The nonlinear stability of a flexible rotor-bearing system supported on finite length journal bearings is addressed. A perturbation method of the Reynolds lubrication equation is presented to calculate the bearing nonlinear dynamic coefficients, a treatment that is suitable to any bearing geometry. A mathematical model, nonlinear coefficient-based model, is proposed for the flexible rotor-bearing system for which the journal forces are represented through linear and nonlinear dynamic coefficients. The proposed model is then used for nonlinear stability analysis in the system. A shooting method is implemented to find the periodic solutions due to Hopf bifurcations. Monodromy matrix associated to the periodic solution is found at any operating point as a by-product of the shooting method. The eigenvalue analysis of the Monodromy matrix is then carried out to assess the bifurcation types and directions due to Hopf bifurcation in the system for speeds beyond the threshold speed of instability. Results show that models with finite coefficients have remarkably better agreement with experiments in identifying the boundary between bifurcation regions. Unbalance trajectories of the nonlinear system are shown to be capable of capturing sub- and super-harmonics which are absent in the linear model trajectories.
Nonlinear stability analysis of rotor-bearing systems
