High Knudsen Number Molecular Rarefaction Effects in Gas-Lubricated Slider Bearings for Computer Flying Heads

1987 ◽  
Vol 109 (2) ◽  
pp. 276-282 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Ohkubo
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Flow Model ◽  
Slip Flow ◽  
Ambient Air ◽  
Mean Free Path ◽  
Lubricating Film ◽  
Modified Reynolds Equation ◽  
Air Film ◽  
Rarefaction Effects

This paper presents a study into the gas lubrication capability of an ultra-thin 0.025 μm film (converted value for ambient air film). The experimental results obtained using subambient helium as the lubricating film are compared with the calculated results using the modified Reynolds equation considering flow slippage due to the molecular mean free path effects. This comparison confirms that the slip flow model holds true within the range of the present experiments, and that the modified Reynolds equation is applicable for designing the computer flying heads operating at such thin spacing. The reason for the excellent agreement is discussed considering the locality of rarefaction effects on the lubricating surfaces and the anisotropy of these effects between the film thickness and the slider width.

Elastohydrodynamic Lubrication of Air-Lubricated Rollers

1996 ◽  
Vol 118 (3) ◽  
pp. 623-628 ◽  
Author(s):  
Y. B. Chang ◽  
F. W. Chambers ◽  
J. J. Shelton
Keyword(s):  
Numerical Model ◽  
Film Thickness ◽  
Free Path ◽  
Close Contact ◽  
Slip Flow ◽  
Elastohydrodynamic Lubrication ◽  
Mean Free Path ◽  
Pressure Profiles ◽  
The Mean ◽  
Air Film

The lubricating air film between two rotating rollers in close contact was studied numerically. The numerical model used in this study accounts for the effects of air compressibility, material deformation, and the slip flow which occurs when the air film thickness is not much larger than the mean-free-path of the air molecules. The air film profiles and the pressure profiles for the nip region between the rollers were calculated. It was found that the calculated air film thicknesses are lower than predicted by the liquid elastohydrodynamic calculation. From this study, equations for the minimum air film thickness, the air film thickness at the center of contact, and the amount of air that passes through the nip were obtained. This study has application to the prediction of the amount of air entrained in a winding roll.

Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip-Flow Model and Considering Surface Accommodation Coefficient

1993 ◽  
Vol 115 (2) ◽  
pp. 289-294 ◽  
Author(s):  
Y. Mitsuya
Keyword(s):  
Thin Film ◽  
Reynolds Equation ◽  
Flow Model ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Second Order ◽  
Flow Models ◽  
Gas Lubrication ◽  
Modified Reynolds Equation ◽  
Ultra Thin Film

A 1.5-order modified Reynolds equation for solving the ultra-thin film gas lubrication problem is derived by using an accurate higher-order slip-flow model. This model features two key differences from the current second-order slip-flow model. One is the involvement of an accommodation coefficient for momentum. The other is that the coefficient of the second-order slip-flow term is 4/9 times smaller than that for the current model. From the physical consideration of momentum transfer, the accommodation coefficient is found to have no affect on the second-order slip-flow term. Numerical calculations using the 1.5-order modified Reynolds equation are performed. The results are compared with those obtained using three kinds of currently employed modified Reynolds equations: those employing the first- and second-order slip-flow models and those utilizing the Boltzmann equation. These comparisons confirm that the present modified Reynolds equation provides intermediate characteristics between those derived from the first- and second-order slip-flow models, and produces an approximation closer to the exact solution resulting from the Boltzmann-Reynolds equation.

Static Characteristics of Gas Foil Thrust Bearing Based on Gas Rarefaction Model

2015 ◽  
Author(s):  
Jiajia Yan ◽  
Guanghui Zhang ◽  
Zhansheng Liu ◽  
Fan Yang
Keyword(s):  
Film Thickness ◽  
Optimization Design ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Rarefied Gas ◽  
Load Capacity ◽  
Structural Parameters ◽  
Lubricating Film ◽  
Lift Off ◽  
Foil Thrust Bearing

A modified Reynolds equation for bump type gas foil thrust bearing was established with consideration of the gas rarefaction coefficient. Under rarefied gas lubrication, the Knudsen number which was affected by the film thickness and pressure was introduced to the Reynolds equation. The coupled modified Reynolds and lubricating film thickness equations were solved using Newton-Raphson Iterative Method and Finite Difference Method. By calculating the load capacity for increasing rotor speeds, the lift-off speed under certain static load was obtained. Parametric studies for a series of structural parameters and assembled clearances were carried out for bearing optimization design. The results indicate that with gas rarefaction effect, the axial load capacity would be decreased, and the lift-off speed would be improved. The rarefied gas has a more remarkable impact under a lower rotating speed and a smaller foil compliance coefficient. When the assembled clearance of the thrust bearing rotor system lies in a small value, the lift-off speed increases dramatically as the assembled clearance decreases further. Therefore, the axial clearance should be controlled carefully in assembling the foil thrust bearing. It’s worth noting that the linear uniform bump foil stiffness model is not exact for large foil compliance ∼0.5, especially for lift-off speed analysis, due to ignoring the interaction between bumps and bending stiffness of the foil.

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.

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.

On Controlling the Film Thickness in Self-Acting Foil Bearings

1970 ◽  
Vol 92 (2) ◽  
pp. 359-362 ◽  
Author(s):  
A. Eshel
Keyword(s):  
Film Thickness ◽  
Free Path ◽  
Marked Effect ◽  
Solid Wall ◽  
Mean Free Path ◽  
Radius Of Curvature ◽  
Air Gaps ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Air Film

Some factors useful in overcoming excessive air gaps in foil bearings are investigated. Since the gaps of interest are small, the foil bearing equations are modified to include the effects of the molecular mean free path. It is shown that by small corners in the solid wall, one can reduce the air film thickness considerably. A change in curvature with continuous slope has also a marked effect on the film thickness. Theoretical prediction curves allowing the calculation of the air gap as a function of corner angle, change in radius of curvature, and the molecular mean free path are presented.

Elastohydrodynamic lubrication of circular contacts at pure squeeze motion with micropolar lubricants

2016 ◽  
Vol 68 (6) ◽  
pp. 640-646 ◽  
Author(s):  
Li Ming Chu ◽  
Jaw-Ren Lin ◽  
Yuh-Ping Chang ◽  
Chung-Chun Wu
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Coupling Parameter ◽  
Elastohydrodynamic Lubrication ◽  
Constant Load ◽  
Polar Coordinates ◽  
Central Pressure ◽  
Content Type ◽  
Deformation Equation ◽  
Modified Reynolds Equation

Purpose This paper aims to explore pure squeeze elastohydrodynamic lubrication (EHL) motion of circular contacts with micropolar lubricants under constant load. The proposed model can reasonably calculate the pressure distributions, film thicknesses and normal squeeze velocities during the pure squeeze process. Design/methodology/approach The transient modified Reynolds equation is derived in polar coordinates using micropolar fluids theory. The finite difference method and the Gauss–Seidel iteration method are used to solve the transient modified Reynolds equation, the elasticity deformation equation, load balance equation and lubricant rheology equations simultaneously. Findings The simulation results reveal that the effect of the micropolar lubricant is equivalent to enhancing the lubricant viscosity. As the film thickness is enlarged, the central pressure and film thickness for micropolar lubricants are larger than those of Newtonian fluids under the same load in the elastic deformation stage. The greater the coupling parameter (N), the greater the maximum central pressure. However, the smaller the characteristic length (L), the greater the maximum central pressure. The time needed to achieve maximum central pressure increases with increasing N and L. Originality/value A numerical method for general applications was developed to investigate the effects of the micropolar lubricants at pure squeeze EHL motion of circular contacts under constant load.

A Numerical Study on Air-Entrainment between a Web and a Convex Guide Roller in a Web Transportation Process

2013 ◽  
Vol 392 ◽  
pp. 110-115 ◽  
Author(s):  
Puttha Jeenkour
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Study ◽  
Air Entrainment ◽  
Convex Shape ◽  
Transportation Process ◽  
Guide Roller ◽  
Shape Equation ◽  
Newton Raphson ◽  
Air Film

This paper presents a characteristic of air-entrainment between a web and a guide roller with modified convex shape. Air film thickness is derived using the modified Reynolds equation, a roller shape equation, and a web deflection equation. A finite difference method and a Newton-Raphson scheme are employed to achieve numerical results, i.e. air film thickness and air pressure distribution profiles, a minimum air film thickness, and an air film thickness at the middle of roller length under varied convex roller shapes. The results show that both minimum and central air film thicknesses decrease when the roller is designed as convex shape, and a parameter of convex roller shape affects a minimum air film thickness position.

Air Film Thickness Estimation in Web Handling Processes

1999 ◽  
Vol 121 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Hiromu Hashimoto
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Experimental Results ◽  
Finite Width ◽  
Web Handling ◽  
Foil Bearing ◽  
Guide Roller ◽  
The Finite Difference Method ◽  
Air Film ◽  
The Web

In this paper, in order to estimate an air film thickness between moving web and guide roller (web spacing height), an air film thickness formula was derived based on the finite width compressible foil bearing theory. In the derivation of the air film thickness formula, the two-dimensional Reynolds equation and foil equilibrium equation were discretized by the finite difference method and solved iteratively to obtain the pressure and air film thickness distributions for various parameters. Based on the numerical results, the simplified convenience formula for the estimation of air film thickness between web and guide roller was obtained. On the other hand, the air film thickness between web and guide roller was measured by an optical sensor, and the experimental results were compared with the calculated results. Moreover, the variation of air film thickness between two layers in web winding processes was analyzed by making use of the air film thickness formula derived above. From the theoretical and experimental results obtained, the effects of air film thickness on the web transporting systems were clarified.

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