Oil whirl of rotors, Part I: vertical shafts

Self excited vibrations are studied which occur in a balanced vertical shaft running on plain lubricated bearings. The effect of weight is excluded; also conditions of full lubrication at the bearings are assumed. A linear theory predicts an exponential increase in the amplitude of vibration. The increase cannot be indefinite, it must be curbed (at the bearings in particular) by non-linear effects. Such effects are studied here and an analysis is carried out of the asymptotic behaviour of rise vibrations for t -> oo. The research is concluded with a numerical analysis of the transition from a small perturbation to a fully, developed whirl.