Vibration analysis of an external-rotor permanent magnet synchronous hub motor considering air-gap deformation

Air-gap non-uniformity directly affects the electromagnetic performance and vibration characteristics of permanent magnet synchronous hub motors. To investigate the combined influence of rotor deformation and stator eccentricity on the vibration behaviour of surface-mounted external-rotor PMSM, this study proposes a vibration analysis method that incorporates air-gap deformation. Based on the magnetic field superposition principle and Maxwell stress tensor, complex relative permeability and air-gap deformation correction coefficients are introduced to establish an analytical electromagnetic force model that accounts for air-gap distortion. The effects of rotor deformation alone, as well as the coupled effects of rotor deformation and stator eccentricity, on radial electromagnetic force and concentrated electromagnetic forces are analysed and validated through finite-element simulations. The resulting electromagnetic forces are subsequently applied as excitations to the finite-element vibration model of the external-rotor system, enabling the examination of the combined influence of different rotor deformation levels and stator eccentricities on rotor vibration. The results indicate that vibration amplitude primarily concentrates at the main electromagnetic excitation and resonance frequencies. As rotor deformation increases, vibration amplitude rises by approximately 15%–20% at low-order frequencies and exhibits additional growth at the ±1-order rotational components. When rotor deformation and stator eccentricity increase simultaneously, vibration amplitude increases by approximately 25%–32% at low-order frequencies, with further amplification observed at the ±1-order and ±2-order rotational components, while high-frequency growth is attributed to modulation effects. Experimental results confirm that air-gap deformation increases electromagnetic force amplitude across multiple frequency bands and correspondingly elevates external-rotor vibration amplitude across the associated frequency ranges. These findings reveal enhanced multi-frequency coupling and resonance behaviour in the motor and provide valuable insights for understanding vibration mechanisms and optimising the structural design of external-rotor permanent magnet synchronous hub motors.