Mongkol Mongkolwongrojn 1*, Ruksakul Boonpuang 2. Thailand 2

Transcription

1 การประช มว ชาการเคร อข ายว ศวกรรมเคร องกลแห งประเทศไทย คร งท พฤศจ กายน 2552 จ งหว ดเช ยงใหม Effect of Ambient Pressure Change on Static Characteristics of a Head Slider under Point Source in Magnetic Storage system Mongkol Mongkolwongrojn 1*, Ruksakul Boonpuang 2 1* Mechanical Engineering Department Faculty of Engineering King Mongkut s Institute of Technology Ladkrabang Bangkok 152 Thailand kmmongko@kmitl.ac.th 2 Western Digital (Thailand) Co.,Ltd, Bangpa-in Industry 14 Moo 2, Udomsorayuth Rd, Klongjig, Bangpa-in Ayutthaya raksakul.boonpuang@wdc.com Abstract This paper presents the effect of ambient pressure change on the static characteristics of sub ambient pressure head sliders with straight rails. The control volume was formulated using the momentum and continuity equations in the air bearing. Numerical scheme based on the finite volume technique was developed to suppress the numerical difficulties caused by the clearance discontinuities in the sliders. The static characteristic of the sub ambient pressure sliders are calculated numerically to obtain the pressure distribution and the flying height with varying the ambient pressure change and heat generated from point source and the other parameters such as rail width, taper length, taper angle, suspension position, preloads and disk velocity. The numerical results show that both ambient pressure change and heat generated from point source have significant effect on the static characteristics of the head sliders in HDD. Keywords: head sliders in HDD, suspension, head sliders with straight rails 1. INTRODUCTION In order to increase the recording density and interface performance of magnetic hard disk drives (HDD), it is essentially to minimize spacing between the slider and disk surface at the trailing edge. Presently, the flying height for commercially available disk drives with a recording density of 1 Gb/in 2 is on the order of 1 nm [1]. Moreover, the rotational velocity of the disk has been increased to improve the transfer rate. Therefore, the geometry and pressure on the air bearing surface become significant for design considerations such as flying heights and flying attitudes. Recently, many research works have been studied to reduce the flying height in HDD system. In those work, the sub-ambient pressure slider were investigated by E. Cha and D.B. Bogy (1995) who developed numerical scheme using control volume formulation to simulate static flying condition and dynamic response of sub-ambient pressure slider with straight rail and guppy slider [2]. J.W. White (1997) presented flying height and air bearing force of transverse and negative pressure contour (TNP) [3]. Y. Hu and D.B. Bogy

2 (1998) solved the high bearing number of magnetic head problem by using multi-grid control volume method [4]. Y. Hu, P.M. Jones and K. Li (1999) shows air bearing suction force, air bearing lifting force and flying height of subambient pressure slider during dynamic unload [5]. Q.H. Zeng and D.B. Bogy (1999) analyzed the characteristics of dynamic air bearing properties by contrast many type of head slider [6]. Hashimoto H. And Hattori Y. (2) developed the optimum design method to find optimum flying height of head slider by using finite difference method and hybrid optimization technique [7]. Having been investigated in this study, the sub-ambient pressure slider is utilized according to figure 1 which can produce subambient pressure at recess region. The air bearing slider utilizes the combination of a thin lubricating air film theory and equation of motion [8] using the finite difference method [9] and adaptive multi-grid method [1] to provide a pressure distribution and flying height. The objective of these studies is to analyze the phenomenon of each parameter on minimum flying height by simulation. 2. THEORETICAL ANALYSIS The schematic diagram of the magnetic head slider considered in this paper is shown in Figure1. The read/write device is located at the trailing edge of the slider. The slider was assumed to have two degree freedom motion, translation perpendicular to the disk surface and rotation around the transverse axis. Figure 1 The model of magnetic head slider Applied the control volume as shown in Figure2 to obtain the continuity equations for air film between slider and disk surface (Head Media interface) can be expressed in steady state condition as: Figure 2 Control volume x x x x ( QI + QII + QIII + QIV ) + y y y y V ( QI + QII + QIII + QIV ) = Qi, j (1)

3 y2 x 3 P Q PH PH dy = ϕ Λ x y1 ( ) (2) CST-245 balanced. The dimension force balance equation can be written as: = ϕ y x1 x2 y 2 3 P Q R PH dx (3) 1/2 1 ( ) F = 2 P 1 dxdy (1) 1/2 Q v = x2 y2 x1 y1 ( PH ) σ dxdy T (4) 1/2 1 ( )( ) M F x = 2 P 1 x x dxdy (11) GS 1/2 G k ( ) F P k ( ) F P + δ P = (5) P ( k ) P = p ( k+ 1) ( k) δ P P P = (6) ( k+ 1) x x x x ( k+ 1) FP ( ) = ( QI ) + ( QII ) ( QIII ) ( QIV ) y y y y ( k+ 1) + ( QI ) + ( QII ) ( QIII ) ( QIV ) (7) Where ϕ(p,h) is the Poiseullie flow factor base on linearization Boltzmann Reynolds model as shown in equation (8) and a, a 1, a 2 and a 3 are the constant that depend on Kn/PH. 2 3 Kn Kn Kn ϕ( PH, ) = a + a1 + a2 + a3 PH PH PH (8) The boundary conditions are given as : 1 1 P(, y) = P(1, y) = P x, = P x, = (9) Equation of motion There are two degree of freedom in the motion of head slider, that is force balance and moment balance, which are necessary to be Modified Reynolds Equation Analyzing lubrication theory, Reynolds equation has been utilized to calculate pressure distribution and flying height. In this study, Reynolds equation is established by combination between Navier-Stokes equation and Continuity equation by the hypothesis that the surface of air bearing and disk are smooth. Lubrication fluid is Newtonian, laminar flow, constant viscosity, ideal gas and isothermal condition. Inertia force and body force of fluid have been neglected because film thickness is very small and the slip condition has been considered. The slip models currently used to predict pressures in head-disk interface in HDD are the first-order slip model [11], second-order slip model [12], 1.5-order slip model [13] and Boltzmann-Reynolds model [14][15]. The governing equation for each of these models and the no-slip model can be written in the dimensionless form as equation (1) [1]. P P + =Λ X X Y Y X ( ) 2 Q λ Q PH (12)

4 Film thickness equation The equation of flying height is analyzed from the surface of air bearing of head slider that can be written in dimensionless form as equation h= htr + ( LTP x) tan θtp + ( L x) tan θ (13) ; x LTP h= htr + ( L x) tan θ (14) ; L x L Table 1 Dimension of taper flat slider Description Dimension L (mm) 2.25 B (mm).5 W (mm) θ TP (mrad) 75 h o (µm).1 h TP (µm) L TP (µm).184 f o (Nm) 73.5 X s (mm) RESULT AND DISCUSSION This paper present, the simulation flying height of the taper flat type head slider, when various shape parameter of the head slider when the ambient pressure change are.85 atm, 1. atm and 1.15 atm respectively, the flying height of the head slider taper flat type, shown based on Figure 3, 4, 5, 6, 7 and 8. In Figure 3 flying height at the leading edge (h LD ) and trailing edge (h TR ) of the slider heads increase related to the rail width and rate, as well as the flying height of the slider air bearing increase significantly with the increase in velocity of the media recording disk, when TP reducing the ambient pressure around the head slider, flying height is decreased and also when increasing the ambient pressure around the slider head, the flying height increase. In Figure 4 flying height of the leading edge (h LD ) decrease and flying height of trailing edge (h TR ) increase by depend on the taper length, except at the low velocity of media disk, the flying height at trailing edge (h TR ) to steady and as well as the flying height of the slider air bearing increase significantly with the increase in velocity of the media recording disk, when reducing the ambient pressure around the head slider, flying height is decreased and when increasing the ambient pressure around the slider head so the flying height is increasing also. Figure 5 flying height at leading edge (h LD ) and trailing edge (h TR ) reduced by increasing the value of a taper angle, with the rate constant and as well as the flying height of the slider air bearing increase significantly with the increase in velocity of the media recording disk, when reducing the ambient pressure around the head slider, flying height is decreased and when increasing the ambient pressure around the slider head so the flying height is increasing also. In Figure 6 the flying height at leading edge (hld) and trailing edge (h TR ) decreased by increasing the length of the suspension position, except at the low velocity of media disk. The flying height at trailing to steady, as well as the flying height of the slider air bearing increase significantly with the increase in velocity of the media recording disk, when reducing the ambient pressure around the head slider, flying height is decreased and when increasing the ambient

5 pressure around the slider head so the flying height is increasing also. In Figure 7 the flying height at leading edge (h LD ) and trailing edge (h TR ) decreased by increasing the pre load, as well as the flying height of the slider air bearing increase significantly with the increase in velocity of the media recording disk, when reducing the ambient pressure around the head slider, flying height is decreased and when increasing the ambient pressure around the slider head so the flying height is increasing also. In Figure 8 flying height at the leading edge (h LD ) and trailing edge (h TR ) of the slider heads as an increase relate to the rail width and the rate, as well as the flying height of the slider air bearing increase significantly with the increase in velocity of the media recording disk, when apply the current source at ma and 13 ma to read/write device, the flying height at trailing edge increase and at leading edge decrease by follow increasing of real width and if increase the temperature, the flying height increase too. Since the ambient pressure around the slider head increasing the flying height at leading edge (h LD ) and trailing edge (h TR ) increase also by follow ambient pressure, ambient pressure is increased by.85 atm, 1. atm and 1.15 atm, respectively. Figure 3 Variation of flying height with varying rail width for different ambient pressure changes. Figure 4 Variation of flying height with varying taper length for different ambient pressure changes.

6 Figure 5 Variation of flying height with varying taper angle for different ambient pressure changes. Figure 7 Variation of flying height with varying pre load for different ambient pressure changes. Figure 6 Variation of flying height with varying suspension position for different ambient pressure changes. Figure 8 Variation of flying height with varying rail width for different electrical current changes for read/write device at 25 C. CONCLUSION The theoretical analysis using by finite volume technique of the sub-ambient pressure slider in HDD are presented and can be concluded that the air bearing geometry is the significant effects on both flying height. A good performance of sub-ambient pressure slider should be a small air bearing with the small rail

7 width, increasing the length of the suspension position and pre load. (i) Head slider rail width and disk velocity have significant effect on trailing edge spacing, (ii) Ambient pressure changes have significant effect on trailing edge and leading edge spacing, when increasing ambient pressure the flying height is increased significantly. (iii) The flying height of leading edge and trailing edge was increased when increasing Suspension position, taper angle, and suspension preload. NOMENCLATURE F Normalized Load, = a f Load F f P LW H Normalized film thickness, a H = hh H TR Normalized trailing edge, HTR = htr ha H LD Normalized leading edge, HLD = hld ha h h a Film thickness Reference film thickness h TR Trailing edge h LD Leading edge K N Knudsen number, KN = λa ha L Slider length P = p p P Normalized pressure, a p p a Pressure Atmosphere pressure X G G Normalized support position, X = x L x g g Support position X,Y Normalized Cartesian coordinates, X = xl, Y= yw x, y Cartesian coordinates U W λ a Disk velocity Slider width Mean free molecular path of gas, λ a 64nm λ Length-width ratio, λ = LW Λ= 6µ UL paha Λ Bearing number, 2 µ Gas viscosity ACKNOWLEDGE This paper was supported by a grant from Western digital (Thailand) Company through Master program fellowship at DSTAR MKITL REFERENCES [1] A.K. Menon, Interface Tribology for 1 Gb/in 2 Tribology International, Vol.33, 2, pp [2] E. Cha. And D.B. Bogy, A Numerical scheme for static and dynamic simulation of sub-ambient pressure shaped rail sliders, ASME Journal of Tribology, Vol.117, 1995, pp [3] J.W. White, Flying Characteristics of the transverse and negative pressure contour (TNP) slider air bearing, Trans. ASME Journal of Tribology, Vol.119, No.2, April 1997, pp [4] Y. Hu. And D.B. Bogy, Solution of the rarefied gas lubrication equation using an additive

8 correction based multi grid control volume method, Trans. ASME Journal of Tribology, Vol.12, 1998, pp [5] Y. Hu., P.M. Jones and K. Li, Trans. Air bearing dynamics of sub-ambient pressure sliders during dynamic unload, ASME Journal of Tribology, Vol.121, 1999, pp [6] Q.H. Zeng and D.B. Bogy, Stiffness and damping evaluation of air bearing sliders and new designs with high damping, Trans. ASME Journal of Tribology, Vol.121, No.2, April 1999, pp [7] H. Hashimoto and Y. Hattori, Improvement of the Static and Dynamic Characteristics of magnetic head sliders by optimum design, Trans. ASME Journal of Tribology, Vol.122, January 2. pp [8] B.J. Hamrock, Fundamentals of Fluid Film Lubrication, New York: McGraw-Hill Inc., [9] S.C. Chapra and R.P. Canale, Numerical Methods for Engineers, 4 th Ed. New York: McGraw-Hill Inc., 22. [1] W.L. Briggs, V.E. Henson and S.F. McCormick, A Multigrid Tutorial, 2 nd Ed. Philadelphia. SIAM, 2. [11] A. Burgdorfer, The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings, ASME Journal of Basic Engineering, Vol.81, 1959, pp [12] Y.T. Hsia And G.A. Domoto, An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances, ASME Journal of Lubrication Technology, Vol.15, 1983, pp [13] Y. Mitsuya, Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slipflow model and considering surface accommodation coefficient, ASME Journal of Tribology, Vol.115, 1993, pp [14] S. Fukui and R. Kaneko, Analysis of ultrathin gas film lubrication based on linearized Boltzmann equation: first report - derivation of a generalized lubrication equation including thermal creep flow, ASME Journal of Tribology, Vol. 11, No.2, April 1988, pp [15] S. Fukui and R. Kaneko, A database for interpolation of Poiseuille flow rates for high Knudsen number lubrication problems, ASME Journal of Tribology, Vol. 112, No.1, January 199, pp [16] M. Anaya Dufresne, 1996 On the Development of a Reynolds Equation for Air Bearings with Contact Ph.D. Dissertation, Carnegie Mellon University.