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.

Dynamic Characterization of an Integral Squeeze Film Bearing Support Damper for a Supercritical CO2 Expander

2017 ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado ◽  
Jeffrey Moore
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Mechanical Impedance ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Damping Behavior ◽  
Impedance Testing ◽  
Stiffness And Damping ◽  
Onset Of Cavitation

The present work advances experimental results and analytical predictions on the dynamic performance of an integral squeeze film damper (ISFD) for application in a high-speed super-critical CO2 (sCO2) expander. The test campaign focused on conducting controlled orbital motion mechanical impedance testing aimed at extracting stiffness and damping coefficients for varying end seal clearances, excitation frequencies, and vibration amplitudes. In addition to the measurement of stiffness and damping; the testing revealed the onset of cavitation for the ISFD. Results show damping behavior that is constant with vibratory velocity for each end seal clearance case until the onset of cavitation/air ingestion, while the direct stiffness measurement was shown to be linear. Measurable added inertia coefficients were also identified. The predictive model uses an isothermal finite element method to solve for dynamic pressures for an incompressible fluid using a modified Reynolds equation accounting for fluid inertia effects. The predictions revealed good correlation for experimentally measured direct damping, but resulted in grossly overpredicted inertia coefficients when compared to experiments.

An Extended Reynolds Equation Including the Lubricant Inertia Effects: Application to Finite Length Water Lubricated Bearings

2015 ◽  
Author(s):  
Saeid Dousti ◽  
Roger L. Fittro
Keyword(s):  
Reynolds Equation ◽  
Load Capacity ◽  
Added Mass ◽  
Turbulent Regime ◽  
Inertia Effects ◽  
Viscous Forces ◽  
Complete Form ◽  
Inertia Model ◽  
Inertia Forces ◽  
Nuclear Coolant

Water lubricated bearings used in nuclear coolant pumps and sub-sea applications exhibit large lubricant inertia forces in the magnitude order of viscous forces. To model these bearings the traditional Reynolds equation is not adequate. An extended Reynolds equation is developed in this study which takes into account the turbulence and inertia effects: both convective and temporal. The most complete form of temporal inertia which applies to the turbulent regime as well, is developed that consists of primary and secondary temporal inertia terms. The convective inertia model follows Constantinescu’s approach [1,2]. The turbulence model is also Constantinescu’s which is tuned with a CFD work. The dynamic coefficients including the lubricant added mass coefficients of a full cylindrical fixed geometry water bearing are obtained. It is observed that the convective inertia increases the load capacity and stability of the bearing. Significant lubricant added mass coefficients comparable to the shaft mass are calculated, which exhibit destabilizing effects in general.

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.

Dynamic Characterization of an Integral Squeeze Film Bearing Support Damper for a Supercritical Co2 Expander

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado ◽  
Jeffrey Moore
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Mechanical Impedance ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Damping Behavior ◽  
Impedance Testing ◽  
Stiffness And Damping ◽  
Onset Of Cavitation

The present work advances experimental results and analytical predictions on the dynamic performance of an integral squeeze film damper (ISFD) for application in a high-speed super-critical CO2 (sCO2) expander. The test campaign focused on conducting controlled orbital motion mechanical impedance testing aimed at extracting stiffness and damping coefficients for varying end seal clearances, excitation frequencies, and vibration amplitudes. In addition to the measurement of stiffness and damping, the testing revealed the onset of cavitation for the ISFD. Results show damping behavior that is constant with vibratory velocity for each end seal clearance case until the onset of cavitation/air ingestion, while the direct stiffness measurement was shown to be linear. Measurable added inertia coefficients were also identified. The predictive model uses an isothermal finite element method to solve for dynamic pressures for an incompressible fluid using a modified Reynolds equation accounting for fluid inertia effects. The predictions revealed good correlation for experimentally measured direct damping, but resulted in grossly overpredicted inertia coefficients when compared to experiments.

scholarly journals Squeeze Film Dampers Executing Small Amplitude Circular-Centered Orbits in High-Speed Turbomachinery

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Sina Hamzehlouia ◽  
Kamran Behdinan
Keyword(s):  
Pressure Distribution ◽  
Small Amplitude ◽  
High Speed ◽  
Fluid Film ◽  
Distribution Model ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Squeeze Film Dampers ◽  
Reaction Forces

This work represents a pressure distribution model for finite length squeeze film dampers (SFDs) executing small amplitude circular-centered orbits (CCOs) with application in high-speed turbomachinery design. The proposed pressure distribution model only accounts for unsteady (temporal) inertia terms, since based on order of magnitude analysis, for small amplitude motions of the journal center, the effect of convective inertia is negligible relative to unsteady (temporal) inertia. In this work, the continuity equation and the momentum transport equations for incompressible lubricants are reduced by assuming that the shapes of the fluid velocity profiles are not strongly influenced by the inertia forces, obtaining an extended form of Reynolds equation for the hydrodynamic pressure distribution that accounts for fluid inertia effects. Furthermore, a numerical procedure is represented to discretize the model equations by applying finite difference approximation (FDA) and to numerically determine the pressure distribution and fluid film reaction forces in SFDs with significant accuracy. Finally, the proposed model is incorporated into a simulation model and the results are compared against existing SFD models. Based on the simulation results, the pressure distribution and fluid film reaction forces are significantly influenced by fluid inertia effects even at small and moderate Reynolds numbers.

Dynamic Analysis of High-Speed Hybrid Thrust Bearings

2013 ◽  
Vol 365-366 ◽  
pp. 304-308
Author(s):  
Lei Wang
Keyword(s):  
Dynamic Analysis ◽  
High Speed ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Orifice Diameter ◽  
Thrust Bearings ◽  
Supply Pressure ◽  
Bearing Stiffness ◽  
Stiffness And Damping

An analysis is conducted and solutions are provided for the dynamic performance of high speed hybrid thrust bearing. By adopting bulk flow theory, the turbulent Reynolds equation is solved numerically with the different orifice diameter and supply pressure. The results show that increasing supply pressure can significantly improve the bearing stiffness and damping, while the orifice diameters make a different effect on the bearing stiffness and damping.

Dynamic Properties of Multi-Lobe Water Lubricated Bearings With Temporal and Convective Inertia Considerations

2017 ◽  
Author(s):  
Saeid Dousti ◽  
Paul Allaire ◽  
Bradley Nichols ◽  
Jianming Cao ◽  
Timothy Dimond
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Added Mass ◽  
Damping Properties ◽  
Inertia Effects ◽  
The Stability ◽  
Water Pumps ◽  
Stiffness And Damping

In this paper, the extended Reynolds equation proposed by Dousti et al. [1] is applied to predict the dynamic behavior of different fixed geometry bearings used in vertical water pumps. The influence of convective and temporal inertia effects is studied in regular and preloaded multi-lobe bearings. It is shown that the convective inertia is more influential at the presence of preload and higher rotational speeds and alters the stiffness and damping properties of the bearing. The temporal inertia leads to the prediction of considerable lubricant added mass coefficients in the order of journal mass. The stability analysis shows depending upon the geometry of the bearing, the new extended Reynolds equation may predict higher or lower logarithmic decrement.

Effects of Turbulence and Viscosity Variation on the Dynamic Coefficients of Fluid Film Journal Bearings

1985 ◽  
Vol 107 (2) ◽  
pp. 256-261 ◽  
Author(s):  
D. F. Wilcock ◽  
O. Pinkus
Keyword(s):  
High Speed ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Fluid Film ◽  
Turbulent Regime ◽  
Dynamic Coefficients ◽  
Damping Characteristics ◽  
Fluid Film Bearings ◽  
Viscosity Variation ◽  
Stiffness And Damping

Many high-speed or large fluid film bearings operate in the turbulent regime. However, relatively little consideration has been given to the effects of turbulence and of the variation in viscosity on the dynamic stiffness and damping characteristics of the bearings. Since the dynamic behavior of the rotor supported on such bearings is often closely tied to the bearing dynamic coefficients, knowledge of them may be critical to both the design and the in-place correction of rotor instabilities. These effects are here considered in some detail on the basis of computer calculated analytical results, both in general dimensionless terms and with regard to a specific numerical example.

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.

Turbulent Hybrid Bearings With Fluid Inertia Effects

1990 ◽  
Vol 112 (4) ◽  
pp. 699-707 ◽  
Author(s):  
Luis San Andre´s
Keyword(s):  
High Speed ◽  
Load Capacity ◽  
Pressure Rise ◽  
Reynolds Numbers ◽  
Dynamic Force ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Friction Factors ◽  
Region Flow ◽  
The Stability

High speed hybrid bearings for cryogenic applications demand large levels of external pressurization to provide substantial load capacity. These conditions give rise to large film Reynolds numbers, and thus, cause the fluid flow within the bearing film to be turbulent and dominated by fluid inertia effects both at the recess edges and at the thin film lands. The analysis includes the effect of recess fluid compressibility and a model for the pressure rise within the recess region. Flow turbulence is simulated by friction factors dependent on the local Reynolds numbers and surface conditions. A perturbation method is used to calculate the zeroth and first flow fields and determine the bearing steady-state and dynamic force response. Comparison of results with existing experimental data shows the accuracy of the present full inertial-turbulent analysis. A roughened bearing surface is shown to improve considerably the stability characteristics of hybrid bearings operating at high speeds.

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