The Effect of Fluid Inertia and Cavitation on the Performance of Oscillatory Squeeze-Film Bearings

Abstract

The underlying objective of this investigation is to provide a simple model and solution for predicting the behaviour of cavitation and its effects. The analytical cavitation model developed is based on experimental observations and is conjined to an incompressible, Newtonian lubricant subjected to a squeezing sinusoidal motion between two parallel, flat circular plates under laminar flow conditions. The combined effects ofjluid inertia and cavitation are considered for conditions of viscous and inertia solutions, Re, = 0 and Re, 2 I respectively. Both dynamic and steady state behaviour of the growth and collapse of a centrally located single bubble are analysed in which the efects ofpuid inertia are examined. The results of analysis are presented in terms of excursion ratio e, Sommerfeld number S, squeeze velocity number N and the normalized bubble parameter a,. The results conjirm the formation of a net force due tofluid inertia and cavitation under different flow conditions. NOTATIONamplitude of vibration (m) coefficients of differential equation cavity radius (m) cavity front velocity (m/s) excursion ratio = a/ho dimensionless velocity = k/h, o frequency, cavitation frequency and normalized frequency (Hz) dynamic and reference load (N) film force, normalized steady force dimensionless acceleration = h/ho w2 instantaneous film gap velocity and acceleration [h = h, -a sin (ot)] mean film gap (m) dimensionless film gap = h/h, dimensionless term = N E / H dimensionless term = N E 2 / H 2 squeeze velocity number = pR2w2/P, local, reference pressure (N/m2) cavity pressure = B , H$B2 H 2 (N/m2) dimensionless term = N G / H PIP, P -Pa P -1 radius of plate (m) modified Reynolds number = p hi w/p Sommerfeld number = p w R 2 / P , hz time (s) radial and axial velocity components (m/s) cavity volume = xB2h (m3) rate of change of cavity volume (m3/s) axial coordinate dimensionless cavity radius coefficients dimensionless radius or width = r/R dynamic viscosity (N s/m2) kinematic viscosity (rn2/s) density (kg/m3) dimensionless time = o t angular velocity = w = 27Ff(rad/s)