Lubrication of a Porous Bearing—Stokes’ Solution

1966 ◽  
Vol 33 (4) ◽  
pp. 753-760 ◽  
Author(s):  
D. D. Joseph ◽  
L. N. Tao
Keyword(s):  
Load Capacity ◽  
Normal Component ◽  
Infinite Cylinder ◽  
Porous Space ◽  
Pressure Gradients ◽  
Porous Flow ◽  
Porous Bearing ◽  
Transverse Pressure ◽  
Stress Resultant ◽  
Compact Approximations

Coupling of flows induced by the rotation of an infinite cylinder in an eccentric cylindrical hole in a fluid-saturated porous space is investigated in the context of a coupled boundary-value problem in which the Stokes flow outside porous regions and the Darcy flow inside porous regions are connected by continuity requirements on the pressure and normal component of velocity. The configuration is used to model the effects of a thick porous bearing. The solution simplifies considerably in the Reynolds limit of small clearance, and compact approximations for the pressure distribution and other relevant physical variables are derived. It is shown that transverse pressure gradients in the lubricant which are normally neglected in the Reynolds limit do increase, but not significantly, as a result of bearing flow. It follows that candidate Reynolds’ equations may ordinarily ignore effects of transverse pressure gradients in the lubricant even when the bearing is porous. A principal effect of the porous flow on the coupled motion is a diminution of pressure differences which would develop if all solids were impermeable. Corresponding changes in the shear stress resultant, which is neglected relative to the pressure resultant in the impermeable Reynolds limit, can become dominant because of the diminished pressures which attend porous flow. For large eccentricity ratios, the shear resultant is negative, and the load capacity may fall to zero and even change sign.

Lubrication of a Porous Bearing—Reynolds’ Solution

1966 ◽  
Vol 33 (4) ◽  
pp. 761-767 ◽  
Author(s):  
C. C. Shir ◽  
D. D. Joseph
Keyword(s):  
Mass Transfer ◽  
Shear Stress ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Radius Ratio ◽  
Total Load ◽  
Porous Bearing ◽  
Stress Resultant

The problem of lubrication of a journal in a porous bearing is considered. A Reynolds equation modified to accommodate mass transfer with the fluid-saturated bearing is solved, and the influence of the permeability and radius ratio of the bearing is examined. The effects of the bearing flow are such as to reduce the magnitude of the pressure and shift the maximum away from the position of minimum gap. In extreme cases, the integrated resultant of the pressure forces is so reduced as to become comparable in magnitude with the normally negligible shear stress resultant. This latter resultant has an opposing sense so that the total load capacity of the bearing is greatly reduced as a result of bearing flow.

Intrapleural fluid movements described by a porous flow model

1992 ◽  
Vol 73 (6) ◽  
pp. 2511-2516 ◽  
Author(s):  
G. Miserocchi ◽  
D. Venturoli ◽  
D. Negrini ◽  
M. C. Gilardi ◽  
R. Bellina
Keyword(s):  
Porous Medium ◽  
Gamma Camera ◽  
Flow Model ◽  
Pleural Space ◽  
Interstitial Tissue ◽  
Hydraulic Pressure ◽  
Pressure Gradients ◽  
Hydraulic Radius ◽  
Porous Flow ◽  
Anesthetized Dogs

We injected technetium-labeled albumin (at a concentration similar to that of the pleural fluid) in the costal region of anesthetized dogs (n = 13) either breathing spontaneously or apneic. The decay rate of labeled activity at the injection site was studied with a gamma camera placed either in the anteroposterior (AP) or laterolateral (LL) projection. In breathing animals (respiratory frequency approximately 10 cycles/min), 10 min after the injection the activity decreased by approximately 50% on AP and approximately 20% on LL imaging; in apneic animals the corresponding decrease in activity was reduced to approximately 15 and approximately 3%, respectively. We considered label translocation from AP and LL imaging as a result of bulk flows of liquid along the costomediastinal and gravity-dependent direction, respectively. We related intrapleural flows to the hydraulic pressure gradients existing along these two directions and to the geometry of the pleural space. The pleural space was considered as a porous medium partially occupied by the mesh of microvilli protruding from mesothelial cells. Solution of the Kozeny-Carman equation for the observed flow velocities and pressure gradients yielded a mean hydraulic radius of the pathways followed by the liquid ranging from 2 to 4 microns. The hydraulic resistivity of the pleural space was estimated at approximately 8.5 x 10(5) dyn.s.cm-4, five orders of magnitude lower than that of interstitial tissue.

scholarly journals ANALYSIS OF THE FIELD TESTS RESULTS OF BORED CONICAL PILES UNDER THE ACTION OF VARIOUS TYPES OF LOADS

2018 ◽  
Vol 3 (3) ◽  
pp. 24-29
Author(s):  
Ирина Рыбникова ◽  
Irina Rybnikova ◽  
Александр Рыбников ◽  
Aleksandr Rybnikov
Keyword(s):  
Bearing Capacity ◽  
Load Capacity ◽  
Normal Component ◽  
Cone Angle ◽  
Field Tests ◽  
Side Surface ◽  
Test Results ◽  
Head Diameter ◽  
Cylindrical Piles ◽  
Bored Piles

One of the methods of improving the bearing capacity of bored piles is giving them a taper. The feature of these (wedge-type) piles is that under load they work "as a thrust" and transfer part of the load due to the normal component to the inclined side surface. Three sizes of tapered bored piles were tested, with the length of 4.5 m, head diameter 0.4; 0.5; 0.6 m and with cone angle 1o and 2,5o. The test results were compared with the test results of cylindrical piles, 4.5 m long, with head diameter 0.4 m and 0.6 m. It has been discovered that with the increasing cone angle, the bearing capacity of piles against the pressing load, especially the specific load capacity for 1 m3 of material, as compared to cylindrical piles, increases significantly. It has been determined that the larger is the diameter of the head of the pile, the higher is the bearing capacity against the horizontal load, and the bearing capacity against the pullout load is equal to the breakout force of a pile from the soil.

Hydrodynamic Lubrication of Partial Porous Metal Bearings

1966 ◽  
Vol 88 (1) ◽  
pp. 53-60 ◽  
Author(s):  
C. A. Rhodes ◽  
W. T. Rouleau
Keyword(s):  
Series Solution ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Metal ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Bearing Material ◽  
Porous Bearing ◽  
The Galerkin Method

Partial porous metal bearings are analyzed to determine their performance during steady-state operating conditions with a full film of lubricant. The pressure distribution is determined by a simultaneous solution of the two-dimensional Reynolds equation in the film region and the Laplace equation within the porous bearing material. An infinite-series solution is obtained for pressure utilizing the Galerkin method to determine coefficients. Numerical values of load capacity and coefficient of friction are presented for bearing arcs of 180, 150, and 120 deg.

scholarly journals Ceramic matrices applied to aerostatic porous journal bearings: material characterization and bearing modeling

Cerâmica ◽  
2010 ◽  
Vol 56 (338) ◽  
pp. 201-211 ◽  
Author(s):  
Z. C Silveira ◽  
R Nicoletti ◽  
C. A Fortulan ◽  
B. M Purquerio
Keyword(s):  
Load Capacity ◽  
Sucrose Concentration ◽  
Porous Matrix ◽  
Numerical Results ◽  
Homogeneous Distribution ◽  
Average Pore ◽  
Porous Bearing ◽  
Bearing Load ◽  
The Mathematical Model ◽  
Ceramic Matrices

This paper presents the development of an advanced ceramic material for manufacturing aerostatic porous bearing. The results show that there is homogeneous distribution of the pores in the alumina matrix by using different concentrations of the added component (sucrose). The average pore diameter remained around 0.14 µm and respective porosity around 28%, with small standard deviation. The mathematical model of the aerostatic porous bearing is presented, and numerical results indicate that the parameter related to porous medium (Г) strongly affects the resultant bearing load capacity and stiffness. Considering the experimental and numerical results, the porous matrix obtained with 40% of sucrose concentration is more suitable for the aerostatic porous bearing application in study.

Sinusoidal Excitation of a Free Turbulent Jet With Constant Amplitude Transverse Pressure Gradients Near the Nozzle Exit: Part II: An A-C Fluidic Model for the Jet Gain

1973 ◽  
Vol 95 (2) ◽  
pp. 174-179
Author(s):  
A. K. Stiffler ◽  
J. L. Shearer
Keyword(s):  
Pressure Gradient ◽  
Control Region ◽  
Input Signal ◽  
Nozzle Exit ◽  
Flow Direction ◽  
Turbulent Jet ◽  
Pressure Gradients ◽  
Constant Amplitude ◽  
Transverse Pressure ◽  
Sinusoidal Excitation

A free turbulent jet is perturbed transverse to the flow direction by a sinusoidal pressure gradient near the nozzle exit. An a-c model for the jet gain, based upon the control region dynamics and a uniform deflection of the jet downstream of this region, is generally verified in conjunction with attenuated mean shear velocities. A method is given to experimentally determine the effective amplitude of the input signal at the interface of the jet.

Effect of Slip-Flow in Narrow Porous Bearings

1973 ◽  
Vol 95 (4) ◽  
pp. 518-523 ◽  
Author(s):  
P. R. K. Murti
Keyword(s):  
Friction Force ◽  
Experimental Work ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Slip Flow ◽  
Velocity Slip ◽  
Low Permeability ◽  
Eccentricity Ratio ◽  
Porous Bearing ◽  
Thin Walled

The experimental work of Beavers, et al., established that velocity slip takes place over a permeable boundary. The presence of slip flow is taken into account while deriving the appropriate modified Reynolds equation that governs the flow of lubricant in a finite porous bearing. The performance of a thin-walled bearing is then analyzed making use of the narrow bearing approximation. It is found that slip flow adversely affects the load capacity and reduces the friction force on the journal; the attitude angle, however, is not significantly affected. Also the analysis indicates that the effects of velocity slip are prominent when the bearing operates at a lower eccentricity ratio and/or the bearing-matrix has a low permeability.

Modified Reynolds Equation for Aerostatic Porous Radial Bearings With Quadratic Forchheimer Pressure-Flow Assumption

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Zilda C. Silveira ◽  
Benedito M. Purquerio
Keyword(s):  
Reynolds Equation ◽  
Load Capacity ◽  
Loading Capacity ◽  
Global Approach ◽  
Pressure Flow ◽  
Stiffness Coefficients ◽  
Porous Bearing ◽  
Bearing Load ◽  
Modified Reynolds Equation ◽  
Precision Machines

Aerostatic porous bearings are becoming important elements in precision machines due to their inherent characteristics. The mathematical modeling of such bearings depends on the pressure-flow assumptions that are adopted for the flow in the porous medium. In this work, one proposes a nondimensional modified Reynolds equations based on the quadratic Forchheimer assumption. In this quadratic approach, the nondimensional parameter Φ strongly affects the bearing load capacity, by defining the nonlinearity level of the system. For values of Φ>10, the results obtained with the modified Reynolds equation with quadratic Forchheimer assumption tend to those obtained with the linear Darcy model, thus showing that this is a more robust and global approach of the problem, and can be used for both pressure-flow assumptions (linear and quadratic). The threshold between linear and quadratic assumptions is numerically investigated for a bronze sintered porous bearing, and the effects of bearing geometry are discussed. Numerical results show that Φ strongly affects the bearing loading capacity and stiffness coefficients.

Static and stability analysis of partial slip texture multi-lobe journal bearings

2019 ◽  
Vol 234 (4) ◽  
pp. 567-587
Author(s):  
TVVLN Rao ◽  
Ahmad M A Rani ◽  
Norani M Mohamed ◽  
Hamdan H Ya ◽  
Mokhtar Awang ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Partial Slip ◽  
Pressure Gradients ◽  
Capacity Coefficient ◽  
Texture Region ◽  
Linearized Stability ◽  
Infinitesimal Perturbation

This paper presents one-dimensional analysis of modified dynamic Reynolds equation derived for partial slip texture multi-lobe journal bearings. The novelty included in this study is the configuration of partial slip texture region on the bottom bearing lobe surface of a multi-lobe journal bearing under a constant vertical load. The nondimensional pressure and shear stress for steady-state and nondimensional pressure gradients for dynamic coefficients for each lobe with partial slip texture configuration are derived based on narrow groove theory. Linearized stability analysis is evaluated using infinitesimal perturbation method. Results of static and stability characteristics of partial slip texture multi-lobe (two-axial groove, elliptical, three-lobe and offset) journal bearings are presented. Partial slip texture configuration significantly enhances load capacity, coefficient of friction, and stability of two-lobe journal bearing.

An Analytical Study of Starved Porous Bearings

1979 ◽  
Vol 101 (1) ◽  
pp. 38-47 ◽  
Author(s):  
C. Cusano
Keyword(s):  
Analytical Study ◽  
Load Capacity ◽  
Porous Wall ◽  
Velocity Slip ◽  
Diameter Ratio ◽  
Radial Clearance ◽  
Oil Film ◽  
Porous Bearing ◽  
Inside Radius ◽  
Outside Diameter

An analytical solution for the performance characteristics of starved porous bearings is obtained. The solution is based on a finite bearing with an arbitrary wall thickness. The Reynolds equation is modified to include the effect of velocity slip at the interface between the oil film and porous wall. The data presented are for a bearing with a length-to-diameter ratio of 1.0, an outside diameter-to-inside diameter ratio of 1.25 and a radial clearance-to-inside radius ratio of 0.0015. The data are presented in a form such that by knowing the oil supplied externally to the porous bearing or by knowing the active oil film arc, the load capacity and coefficient of friction of the bearing can be obtained for given eccentricity ratios and permeability parameters.

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