Stability and Transient Motion of a Vertical Three-Lobe Bearing System

The stability characteristics and general transient motion of the finite-width three-lobe bearing assuming an incompressible fluid with cavitation are presented. The hydro-dynamic bearing forces are evaluated by both a finite-difference analysis and an approximate method. The approximate method consists of the infinite bearing solution corrected for end leakage. The approximate method is compared to the finite-difference solution of Reynolds equation and yields acceptable accuracy while running 100 times faster. Linearized bearing stiffness and damping coefficients are determined numerically and used to calculate the threshold of instability for a rigid vertical rotor. The stability curves developed are compared to NASA experimental data as well as analytic work performed by Lund. The nonlinear transient orbits for a balanced rotor are computed and plotted for comparison to the linear stability curves and the NASA test data. The influence of rotor unbalance above and below the stability threshold is investigated. The stability of the three-lobe bearing is optimized with respect to minimum film thickness. It is found that the optimum preload factor varies from 0.59 to 0.47 and the corresponding offset factor ranges from 0.8 to 1.0 for an aspect ratio L/D = 1.0.