Averaged Reynolds Equation Based on the Homogenization Theory for Gas Film Lubrication in the Head/Disk Interface

In order to improve the magnetic recording density of hard disk drives, discrete track disks and/or bit patterned disks are being considered. The gas film lubrication characteristics of a disk with microscale geometric surface features are different from those of traditional “smooth” disks. In this paper, an averaged Reynolds equation suitable for the analysis of gas film lubrication with discrete track recording (DTR) disks is derived based on the homogenization theory and a simplified model of the Reynolds equation with linearized flow rate (LFR). The averaged Reynolds equation and the LFR model are solved simultaneously using the finite volume method. Numerical results show that the pressure solution of the averaged Reynolds equation agrees well with the LFR model for DTR disks. The exact pressure values fluctuate in the neighborhood of those of the averaged pressure distribution curve. The pressure distributions of a complex slider for different groove depths are presented to investigate the effects of groove depth on pressure profiles. The proposed approach is shown to have a high computational efficiency.

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

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.