Analysis of the Flux Density and Back EMF in Eccentric Permanent Magnet Machines Based on 2-D Air-Gap Modulation Theory

In this article, the unified 2-D air-gap field modulation (AFM) model is established to analyze the flux density and back electromagnetic force (EMF) in both rotor-permanent magnet (PM) and stator-PM machines under eccentricity. For the temporal distribution of flux density, the static eccentricity (SE) causes amplitude unbalance, while the dynamic eccentricity (DE) leads to sideband harmonic components. The sideband harmonic is commonly regarded as a double-sideband (DSB) modulation effect, but it may be a single sideband (SSB) modulation effect in some specific cases, which is analytically and experimentally proved in this article. More importantly, a quantitative description of how eccentricity influences the phase back EMF is provided, which is only qualitatively expressed in the existing literature. A standardized analysis process is also given, which can be used for different machine topologies. The aforementioned conclusions are validated by the simulations and experiments on two prototyped machines, namely, an 18-slot 20-pole (18s/20p) surface-mounted PM (SPM) machine and a 12s/10p flux-switching PM (FSPM) machine.