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Forces due to nonuniform airgaps in rotating electrical machines have been a research topic for over 100 years. However, most research in the area of rotating electrical machines has been performed on motors. Large forces in hydropower generators can lead to expensive damage and failures. Therefore, it is of interest to calculate the forces that arise in a large synchronous generator with an eccentric rotor and study the influence these forces have on the stability of the generator rotor. A 74 MVA synchronous hydropower generator was simulated with an eccentric rotor, using a time-stepping finite-element technique. The forces were calculated using Coulomb's virtual-work method and simulations were performed for no-load and load cases. The resulting force was found to be reduced significantly when a damper winding was taken into account. An interesting effect of the rotor damper winding was that it reduced the eccentricity force and introduced a force component perpendicular to the direction of eccentricity. The results from the finite-element simulations were used to determine how the forces affect the stability of the generator rotor. Damped natural eigenfrequencies and damping ratio for load and no-load conditions are presented. When applying the forces computed in the time-dependent model, the damped natural eigenfrequencies were found to increase and the stability of the generator rotor was found to be reduced compared with when the forces were computed in a stationary model.