scholarly journals Derivation of Rarefaction-Modified Reynolds Equation Considering Porosity of Thin Lubricant Film.

1996 ◽  
Vol 62 (595) ◽  
pp. 1060-1067
Author(s):  
Yasunaga MITSUYA ◽  
Zhisheng DENG ◽  
Masahiro OHKA
Keyword(s):  
Reynolds Equation ◽  
Lubricant Film ◽  
Modified Reynolds Equation

Derivation of Rarefaction-Modified Reynolds Equation Considering Porosity of Thin Lubricant Film

1997 ◽  
Vol 119 (4) ◽  
pp. 653-659 ◽  
Author(s):  
Yasunaga Mitsuya ◽  
Zhisheng Deng ◽  
Masahiro Ohka
Keyword(s):  
Reynolds Equation ◽  
Lubricant Film ◽  
The Other ◽  
Magnetic Head ◽  
Permeable Material ◽  
Magnetic Medium ◽  
Magnetic Disk ◽  
Head Slider ◽  
Liquid Lubricant ◽  
Modified Reynolds Equation

A new lubrication model is derived for solving ultra-thin gas lubrication problems encountered in the analysis of a magnetic head slider flying over a magnetic disk coated with giant-molecule lubricant film. In this model, the liquid lubricant film is replaced with a permeable material, and the boundary between the gas and liquid is subject to two kinds of velocity slippage: one due to the rarefaction effect and the other to the porous effect. Using this model, a rarefaction-modified Reynolds equation is derived considering the permeability of the running surface. This equation is then applied to the lubrication of head sliders flying over a magnetic medium. An interesting condition is found to arise wherein total apparent slippage seems to disappear due to the cancellation of the two slippages and the permeability effects are larger for a slider having a steeper pressure gradient.

Dynamic Analysis of the Rarefaction-Modified Reynolds Equation Considering Porosity of Thin Liquid Lubricant Film

1999 ◽  
Vol 121 (4) ◽  
pp. 864-871 ◽  
Author(s):  
Yasunaga Mitsuya ◽  
Zhisheng Deng ◽  
Masahiro Ohka
Keyword(s):  
Reynolds Equation ◽  
Mean Free Path ◽  
Lubricant Film ◽  
Correction Coefficient ◽  
Dynamic Problems ◽  
Head Slider ◽  
Liquid Lubricant ◽  
Damping Coefficients ◽  
Modified Reynolds Equation ◽  
Velocity Region

A rarefaction-modified Reynolds equation was derived to solve dynamic problems of a thin liquid lubricant film coated on a sliding surface. Applying the perturbation method, a calculation procedure based on FEM was formulated to obtain the stiffnesses and damping coefficients of gas lubricating films over a permeable liquid lubricant. Calculations were performed for a specified flying head slider. First, the effects of the permeability and porosity correction coefficients, which serve to increase the molecular mean free path, were presented focusing on landing on/off characteristics. Next, the effects of those on the stiffnesses and damping coefficients were demonstrated using the frequency domain. The results showed that the permeability and porosity correction coefficient increasingly had an influence on the landing on/off characteristics more in the higher velocity region, and that the permeability was effective in increasing the damping of lubricating films.

Two Dimensional Modified Reynolds Equation Including Pressure Dependent Viscosity Effect

2012 ◽  
Author(s):  
Jung Gu Lee ◽  
Alan Palazzolo
Keyword(s):  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Fluid Film ◽  
Maximum Pressure ◽  
Elastic Solids ◽  
Pressure Distributions ◽  
Pressure Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity ◽  
Modified Equation

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

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

2007 ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Zilda C. Silveira ◽  
Benedito M. Purquerio
Keyword(s):  
Mathematical Modeling ◽  
Porous Medium ◽  
Linear Model ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Dimensional Parameter ◽  
Pressure Flow ◽  
Darcy Model ◽  
Linear Effects ◽  
Modified Reynolds Equation

The mathematical modeling of aerostatic porous bearings, represented by the Reynolds equation, depends on the assumptions for the flow in the porous medium. One proposes a modified Reynolds equation based on the quadratic Forchheimer assumption, which can be used for both linear and quadratic conditions. Numerical results are compared to those obtained with the linear Darcy model. It is shown that, the non-dimensional parameter Φ, related to non-linear effects, strongly affects the bearing dynamic characteristics, but for values of Φ > 10, the results tend to those obtained with the linear model.

The Effect of a Hydrophobic Coating Material on Friction in a Micro-Slider Bearing: A Numerical Analysis

2015 ◽  
Vol 1123 ◽  
pp. 42-45
Author(s):  
Mohammad Tauviqirrahman ◽  
Muchammad ◽  
Rifky Ismail ◽  
J. Jamari ◽  
D.J. Schipper
Keyword(s):  
Numerical Analysis ◽  
Reynolds Equation ◽  
Poor Performance ◽  
Coating Material ◽  
Slider Bearing ◽  
Hydrophobic Coating ◽  
Modified Surface ◽  
Modified Reynolds Equation ◽  
Inappropriate Choice

The use of conventional lubricant such as hexadecane and toluene in micro-bearings has shown poor performance due to their hydrophilicity. High friction between the lubricated surfaces could lead to the occurrence of stiction which limits the functionality of a micro-bearing. In order to assess this strategy, a lubrication model of a micro-slider bearing with modified surface was used to simulate the technology. Friction, hydrophobic zone and hydrophobicity coefficient were evaluated based on the modified Reynolds equation. Results showed that in general the application of a hydrophobic coating has a significant improvement in reducing friction. Further, particular care must be taken in choosing the hydrophobic coating zone; an inappropriate choice of this zone will lead to a deterioration of the friction. This finding may have useful implications to accelerate the development of micro-bearings.

Effects of Electrokinetic Slip Flow on Lubrication Theory

2007 ◽  
Author(s):  
Wang-Long Li
Keyword(s):  
Reynolds Equation ◽  
Slip Flow ◽  
Electrical Potential ◽  
Lubrication Theory ◽  
Boundary Slip ◽  
Navier Stokes Equation ◽  
Electroviscous Effect ◽  
Navier Slip ◽  
Navier Slip Boundary Conditions ◽  
Modified Reynolds Equation

A lubrication theory that includes the effects of electric double layer (EDL) and boundary slip is developed. Both effects are important in microflow, and thus in lubrication problems. They have opposite effects on velocity distributions between lubricating surfaces. Also, the velocity distribution induced by the EDL stream potential (electroviscous effect) is affected by the boundary slip. Under the usual assumptions of lubrication and Debye-Hu¨ckel approximation for low surface potential, the Navier-Stokes equation with body force due to the electrical potential as well as the widely accepted Navier slip boundary conditions is utilized on deriving the modified Reynolds equation. Effects of EDL and boundary slip on the 1-D bearing performance are discussed by solving the modified Reynolds equation numerically.

scholarly journals Pressure Distribution in a Porous Squeeze Film Bearing Lubricated with a Herschel-Bulkley Fluid

2016 ◽  
Vol 21 (4) ◽  
pp. 951-965
Author(s):  
A. Walicka ◽  
P. Jurczak
Keyword(s):  
Pressure Distribution ◽  
Successive Approximation ◽  
Porous Layer ◽  
Reynolds Equation ◽  
Viscoplastic Fluid ◽  
Squeeze Film ◽  
Bearing Clearance ◽  
Parallel Disks ◽  
Modified Reynolds Equation

Abstract The influence of a wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated with a lubricant being a viscoplastic fluid of a Herschel-Bulkley type is considered. After general considerations on the flow of the viscoplastic fluid (lubricant) in a bearing clearance and in a porous layer the modified Reynolds equation for the curvilinear squeeze film bearing with a Herschel-Bulkley lubricant is given. The solution of this equation is obtained by a method of successive approximation. As a result one obtains a formula expressing the pressure distribution. The example of squeeze films in a step bearing (modeled by two parallel disks) is discussed in detail.

Some Remarks on the Validity of Reynolds Equation in the Modeling of Lubricant Film Flows on the Surface Roughness Scale

2004 ◽  
Vol 126 (4) ◽  
pp. 703-710 ◽  
Author(s):  
T. Almqvist ◽  
R. Larsson
Keyword(s):  
Surface Roughness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Fluid Dynamic ◽  
Lubricant Film ◽  
Continuity Equations ◽  
Newtonian Case ◽  
Eyring Model ◽  
Wavelength Scale ◽  
Film Flows

The objective of this paper is to investigate the flow in a lubricant film on the surface roughness scale and to compare the numerical solutions obtained by two different solution approaches. This is accomplished firstly by the CFD-approach (computational fluid dynamic approach) where the momentum and continuity equations are solved separately, and secondly the Reynolds equation approach, which is a combination and a simplification of the above equations. The rheology is assumed to be both Newtonian and non-Newtonian. An Eyring model is used in the non-Newtonian case. The result shows that discrepancies between the two approaches may occur, primarily due to a singularity which appears in the momentum equations when the stresses in the lubricant attain magnitudes that are common in EHL. This singularity is not represented by the Reynolds equation. If, however, the rheology is shifted to a non-Newtonian Eyring model the deviations between the two solution approaches is removed or reduced. The second source of discrepancies between the two approaches is the film thickness to wavelength scale ω. It will be shown that the Reynolds equation is valid until this ratio is approximately O10−2.

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