A new approach to solve for oil-whirl and oil-whip limit-cycle response

Abstract

Oil whirl/whip phenomena have been observed for some lightly loaded or unloaded rotor-hydrodynamic bearing systems. To describe and analyze this type of unstable motion, nonlinear hydrodynamic bearing models have been used as well as numerical-integration approaches that eventually converge to limit-cycle orbits. However, if a system includes a large number of bearings, a numerical approach can be time consuming and slow to converge. This paper presents a new way to solve for the limit-cycle orbits of oil whirl/whip. A flexible lumped rotor is modeled as supported by two massless hydrodynamic bearings. Oil film force expressions in terms of the frequency and amplitude of the oil whirl/whip limit cycle are developed for both cavitating and non-cavitating bearings. Free-body analysis is conducted for the rotor and bearing, and then the Newton-Raphson Method (NRM) is adopted to obtain the stable oil whirl/whip response. The stability of NRM solutions is checked. Another approach using conventional nonlinear hydrodynamic bearing model and Runge-Kutta method is employed to confirm the reliability of the new approach. The effects of bearing cavitation, external damping, and imbalance are studied.