Conditions for the Rupture of a Lubricating Film—Part II: New Boundary Conditions for Reynolds Equation

1971 ◽  
Vol 93 (1) ◽  
pp. 156-167 ◽  
Author(s):  
J. C. Coyne ◽  
H. G. Elrod
Keyword(s):  
Surface Tension ◽  
Boundary Conditions ◽  
Reynolds Equation ◽  
Dimensionless Parameter ◽  
Glass Plate ◽  
Flow Conditions ◽  
Lubricating Film ◽  
Load Carrying ◽  
Bearing Load ◽  
Good Agreement

The pressure and flow conditions upstream of the rupture point of a lubricating film are analyzed with the theoretical model derived in Part I. The boundary conditions on the pressure and pressure gradient for use with Reynolds’ equation are developed as functions of a dimensionless parameter involving viscosity, speed, and surface tension. The load-carrying capacity which results from the use of these new boundary conditions does not differ appreciably from that of other boundary conditions in current use, except when the bearing load is extremely light, or when surface tension is large compared with the product of speed and viscosity. A simple experiment was conducted using a cylindrical lens bearing on a rotating oil-lubricated glass plate. Measurements of the bearing load and the location of the film attachment to the lens were in good agreement with the theory.

Analysis of a Hydrodynamic Thrust Bearing With Incomplete Film

1981 ◽  
Vol 103 (3) ◽  
pp. 355-359 ◽  
Author(s):  
I. Etsion ◽  
I. Barkon
Keyword(s):  
Reynolds Equation ◽  
Iterative Solution ◽  
Flow Equation ◽  
Load Carrying Capacity ◽  
Free Boundaries ◽  
Thrust Bearings ◽  
Lubricating Film ◽  
Load Carrying ◽  
Bearing Load ◽  
Wetted Area

The possibility of an incomplete lubricating film due to directed lubrication in hydrodynamic thrust bearings is considered. The free boundaries of the wetted area on a flat sector-shaped pad are determined by a simultaneous iterative solution of the Reynolds equation and a flow equation. Bearing load carrying capacity and power loss are calculated for a variety of inlet geometries, and a comparison is made with a complete fluid film bearing. It is found that bearing performance can be very much affected by the radial location of lubricant supply to the pads.

Load-Carrying Capacity of the Lubricating Film in the Gap Between Surfaces Textured by Hemispherical Pores

2021 ◽  
Vol 9 (2) ◽  
pp. 1-23
Author(s):  
Leonid Burstein
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Pore Diameter ◽  
Pore Radius ◽  
Load Carrying Capacity ◽  
Mechanical Parts ◽  
Lubricating Film ◽  
Small Pore ◽  
Cell Dimensions ◽  
Load Carrying

The load support of a lubricating film that separates the surfaces textured by identical equidistant spaced hemispherical pores was investigated. Two-dimensional time-dependent Reynolds equation is solved numerically for different pore-radius-to-gap and cell-dimension-to-pore-radius ratios and for different relative pore positions of opposite surfaces. The results are compared with the data obtained for the case when only one of the opposite surfaces is covered with pores. The obtained data show a maximum in the carrying capacity of the lubricating film when the cell-to-pore-radii ratio is approximately equal to two, in the case of two opposite surfaces with pores. At small pore radii and with increasing cell dimensions, the load support of two surfaces with pores is much greater than in the case of one surface with pores. This behavior reverses with increasing pore diameter. The presented analysis and the provided MATLAB programs are applicable for mechanisms having rubbing mechanical parts with surfaces covered with pores.

A Simplified One-Dimensional Thermal Model for Journal Bearings

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Daquan Liu ◽  
Wen Zhang ◽  
Tiesheng Zheng
Keyword(s):  
Thermal Effects ◽  
Thermal Model ◽  
Reynolds Equation ◽  
Computing Time ◽  
One Dimensional ◽  
Lubricating Film ◽  
Direct Solution Method ◽  
The One ◽  
Generalized Reynolds Equation ◽  
Good Agreement

The variational approach, which is used to solve the Reynolds equation based on the assumption of constant temperature, is extended to the generalized Reynolds equation calculation. The direct solution method of the generalized Reynolds equation is presented, where the pressure of the nodal points and the cavitation zone boundary of the film can be determined without iterating. A simplified one-dimensional thermal model is built on the basis of the original two-dimensional thermal model. The model not only concerns the thermal effects of the lubricating film, but also offers a direct and rapid numerical algorithm for solving lubricating film temperature field. The numerical results of the temperature distributions for the one model are in good agreement with experiment, and less computing time is needed.

Study on Lubrication Simulation and Capability of Three-Lobe Journal Bearing

2014 ◽  
Vol 709 ◽  
pp. 210-214
Author(s):  
Kun Qian ◽  
Wei Gang Guo
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Rotation Speed ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Bearing Load ◽  
The Stability ◽  
Eccentric Distance

The lubrication state of three-lobe bearing is simulated by using Reynolds equation. It concluded that the load-carrying capability of three-lobe bearing increases with the eccentric distance between the centers of axis and bearing with a nonlinear way. The largest bearing load-carrying capacity occurs in the eccentric direction of 30 °and making sure the eccentric direction can improve the stability of the system. To improve the rotation speed of the axis is beneficial to promote the load-carrying capacity.

The Influence of Surface Tension on Bearings Lubricated With Bubbly Liquids

1980 ◽  
Vol 102 (1) ◽  
pp. 91-96 ◽  
Author(s):  
E. H. Smith
Keyword(s):  
Surface Tension ◽  
Bubble Surface ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Bubbly Liquids ◽  
Viscous Forces ◽  
Tilting Pad ◽  
Load Carrying ◽  
Bearing Load ◽  
Order Of Magnitude

An order of magnitude analysis of the Rayleigh-Plesset equation of motion of a bubble surface reveals that inertia and viscous forces can be ignored in realistic bearing configurations and that surface tension plays an important role. The influence of gas bubbles in liquid lubrication is examined with particular reference to the steadily-loaded plane-inclined slider-bearing. Load carrying capacity is virtually unaffected by lubricant gasification. The centre of pressure can be considerably modified, depending partially on the value of a new dimensionless group—the configuration number φ. It appears that the tilting-pad thrust bearing will sometimes be unstable in operation, resulting in bearing failure.

Analysis of Short Journal Bearings With New Upstream Boundary Conditions

1974 ◽  
Vol 96 (3) ◽  
pp. 489-496 ◽  
Author(s):  
I. Etsion ◽  
O. Pinkus
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Reynolds Equation ◽  
Journal Bearings ◽  
Diameter Ratio ◽  
General Analysis ◽  
New Approach ◽  
Starting Condition ◽  
Lubricating Film ◽  
Limiting Case

The Reynolds equation, for short journal bearings, is treated with a new approach to the boundary condition at the beginning of the lubricating film. The nondimensional hydrodynamic side leakage and other performance characteristics of the bearing are shown to be a function not only of Sommerfeld number and width over diameter ratio but also of another parameter which depends on the starting condition at the film inlet. The results obtained by other investigators till now are shown to be only a limiting case of the more general analysis given here. This work is the first part of a larger work embracing the analysis of finite bearings.

Perturbation Solution of the 1-D Reynolds Equation With Slip Boundary Conditions

1978 ◽  
Vol 100 (1) ◽  
pp. 70-73 ◽  
Author(s):  
Aron Sereny ◽  
Vittorio Castelli
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Load Carrying Capacity ◽  
Slip Boundary Conditions ◽  
Slider Bearing ◽  
Slip Boundary ◽  
Load Carrying ◽  
Bearing Number

The method of matched asymptotic expansion is applied to obtain the pressure distribution and the load carrying capacity for an infinitely long slider bearing, operating under high-speed, low-height, with slip boundary conditions. The pressure distribution is easily applicable as the starting solution for the iterative numerical solution of Reynolds equation. Two examples given show extremely good correlation between this expansion and the numerical solution. It is shown that, for a tapered slider bearing with a bearing number above 100, the reduction in load because of slip is minimal and that, for a parabolic slider, there exists a certain unique bearing number for which the load carrying capacity is independent of the parabolic crown of the slider. It is shown that for a wide slider bearing with large bearing number, the effect of slip is on the order of 1/A.

A High Performance Journal Bearing With Controlled Elastic Deflection

1995 ◽  
Vol 117 (4) ◽  
pp. 702-708 ◽  
Author(s):  
A. K. Tieu ◽  
N. O. Freund
Keyword(s):  
Thermal Effects ◽  
High Performance ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Pressure ◽  
Hydrodynamic Analysis ◽  
Elastic Deflection ◽  
Load Carrying ◽  
Bearing Load ◽  
Generalized Reynolds Equation

A thermo-elasto-hydrodynamic analysis of an undercut journal bearing is presented whereby elastic deflection is introduced in a certain area of the bearing surface. The hydrodynamic pressure is computed from the generalized Reynolds equation, which takes into account thermal effects on viscosity. This is accomplished by solving the full energy equation for temperature. The elastic deflection is obtained from the elasticity equation. This study is then complemented with an elasto-hydrodynamic analysis of the full bearing. The controlled elastic deflection increases the bearing load carrying capacity and reduces friction.

Modeling of mass transfer in biofilms in oscillatory flow conditions using k-ɛ turbulence model

2003 ◽  
Vol 3 (1-2) ◽  
pp. 201-207
Author(s):  
H. Nagaoka ◽  
T. Nakano ◽  
D. Akimoto
Keyword(s):  
Numerical Simulation ◽  
Mass Transfer ◽  
Turbulence Model ◽  
Uptake Rate ◽  
Oscillatory Flow ◽  
Substrate Uptake ◽  
Flow Conditions ◽  
Mass Transfer Mechanism ◽  
Substrate Uptake Rate ◽  
Good Agreement

The objective of this research is to investigate mass transfer mechanism in biofilms under oscillatory flow conditions. Numerical simulation of turbulence near a biofilm was conducted using the low Reynold’s number k-ɛ turbulence model. Substrate transfer in biofilms under oscillatory flow conditions was assumed to be carried out by turbulent diffusion caused by fluid movement and substrate concentration profile in biofilm was calculated. An experiment was carried out to measure velocity profile near a biofilm under oscillatory flow conditions and the influence of the turbulence on substrate uptake rate by the biofilm was also measured. Measured turbulence was in good agreement with the calculated one and the influence of the turbulence on the substrate uptake rate was well explained by the simulation.

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