Surface Roughness Effects on Air Bearing Performance Over a Wide Range of Knudsen and Wave Numbers

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Data Storage ◽  
Knudsen Number ◽  
Poiseuille Flow ◽  
Air Bearing ◽  
Roughness Effects ◽  
Averaging Methods ◽  
Lubrication Equation ◽  
Wide Range ◽  
Averaging Techniques

Design of a near contact air bearing interface such as that created by a recording head slider and data storage disk requires consideration of a lubrication equation that is appropriate for high Knudsen number flows. The Poiseuille flow database reported by Fukui and Kaneko, 1990 [“A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems,” ASME J. Tribol., 112, pp. 78–83] is appropriate over a wide range of Knudsen numbers and is used throughout the data storage industry for analysis of the low flying recording head slider air bearing. However, at such low clearances, the topography of the air bearing surfaces also comes into question, making it important to consider both rarefaction and surface roughness effects in the air bearing design. In order to simplify the air bearing analysis of rough surfaces, averaging techniques for the lubrication equation have been developed for situations where the number of roughness elements (or waves) is either much greater or much less than the gas bearing number. Between these two extremes there are currently no roughness averaging methods available. Although some analytical and numerical studies have been reported for continuum and first-order slip conditions with simple geometries, little or no results have appeared that include both surface roughness and high Knudsen number flows outside the limited ranges where surface averaging techniques are used. In order to better understand the influence of transverse surface roughness over a wide range of Knudsen numbers and the relationship of key parameters involved, this paper describes a primarily analytical air bearing study of a wide, rough surface slider bearing using the Poiseuille flow database reported by Fukui and Kaneko. The work is focused outside the limited ranges where current surface averaging methods for the lubrication equation are expected to be valid.

Comparison of Moving and Stationary Surface Roughness Effects on Bearing Performance, With Emphasis on High Knudsen Number Flow

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Knudsen Number ◽  
Multiple Scale ◽  
Air Bearing ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Wide Range ◽  
Transverse Roughness ◽  
Number Flow ◽  
Gas Bearing

Low clearance gas bearing applications require an understanding of surface roughness effects at increased levels of Knudsen number. Because very little information has been reported on the relative air-bearing influence of roughness location, this paper is focused on a comparison of the effects of moving and stationary striated surface roughness under high Knudsen number conditions. First, an appropriate lubrication equation will be derived based on multiple-scale analysis that extends the work of White (2010, “A Gas Lubrication Equation for High Knudsen Number Flows and Striated Rough Surfaces,” ASME J. Tribol., 132, p. 021701). The resulting roughness averaged equation, applicable for both moving and stationary roughness over a wide range of Knudsen numbers, allows an arbitrary striated roughness orientation with regard to both (1) the direction of surface translation and (2) the bearing coordinates. Next, the derived lubrication equation is used to analyze and compare the influences produced by a stepped transverse roughness pattern located on the moving and the stationary bearing surface of a wedge bearing geometry of variable inclination. Computed results are obtained for both incompressible and compressible lubricants, but with an emphasis on high Knudsen number flow. Significant differences in air-bearing performance are found to occur for moving versus stationary roughness.

A Gas Lubrication Equation for High Knudsen Number Flows and Striated Rough Surfaces

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Knudsen Number ◽  
Poiseuille Flow ◽  
Rough Surfaces ◽  
Multiple Scale ◽  
Scale Analysis ◽  
Recording Head ◽  
Lubrication Equation ◽  
Highly Nonlinear ◽  
Multiple Scale Analysis

This paper describes the derivation and numerical solution of a lubrication equation appropriate for high Knudsen number flows and certain types of striated rough surfaces. The derivation begins with the compressible form of the lubrication equation together with the nonlinear series form of the Poiseuille flow reported by Fukui and Kaneko (1990, “A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems,” ASME J. Tribol., 112, pp. 78–83.). A multiple-scale analysis is performed on the lubrication equation for a finite-width time-dependent bearing and is limited to either stationary-transverse or longitudinal striated surface roughness of very short length scale. The rough surface averaging that takes place within the multiple-scale analysis includes a fully coupled treatment of the Poiseuille flow. What results is an especially nonlinear lubrication equation with averaged surface roughness effects that is appropriate for high Knudsen number analysis. A rotational transformation is also introduced to provide the roughness averaged lubrication equation in a form that allows analysis of the skewed orientation of a recording head slider with roughness defined relative to the direction of disk motion but with the lubrication equation conveniently expressed in the coordinate system of the slider. A factored-implicit numerical algorithm is described that provides the solution of the roughness averaged lubrication equation. Even though the lubrication equation is highly nonlinear, the numerical scheme is crafted to be fully second-order, time-accurate, and noniterative for tracking the solution in time either to an asymptotic steady-state or in response to a dynamic event. Numerical solutions of several simple geometry bearings are presented that utilize parameters that are typical of the slider-disk interface of current hard disk drives. It is anticipated that the primary benefit of this work may be the ability to accurately and efficiently include the influence of discrete disk data tracks in the air bearing design of very low clearance recording head sliders.

Combined Effects of Surface Roughness and Rarefaction in the Region Between High Wave Number-Limited and High Bearing Number-Limited Lubricant Flows

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Knudsen Number ◽  
Analytical Methods ◽  
Wave Number ◽  
Solution Technique ◽  
High Wave Number ◽  
High Wave ◽  
Lubrication Equation ◽  
Wide Range ◽  
Bearing Number

Analytical methods and techniques are required for design and analysis of low clearance gas-bearings that account for the combined influence of surface roughness and Knudsen number. Analytical methods for the lubrication equation are currently available for bearings that are either high wave number-limited or high bearing number-limited. There are few useful analytical methods in the range between these limiting extremes that account for the combined effect of roughness and rarefaction. That is the focus of this paper as it extends the work reported by White (2013, “Surface Roughness Effects in the Region Between High Wave Number and High Bearing Number-Limited Lubricant Flows,” ASME J. Tribol., 135(4), p. 041706) to include rarefaction effects. Results of an analytical study will be reported that investigates a wedge bearing geometry using perturbation methods and multiple-scale analysis over a wide range of Knudsen numbers for roughness on moving and stationary surfaces. The solution technique developed allows nonlinear aspects of the lubrication equation to be retained in the analysis. Solutions will be presented graphically and discussed. Results indicate that most of the bearing sensitivity to Knudsen number can be accounted for by a modified form of the bearing number.

Numerical Solution of the Boltzmann Based Lubrication Equation for the Air-Bearing Interface Between a Skewed Slider and a Disk With Discrete Data Tracks

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
James White
Keyword(s):  
Numerical Solution ◽  
Data Storage ◽  
Knudsen Number ◽  
Numerical Solutions ◽  
Disk Surface ◽  
Air Bearing ◽  
Skew Angle ◽  
Lubrication Equation ◽  
Highly Nonlinear ◽  
Discrete Track

Discrete track recording (DTR) is a method for increasing the recording density of a data storage disk by use of a pattern arrangement of discrete tracks. The DTR track structure consists of a pattern of very narrow concentric raised areas and recessed areas underneath a magnetic recording layer. In order to design the air-bearing slider platform that houses the magnetic transducer for DTR application at very low fly heights, the influence of the disk surface topography as a surface roughness effect must be taken into account. This paper is focused on the numerical solution of the roughness averaged lubrication equation reported recently in the work of White (2010, “A Gas Lubrication Equation for High Knudsen Number Flows and Striated Rough Surfaces,” ASME J. Tribol., 132, p. 021701) and is specialized for the influence of discrete disk data tracks on the recording head slider-disk air-bearing interface subject to a nonzero skew angle formed between the slider longitudinal axis and the direction of disk motion. The generalized lubrication equation for a smooth surface bearing and appropriate for high Knudsen number analysis is quite nonlinear. And including the averaging process required for treatment of a nonsmooth disk surface, as well as the rotational transformation required to allow for a nonzero skew angle, increases further the nonlinearity and general complexity of the lubrication equation. Emphasis is placed on development of a numerical algorithm that is fast, accurate, and robust for air-bearing analysis of complex slider surfaces. The numerical solution procedure developed utilizes a time integration of the lubrication equation for both steady-state and dynamic analyses. The factored-implicit scheme, a form of the more general alternating-direction-implicit numerical approach, was chosen to deal with the two-dimensional and highly nonlinear aspects of the problem. Factoring produces tightly banded coefficient matrices and results in an algorithm that is second-order accurate in time while requiring only the solution of tridiagonal systems of linear equations in advancing the computation from one time level to the next. Numerical solutions are presented that demonstrate the performance of the computational scheme and illustrate the influence of some discrete track parameters on skewed air-bearing performance as compared with a flat surface data storage disk.

A Lubrication Equation Incorporating Two-Dimensional Roughness Effects, With Emphasis on the Patterned Data Islands of a Recording Disk

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Multiple Scale ◽  
Industrial Applications ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Design And Optimization ◽  
Lubrication Equation ◽  
Wide Range ◽  
Level Of Understanding ◽  
Dimensional Surface

Current industrial applications require a consideration of two-dimensional surface roughness effects in design and optimization of fluid bearings. Although the influence of striated surface roughness on fluid lubrication is now at a fairly mature level of understanding, the knowledge and understanding of two-dimensional roughness effects is not nearly at the same level as that achieved over the past several decades for one-dimensional striations. The subject of this paper includes the formulation of a practical “roughness averaged” lubrication equation that is appropriate for two-dimensional surface roughness and applicable over a wide range of Knudsen numbers. After derivation by multiple-scale analysis, the resulting lubrication equation is specialized to treat the patterned data islands located on a storage medium as a two-dimensional roughness pattern, and then used to determine the effect of this roughness on the air-bearing interface between recording head slider and disk. The roughness averaged lubrication equation is solved numerically by a variable-grid finite-difference algorithm, and computed results are included for several bearing geometries.

Plane Thermal Transpiration of a Rarefied Gas Between Two Walls of Maxwell-Type Boundaries With Different Accommodation Coefficients

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Boltzmann Equation ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Poiseuille Flow ◽  
Rarefied Gas ◽  
Thermal Transpiration ◽  
Wide Range ◽  
Accommodation Coefficients

Plane thermal transpiration of a rarefied gas between two walls of Maxwell-type boundaries with different accommodation coefficients is studied based on the linearized Boltzmann equation for a hard-sphere molecular gas. The Boltzmann equation is solved numerically using a finite difference method, in which the collision integral is evaluated by the numerical kernel method. The detailed numerical data, including the mass and heat flow rates of the gas, are provided over a wide range of the Knudsen number and the entire range of the accommodation coefficients. Unlike in the plane Poiseuille flow, the dependence of the mass flow rate on the accommodation coefficients shows different characteristics depending on the Knudsen number. When the Knudsen number is relatively large, the mass flow rate of the gas increases monotonically with the decrease in either of the accommodation coefficients like in Poiseuille flow. When the Knudsen number is small, in contrast, the mass flow rate does not vary monotonically but exhibits a minimum with the decrease in either of the accommodation coefficients. The mechanism of this phenomenon is discussed based on the flow field of the gas.

Theoretical Approach to Turbulent Lubrication Problems Including Surface Roughness Effects

1989 ◽  
Vol 111 (1) ◽  
pp. 17-22 ◽  
Author(s):  
H. Hashimoto ◽  
S. Wada
Keyword(s):  
Surface Roughness ◽  
Velocity Distribution ◽  
Boundary Layers ◽  
Theoretical Approach ◽  
Turbulent Boundary Layers ◽  
Distribution Law ◽  
Roughness Effects ◽  
Relative Roughness ◽  
Lubrication Equation ◽  
Lubrication Characteristics

A new theoretical approach to turbulent lubrication problems including the surface roughness effects is described. On the basis of a logarithmic velocity distribution law in the turbulent boundary layers, the resistance laws for pressure and shear flows in the lubricant film are formulated separately in both cases of smooth and homogeneous rough surfaces. Moreover, combining the bulk flow concept proposed by Hirs with the formulated resistance laws, the generalized turbulent lubrication equation including the surface roughness effects is derived. Some numerical results for the modified turbulence coefficients are presented in the graphic form for different values of relative roughness, and the effects of surface roughness on the turbulent lubrication characteristics are generally discussed.

Measurements and Predictions of Surface Roughness Effects on the Turbine Vane Aerodynamics

2003 ◽  
Author(s):  
R. J. Boyle ◽  
R. G. Senyitko
Keyword(s):  
Surface Roughness ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Aerodynamic Performance ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Linear Cascade ◽  
Wide Range ◽  
Turbine Vane

The aerodynamic performance of a turbine vane was measured in a linear cascade. These measurements were conducted for exit-true chord Reynolds numbers between 150,000 and 1,800,000. The vane surface rms roughness-to-true chord ratio was approximately 2 × 10−4. Measurements were made for exit Mach numbers between 0.3 and 0.9 to achieve different loading distributions. Measurements were made at three different inlet turbulence levels. High and intermediate turbulence levels were generated using two different blown grids. The turbulence was low when no grid was present. The wide range of Reynolds numbers was chosen so that, at the lower Reynolds numbers the rough surfaces would be hydraulically smooth. The primary purpose of the tests was to provide data to verify CFD predictions of surface roughness effects on aerodynamic performance. Data comparisons are made using a two-dimensional Navier-Stokes analysis. Both two-equation and algebraic roughness turbulence models were used. A model is proposed to account for the increase in loss due to roughness as the Reynolds number increases.

Surface Roughness Effects on the Load Carrying Capacity of Very Thin Compressible Lubricating Films

1980 ◽  
Vol 102 (4) ◽  
pp. 445-451 ◽  
Author(s):  
J. W. White
Keyword(s):  
Surface Roughness ◽  
Exact Solutions ◽  
Carrying Capacity ◽  
Current Method ◽  
Previous Method ◽  
Finite Width ◽  
Load Carrying Capacity ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Load Carrying

The effect of surface roughness on load carrying capacity of very low clearance gas bearings is analyzed. A model lubrication equation appropriate for high bearing number, finite width films is first derived. Then, by obtaining exact solutions to several simple geometry bearings, the “closure problem” or statistical relationship of pressure and spacing is revealed. The lubrication equation is then ensamble averaged and solved for several test cases. The seemingly subtle differences in ensamble averaging the transverse terms in the lubrication equation are compared for the current theory and a previous method and are shown to produce vast differences in load carrying capacity. The current method is expected to be the correct approach since it is based on a generalization of exact solutions.

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