Temporal and Convective Inertia Effects in Plain Journal Bearings With Eccentricity, Velocity and Acceleration

Abstract

Fluid film bearings are commonly analyzed with the conventional Reynolds equation, without any temporal inertia effects, developed for oil or other high viscosity lubricants. In applications with rapidly time varying external loads, e.g. ships on wavy oceans, temporal inertia effect should be taken into account. As rotating speeds increase in industrial machines and the reduced Reynolds number increases above the turbulent threshold, a form of linearized turbulence model is often used to increase the effective viscosity to take the turbulence into account. Other than the turbulence effect, with high reduced Reynolds number, convective inertia effect gains importance. Water or other low viscosity fluid film bearings used in subsea machines and compressors are potential applications with a highly reduced Reynolds number.” This paper extends the theory originally developed by Tichy [1] for impulsive loads to high reduced Reynolds number lubrication in different bearing configurations. Both fluid shear and pressure gradient terms are included in the velocity profiles across the lubricant film. The incompressible continuity equation and Navier Stokes equations, including the temporal inertia term, are simplified using an averaged velocity approach to obtain an extended form of Reynolds equation which applies to both laminar and turbulent flow. All terms in the Navier Stokes equation, including both the convective and temporal inertia terms are included in the analysis. The inclusion of the temporal inertia term creates a fluid acceleration term in the extended Reynolds equation. A primary advantage of this formulation is that fluid film bearings lubricated with low viscosity lubricants which are subject to high force slew rates can be analyzed with this extended Reynolds equation. A short bearing form of the extended Reynolds equation is developed with appropriate boundary conditions. A full kinematic analysis of the short journal bearing is developed including time derivatives up to and including shaft accelerations. Linearized stiffness, damping and mass coefficients are developed for a plain short journal bearing. A time transient solution is developed for the pressure and bearing loads in plain journal bearings supporting a symmetric rigid rotor when the rotor is subjected to rapidly applied large forces. The change in the rotor displacements when subjected to unbalance forces is explored. Several comparisons between conventional Reynolds equation solutions and the extended Reynolds number form with temporal inertia effects will be presented and discussed.

A Study of Lubricant Inertia Effects for Squeeze Film Dampers Incorporated into High-Speed Turbomachinery

“…They suggested that at small eccentricity ratios, where the effect of temporal inertia is dominant, an added mass is produced, which corresponds to the radial direct inertia coefficient, however, at large eccentricity ratios, where the effect of convective inertia is superior, this effect is completely reversed. Dousti et al [18] developed an extended short bearing Reynolds equation that is applicable to both laminar and turbulent flow regimes. Alternatively, according to the perturbation technique [10,19,20], a small first-order perturbation by means of the expressions for the fluid film velocity components and the lubricant pressure distribution that are typically expanded in power series of the squeeze film Reynolds number is applied to the flow equations.…”

An extended Reynold equation applicable to high reduced Reynolds number operation of journal bearings

“…The reduction of momentum equations based on the short bearing assumption leads to the neglect of all shear and inertia terms in the circumferential direction, which limits the applicability of the obtained extended Reynolds equation to short bearings in this work. The current paper can be considered a continuation of the earlier work by Dousti et al [38] including all relevant inertia terms for finite length bearings.…”

“…This motion entails centrifugal acceleration, which necessitates the inclusion of temporal inertia in the extended Reynolds equation. Dousti et al [38] developed a new extended Reynolds equation for short fixed geometry bearings. They adopted Constantinescu's model to include turbulence and convective inertia terms [27,30], and accounted for temporal inertia as well.…”

“…Tichy and Bou-Said [28] included the temporal inertia effects in a transient analysis of a short bearing. Dousti et al [38] included the temporal inertia effects in the analysis of a short bearing and calculated the added mass effects for both laminar and turbulent regimes. San Andres and Delgado included a temporal inertia term in their version of Reynolds equation developed using bulk flow method and for laminar regime [40].…”

Effects of Nanoparticle Enhanced Lubricant Films in Dynamic Properties of Plain Journal Bearings at High Reynolds Numbers

“…A comprehensive debate on the properties of inertial effects of fluid on lubricant bearing steadiness observing that inertial special contribution are noteworthy in calculation of the rotor steadiness quantities is done by Kakoty and Majumadar [34]. As presented in recent researches [35][36][37][38][39][40][41][42] the inspiration of the ultrafine extracts on hydrodynamic oils lubrication and vibration and friction of the fluid flow film bearings greased with the with ultrafine spices.…”