Comparisons of Slip-Corrected Reynolds Lubrication Equations for the Air Bearing Film in the Head-Disk Interface of Hard Disk Drives

Tribology Letters - Tập 37 - Trang 191-201 - 2009
Du Chen1, David B. Bogy1
1Computer Mechanics Laboratory, Department of Mechanical Engineering, University of California, Berkeley, USA

Tóm tắt

Slip-corrected Reynolds equations have not been widely used in the air bearing simulations for the head-disk interface in hard disk drives since Fukui and Kaneko [Trans ASME J Tribol 110:253–262, 1988] published a more accurate generalized lubrication equation (FK model) based on the linearized Boltzmann equation for molecular gas lubrication. However, new slip models and slip-corrected Reynolds equations continue to be proposed with certain improvements or with the more physical basis of kinetic theory. Here, we reanalyze those slip models and lubrication equations developed after the FK model was published. It is found that all of the slip-corrected Reynolds equations are of limited use in the air bearing simulations, and that these new slip-corrected Reynolds equations cannot replace the FK model for calculating an accurate pressure distribution of molecular gas lubrication.

Tài liệu tham khảo

Fukui, S., Kaneko, R.: Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report-derivation of a generalized lubrication equation including thermal creep flow. Trans. ASME J. Tribol. 110, 253–262 (1988) Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525 (1954). doi:10.1103/PhysRev.94.511 Kennard, E.H.: Kinetic Theory of Gasses. MacGraw-Hill Book Co. Inc., New York (1938) Burgdorfer, A.: The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings. ASME J. Basic Eng. 81, 94–100 (1959) Hsia, Y.T., Domoto, G.A.: An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearance. Trans. ASEM J. Tribol. 105, 120–130 (1983) Mitsuya, Y.: Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient. Trans. ASME J. Tribol. 115, 289–294 (1993). doi:10.1115/1.2921004 Wu, L., Bogy, D.B.: A generalized compressible Reynolds lubrication equation with bounded contact pressure. Phys. Fluids 13, 2237–2244 (2001). doi:10.1063/1.1384867 Wu, L., Bogy, D.B.: New first and second order slip models for the compressible Reynolds Equation. Trans. ASME J. Tribol. 125, 558–561 (2003). doi:10.1115/1.1538620 Shen, S., Chen, G.: A kinetic-theory based first order slip boundary condition for gas flow. Phys. Fluids 19, 086101 (2007). doi:10.1063/1.2754373 Peng, Y., Lu, X., Luo, J.: Nanoscale effect on ultrathin gas film lubrication in hard disk drives. Trans. ASME J. Tribol. 126, 347–352 (2004). doi:10.1115/1.1614824 Bahukudumbi, P., Beskok, A.: A phenomenological lubrication model for the entire Knudsen regime. J. Micromech. Microeng. 13, 873–884 (2003). doi:10.1088/0960-1317/13/6/310 Bahukudumbi, P., Park, J.H., Beskok, A.: A unified engineering model for steady and quasi-steady shear driven gas micro flows. Microscale Thermophys. Eng. 7, 291–315 (2003). doi:10.1080/10893950390243581 Beskok, A., Karniadakis, G.E.: A model for flows in channels, pipes and ducts at micro and nano scales. Microscale Thermophys. Eng. 3, 43–77 (1999). doi:10.1080/108939599199864 Schaaf, S.A., Sherman, F.S.: Skin friction in slip flow. J. Aeronaut. Sci. 21, 85–90 (1953) Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases, 3rd edn. Cambridge University Press, New York (1991) Fukui, S., Kaneko, R.: A database for interpolation of Poiseuille flow rates for high Knudsen number lubrication problems. Trans. ASME J. Tribol. 112, 78–83 (1990). doi:10.1115/1.2920234 Schamberg, R.: The fundamental differential equations and the boundary conditions for high speed slip-flow, and their application to several specific problems. Ph.D. thesis, California Institute of Technology (1947) Cercignani, C., Daneri, A.: Flow of a rarefied gas between two parallel plates. J. Appl. Phys. 43, 3509–3513 (1963). doi:10.1063/1.1729249 Deissler, R.G.: An analysis of second-order slip flow and temperature jump boundary conditions for rarefied gases. Int. J. Heat Mass Trans. 7, 681–694 (1964). doi:10.1016/0017-9310(64)90161-9 Hadjiconstantinou, N.G.: Comment on Cercignani’s second-order slip coefficient. Phys. Fluids 15, 2352–2354 (2003). doi:10.1063/1.1587155 Ascroft, N.W., Mermin, N.D.: Solid State Physics. Saunders College press, Philadelphia (1976) Sun, Y., Chan, W.K., Liu, N.: A slip model with molecular dynamics. J. Micromech. Microeng. 12, 316–322 (2002). doi:10.1088/0960-1317/12/3/318 Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford University press, Clarendon (1994) Koura, K., Matsumoto, H.: Variable soft sphere molecular model for inverse -power-law or Lennard-Jones potential. Phys. Fluids 4, 1083–1085 (1992). doi:10.1063/1.858262