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Simplified model of Reynolds equation with linearized flow rate for ultra-thin gas film lubrication in hard disk drives

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Abstract

In a hard disk drive (HDD), when the spacing between the flying head and the rotating disk approximates the molecular mean-free path or less, the gas dynamics cannot be described from the continuum transport theory directly, and the gaseous rarefaction effects must be taken into account in this case. In this paper we start from a widely used FK model of Reynolds equation and propose a simplified model, called linearized flow rate Reynolds equation, to simulate the ultra-thin gas film lubrication in HDDs. We use a piecewise continuous linear function to approximate the flow rate. This simplified model of Reynolds equation possesses simpler mathematical form than that of FK model. This simplified model is solved by using the finite volume method and the resultant numerical solutions are compared with those of FK model. We find that their numerical results of these two models are in very good agreement with very small relative errors, while the simplified model has higher computational efficiency than that of FK model.

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Acknowledgment

This work was supported in part by the National Natural Science of Foundation of China (Grant Nos. 50775132, U0635002) and the Natural Science of Foundation of Shandong Province, China (Grant No. Z2008F06).

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Authors and Affiliations

  1. School of Mechanical and Electronic Engineering, Shandong Jianzhu University, Jinan, 250101, China

    Bao-Jun Shi & Ting-Yi Yang

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  1. Bao-Jun Shi
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  2. Ting-Yi Yang
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Correspondence to Bao-Jun Shi.

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Shi, BJ., Yang, TY. Simplified model of Reynolds equation with linearized flow rate for ultra-thin gas film lubrication in hard disk drives. Microsyst Technol 16, 1727–1734 (2010). https://doi.org/10.1007/s00542-010-1107-8

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  • DOI: https://doi.org/10.1007/s00542-010-1107-8

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