微尺度气体润滑的非平衡流效应分析
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摘要
微尺度气体润滑中,引起微尺度气体润滑压力降低的原因在于润滑流的非平衡流效应。微尺度气体润滑的非平衡流效应不仅会引起壁面气流速度滑移,而且会引起润滑气流热通量的变化。本文首先给出了基于Boltzmann矩方程的微尺度气体润滑模型(矩方程润滑模型);其次,与FK润滑模型和直接模拟Monte Carlo方法的分析结果比较,验证基于矩方程润滑模型的有效性;再次,基于矩方程润滑模型,分析不同轴承数情形下微尺度气体润滑的非平衡流效应。研究表明,随着轴承数的增大,微尺度气体润滑的非平衡流效应增强,表现为壁面速度滑移及热通量均增大。与壁面速度滑移的变化相反,随着轴承数的增大,非平衡流效应引起气膜压力及承载力的变化较小。这一反常现象的原因在于气体的可压缩性。
The micro scale gas lubrication was mathematically formulated withthe moment equationslubrication model,derived on Boltzmann moment equations,and numerically simulated in Monte Carlo method.The effect of the non-equilibrium flow at different bearing numbers on the decrease of the lubrication pressure,possibly originated from the velocity-slip on the wall and changes in heat flux,was investigated.The pressure profile evaluated with the novel moment equationslubrication modelwas roughly in agreement with those calculated with FK model and simulated in direct Monte Carlomethod.The simulated results show that thenon-equilibrium flow has a major impact.For instance,as the bearing number increased,the non-equilibrium flow effect becomes stronger because of the rapid increases of velocity slip and heat flux; in contrast,the gas film pressure and load capacitychangedrather weakly,possibly because of the compressibility of gases.
The micro scale gas lubrication was mathematically formulated withthe moment equationslubrication model,derived on Boltzmann moment equations,and numerically simulated in Monte Carlo method.The effect of the non-equilibrium flow at different bearing numbers on the decrease of the lubrication pressure,possibly originated from the velocity-slip on the wall and changes in heat flux,was investigated.The pressure profile evaluated with the novel moment equationslubrication modelwas roughly in agreement with those calculated with FK model and simulated in direct Monte Carlomethod.The simulated results show that thenon-equilibrium flow has a major impact.For instance,as the bearing number increased,the non-equilibrium flow effect becomes stronger because of the rapid increases of velocity slip and heat flux; in contrast,the gas film pressure and load capacitychangedrather weakly,possibly because of the compressibility of gases.
引文
[1]孟光,张文明.微机电系统动力学[M].北京:科学出版社,2008:1-26
[2]Bao M.Analysis and Design Principles of MEMS Devices[M].Amsterdam:Elsevier,2005
[3]Chen D,Bogy DB.Comparisons of Slip-Corrected Reynolds Lubrication Equations for the Air Bearing Film in the Head-Disk Interface of Har Ddisk Drives[J].Tribology Letter,2010,37(191-201
[4]张海军,祝长生,杨琴.基于稀薄效应的微气体径向轴承稳态性能[J].力学学报,2009,41(6):941-946
[5]张文明,孟光,陈迪.微转子径向气体轴承特性[J].机械工程学报,2008,44(5):25-33
[6]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[J].Journal of Tribology,Transactions of the ASME,1988,110(2):253-262
[7]Fukui S,Kaneko R.A Database for Interpolation of Poiseuille flow Rates for High Knudsen Number Lubrication Problems[J].Journal of Tribology,Transactions of the ASME,1990,112(1):78-83
[8]Alexander F,Garcia A,Alder B.Direct Simulation Monte Carlo for Thin-Film Bearings[J].Physics of Fluids,1994,6(12):3854-3860
[9]Liu N Y,Ng E Y.The Posture Effects of a Slider air Bearing on its Performance with a Direct Simulation Monte Carlo Method[J].Journal of Micromechanics and Microengineering,2001,11(463-473)
[10]黄平,许兰贵,孟永钢,等.求解磁头/磁盘超薄气膜润滑性能的有效有限差分算法[J].机械工程学报,2007,43(3):43-49
[11]白少先,彭旭东,孟永钢,等.范德华力对磁头/硬盘薄膜气体润滑动态特性的影响[J].摩擦学学报,2008,28(5):438-442
[12]Shi B,Feng Y,Ji J,et al.Simplified Precise Model of Reynolds Equation for Simulating Ultral-Thin Gas Film Lubrication in Hard Disk Drives[J].Microsystem Techonologies,2015,21(12):2517-2522
[13]Burgdorfer A.The Influence of the Molecular Mean Free Path on the Performance of Hydrodynamic Gas Lubricated Bearings[J].Journal of Basic Engineering,1959,81(1):94-100
[14]Hsia Y T,Domoto G A.An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances[J].Journal of Lubrication Technology,1983,105(1):120-130
[15]Mitsuya Y.Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip Flow Model and Considering Surface Accommodation Coefficient[J].Journal of Tribology,Transactions of the ASME,1993,115(2):289-294
[16]Sun Y H,Chan W K,Liu N Y.A Slip Model for Gas Lubrication Based on an Effective Viscosity Concept[J].Journal of Engineering Tribology,2003,217(187-196)
[17]Zhang H,Zhu C,Yang Q.Characteristics of Micro Gas Journal Bearings Based on Effective Viscosity[J].Journal of Tribology,Transactions of ASME,2009,131(4):041707
[18]Yang Q.Zhang H,Liu Y.Improved Modified Reynolds Equation for Thin-Film Gas Lubrication From an Extended Slip Velocity Boundary Condition[J].Microsystem Technologies,2016,22:2869-2875
[19]樊菁.稀薄气体动力学:进展与应用[J].力学进展,2013,43(2):185-201
[20]Myo K S,Zhou W,Yu S,et al.Direct Monte Carlo Simulation of Air Bearing Effects in Heat-Assisted Magnetic Recording[J].Microsystem Technologies,2011,17(5):903-909
[21]李志辉,蒋新宇,吴俊林,等.转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用[J].力学学报,2014,46(3):336-351
[22]Gu X,Zhang H,Emerson D R.A New Extended Reynolds Equation for Gas Bearing Lubrication Based on the Method of Moments[J].Microfluidics and Nanofluidics,2016,20:23
[2]Bao M.Analysis and Design Principles of MEMS Devices[M].Amsterdam:Elsevier,2005
[3]Chen D,Bogy DB.Comparisons of Slip-Corrected Reynolds Lubrication Equations for the Air Bearing Film in the Head-Disk Interface of Har Ddisk Drives[J].Tribology Letter,2010,37(191-201
[4]张海军,祝长生,杨琴.基于稀薄效应的微气体径向轴承稳态性能[J].力学学报,2009,41(6):941-946
[5]张文明,孟光,陈迪.微转子径向气体轴承特性[J].机械工程学报,2008,44(5):25-33
[6]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[J].Journal of Tribology,Transactions of the ASME,1988,110(2):253-262
[7]Fukui S,Kaneko R.A Database for Interpolation of Poiseuille flow Rates for High Knudsen Number Lubrication Problems[J].Journal of Tribology,Transactions of the ASME,1990,112(1):78-83
[8]Alexander F,Garcia A,Alder B.Direct Simulation Monte Carlo for Thin-Film Bearings[J].Physics of Fluids,1994,6(12):3854-3860
[9]Liu N Y,Ng E Y.The Posture Effects of a Slider air Bearing on its Performance with a Direct Simulation Monte Carlo Method[J].Journal of Micromechanics and Microengineering,2001,11(463-473)
[10]黄平,许兰贵,孟永钢,等.求解磁头/磁盘超薄气膜润滑性能的有效有限差分算法[J].机械工程学报,2007,43(3):43-49
[11]白少先,彭旭东,孟永钢,等.范德华力对磁头/硬盘薄膜气体润滑动态特性的影响[J].摩擦学学报,2008,28(5):438-442
[12]Shi B,Feng Y,Ji J,et al.Simplified Precise Model of Reynolds Equation for Simulating Ultral-Thin Gas Film Lubrication in Hard Disk Drives[J].Microsystem Techonologies,2015,21(12):2517-2522
[13]Burgdorfer A.The Influence of the Molecular Mean Free Path on the Performance of Hydrodynamic Gas Lubricated Bearings[J].Journal of Basic Engineering,1959,81(1):94-100
[14]Hsia Y T,Domoto G A.An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances[J].Journal of Lubrication Technology,1983,105(1):120-130
[15]Mitsuya Y.Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip Flow Model and Considering Surface Accommodation Coefficient[J].Journal of Tribology,Transactions of the ASME,1993,115(2):289-294
[16]Sun Y H,Chan W K,Liu N Y.A Slip Model for Gas Lubrication Based on an Effective Viscosity Concept[J].Journal of Engineering Tribology,2003,217(187-196)
[17]Zhang H,Zhu C,Yang Q.Characteristics of Micro Gas Journal Bearings Based on Effective Viscosity[J].Journal of Tribology,Transactions of ASME,2009,131(4):041707
[18]Yang Q.Zhang H,Liu Y.Improved Modified Reynolds Equation for Thin-Film Gas Lubrication From an Extended Slip Velocity Boundary Condition[J].Microsystem Technologies,2016,22:2869-2875
[19]樊菁.稀薄气体动力学:进展与应用[J].力学进展,2013,43(2):185-201
[20]Myo K S,Zhou W,Yu S,et al.Direct Monte Carlo Simulation of Air Bearing Effects in Heat-Assisted Magnetic Recording[J].Microsystem Technologies,2011,17(5):903-909
[21]李志辉,蒋新宇,吴俊林,等.转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用[J].力学学报,2014,46(3):336-351
[22]Gu X,Zhang H,Emerson D R.A New Extended Reynolds Equation for Gas Bearing Lubrication Based on the Method of Moments[J].Microfluidics and Nanofluidics,2016,20:23