Dynamic Behavior Analysis of a Rotor System Based on a Nonlinear Labyrinth-Seal Forces Model

Abstract

Taking the flow field features of labyrinth seal into consideration, the fluid force generated from the seal cavity, which is spatially separated into two regions, is modeled with the perturbation method. The rotor orbit defined in the perturbation analysis is spatio-temporal varied, which is quite different from the usually preconditioned elliptical track. Meanwhile, the nonlinear fluid force originating from the seal clearance is delineated by the Muszynska's model. Based on the short bearings assumption, a nonlinear oil-film force model is employed. The rotating shaft is simulated by Timoshenko beam finite element with the consideration of geometric asymmetry. Applying the Lagrange's equations, the motion equations of the rotor-bearing-labyrinth seal system are derived. By means of spectrum cascades, bifurcation diagrams, Poincaré maps, etc., the numerical analysis of the system dynamic characteristics is conducted. The results show that abundant nonlinear behaviors can be triggered in the speed-up. The instability threshold and the vibration amplitude of the rotor system are, respectively, enhanced and reduced by the increasing inlet pressure. With shorter seal length, the sealing effect is decreased, whereas the system stability is improved. The fluid-whip phenomenon can be eliminated by increasing the mass unbalance eccentricity at a certain rotational speed.