An analysis of the self-excited oscillations, known as “oil whip,” of a rotor supported in fluid film bearings is presented. The source of the instability is the hydrodynamic forces of the bearing fluid film. The equations of motion are nonlinear, and they are studied to determine the limit cycles of the system, also called the whirl orbits. The nonlinear equations are solved by the method of averaging whereby the whirl orbits are obtained directly. The results are dimensionless and are given in graphical form. They show under which conditions whirl orbits can exist, and the position and the size of the orbits are also given. It is found that the orbits are only encountered in a relatively narrow speed interval around the speed at which the static equilibrium becomes unstable.

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