Orbit Model Force Coefficients for Fluid Film Bearings: A Step Beyond Linearization

Abstract

Highperformance turbomachinery demands high shaft speeds, increased rotor flexibility, tighter clearances in the flow passages, advanced materials, and increased tolerance to imbalances. Operation at high speeds induces severe dynamic loading with large amplitude shaft motions at the bearing supports. Typical rotordynamic models rely on linearized force coefficients (stiffness K, damping C, and inertia M) to model the reaction forces from fluid film bearings and seal elements. These true linear force coefficients are derived from infinitesimally small amplitude motions about an equilibrium position. Often, however, a rotor–bearing system does not reach an equilibrium position and displaces with motions amounting to a sizable portion of the film clearance; the most notable example being a squeeze film damper (SFD). Clearly, linearized force coefficients cannot be used in situations exceeding its basic formulation. Conversely, the current speed of computing permits to evaluate fluid film element reaction forces in real time for ready numerical integration of the transient response of complex rotor–bearing systems. This approach albeit fast does not help to gauge the importance of individual effects on system response. Presently, an orbit analysis method estimates force coefficients from numerical simulations of specified journal motions and predicted fluid film reaction forces. For identical operating conditions in static eccentricity and whirl amplitude and frequency as those in measurements, the computational physics model calculates instantaneous damper reaction forces during one full period of motion and performs a Fourier analysis to characterize the fundamental components of the dynamic forces. The procedure is repeated over a range of frequencies to accumulate sets of forces and displacements building mechanical transfer functions from which force coefficients are identified. These coefficients thus represent best fits to the motion over a frequency range and dissipate the same mechanical energy as the nonlinear mechanical element. More accurate than the true linearized coefficients, force coefficients from the orbit analysis correlate best with SFD test data, in particular for large amplitude motions, statically offcentered. The comparisons also reveal the fallacy in representing nonlinear systems as simple K–C–M models impervious to the kinematics of motion.