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This paper presents a method to analyse the dynamical behaviour of large-size generators due to the magnetic pull. In rotating electrical machines, the electromagnetic radial forces acting upon rotor and stator surfaces are very large, but they are balanced when the rotor is concentric with the stator. Similarly, the tangential forces produce only an axially rotating moment. If the rotor becomes eccentric, then an imbalance of these forces occurs, so that a net radial electromagnetic force, known as Unbalanced Magnetic Pull (UMP), is developed. The models traditionally proposed in the literature to study the UMP can be considered as reliable in case of small size electrical machines supported by rolling bearings. On the contrary, in case of large-size machines, such as turbo-generators supported by oil-film bearings, the approximation of circular orbit for the geometric centre of the rotor is not acceptable. Nevertheless, the authors who have dealt with UMP in large generators have disregarded that these filtered orbits of the rotor are elliptical and generally the orbit centre is not concentric with the stator. A more realistic model is introduced in this work and the actual distribution of the air-gap length during the rotation will be determined in analytical terms, by taking into account the effects produced by the actual rotor orbit. The actual UMP is calculated by using the air-gap permeance approach and the simulation of the dynamical behaviour of a 320 MVA generator is presented, showing the harmonic content of the UMP and the presence of nonlinearities.