concentrated force and additional bending moment and is related to slot/pole combinations and pole-arc coefficient, which lays the foundation for vibration reduction.