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Theoretical analysis and numerical FEM calculations, together with segmental experiment studies, are used to study the impact of the static air-gap eccentricity forms on the rotor unbalanced magnetic pull (UMP) of turbogenerator. The universal expression of the magnetic flux density under different forms of SAGE is firstly deduced, based on which the detailed UMP formulas for the normal condition and three SAGE cases are obtained, respectively. Then the exciting characteristics of the UMP for each SAGE form to generate vibrations are analyzed. Finally, numerical FEM calculations and segmental experiments are carried out to investigate the effect of SAGE forms on the rotor UMP, taking the SDF-9 type non-salient-pole fault simulating generator as the object. It is shown that, no matter what kind of SAGE occurs, amplitude increments at each even harmonic component of the UMP and the rotor vibration, especially the 2nd harmonic component, will be brought in. Meanwhile, the UMP keeps directing to the very position where the minimum radial air-gap is. Among the different SAGE forms, the rotor offset has the most sensitive effect on the rotor UMP and vibration, while the stator ellipse deformation has the weakest impact. [ABSTRACT FROM AUTHOR]