Theoretical Investigation of Fluid Inertia Effects and Stability of Self-Acting Gas Journal Bearings

1999 ◽  
Vol 121 (4) ◽  
pp. 836-843 ◽  
Author(s):  
G. Belforte ◽  
T. Raparelli ◽  
V. Viktorov
Keyword(s):  
Reynolds Equation ◽  
Equation Of Motion ◽  
Journal Bearings ◽  
Fluid Inertia ◽  
Stability Parameters ◽  
Inertia Effects ◽  
Stability Diagrams ◽  
Intensive Use ◽  
Stability Limits ◽  
Theoretical Results

The journal equation of motion and the complete Reynolds equation of compressible fluid film are numerically solved and a computer program is developed. The formulas are for externally pressurized bearings, but results are shown only for self-acting bearings. For certain cases, the validity of the theoretical results is verified by comparison with the experimental data available from the literature. Through intensive use of the program, journal center trajectories are obtained and effects of fluid inertia are investigated. New stability parameters are presented and stability diagrams are established for bearings with L/D = 0.25, 0.5, 1, 1.5, and 2. The rotor unbalance effects on bearing stability limits are illustrated for several cases.

Annular Squeeze Films With Inertial Effects

1983 ◽  
Vol 105 (3) ◽  
pp. 361-363 ◽  
Author(s):  
S. R. Turns
Keyword(s):  
Annular Plate ◽  
Equation Of Motion ◽  
Plate Motion ◽  
Squeezing Flow ◽  
Approximation Technique ◽  
Inertial Effects ◽  
Fluid Inertia ◽  
Governing Equations ◽  
Inertia Effects ◽  
Incompressible Newtonian Fluid

An analysis of the laminar squeezing flow of an incompressible Newtonian fluid between parallel plane annuli is presented in which a successive approximation technique is used to account for fluid inertia effects. An expression for the force generated by the fluid is developed and coupled to the equation of motion for the annular plate. Results are presented from the numerical integration of the governing equations for the plate motion.

Lubricant Inertia in Water Lubricated Bearings

2017 ◽  
Author(s):  
Xin Deng ◽  
Cori Watson ◽  
Brian Weaver ◽  
Houston Wood ◽  
Roger Fittro
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Current Status ◽  
Shear Stresses ◽  
Turbulent Regime ◽  
Fluid Inertia ◽  
Film Pressure ◽  
Inertia Effects ◽  
Inertia Model ◽  
Stiffness And Damping

Oil-lubricated bearings are widely used in high speed rotating machines such as those used in the aerospace and automotive industries. However, with some applications including underwater machinery and environmentally friendly applications, water lubricated bearings have become increasingly used. Due to the different fluid properties between oil and water — namely viscosity — the use of water increases the Reynolds numbers drastically and, therefore, makes water-lubricated bearings prone to turbulence and fluid inertia effects. In other words, the linear approximation of the fluid film reaction forces due to the stiffness and damping parameters — as suggested in the traditional Reynolds equation — is not adequate and should be amended to include lubricant added mass. This is because water-lubricated bearings exhibit large lubricant inertia forces on the order of viscous forces. Additionally, stiffness and damping coefficients should be calculated with the turbulence effects included. The aim of this study was to investigate the methodology of modifying the traditional Reynolds equation to include lubricant inertia effects. This paper reviews the current status of research in the lubricant inertia of bearings and explores the development of methodologies to modify the Reynolds equation to include lubricant inertia in bearings. The Reynolds equation is a partial differential equation governing the pressure distribution of thin viscous fluid films in lubrication theory. The thin film hypothesis is used to directly relate the bearing film thickness to the lubricant film pressure. Adding lubricant inertia to the Reynolds equation is vital to improving the accuracy of the bearing model and more specifically its film pressure which is essential to predicting load carrying capabilities. The film pressure relates the gradient of the velocity tensor through the Reynolds equation, and resulting shear stresses then allow the turbulent momentum equations to be written in terms of an eddy-viscosity value. An extended Reynolds equation should be developed which takes into account turbulence and both convective and temporal inertia. The most complete form of the temporal inertia effect model should be developed and applied to the turbulent regime, consisting of both primary and secondary temporal inertia terms. The convective inertia model follows Constantinescu’s approach. This analysis develops a lubricant inertia model applicable to water-lubricated bearings. The results of this study could aid in improving future designs and models of water-lubricated bearings.

Stability analysis of a rigid rotor supported by two-lobe hydrodynamic journal bearings operating with a non-Newtonian lubricant

2018 ◽  
Vol 233 (6) ◽  
pp. 884-898 ◽  
Author(s):  
Saurabh K Yadav ◽  
Arvind K Rajput ◽  
Nathi Ram ◽  
Satish C Sharma
Keyword(s):  
Reynolds Equation ◽  
Pressure Field ◽  
Equation Of Motion ◽  
Journal Bearings ◽  
Rigid Rotor ◽  
Linear Finite Element ◽  
Runge Kutta Method ◽  
The Stability ◽  
Ellipticity Ratio ◽  
Bearing System

In the present work, an investigation has been performed on a rigid rotor supported by two-lobe journal bearings operating with a non-Newtonian lubricant. The governing Reynolds equation for pressure field is solved by using non-linear finite element method. Further to study the dynamic stability of the bearing system, governing equation of motion for the rotor position is solved by fourth order Runge–Kutta method. Bifurcation and Poincaré maps of two-lobe bearings are presented for different values of the non-Newtonian parameter and bearing ellipticity ratio. The numerical results illustrate that the ellipticity of a bearing with a dilatant lubricant improve the stability of the rotordynamic system.

Non-Newtonian Effects on the Static Characteristics of One-Dimensional Slider Bearings in the Inertial Flow Regime

1994 ◽  
Vol 116 (2) ◽  
pp. 303-309 ◽  
Author(s):  
H. Hashimoto
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Reynolds Equation ◽  
Perturbation Technique ◽  
Static Characteristics ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
One Dimensional ◽  
Slider Bearings ◽  
Modified Reynolds Equation

In this paper, the non-Newtonian effects of lubricants on the static characteristics of one-dimensional, high-speed slider bearings are examined theoretically by considering the fluid inertia effects. In the derivation of the modified Reynolds equation, the fluid inertia term in the momentum equation for the non-Newtonian lubricant films is averaged over the film thickness, and the Rabinowitsch empirical model is used as a constitutive equation for non-Newtonian fluids. Applying the modified Reynolds equation to the one-dimensional slider bearings and solving the equation analytically based on the perturbation technique, the film pressure, load carrying capacity, friction force, and inlet flow rate are obtained under various values of the dimensionless nonlinear factor and film thickness ratio. The combined effects of fluid inertia and non-Newtonian characteristics on these static characteristics of lubricants are discussed.

Fluid Inertia Effects on the Load Capacity of Spherical Spiral Groove Bearings

1986 ◽  
Vol 108 (1) ◽  
pp. 65-69 ◽  
Author(s):  
Yuichi Sato
Keyword(s):  
Incompressible Fluid ◽  
Centrifugal Force ◽  
Load Capacity ◽  
Inertia Force ◽  
Laminar Regime ◽  
Fluid Inertia ◽  
Spiral Groove ◽  
Centrifugal Effect ◽  
Inertia Effects ◽  
Theoretical Results

The effects of centrifugal force on the load capacity of inwardly and outwardly spherical spiral groove bearings, operated in laminar regime and lubricated with incompressible fluid, have been investigated. The narrow groove theory has been generalized to include the centrifugal effect of lubricant. The analysis demonstrates that the fluid inertia force reduces the load capacity of an inwardly pumping bearing, whereas it increases the load capacity of an outwardly pumping bearing. The theoretical results are compared with the experimental ones.

Approximate Analysis of Turbulent Hybrid Bearings. Static and Dynamic Performance for Centered Operation

1990 ◽  
Vol 112 (4) ◽  
pp. 692-698 ◽  
Author(s):  
Luis San Andre´s
Keyword(s):  
Analytical Study ◽  
Dynamic Performance ◽  
Journal Bearings ◽  
Dynamic Force ◽  
Force Response ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Numerical Predictions ◽  
Hybrid Bearing ◽  
Close Form

An analytical study for the flow and dynamic force response in turbulent hybrid journal bearings is presented. Fluid inertia effects at the recess edges and film lands are included. For small amplitude motions about the centered position, the equations for the flow on the film lands and recesses are solved in close form by invoking the thin-land assumption. Predictions from the present simplified analytical theory agree well with full numerical predictions. The effect of recess pressure on the dynamic force response of a L02 hybrid bearing is discussed in detail.

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

2011 ◽  
Author(s):  
Saeid Dousti ◽  
Jianming Cao ◽  
Amir Younan ◽  
Paul Allaire ◽  
Tim Dimond
Keyword(s):  
Reynolds Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Navier Stokes ◽  
Inertia Effect ◽  
Inertia Effects ◽  
Low Viscosity ◽  
Fluid Film Bearings

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.

Static and Dynamic Characteristics for a Pressure-Dam Bearing

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Bader Al-Jughaiman ◽  
Dara Childs
Keyword(s):  
Frequency Ratio ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Added Mass ◽  
Equation Model ◽  
Journal Bearings ◽  
Infinite Length ◽  
Fluid Inertia ◽  
Test Conditions ◽  
Load Conditions

Measured rotordynamic force coefficients (stiffness, damping, and added mass) and static characteristics (eccentricity and attitude angle) of a pressure-dam bearing are presented and compared to predictions from a Reynolds-equation model, using an isothermal and isoviscous laminar analysis. The bearing’s groove dimensions are close to the optimum predictions of Nicholas and Allaire (1980, “Analysis of Step Journal Bearings-Infinite Length and Stability,” ASLE Trans., 22, pp. 197–207) and are consistent with current field applications. Test conditions include four shaft speeds (4000rpm, 6000rpm, 8000rpm, and 10000rpm) and bearing unit loads from 0kPato1034kPa(150psi). Laminar flow was produced for all test conditions. A finite-element algorithm was used to generate solutions to the Reynolds-equation model. Excellent agreement was found between predictions and measurements for the eccentricity ratio and attitude angles. Predictions of stiffness and damping coefficients are in reasonable agreement with measurements. However, experimental results show that the bearing has significant added mass of about 60kg at no-load conditions, versus zero mass for predictions from the Reynolds-equation model and 40kg using Reinhardt and Lund’s (1975, “The Influence of Fluid Inertia on the Dynamic Properties of Journal Bearings,” ASME J. Lubr. Technol., 97, pp. 159–167) extended Reynolds-equation model for a plain journal bearing. The added mass quickly drops to zero as the load increases. Measured results also show a whirl frequency ratio near 0.36 at no-load conditions; however, a zero whirl frequency ratio was obtained at all loaded conditions, indicating an inherently stable bearing from a rotordynamics viewpoint.

Bifurcation Analysis of Self-Acting Gas Journal Bearings

2001 ◽  
Vol 123 (4) ◽  
pp. 755-767 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cha’o-Ku`ang Chen
Keyword(s):  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Rotational Velocity ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Finite Differences Method ◽  
Subharmonic Response ◽  
Rotor Center ◽  
Rotor Mass

This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

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