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.

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.

Static Characteristics of Gas-Lubricated Slider Bearings Operating in a Helium-Air Mixture

1989 ◽  
Vol 111 (4) ◽  
pp. 620-627 ◽  
Author(s):  
T. Ohkubo ◽  
S. Fukui ◽  
K. Kogure
Keyword(s):  
Reynolds Equation ◽  
Mean Free Path ◽  
Linear Interpolation ◽  
Numerical Results ◽  
Experimental Results ◽  
Experimental Investigations ◽  
Static Characteristics ◽  
Slider Bearings ◽  
Lubrication Equation ◽  
Modified Reynolds Equation

This paper outlines experimental investigations of the static characteristics of self-acting gas-lubricated slider bearings operating in a helium-air mixture. The experimental results are compared with numerical results obtained by solving a modified Reynolds equation and a generalized lubrication equation based on an equivalent molecular mean free path (MMFP) and on an equivalent viscosity derived from molecular gas dynamics. At any mole ratio of air α, the values of the equivalent MMFP are generally expected to be smaller than those of the MMFP derived from linear interpolation, whereas the values of equivalent viscosity are expected to be larger. The numerical results agree well with the experimental results within the range of α from 1.0 to 0.6. Lower values of α give a bigger difference between numerical and experimental results, and make the experimental results lower than the numerical results. Moreover, results of a generalized lubrication equation based on the Boltzmann equation give a closer prediction or qualitative tendency to the experimental results than do those based on the modified Reynolds equation.

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.

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.

Effects of Surface Roughness and Additives in Lubrication: Generalized Reynolds Equation and its Application to Elastohydrodynamic Film

1987 ◽  
Vol 201 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P Sinha ◽  
J S Kennedy ◽  
C M Rodkiewicz ◽  
P Chandra ◽  
R Sharma ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Molecular Size ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Minimum Film Thickness ◽  
Porous Matrices ◽  
The Mean ◽  
Generalized Reynolds Equation

To study the effects of surface roughness and additives in lubrication, a generalized form of Reynolds equation is derived by taking into account the roughness interaction zones adjacent to the moving rough surfaces as sparsely porous matrices and purely hydrodynamic film of micropolar fluid characterizing the lubricant with additives. A particular, one-dimensional form of this equation is used to study these effects on the elastohydrodynamic (EHD) minimum film thickness at the inlet, between two rough rollers. It is shown that for the low permeability of the roughness zone, the EHD film thickness increases as the mean height of the asperities increases, whereas for the high permeability it decreases. The EHD film thickness is also found to increase with the concentration of the additives and the molecular size of the particles. These results are in conformity at least qualitatively, with various experimental and theoretical investigations, cited in the paper.

Static characteristics of hydrostatic doubled-layered porous journal bearings with slip flow including additives percolation into pores under coupled stress lubrication

2017 ◽  
Vol 232 (8) ◽  
pp. 927-939 ◽  
Author(s):  
Shitendu Some ◽  
Sisir K Guha
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Journal Bearings ◽  
Static Characteristics ◽  
Governing Equations ◽  
Modified Reynolds Equation ◽  
Film Interface ◽  
Coupled Stress ◽  
Steady State Performance

A theoretical analysis of the steady-state characteristics of finite hydrostatic double-layered porous journal bearings dealing with the effects of slip flow at the fine porous layer–film interface and percolation of additives into pores under the coupled stress fluid lubrication is presented. Based on the Beavers–Joseph’s criterion for slip flow, the modified Reynolds equation applicable to finite porous journal bearings lubricated with coupled stress fluids have been derived. The governing equations for flow in the coarse and fine layers of porous medium incorporating the percolation of polar additives of lubricant and the modified Reynolds equation are solved simultaneously using finite difference method satisfying appropriate boundary conditions to obtain the steady-state performance characteristics for various parameter namely percolation factor, slip coefficient, bearing feeding parameter, coupled stress parameter, and eccentricity ratio. The results are exhibited in the form of graphs, which may be useful for design of such bearing.

Statics of Gas-Lubricated Slider Bearings in Magnetic Recording Disk Files

1992 ◽  
Vol 206 (1) ◽  
pp. 13-17
Author(s):  
Z Zheming ◽  
S Wenkang
Keyword(s):  
Pitch Angle ◽  
Reynolds Equation ◽  
Flying Height ◽  
Response Analysis ◽  
Static Characteristics ◽  
Magnetic Disk ◽  
Numerical Heat Transfer ◽  
Slider Bearings ◽  
Transient Response Analysis ◽  
Theoretical Results

This paper presents theoretical and experimental analyses of the static characteristics of gas-lubricated slider bearings. An implicit scheme, based on the Patankar-Spalding method, which is commonly utilized in the numerical heat transfer and fluid flow, is developed for the numerical solution of the Reynolds equation. Further investigations on the steady static minimum flying height and the pitch angle are presented by use of a transient response analysis. Theoretical results are experimentally verified to be correct and reliable. By comparing a grooved slider with a non-grooved one in the surface of bearing rails, it is concluded that the grooves in the surface of bearing rails may effectively improve statics of gas-lubricated slider bearings in magnetic disk storages.

On the study of Rayleigh step slider bearings lubricated with non-Newtonian Rabinowitsch fluid

2017 ◽  
Vol 69 (5) ◽  
pp. 666-672
Author(s):  
N.B. Naduvinamani ◽  
Siddharam Patil ◽  
S.S. Siddapur
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Maximum Load ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Content Type ◽  
Slider Bearings ◽  
Load Carrying ◽  
Modified Reynolds Equation ◽  
Frictional Coefficients

Purpose Nowadays, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of non-Newtonian fluids has gained importance. This paper presents an analysis of the static characteristics of Rayleigh step slider bearing lubricated with non-Newtonian Rabinowitsch fluid, which has not been studied so far. The purpose of this paper is to derive the modified Reynolds equation for Rabinowitsch fluids for two regions and to obtain the optimum bearing parameters for the Rayleigh step slider bearings. Design/methodology/approach The governing equations relevant to the problem under consideration are derived. The modified Reynolds equation is derived, and it is found to be highly non-linear and hence small perturbation method is adopted to find solution. Findings From this study it is found that there is an increase in the load-carrying capacity, pressure and frictional coefficients for dilatant fluids as compared to the corresponding Newtonian case. Further, for dilatant lubricants the maximum load-carrying capacity is attained for the slightly larger values of entry region length of Rayleigh step bearing as compared to Newtonian and pseudoplastic lubricants. Originality/value Rabinowitsch fluid is used for the study of lubrication characteristics of Rayleigh step bearings. The author believes that the paper presents these results for the first time.

Generalized Reynolds Equation for Micropolar Lubricants and its Application to Optimum One-Dimensional Slider Bearings: Effects of Solid-Particle Additives in Solution

1975 ◽  
Vol 17 (5) ◽  
pp. 280-284 ◽  
Author(s):  
J. B. Shukla ◽  
M. Isa
Keyword(s):  
Calculus Of Variations ◽  
Solid Particle ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slider Bearing ◽  
One Dimensional ◽  
Slider Bearings ◽  
Generalized Reynolds Equation

The effects of solid-particle additives in the lubricant are considered by characterizing this suspension as a micropolar fluid. The generalized Reynolds equation for this case has been derived and the optimum one-dimensional slider bearing is studied by using the techniques of the calculus of variations.

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