Abstract
A new slip model derived by molecular dynamics has been used to investigate the ultra-thin gas-lubricated slider bearings beneath the three bushings of an electrostatic micromotor in micro-electro-mechanical systems (MEMS). Modified Reynolds equation is proposed based on the modified slip model. Analytical solutions for flow rate, pressure distribution, load carrying capacity and streamwise location using the modified Reynolds equation are obtained and compared with the results gained from those in the literature. It demonstrates that the new second-order slip model is of greater accuracy than that predicted by the first-order, second-order slip models and MMGL model and produces a good approximation to variable hard sphere (VHS) and variable soft sphere (VSS) models, which agree well with the solution obtained from the linearized Boltzmann equation. It is indicated that the slip effect reduces the pressure distribution and load carrying capacity, and shifts the streamwise location of the load carrying capacity, which should not be ignored to study the step-shaped slider bearings in micromotors for MEMS devices.
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References
Bahukudumbi P, Beskok A (2003) A phenomenological lubrication model for the entire Knudsen regime. J Micromech Microeng 13:873–884. doi:10.1088/0960-1317/13/6/310
Bart SF, Mehregany M, Tavrow LS, Lang JH (1992) Electric micromotor dynamics. IEEE Trans Electron Dev 39(3):566–575. doi:10.1109/16.123479
Burgdorfer A (1959) The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearing. ASME J Basic Eng 81(1):94–100
Chen MD, Lin JW, Lee SC, Chang KM, Li WL (2004) Application of modified molecular gas lubrication equation to the analysis of micromotor bushings. Tribology Int 37:507–513. doi:10.1016/j.triboint.2004.01.006
Egawa S, Higuchi T (1990) Multi-layered electrostatic film actuator. In: Proceeding of IEEE MEMS. IEEE, Napa Valley, CA, pp 166–171
Fukui S, Kaneko R (1993) Estimation of gas film lubrication effects beneath sliding bushings of micromotors using a molecular gas film lubrication equation. Wear 168:175–179. doi:10.1016/0043-1648(93)90214-7
Hsia YT, Domoto GA (1983) An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances. ASME J Tribology 81:94–100
Huang JB, Tong QY, Mao PS (1992) Gas-lubricated microbearing for microactuators. Sens Actuators A Phys 35:69–75. doi:10.1016/0924-4247(92)87009-6
Kennard EH (1938) Kinetic theory of gases. McGraw-Hill Book Co., New York
Kim D, Lee S, Jin Y, Desta Y, Bryant MD, Goettert J (2004) Micro gas bearings fabricated by deep X-ray lithography. Microsyst Technol 10:456–461. doi:10.1007/s00542-004-0369-4
Kumar S, Cho D, Carr W (1991) Electric levitation bearings for micromotors. In: Proceedings of 6th international conference on solid-state sensors and actuators, San Francisco, CA, USA, pp 882–885
Liu N, Ng YK (2001) The posture effects of a slider air bearing on its performance with a direct simulation Monte Carlo method. J Micromech Microeng 11:463–473. doi:10.1088/0960-1317/11/5/304
Mehregany M, Senturia SD, Lang JH (1990) Friction and wear in micro-fabricated harmonic side-drive motors. In: Technical digest: IEEE solid-state sensor and actuator workshop. IEEE, Hilton Head, SC, pp. 17–22
Mitsuya Y (1993) Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient. ASME J Tribology 115:289–294. doi:10.1115/1.2921004
Gad-el-Hak M (2001) Review: flow physics in MEMS. Mec Ind 2:314–341
Pister KSJ, Fearing RS, Howe RT (1990) A planar air levitated electro-static actuator system. In: Proceedings of IEEE MEMS workshop. IEEE, Napa Valley, CA, pp 670–677
Rymuza Z (1999) Control tribological and mechanical properties of MEMS surfaces. Microsyst Technol 5:173–180. doi:10.1007/s005420050160
Stokes VK (1966) Couple stresses in fluids. Phys Fluids 9:1705–1715. doi:10.1063/1.1761925
Sun YH, Chan WK, Liu NY (2002) A slip model with molecular dynamics. J Micromech Microeng 12:316–322. doi:10.1088/0960-1317/12/3/318
Wu L, Bogy DB (2003) New first and second order slip models for the compressible Reynolds equation. ASME J Tribology 125:558–561. doi:10.1115/1.1538620
Zhang WM, Meng G (2005) Contact dynamics between the rotor and bearing hub in an electrostatic micromotor. Microsyst Technol 11:438–443. doi:10.1007/s00542-004-0493-1
Zhang WM, Meng G (2006a) Numerical simulation of sliding wear between the rotor bushing and ground plane in micromotors. Sens Actuators A Phys 126:15–24. doi:10.1016/j.sna.2005.08.004
Zhang WM, Meng G (2006b) Friction and wear study of the hemispherical rotor bushing in a variable capacitance micromotor. Microsyst Technol 12(4):283–292. doi:10.1007/s00542-005-0064-0
Zhang QD, Shan XC (2008) Dynamic characteristics of micro air bearing for Microsystems. Microsyst Technol 14:229–234. doi:10.1007/s00542-007-0414-1
Zhao Z, Bhushan B (1996) Effect of bonded-lubricant films on the tribological performance of magnetic thin-film rigid disks. Wear 202:50–59. doi:10.1016/S0043-1648(96)07307-3
Acknowledgments
The authors are grateful to Prof. H. G. Li and Dr. H. Huang for their fruitful suggestions and discussions. This work was supported by the National Natural Science Foundation of China under Grant No. 10602033, the National Outstanding Youth Foundation of China under Grant No. 10325209, and the China Postdoctoral Science Foundation under Grant No. 20060400165.
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Zhang, WM., Meng, G., Zhou, JB. et al. Slip model for the ultra-thin gas-lubricated slider bearings of an electrostatic micromotor in MEMS. Microsyst Technol 15, 953–961 (2009). https://doi.org/10.1007/s00542-009-0828-z
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DOI: https://doi.org/10.1007/s00542-009-0828-z