In this paper we present new results for the dynamics of a problem for the interaction of a compressible gas flow with a movable rigid surface. Compressible lubrication theory is applied to describe the dynamics of the vertical motion of air bearing sliders used in computer hard disk drives. In the limit of large bearing number we show this problem can be reduced to a nonlinear integrodifferential equation. Linear stability analysis and perturbation methods show that over the range of possible slider positions there is an infinite sequence of Hopf bifurcations yielding stable large amplitude periodic orbits. The dynamics of near-crash behavior and interaction with a moving disk surface are also addressed.
REFERENCES
1.
R. F. Hoyt, “Head-disk Interface,” in Magnetic Disk Drive Technology: Heads, Media, Channel, Interfaces and Integration, edited by K. G. Ashar (IEEE press, New York, 1977).
2.
M. Chipot and M. Luskin, “The compressible Reynolds lubrication equation,” in Metastability and Incompletely Posed Problems, edited by S. Antman (Springer-Verlag, New York, 1987), pp. 61–75.
3.
J. Chandra and P. W. Davis, “Applications of differential inequalities to gas lubrication theory,” in Nonlinear Phenomena in Mathematical Sciences, edited by V. Lakshimikantham (Academic, New York, 1982), pp. 235–239.
4.
A. Friedman, Mathematics in Industrial Problems, Part 4 (Springer-Verlag, New York, 1991).
5.
A. Friedman and B. Hu, “Head-media interaction in magnetic recording,” IMA Preprint series 1363 (1995).
6.
W.
Huang
and D. B.
Bogy
, “Three-dimensional direct simulation Monte Carlo method for slider air bearings
,” Phys. Fluids
9
, 1764
(1997
).7.
S.
Zhang
and D. B.
Bogy
, “Effects of lift on the motion of particles in the recessed regions of a slider
,” Phys. Fluids
9
, 1265
(1997
).8.
F. J.
Alexander
, A. L.
Garcia
, and B. J.
Alder
, “Direct simulation Monte Carlo for thin-film bearings
,” Phys. Fluids
6
, 3854
(1994
).9.
S.
Fukui
and R.
Kaneko
, “Dynamic analysis of flying head sliders with ultra-thin spacing based on the Boltzmann equation (Comparison with two limiting approximations)
,” JSME Int. J., Series III
33
, 76
(1990
).10.
W. D.
Henshaw
, L. G.
Reyna
, and J. A.
Zufria
, “Compressible Navier–Stokes computations for slider air-bearings
,” J. Tribol.
113
, 73
(1991
).11.
T. Hayashi and T. Ohkubo, “Comparison of the direct numerical solution and the perturbation solution in the dynamic analysis of a flying head slider for magnetic disk storage operating at very low spacing,” Adv. Information Storage Systems 2, 113 (1991).
12.
R. M. Crone, M. S. Jhon, T. E. Karis, and B. Bhushan, “The behavior of a magnetic slider over a rigid-disk surface:a comparison of several approximations of the modified Reynolds equations,” Adv. Information Storage Systems 4, 105 (1992).
13.
K.
Ono
, “Dynamic characteristics of air-lubricated slider bearing for noncontact magnetic recording
,” ASME J. Lub. Technol.
97
, 250
(1975
).14.
R. C.
DiPrima
, “Asymptotic methods for an infinitely long slider squeeze-film bearing
,” ASME J. Lub. Technol.
90
, 173
(1968
).15.
J. W. White, “Analytical study of Air Bearing Damping for low clearance magnetic head sliders,” STLE special publication SP-26 Tribology and Mechanics of Magnetic Storage Systems 6, 141 (1989).
16.
T. P. Witelski and F. Hendriks, “Stability of gas bearing sliders for large bearing number: convective instability of the tapered slider,” submitted to Tribol. Trans. (1997).
17.
T. P. Witelski and F. Hendriks, “Large bearing number stability analysis for tango class gas bearing sliders,” submitted to Tribol. Trans. (1997).
18.
L. G. Leal, Laminar Flow and Convective Transport Processes (Butterworth-Heinemann, Boston, 1992).
19.
H. Ockendon and J. R. Ockendon, Viscous Flow (Cambridge University Press, Cambridge, 1995).
20.
W. A. Gross, Gas Film Lubrication (Wiley, New York, 1962).
21.
C.
Borgers
, C.
Greengard
, and E.
Thomann
, “The diffusion limit of free molecular flow in thin plane channels
,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
52
, 1057
(1992
).22.
R. E. Bellman and K. L. Cooke, Differential-Difference Equations (Academic, New York, 1963).
23.
J. Hale, Theory of Functional Differential Equations (Springer-Verlag, New York, 1977).
24.
C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
25.
S. Fukui, Y. Mitsua, and K. Kogure, “Dynamic characteristics of flying-head sliders on running wave disk,” Tribology and Mechanics of Magnetic Storage Systems 2, ASLE Special Publication SP-19 (1985).
26.
A. E. V.
Ponnaganti
, R.
Noteboom
, “On nonlinear response of head-disk interface to wavy excitation
,” IEEE Trans. Magn.
22
, 1008
(1986
).27.
J. E. Marsden and M. McCracken, The Hopf Bifurcation and its Applications (Springer-Verlag, New York, 1976).
28.
S. N.
Chow
and J.
Mallet-Paret
, “Integral averaging and bifurcation
,” J. Diff. Eqns.
26
, 112
(1977
).29.
J. M. Franke and H. W. Stech, “Extensions of an Algorithm for the analysis of nongeneric Hopf Bifurcations with applications to delay-difference equations,” in Delay Differential Equations and Dynamical Systems, edited by S. Busenberg and M. Martelli, Lecture Notes in mathematics 1475 (Springer-Verlag, Berlin, 1991), pp. 161–175.
30.
H. W. Stech, “Hopf bifurcation in a class of scalar functional differential equations,” in Physical Mathematics and Nonlinear Partial Differential Equations, edited by J. H. Lightbourne and S. M. Rankin (Marcel Dekker, New York, 1988), Lecture Notes in Pure and Applied Mathematics 102, pp. 175–185.
31.
J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics (Springer-Verlag, New York, 1981).
32.
A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley Interscience, New York, 1981).
33.
D. S. Schmidt, “Hopf’s bifurcation and the center theorem of Liapunov,” in The Hopf Bifurcation and its Applications, edited by J. E. Marsden and M. McCracken (Springer-Verlag, New York, 1976).
34.
R. B. Grafton, “Existence and uniqueness theorems for differential equations with deviating arguments of mixed type,” in Delay and Functional Differential Equations and their Applications, edited by K. Schmitt (Academic, New York, 1972), pp. 309–334.
35.
F.
Hendriks
, “Speed Dependence, Takeoff and Stiction of a New Class of Gas Bearing Sliders
,” Tribol. Trans.
39
, 603
(1996
).36.
E. O.
Tuck
, “An inviscid theory for sliding flexible sheets
,” J. Aust. Math. Soc. B, Appl. Math.
23
, 403
(1982
).37.
E. O.
Tuck
and M.
Bentwich
, “Sliding sheets: lubrication with comparable viscous and inertia forces
,” J. Fluid Mech.
135
, 51
(1983
).
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