Dry-Friction Whirl and Whip Between a Rotor and a Stator: Effect of Rotor-Stator Coupling Due to Seals and Rotor Rigid-Body Dynamics

Abstract

Dry friction backward whirl phenomena have been studied for some time, the most notable work starting with Black in 1967 and 1968. Other notable contributions include those of Crandall (1990) and Lingener (1990), and Bartha (2000). The authors (2007) extended those earlier studies that used lumped-parameter models to a multiple-degree-of-freedom rotor model showing excellent agreement between predictions and available measurements for whip frequencies and the transition frequencies from whirl to whip. One obvious question remains unanswered, namely: Why are dry friction whirl and whip readily induced in test rigs but rarely observed in turbomachinery? This question is addressed here by studying the effect of cross-coupled stiffness and direct damping connections between the rotor and stator (as provided by annular seals), support damping at the stator, and polar and diametral moments of inertia on regions of dry-friction whirl and whip. “Positive” cross-coupled-stiffness coefficients arise in fluid film bearings and fluid seals due to shaft and fluid rotation and produce a reaction force between the rotor and stator. They act to destabilize forward (in the direction of shaft rotation) precessional modes while stabilizing reverse-precession modes. The present predictions show that increasing positive cross-coupled-stiffness-coefficient magnitudes increases the Coulomb friction coefficient that is required to support whirl thus acting to suppress dry-friction whirl. Direct damping that is related to the relative velocity between the rotor and stator acts in exactly the same fashion. Direct damping that connects the stator to ground also acts to suppress whirl and whip. For the models considered here, enough stator damping eliminated the whip region. Test results of axial-compressor stages have shown “negative” cross-coupled-stiffness coefficients. The present study shows that negative cross-coupled stiffness coefficients can make dry-friction whirl more likely by reducing the magnitude of Coulomb friction required to sustain it. The influence of polar and diametral moments of inertia were investigated using a Stodola model comprised of a disk supported at the end of a cantilevered beam. Gyroscopic moments arising from the polar moment of inertia plus running speed had a negligible impact on the whirl-whip regimes. The diametral moment of inertia added an additional degree of freedom, creating an additional whip regime. However, it had no fundamental impact on the whirl-whip regimes.