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Research Papers: Magnetic Storage

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

[+] Author and Article Information
James White

6017 Glenmary Road, Knoxville, TN 37919

J. Tribol 133(2), 021901 (Mar 17, 2011) (14 pages) doi:10.1115/1.4003413 History: Received July 12, 2010; Revised December 14, 2010; Published March 17, 2011; Online March 17, 2011

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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

The slider and disk orientation: (a) disk motion at a skew angle and (b) DTR disk topography

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Figure 2

Pressure contours as functions of the dimensionless slider coordinates for the compression step slider and DTR disk: (a) skew angle=0 and (b) skew angle=20 deg

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Figure 3

Three-dimensional pressure profiles as functions of the dimensionless slider coordinates for the compression step slider and DTR disk: (a) skew angle=0, (b) skew angle=10 deg, and (c) skew angle=20 deg

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Figure 4

Convergence history of the compression step slider for several values of pitch angle

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Figure 5

Pressure contours as functions of the dimensionless slider coordinates for the compression step slider and flat disk: (a) skew angle=0 deg and (b) skew angle=20 deg

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Figure 6

Pressure contours as functions of the dimensionless slider coordinates for the subambient pressure slider and DTR disk: (a) skew angle=0 deg and (b) skew angle=20 deg

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Figure 7

Three-dimensional pressure profiles as functions of the dimensionless slider coordinates for the subambient pressure slider and DTR disk: (a) skew angle=0 deg and (b) skew angle=20 deg

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Figure 8

Pressure contours as functions of the dimensionless slider coordinates for the subambient pressure slider and flat disk: (a) skew angle=0 deg and (b) skew angle=20 deg

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Figure 9

Effect of the DTR disk dimensional recess depth on net air-bearing force: a comparison of the compression step and subambient pressure sliders

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Figure 14

Pressure contours as functions of the dimensionless slider coordinates for the vacuum cavity slider with complex air-bearing surface flying on a flat disk at a skew angle of 20 deg

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Figure 10

Vacuum cavity type slider with complex air-bearing surface

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Figure 11

Three-dimensional pressure profiles as functions of the dimensionless slider coordinates for the vacuum cavity slider with complex air-bearing surface flying on a DTR disk: (a) skew angle=0 deg and (b) skew angle=20 deg

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Figure 12

Three-dimensional pressure profiles as functions of the dimensionless slider coordinates for the vacuum cavity slider with complex air-bearing surface flying on a flat disk: (a) skew angle=0 deg and (b) skew angle=20 deg

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Figure 13

Pressure contours as functions of the dimensionless slider coordinates for the vacuum cavity slider with complex air-bearing surface flying on a DTR disk: (a) skew angle=0 deg and (b) skew angle=20 deg

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