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In this paper, a generalized theory is developed to detect eccentricity fault in synchronous machines. This theory is independent of synchronous machines configurations and structures. Using this theory, a frequency pattern is proposed for eccentricity fault diagnosis in any synchronous machine. Amplitude of the side-band components at the above mentioned frequencies is introduced as a proper index to identify eccentricity fault in synchronous machines. Here, an interior permanent magnet synchronous motor and a surface mounted permanent magnet synchronous motors are selected for modeling and analyzing. The aforementioned motors are simulated using two-dimensional time stepping finite element method. In this modeling method, non-linearity of the permanent magnets and core materials, spatial distribution of stator windings and non-uniformity of the airgap due to static and dynamic eccentricities are taken into account. By this modeling method, Stator currents are calculated for processing and feature extracting. The spectra of the aforementioned signals are computed to certificate extracted features and recognized patterns from presented theory. The simulation results are verified by the experimental results.