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.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

1957 ◽  
Vol 24 (4) ◽  
pp. 494-496
Author(s):  
J. F. Osterle ◽  
Y. T. Chou ◽  
E. A. Saibel
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Theory ◽  
Simple Relationship ◽  
Inertia Effect ◽  
Laminar Regime ◽  
Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

Empirical Treatment of Hydrodynamic Journal Bearing Performance in the Superlaminar Regime

1970 ◽  
Vol 12 (2) ◽  
pp. 116-122 ◽  
Author(s):  
H. F. Black
Keyword(s):  
Reynolds Number ◽  
Field Equation ◽  
Experimental Work ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Theoretical Treatment ◽  
Hydrodynamic Journal Bearing

The application of a perturbation in terms of simple correlations for friction in turbulent Couette and ‘screw’ flows, together with a further empirical assumption consonant with the experimental work of Smith and Fuller (1), leads to a pressure field equation identical in form with the Reynolds equation. The load capacity of journal bearings throughout most of the superlaminar range may be represented by a single curve, and existing laminar solutions may be applied with the parameters modified by Reynolds number. The theory is compared with published experimental results, and with the most successful theoretical treatment (4). The correlations obtained confirm the adequacy of the theory to predict performance in the superlaminar régime.

A Multiscale Method Modeling Surface Texture Effects

2006 ◽  
Vol 129 (2) ◽  
pp. 221-230 ◽  
Author(s):  
Alex de Kraker ◽  
Ron A. J. van Ostayen ◽  
A. van Beek ◽  
Daniel J. Rixen
Keyword(s):  
Surface Texture ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Multiscale Method ◽  
Operating Conditions ◽  
Contact Load ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Inertia Effects

In this paper a multiscale method is presented that includes surface texture in a mixed lubrication journal bearing model. Recent publications have shown that the pressure generating effect of surface texture in bearings that operate in full film conditions may be the result of micro-cavitation and/or convective inertia. To include inertia effects, the Navier–Stokes equations have to be used instead of the Reynolds equation. It has been shown in earlier work (de Kraker et al., 2006, Tribol. Trans., in press) that the coupled two-dimensional (2D) Reynolds and 3D structure deformation problem with partial contact resulting from the soft EHL journal bearing model is not easy to solve due to the strong nonlinear coupling, especially for soft surfaces. Therefore, replacing the 2D Reynolds equation by the 3D Navier–Stokes equations in this coupled problem will need an enormous amount of computing power that is not readily available nowadays. In this paper, the development of a micro–macro multiscale method is described. The local (micro) flow effects for a single surface pocket are analyzed using the Navier–Stokes equations and compared to the Reynolds solution for a similar smooth piece of surface. It is shown how flow factors can be derived and added to the macroscopic smooth flow problem, that is modeled by the 2D Reynolds equation. The flow factors are a function of the operating conditions such as the ratio between the film height and the pocket dimensions, the surface velocity, and the pressure gradient over a surface texture unit cell. To account for an additional pressure buildup in the texture cell due to inertia effects, a pressure gain is introduced at macroscopic level. The method also allows for microcavitation. Microcavitation occurs when the pressure variation due to surface texture is larger than the average pressure level at that particular bearing location. In contrast with the work of Patir and Cheng (1978, J. Lubrication Technol., 78, pp. 1–10), where the microlevel is solved by the Reynolds equation, and the Navier–Stokes equations are used at the microlevel. Depending on the texture geometry and film height, the Reynolds equation may become invalid. A second pocket effect occurs when the pocket is located in the moving surface. In mixed lubrication, fluid can become trapped inside a pocket and squeezed out when the pocket is running into an area with higher contact load. To include this effect, an additional source term that represents the average fluid inflow due to the deformation of the surface around the pocket is added to the Reynolds equation at macrolevel. The additional inflow is computed at microlevel by numerical solution of the surface deformation for a single pocket that is subject to a contact load. The pocket volume is a function of the contact pressure. It must be emphasized that before ready-to-use results can be presented, a large number of simulations to determine the flow factors and pressure gain as a function of the texture parameters and operating conditions have yet to be done. Before conclusions can be drawn, regarding the dominanant mechanism(s), the flow factors and pressure gain have to be added to the macrobearing model. In this paper, only a limited number of preliminary illustrative simulation results, calculating the flow factors for a single 2D texture geometry, are shown to give insight into the method.

A Compressible Thermohydrodynamic Analysis of Journal Bearings Lubricated With Supercritical CO2

2017 ◽  
Author(s):  
Ssu-Ying Chien ◽  
Mark Cramer ◽  
Alexandrina Untaroiu
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Flow Dynamics ◽  
Navier Stokes ◽  
Supercritical Regime ◽  
Effective Bulk Modulus ◽  
Thermodynamic Critical Point ◽  
Temperature Boundary ◽  
Compressible Lubricant

In this study, a compressible thermohydrodynamic (THD) model was developed to examine the flow dynamics of a journal bearing lubricated with supercritical carbon dioxide (sCO2). This model employed a general form of the Reynolds equation governing compressible lubricant flows with a well-known analytical equation of state, and a viscosity model that depends on both pressure and temperature. In order to verify the model, we first compared the results of this compressible Reynolds equation to the full Navier-Stokes solutions. The accuracy of the model was found to be reasonable when the operating condition is sufficiently far from the thermodynamic critical point. Additionally, the numerical solution suggests that different temperature boundary conditions give slight different results due to the small variations of density and temperature across the gap. Finally, the general approach presented in this study introduces a new single parameter — effective bulk modulus that characterize both the frictional and thermodynamic fluid response. The model developed in this study can provide guidance for further studies of CO2-lubricated bearings operating in the full supercritical regime.

scholarly journals Vibration Characteristics of Hydrodynamic Fluid Film Pocket Journal Bearings

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
N. S. Feng ◽  
E. J. Hahn
Keyword(s):  
Reynolds Equation ◽  
Natural Frequencies ◽  
Journal Bearings ◽  
Vibration Characteristics ◽  
Fluid Film ◽  
Critical Speeds ◽  
Fluid Film Bearings ◽  
Theoretical Analyses

Theoretical analyses of hydrodynamic fluid film bearings with different bearing profiles rely on solutions of the Reynolds equation. This paper presents an approach used for analysing the so-called pocket bearings formed from a combination of offset circular bearing profiles. The results show that the variation of the dynamic bearing characteristics with different load inclinations for the pocket bearings is less than that for the elliptic bearing counterpart. It is shown that the natural frequencies as well as the critical speeds, and hence the vibrational behaviour, can also be significantly different for an industrial rotor supported by the different bearings.

Inertia Effect in Hydrodynamic Lubrication With Film Rupture

1987 ◽  
Vol 109 (1) ◽  
pp. 86-90 ◽  
Author(s):  
H. I. You ◽  
S. S. Lu
Keyword(s):  
Reynolds Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Inertia Effect ◽  
Fluid Inertia ◽  
Film Rupture ◽  
Minimum Film Thickness ◽  
Rupture Model ◽  
Modified Reynolds Equation

The modified Reynolds equation in conjunction with the modified Coyne-Elrod rupture model is used to investigate the inertia effect on the pressure distribution in converging-diverging bearings. The modified Reynolds equation is solved analytically for infinitely long bearings, including the cylinder-plane bearing and the journal bearing. The results showed that the fluid inertia tends to stretch the fluid film and to move the film rupture point farther downstream. The effects are profound even at a moderate value of the reduced Reynolds number, Re* ≈ 0.13 based on the minimum film thickness.

scholarly journals Improvement of Tilting-Pad Journal Bearing Operating Characteristics by Application of Eddy Grooves

Lubricants ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 18
Author(s):  
Eckhard Schüler ◽  
Olaf Berner
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Load Capacity ◽  
Fluid Film ◽  
Operating Characteristics ◽  
Fluid Film Bearings ◽  
Tilting Pad ◽  
Bearing Load ◽  
Bearing Loads ◽  
Tilting Pad Journal Bearing

In high speed, high load fluid-film bearings, the laminar-turbulent flow transition can lead to a considerable reduction of the maximum bearing temperatures, due to a homogenization of the fluid-film temperature in radial direction. Since this phenomenon only occurs significantly in large bearings or at very high sliding speeds, means to achieve the effect at lower speeds have been investigated in the past. This paper shows an experimental investigation of this effect and how it can be used for smaller bearings by optimized eddy grooves, machined into the bearing surface. The investigations were carried out on a Miba journal bearing test rig with Ø120 mm shaft diameter at speeds between 50 m/s–110 m/s and at specific bearing loads up to 4.0 MPa. To investigate the potential of this technology, additional temperature probes were installed at the crucial position directly in the sliding surface of an up-to-date tilting pad journal bearing. The results show that the achieved surface temperature reduction with the optimized eddy grooves is significant and represents a considerable enhancement of bearing load capacity. This increase in performance opens new options for the design of bearings and related turbomachinery applications.

Numerical and Experimental Investigations on Preload Effects in Air Foil Journal Bearings

2017 ◽  
Author(s):  
Marcel Mahner ◽  
Pu Li ◽  
Andreas Lehn ◽  
Bernhard Schweizer
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Compressible Fluids ◽  
Experimental Investigations ◽  
Hysteresis Curves ◽  
Numerical Predictions ◽  
Bearing Stiffness ◽  
Gasdynamic Model ◽  
Good Agreement

A detailed elasto-gasdynamic model of a preloaded three-pad air foil journal bearing is presented. Bump and top foil deflections are herein calculated with a nonlinear beamshell theory according to Reissner. The 2D pressure distribution in each bearing pad is described by the Reynolds equation for compressible fluids. With this model, the influence of the assembly preload on the static bearing hysteresis as well as on the aerodynamic bearing performance is investigated. For the purpose of model validation, the predicted hysteresis curves are compared with measured curves. The numerically predicted and the measured hysteresis curves show a good agreement. The numerical predictions exhibit that the assembly preload increases the bearing stiffness (in particular for moderate shaft displacements) and the bearing damping.

Magneto-rheological fluid slot-entry journal bearing considering thermal effects

2019 ◽  
Vol 30 (18-19) ◽  
pp. 2831-2852 ◽  
Author(s):  
Krishnkant Sahu ◽  
Satish C Sharma
Keyword(s):  
Thermal Effects ◽  
Journal Bearing ◽  
Fluid Model ◽  
Viscous Friction ◽  
Fluid Film ◽  
Applied Current ◽  
Bingham Model ◽  
Geometric Imperfection ◽  
Fluid Film Bearings ◽  
Magneto Rheological

In recent times, controlling the performance of fluid film bearings smartly has become an important area for the fluid film bearing designers. This study deals with the numerical simulation of a magneto-rheological fluid–lubricated two-lobe hybrid slot-entry journal bearing. To make the operating condition more exact and realistic, the influence of geometric imperfection of the journal arising from manufacturing inaccuracies and thermal effect has been considered. Dave magneto-rheological fluid model, a constitutive relation of the Bingham model, and finite element method have been used in this article to simulate the behavior of the magneto-rheological fluid in a slot-entry bearing. The results indicate that the heat generated because of viscous friction rises the temperature of the magneto-rheological fluid, which changes the bearing performance significantly. Considering barrel-shaped journal and magneto-rheological fluid (applied current, Ic = 4 A), the performance of two-lobe slot-entry bearing is superior in terms of the value of [Formula: see text] approximately by a magnitude of 2%, 41%, 181%, 168%, 75%, and 41%, respectively, as compared to that of the base bearing (smooth [Formula: see text], two-lobe bearing, operating with a Newtonian fluid, Ic = 0 A).

Sign in / Sign up

Export Citation Format

Share Document