Analytical modeling of stator vibration for surface mount permanent magnet brushless motors

An analytical method of dynamic vibration response for the surface mount permanent magnet brushless motors was proposed. It is based on the modal superposition method and Love's thin shell theory. The analytical solution explicitly explained the relationship between the radial force, the natural frequency, the mode shape and the vibration. It offered a simple approach to avoid the potential vibration issues during the motor preliminary design stage. The accuracy was verified by comparing to finite element method results. The major findings from the analytical solution include: 1) all the odd modes in axial direction contribute to the motor vibration. 2) The vibration damping not only reduced the vibration amplitude, but also made response lagging behind by a phase angle. 3) The vibration at the middle of the stator is greater than the vibration near the end bell.