A numerical method on estimation of stable regions of rotor systems supported on lubricated bearings

The stability degree of periodic solution of nonlinear nonautonomous system was defined by means of the Floquet theory. A method evaluating the stability degree of periodic solution based on transient response was presented by the aid of the concept of dynamic systems or flows. The critical value of a system was determined by the condition, i.e., its stability degree equals zero. Stable regions of rotor systems with balanced and unbalanced disk supported on lubricated bearings were calculated. The study shows that stable region decreases with the increase of speed for a balanced rotor system and decreases with the increase of unbalance for an unbalanced rotor system. Stable regions of periodic solutions are less than that of equilibrium points under the same systematic conditions.