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.

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.

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.

Static Characteristics of Gas-Lubricated Slider Bearings Operating in a Helium-Air Mixture

1989 ◽  
Vol 111 (4) ◽  
pp. 620-627 ◽  
Author(s):  
T. Ohkubo ◽  
S. Fukui ◽  
K. Kogure
Keyword(s):  
Reynolds Equation ◽  
Mean Free Path ◽  
Linear Interpolation ◽  
Numerical Results ◽  
Experimental Results ◽  
Experimental Investigations ◽  
Static Characteristics ◽  
Slider Bearings ◽  
Lubrication Equation ◽  
Modified Reynolds Equation

This paper outlines experimental investigations of the static characteristics of self-acting gas-lubricated slider bearings operating in a helium-air mixture. The experimental results are compared with numerical results obtained by solving a modified Reynolds equation and a generalized lubrication equation based on an equivalent molecular mean free path (MMFP) and on an equivalent viscosity derived from molecular gas dynamics. At any mole ratio of air α, the values of the equivalent MMFP are generally expected to be smaller than those of the MMFP derived from linear interpolation, whereas the values of equivalent viscosity are expected to be larger. The numerical results agree well with the experimental results within the range of α from 1.0 to 0.6. Lower values of α give a bigger difference between numerical and experimental results, and make the experimental results lower than the numerical results. Moreover, results of a generalized lubrication equation based on the Boltzmann equation give a closer prediction or qualitative tendency to the experimental results than do those based on the modified Reynolds equation.

The Effect of Porosity on the Head-Media Interface

2000 ◽  
Vol 123 (3) ◽  
pp. 555-560 ◽  
Author(s):  
James K. Knudsen ◽  
Kenneth E. Palmquist
Keyword(s):  
Experimental Data ◽  
Porous Layer ◽  
Reynolds Equation ◽  
Velocity Slip ◽  
Element Model ◽  
Liquid Lubricant ◽  
Slip Effects ◽  
Porosity And Permeability ◽  
The Media ◽  
Modified Reynolds Equation

A lubrication model for the head-media interface is presented which includes the effect of porosity in the media coating. Experimental data is shown which illustrates the reduction in head-media spacing as porosity is increased. A modified Reynolds equation is derived to account for the effects of coating porosity. Other authors have considered a very thin porous layer to simulate a liquid lubricant or surface microstructure on a nonporous substrate. This study considers a porous layer that can be much larger than the bearing clearance. Darcy’s law is used in the porous layer. Velocity-slip effects, resulting both from rarefaction and the porous boundary, are considered. The modified Reynolds equation is applied to a simple capillary model of a porous layer as an illustrative example. The modified Reynolds equation was incorporated into a finite-element model for the head-media interface. Computations show reduced head-media clearance as porosity and permeability are increased in agreement with experimental data.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

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.

Sign in / Sign up

Export Citation Format

Share Document