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.

Effect of Slip Flow in Narrow Porous Bearings With Arbitrary Wall Thickness

1975 ◽  
Vol 42 (2) ◽  
pp. 305-310 ◽  
Author(s):  
P. R. K. Murti
Keyword(s):  
Wall Thickness ◽  
Reynolds Equation ◽  
Bessel Functions ◽  
Load Capacity ◽  
Slip Flow ◽  
Velocity Slip ◽  
Low Permeability ◽  
Bearing Material ◽  
Porous Bearing ◽  
The Galerkin Method

The experimental work of Beavers, et al., established that velocity slip takes place over a permeable boundary. The Reynolds equation governing the flow of lubricant in a finite porous bearing is appropriately modified to include the effect of velocity slip at the permeable boundary. The performance of a bearing with arbitrary wall thickness is then analyzed adopting the narrow bearing approximation. An exact solution is given for the pressure of the lubricant in the bearing material using modified Bessel functions and the modified Reynolds equation for the problem is solved by the Galerkin method. Numerical results obtained with a digital computer indicate 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 higher eccentricity ratio and/or the bearing matrix has a low permeability. The results are presented in graphical and tabular forms and guidelines are outlined to enable designers in assessing bearing performance using the results.

Effect of velocity slip in a narrow rough porous journal bearing

2003 ◽  
Vol 217 (1) ◽  
pp. 59-70 ◽  
Author(s):  
K Gururajan ◽  
J Prakash
Keyword(s):  
Porous Material ◽  
Coefficient Of Friction ◽  
Strong Interaction ◽  
Journal Bearing ◽  
Load Capacity ◽  
Tangential Velocity ◽  
Velocity Slip ◽  
Qualitative And Quantitative ◽  
Slip Effects ◽  
Thin Walled

The paper examines the effect of velocity slip in a thin-walled infinitely short rough porous journal bearing operating under steady conditions in a hydrodynamic regime. The analysis extends earlier work [1] in which the tangential velocity at the surface of the porous material was neglected. The problem is solved analytically together with associated boundary conditions. It is found that there exists a strong interaction between roughness and slip effects. A comparison with the case of an infinitely long journal bearing [2] shows that there are significant qualitative and quantitative differences in load capacity and coefficient of friction. However, the slip-induced variations in friction force are similar to those for an infinitely long journal bearing.

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.

On the linear stability analysis of finite-hydrodynamic porous journal bearings under coupled stress lubrication

2007 ◽  
Vol 221 (7) ◽  
pp. 831-840 ◽  
Author(s):  
S. K. Guha ◽  
A. K. Chattopadhyay
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Slip Flow ◽  
Tangential Velocity ◽  
Continuum Theory ◽  
Transient State ◽  
Velocity Slip ◽  
Journal Bearings ◽  
The Stability ◽  
Coupled Stress

The objective of the present investigation is to study theoretically, using the finite-difference techniques, the dynamic performance characteristics of finite-hydrodynamic porous journal bearings lubricated with coupled stress fluids. In the analysis based on the Stokes micro-continuum theory of the rheological effects of coupled stress fluids, a modified form of Reynolds equation governing the transient-state hydrodynamic film pressures in porous journal bearings with the effect of slip flow of coupled stress fluid as lubricant is obtained. Moreover, the tangential velocity slip at the surface of porous bush has been considered by using Beavers-Joseph criterion. Using the first-order perturbation of the modified Reynolds equation, the stability characteristics in terms of threshold stability parameter and whirl ratios are obtained for various parameters viz. permeability factor, slip coefficient, bearing feeding parameter, and eccentricity ratio. The results show that the coupled stress fluid exhibits better stability in comparison with Newtonian fluid.

scholarly journals Mathematical Model and Analysis of the Water-Lubricated Hydrostatic Journal Bearings considering the Translational and Tilting Motions

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui-Hui Feng ◽  
Chun-Dong Xu ◽  
Jie Wan
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Linear Perturbation ◽  
Eccentricity Ratio ◽  
Dynamic Coefficients ◽  
Pressure Fields ◽  
Dynamic Performances ◽  
Rotary Speed

The water-lubricated bearings have been paid attention for their advantages to reduce the power loss and temperature rise and increase load capacity at high speed. To fully study the complete dynamic coefficients of two water-lubricated, hydrostatic journal bearings used to support a rigid rotor, a four-degree-of-freedom model considering the translational and tilting motion is presented. The effects of tilting ratio, rotary speed, and eccentricity ratio on the static and dynamic performances of the bearings are investigated. The bulk turbulent Reynolds equation is adopted. The finite difference method and a linear perturbation method are used to calculate the zeroth- and first-order pressure fields to obtain the static and dynamic coefficients. The results suggest that when the tilting ratio is smaller than 0.4 or the eccentricity ratio is smaller than 0.1, the static and dynamic characteristics are relatively insensitive to the tilting and eccentricity ratios; however, for larger tilting or eccentricity ratios, the tilting and eccentric effects should be fully considered. Meanwhile, the rotary speed significantly affects the performance of the hydrostatic, water-lubricated bearings.

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.

Hydrodynamic Behaviors of the Gas-Lubricated Film in Wedge-Shaped Microchannel

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Xueqing Zhang ◽  
Qinghua Chen ◽  
Juanfang Liu
Keyword(s):  
Wall Temperature ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Stokes Equations ◽  
Load Capacity ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Hydrodynamic Properties ◽  
Obvious Effect ◽  
Navier Stokes Equations

As for the micro gas bearing operating at a high temperature and speed, one wedge-shaped microchannel is established, and the hydrodynamic properties of the wedge-shaped gas film are comprehensively investigated. The Reynolds equation, modified Reynolds equation, energy equation, and Navier–Stokes equations are employed to describe and analyze the hydrodynamics of the gas film. Furthermore, the comparisons among the hydrodynamic properties predicted by various models were performed for the different wedge factors and the different wall temperatures. The results show that coupling the simplified energy equation with the Reynolds or modified Reynolds equations has an obvious effect on the change of the friction force acting on the horizontal plate and the load capacity of the gas film at the higher wedge factor and the lower wall temperature. The velocity slip weakens the squeeze of the gas film and strengths the gas backflow. A larger wedge factor or a higher wall temperature leads to a higher gas film temperature and thus enhances the rarefaction effect. As the wall temperature is elevated, the load capacity obtained by the Reynolds equation increases, while the results by the Navier–Stokes equations coupled with the full energy equation rapidly decrease. Additionally, the vertical flow across the gas film in the Navier–Stokes equations weakens the squeeze between the gas film and the tilt plate and the gas backflow.

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.

Geometrical analysis of elliptical journal bearings and its effects on friction and load capacity

2019 ◽  
Vol 234 (5) ◽  
pp. 743-750
Author(s):  
Ali Ebrahimi ◽  
Saleh Akbarzadeh ◽  
Hassan Moosavi
Keyword(s):  
Friction Force ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Major Axis ◽  
Journal Bearings ◽  
Maximum Pressure ◽  
Geometrical Parameters ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Lower Temperature

Elliptical bearings are one type of non-circular journal bearings which has two main advantages over the conventional circular bearings: lower temperature rise and lower vibrations. In this study, the energy equation and Reynolds equation are simultaneously solved under adiabatic boundary conditions. The predicted pressure and temperature are compared to the results of published literature for verification purposes. A parametric study is then conducted on the effect of geometrical parameters of the elliptical journal bearing on the load capacity, friction force, pressure, and oil temperature. Effect of geometric parameters of the bearing on the performance is studied. The results show that non-circularity parameter is the most influential parameter in the bearing, and an increase in the non-circularity results in the decrease in maximum pressure and temperature as well as the friction force. Increasing the eccentricity ratio, on the other hand, will cause an increase in the pressure, temperature, and the friction force. Changes in the angle between the major axis of the bearing and load direction decrease the load-carrying capacity and the non-dimensional pressure and results in an increase in the friction coefficient.

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.

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