A Nonlinear Model for Short Length, Cylindrical Squeeze Films With Large Planar Motions

Abstract

A rotating shaft vibrating in a squeeze film bearing and a tube in a heat exchanger oscillating with fluid-filled cylindrical supports both involve cylindrical squeeze films. Many theoretical and experimental results show that the squeeze film force consists of both a damping force and an inertia force. For relatively large amplitude motions or when the initial eccentricity is large, the time waveform of the squeeze force is significantly nonlinear. In order to predict the transient response of a rotor with squeeze film bearings or a heat exchanger tube subject to flow induced vibration, the nonlinear instantaneous squeeze force must be calculated. This paper presents a model for the instantaneous cylindrical squeeze film force for planar motion. The squeeze film model for a two-dimensional plate shows that there are three nonlinear terms included in the squeeze force. Based on this model, an equation for the short length, cylindrical squeeze film force for moderately large eccentricities is developed. The equation includes the three nonlinear terms: the viscous term, the unsteady inertia term, and the convective inertia term. All three terms are functions of instantaneous eccentricity. The equation predicts the nonlinear multi-harmonic and unsymmetrical time waveforms of the instantaneous squeeze film force for planar motions with both in-line and out-of-line initial eccentricities. The results are compared with experimentally measured squeeze force waveforms obtained with a length to diameter ratio of 0.75 and instantaneous eccentricities less than 0.75. The squeeze force waveforms for this finite length geometry can be reasonably predicted if correction coefficients, which account for the circumferential flow, are applied to the three nonlinear force terms. These coefficients are themselves functions of frequency, initial eccentricity and amplitude.