This paper aims to clarify global and local force harmonics and their effects on vibration in permanent magnet (PM) synchronous machines. The local force includes both the tangential and radial forces distributing on the stator bore while global force refers to cogging torque and torque ripple. First, the expressions of local tangential and radial forces are derived based on the periodicity of magnetic field. The relationship between local tangential force and global force is also established. Then, the work continues with the effects of global and local forces on vibration. It is found global force may induce remarkable lateral motion when the mounting stiffness is low, while the main combined effect of local radial and tangential forces is inducing radial vibration. At last, influence of reducing global force on the vibration is investigated. It is shown even the vibration induced by global force itself does not always decrease, because this sort of vibration depends on both the harmonic components of optimized global force and the specific mounting conditions. The influence on vibration induced by local force is determined by the overall variation of flux density harmonics. Moreover, it is shown that PM arc shaping is a promising candidate for vibration mitigation.
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