On the notion of a rotating fluid force induced by swirling flow

The Bently/Muszynska (B/M) model shows that oil whirl and oil whip are both self-sustained vibrations associated with two unstable modes of a rotor–fluid system. The model includes a rotating fluid damping and inertia force. In certain configurations, the rotating damping force overcomes the frictional internal damping of the rotor and pushes the rotor into a stable limit cycle of circular orbiting. Such a notion of a rotating fluid force is based on bulk-flow models of fluid-filled clearances that could be approximated as narrow since the tangential velocity of the fluid then translates to one angular velocity at a certain radial distance defined by an average radius. This paper scrutinizes the assumption of a rotating fluid inertia force and pinpoints the additional inertial effects of the swirling flow as the gap width increases. These effects are clarified by deriving the equation of motion of a body with a mass subjected to motion-induced fluid forces of a confined swirling flow. We show that the inertial effects of the swirling flow counteract the destabilizing effect of the rotating damping force. However, if the body mass is larger than the displaced fluid mass, instability follows. The frequency of the unstable mode is unchanged by the additional inertial effects and is always equal to the frequency of the damping that induces the instability.