微涡轮发动机气体轴承—转子系统非线性动力学研究
|
摘要
气体润滑轴承是支撑高功率密度微涡轮发动机超高速转子的最佳选择。超小宽径比及气膜间隙、超高转子转速及工作温度以及不可避免的硅微加工缺陷是微涡轮发动机气体轴承系统面临的特殊挑战，然而目前对上述因素如何影响微气体轴承的性能还缺乏系统研究。本文综合考虑了稀薄气体效应、工作气体温度、黏性摩擦力以及硅微加工缺陷等影响因素，研究了微涡轮发动机气体轴承-转子系统的刚度及阻尼系数、涡动稳定界限以及非线性动力学行为。主要内容如下：
从适用于任意逆努森数的超薄气膜润滑Reynolds方程出发，建立气膜刚度及阻尼系数、转子涡动稳定界限及分岔特性的求解模型，发展高效的数值方法，研究了稀薄气体效应对微轴承性能的影响。
将侧壁Taper及Bow型硅微加工缺陷的膜厚方程与超薄气膜润滑理论相结合，推导了同时考虑硅微加工缺陷及稀薄气体效应的微气体轴承润滑方程，研究了硅微加工缺陷对轴承润滑特性及动力学特性的影响。结果表明：硅微加工缺陷的存在会降低气体轴承系统的承载能力，影响其动力学稳定性，缩小稳定运转范围，增大碰磨失效发生的几率。
微涡轮发动机气体轴承温度高达1300～1700K。随着温度的升高，稀薄气体效应更加明显，而与此同时气体的动力黏度也随之增大，因此需要考察高温对微气体轴承润滑性能和动力学性能所产生的最终影响。研究表明：温度对微气体推力轴承性能的影响可以分为黏度效应占优和稀薄效应占优两个区域。在黏度效应占优区，温度对气体黏度的影响占主导地位，从而承载力随温度的升高而增大；在稀薄效应占优区则相反。温度对微气体径向轴承-转子系统的非线性动力学特性影响非常复杂，总体来说，系统在高温时的振动幅度更大。
研究发现：在微气体径向轴承所处的宽径比范围内，黏性摩擦力与气膜承载力在同一量级。建立了计入黏性摩擦力的超小宽径比气体径向轴承系统的运动学方程，计算了考虑黏性摩擦力情形下系统的轴心轨迹、相图、Poincaré图、频率谱图以及升速频率瀑布图。结果表明：当计入黏性摩擦力时，转子的非线性运动状态比忽略黏性摩擦力时得到的结果更为稳定；当转子质量较大、轴承数较大时，低频、大幅度自激振动比不考虑黏性摩擦力时出现的概率低。这是因为黏性摩擦力吸收了转子涡动的能量，使得转子振动幅度减小，因而运动状态更为稳定。
对影响硅微涡轮发动机转子平衡的微透平及微密封流场进行了CFD数值仿真，研究了其压力分布、速度分布和质量流量等性能，探讨了供气压力对气体质量流量、转子受力的影响规律，为各流场的协调供气、转子的稳定运转提供了可靠的理论依据。
提出了将圆锥气体轴承应用于金属材料微型涡轮发动机的设想，设计并制作了能给微型转子提供径向及轴向联合支撑的圆锥轴承，实现了高功率密度微涡轮发动机对于轴承系统的紧凑性的要求；发展了迭代求解微型圆锥气体轴承润滑方程与供气孔流量方程的数值方法，探讨了圆锥气体轴承的承载力及耗气规律，发现减小气膜间隙是提高轴承承载力及节约耗气量的有效手段。
自主研发了一套可在线监测转子转速、气体压力和质量流量的测试平台，实现了对轴承的质量流量——供气压力曲线的测试；实验测试了升速过程中的流量及压力曲线，该结果与理论计算结果取得了良好的一致。
Micro-gas-lubricated bearings are the best candidates for supporting the high speedrotors in microengine. The implementation of micro-gas-lubricated bearings encounterschallenges because of their characteristics which are different from their conventional onesas follows: the extremely low length-to-diameter ratio and film thickness, the very highrotating speed and operating temperature. However, influences of those above factors oncharacteristics of micro gas bearings have not been fully understood yet. In this dissertation,influences of the gas rarefaction effects, the operating temperature, the viscous frictionforce and the microfabrication defects are taken into account to study the charcteristics ofthe bearing, including the the stiffness and damping coefficients, the whirl stable region,and the non-linear dynamic performance.
Based on the Molecular Gas-film Lubrication model valid for arbitrary inverseKnudsen numbers, the numerical models to obtain the stiffness and damping coefficients,the threshold of whirl stability and the bifurcation behavior of the system are developed,and the numerical methods are established to study the gas rarefaction effects on theperformance of the micro gas bearings.
Gas film thickness equation of the tapered or bowed bearing is combined with theMolecular Gas-film Lubrication model so that both the gas rarefaction effects and the Taperor Bow effects are introduced simultaneously to study the steady-state performance and thestability charts of micro bearings. Compared with the ideal bearing with the same minimumclearance, the Taper and Bow effects weaken the load capacity, increase the required stableminimum eccentricity and narrow the stable static load region.
The operating temperature of the micro gas bearing system for microengine is up to1300K～1700K. As the operating temperature goes higher, the gas rarefaction effectsbecome stronger and the gas viscosity increases at the same time. Thus the final impact oftemperature on the steady-state and dynamic performance of the system should beinspected. The results show that the influence of temperature on micro gas thrust bearingcould be divided into the viscosity effect domain region and the rarefaction effects domainregion. As temperature increases, the load capacity becomes larger in the viscosity effectdomain region and weaker in the rarefaction effects domain region. In the junction zonebetween the two regions, the load carrying capacity is the highest, but the stability is the weakest of all. Influences of temperature on the non-linear dynamic performance of themicro gas journal bearing is rather complex, and when the temperature increases, theamplitute of the rotor goes larger in general.
It is found that the viscous friction force is comparable to the load carrying capacityfor the micro gas bearing system with low L/D ratio. The rotor kinetic equations, whichconsidering the effects of viscous friction force, are derived. The center orbits, phaseportraits, Poincaré maps, and FFT spectra of the system response and the correspondingbifurcation diagrams are studied. The results indicate that, when the viscous friction force istaken into account, the rotor motion shows more stable, for the low-frequencylarge-amplitude self-excited whirl motion would not appear so frequently. The reason isthat the viscous friction force absorbs the energy of the whirl motion and thus decreases thewhirling amplitude and a more stable rotor motion then appears.
The flow fields of the micro turbine and the micro seal, which could influence thebalance of the microengine rotor, are simulated by CFD software. The pressure distribution,the velocity distribution and the mass flow rate of those fields are studied to estiblish theconnection between the supply pressure and the corresponding force on the rotor.
The idea of adopting the conical bearings to support the high-speed microengine rotorin both axial and radial direction is proposed, and the simplified bearing system forcompactive micro engine is designed and manufactured. Numerical method is developed toinspect the load carrying capacity and the gas consumption law of the conical bearings. Theresults show that thiner gas film thickness implies larger load capacity but less gasconsumption.
An integrated in-situ measurment system is developed to measure the rotor speed, thesupply pressure and the mass flow rate of the micro gas bearing system. Curves of massflow rate versus supply pressure are tested and show good agreement with the numericalresults. Mass flow rate, supply pressure and axial vibration in start up process are studiedand analysed.
从适用于任意逆努森数的超薄气膜润滑Reynolds方程出发，建立气膜刚度及阻尼系数、转子涡动稳定界限及分岔特性的求解模型，发展高效的数值方法，研究了稀薄气体效应对微轴承性能的影响。
将侧壁Taper及Bow型硅微加工缺陷的膜厚方程与超薄气膜润滑理论相结合，推导了同时考虑硅微加工缺陷及稀薄气体效应的微气体轴承润滑方程，研究了硅微加工缺陷对轴承润滑特性及动力学特性的影响。结果表明：硅微加工缺陷的存在会降低气体轴承系统的承载能力，影响其动力学稳定性，缩小稳定运转范围，增大碰磨失效发生的几率。
微涡轮发动机气体轴承温度高达1300～1700K。随着温度的升高，稀薄气体效应更加明显，而与此同时气体的动力黏度也随之增大，因此需要考察高温对微气体轴承润滑性能和动力学性能所产生的最终影响。研究表明：温度对微气体推力轴承性能的影响可以分为黏度效应占优和稀薄效应占优两个区域。在黏度效应占优区，温度对气体黏度的影响占主导地位，从而承载力随温度的升高而增大；在稀薄效应占优区则相反。温度对微气体径向轴承-转子系统的非线性动力学特性影响非常复杂，总体来说，系统在高温时的振动幅度更大。
研究发现：在微气体径向轴承所处的宽径比范围内，黏性摩擦力与气膜承载力在同一量级。建立了计入黏性摩擦力的超小宽径比气体径向轴承系统的运动学方程，计算了考虑黏性摩擦力情形下系统的轴心轨迹、相图、Poincaré图、频率谱图以及升速频率瀑布图。结果表明：当计入黏性摩擦力时，转子的非线性运动状态比忽略黏性摩擦力时得到的结果更为稳定；当转子质量较大、轴承数较大时，低频、大幅度自激振动比不考虑黏性摩擦力时出现的概率低。这是因为黏性摩擦力吸收了转子涡动的能量，使得转子振动幅度减小，因而运动状态更为稳定。
对影响硅微涡轮发动机转子平衡的微透平及微密封流场进行了CFD数值仿真，研究了其压力分布、速度分布和质量流量等性能，探讨了供气压力对气体质量流量、转子受力的影响规律，为各流场的协调供气、转子的稳定运转提供了可靠的理论依据。
提出了将圆锥气体轴承应用于金属材料微型涡轮发动机的设想，设计并制作了能给微型转子提供径向及轴向联合支撑的圆锥轴承，实现了高功率密度微涡轮发动机对于轴承系统的紧凑性的要求；发展了迭代求解微型圆锥气体轴承润滑方程与供气孔流量方程的数值方法，探讨了圆锥气体轴承的承载力及耗气规律，发现减小气膜间隙是提高轴承承载力及节约耗气量的有效手段。
自主研发了一套可在线监测转子转速、气体压力和质量流量的测试平台，实现了对轴承的质量流量——供气压力曲线的测试；实验测试了升速过程中的流量及压力曲线，该结果与理论计算结果取得了良好的一致。
Micro-gas-lubricated bearings are the best candidates for supporting the high speedrotors in microengine. The implementation of micro-gas-lubricated bearings encounterschallenges because of their characteristics which are different from their conventional onesas follows: the extremely low length-to-diameter ratio and film thickness, the very highrotating speed and operating temperature. However, influences of those above factors oncharacteristics of micro gas bearings have not been fully understood yet. In this dissertation,influences of the gas rarefaction effects, the operating temperature, the viscous frictionforce and the microfabrication defects are taken into account to study the charcteristics ofthe bearing, including the the stiffness and damping coefficients, the whirl stable region,and the non-linear dynamic performance.
Based on the Molecular Gas-film Lubrication model valid for arbitrary inverseKnudsen numbers, the numerical models to obtain the stiffness and damping coefficients,the threshold of whirl stability and the bifurcation behavior of the system are developed,and the numerical methods are established to study the gas rarefaction effects on theperformance of the micro gas bearings.
Gas film thickness equation of the tapered or bowed bearing is combined with theMolecular Gas-film Lubrication model so that both the gas rarefaction effects and the Taperor Bow effects are introduced simultaneously to study the steady-state performance and thestability charts of micro bearings. Compared with the ideal bearing with the same minimumclearance, the Taper and Bow effects weaken the load capacity, increase the required stableminimum eccentricity and narrow the stable static load region.
The operating temperature of the micro gas bearing system for microengine is up to1300K～1700K. As the operating temperature goes higher, the gas rarefaction effectsbecome stronger and the gas viscosity increases at the same time. Thus the final impact oftemperature on the steady-state and dynamic performance of the system should beinspected. The results show that the influence of temperature on micro gas thrust bearingcould be divided into the viscosity effect domain region and the rarefaction effects domainregion. As temperature increases, the load capacity becomes larger in the viscosity effectdomain region and weaker in the rarefaction effects domain region. In the junction zonebetween the two regions, the load carrying capacity is the highest, but the stability is the weakest of all. Influences of temperature on the non-linear dynamic performance of themicro gas journal bearing is rather complex, and when the temperature increases, theamplitute of the rotor goes larger in general.
It is found that the viscous friction force is comparable to the load carrying capacityfor the micro gas bearing system with low L/D ratio. The rotor kinetic equations, whichconsidering the effects of viscous friction force, are derived. The center orbits, phaseportraits, Poincaré maps, and FFT spectra of the system response and the correspondingbifurcation diagrams are studied. The results indicate that, when the viscous friction force istaken into account, the rotor motion shows more stable, for the low-frequencylarge-amplitude self-excited whirl motion would not appear so frequently. The reason isthat the viscous friction force absorbs the energy of the whirl motion and thus decreases thewhirling amplitude and a more stable rotor motion then appears.
The flow fields of the micro turbine and the micro seal, which could influence thebalance of the microengine rotor, are simulated by CFD software. The pressure distribution,the velocity distribution and the mass flow rate of those fields are studied to estiblish theconnection between the supply pressure and the corresponding force on the rotor.
The idea of adopting the conical bearings to support the high-speed microengine rotorin both axial and radial direction is proposed, and the simplified bearing system forcompactive micro engine is designed and manufactured. Numerical method is developed toinspect the load carrying capacity and the gas consumption law of the conical bearings. Theresults show that thiner gas film thickness implies larger load capacity but less gasconsumption.
An integrated in-situ measurment system is developed to measure the rotor speed, thesupply pressure and the mass flow rate of the micro gas bearing system. Curves of massflow rate versus supply pressure are tested and show good agreement with the numericalresults. Mass flow rate, supply pressure and axial vibration in start up process are studiedand analysed.
引文
[1] Feynman RP. There’s Plenty of Room at the Bottom[J].Journal of Microelectromechanicalsystems,1992,1(1):60-66.
[2] Thompson M, Whalen S. Design, Fabrication, and Testing of a Micro Heat Engine[J]. AIAA2002-5729.
[3] London AP, Epstein AH, Kerrebrock JL. A high Pressure Bipropellant Micro-Rocket Engine.36thAIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit[C],16-19July2000Huntsville,Alabama
[4] Thompson M, Whalen S. Design, Fabrication, and Testing of a Micro Heat Engine. AIAA2002-5729.
[5] Skinner J, Olson A, Bahr D, Richards C, Richards. A Piezoelectric Membrane Generator forMEMS Power. NanoTech2002-"At the Edge of Revolution"9-12September2002, Houston,Texas, AIAA2002-5745:1-7.
[6] Larangot B, Rossi1C, Camps1T, Berthold A, et. al. Solid Propellant Micro-Rockets-towards aNew Type of Power MEMS. NanoTech2002-"At the Edge of Revolution"9-12September2002,Houston, Texas, AIAA2002-5756.
[7] Lysherski SE. MEMS and NEMS: Systems, Devices, and Structures. CRC Press, Boca Raton,FL,2002.
[8]王琪民．微型机械导论[M].合肥:中国科技大学出版社，2003.3,
[9]刘广玉，樊尚春，周浩敏．微机械电子系统及其应用[M].北京:北京航空航天大学出版社，2003.2,
[10] Fujita H. Microactuators and Micromachines. In: Proceedings of IEEE[C], August1998,86(8):1721-1732.
[11] Carol Livermore, Anthony RF, Theodore L, Stephen DU, et al. A High-Power MEMS ElectricInduction Motor[J]. Journal of Micro-electro-mechanical Systems,2004,13(3):465-471.
[12] Senturia SD. Simulation and Design of Microsystems: a10-year perspective[J].Sensors andActuators A,1998,67:1-7.
[13] Epstein AH. Micro-Engines Scholar Lecture[J]. ASME Journal of Turbo-machinery,2004,5(2):204-211.
[14] Epstein AH. Millimeter-Scale Micro-Electro-Mechanical Systems Gas Turbine Engines[J]. Journalof Engineering for Gas Turbines and Power,2004,126(4):205-226.
[15] Lin CC. Development of a Microfabricated Turbine-Driven Air Bearing Rig[D]. Cambridge:Massachusetts Institute of Technology,1999.
[16] Epstein AH, Senturia SD. Power MEMS and Micro Engines. IEEE,1997lnfernational Conferenceon Solid-state Sensors and Actuators Chicago[C], June16-19,1997.
[17] Epstein AH, Senturia SD. Macro Power From Micro Machinery[J].Science,1997,276(5316):1211.
[18] Shan XC, Zhang QD, Sun YF, Wang ZF. Design, Fabrication and Characterization of an Air-drivenMicro Turbine Device[C]. Institute of Physics Publishing Journal of Physics: Conference Series,2006,34:316-321.
[19] Shan XC, Zhang QD, Sun YF, Maeda R. Studies on a Micro Turbine Device with Both Journal-andThrust-air Bearings[J]. Microsyst Technol,2007,13:1501-1508.
[20] Zhang QD, Shan XC, Guo GX, Wong S. Performance Analysis of Air Bearing in a MicroSystem[J]. Materials Science and Engineering A,2006,423:225-229.
[21] Zhang QD, Shan XC. Dynamic Characteristics of Micro Air Bearings for Microsystems[J].Microsyst Technol,2008,14:229-234.
[22] Zhang QD, Shan XC. Micro Air Bearing for a Microturbine[J]. IEEE Sens J,2008,8(5):435-440.
[23] Tanaka S, Hikichi K, Togo S, et al．World’s Smallest Gas Turbine Establishing Brayton Cycle[C].The7th international workshop on micro and nanothchnology for power generation and energyconversion application,2007:359-362．
[24] Kousuke I, Shuji T, et.at. Development of Micromachine Gas Turbine for Portable PowerGeneration[J]. JSME International Journal Series B,2004,47(3):459-464.
[25] Kousuke I, Shinichi T, Kousuke H, Satoshi G, Shuji T.Analytical and Experimental Study ofHydroinertia Gas Bearings For Micromachine Gas Turbines[C]. Proceedings of the ASME TurboExpo, Power for Land, Sea and Air,2005:1-9.
[26] Kousuke I, Shuji T, ShinIchi, T, Togo, S, Esashi M. Development of High-Speed Micro-GasBearings for Three-dimensional Micro-turbo Machines[J]. Journal of Micromechanics andMicroengineering,2005,15(9):S222-227.
[27] Isomura K, Murayama M, Teramoto S, Hikichi K, Endo Y, Togo S. Experimental Verification ofthe Feasibility of a100W Class Micro-Scale Gas Turbine at an Impeller Diameter of10mm [J].Journal of Micromechanics and Microengineering,2006,16(9):254-561.
[28] Peirs J, Reynaerts D, Verplaetsen F. A Microturbine For Electric Power Generation[J]. Sensors andActuators,A113(2004):86-93.
[29] Peirs J, Reynaerts D, Verplaetsen FA. Development of an Axial Microturbine for a Portable GasTurbine Generato[J]. Journal of Micromechanics and Microengineering,2003,13: S190-195．
[30] Almasi A. New Application of Micro-Turbine:Nuclear Emergency Cooling[J]. Proc IMechE PartA:J Power and Energy,2012.226(8):1076-1080.
[31]李军伟,钟北京,王建华,魏志军,王宁飞.空气槽对微型Swiss-Roll燃烧器工作特性的影响.北京理工大学学报,2010,30(2):140-144.
[32]李军伟,钟北京.微细直管燃烧器的散热损失研究[J].中国电机工程学报,2007,27(20):59-64.
[33]张永生,周俊虎,杨卫娟,刘茂省,岑可法.微燃烧稳定性分析和微细管道燃烧实验研究[J].浙江大学学报(工学版),2006,40(7):1178-1182.
[34]周俊虎,刘茂省,杨卫娟,张永生,周志军,岑可法.微燃烧发动机应用于微型飞行器的性能分析[J].燃烧科学与技术,2006,12(3):193-197.
[35]胡国新,王明磊.微细通道内可燃气体预混燃烧实验与微型发动机燃烧方案[J].热能动力工程,2003,18(4):352-355.
[36]梁德旺,黄国平.厘米级微型涡轮喷气发动机主要研究进展[J].燃气涡轮试验与研究,2004,17(2):9-13.
[37]黄国平,梁德旺,何志强.大型飞机辅助动力装置与微型涡轮发动机技术特点对比[J].航空动力学报,2008,23(2):383-388
[38]戚峰.微尺度射流、平板边界层及叶栅流动实验研究[D].南京:南京航空航天大学,2006.
[39]唐振寰.微型发动机整机振动分析[D].南京：南京航空航天大学,2009.
[40]徐进良,胡建军,曹海亮.微燃烧透平发电系统的研制及性能测试[J].中国机械工程,2008,19(12):1399-1405.
[41]周杨,刘火星,邹正平.微小型发动机涡轮气动设计研究[J].推进技术,2010,1:64-69.
[42]郑东亚,杜发荣,丁水汀,韩树军,张奇.微小型涡喷发动机转子涡动控制方法研究[J].推进技术,2010,31(1):52-55.
[43]曾昭奇.一种微型燃气涡轮发动机及其组合微细电加工技术研究[D].哈尔滨:哈尔滨工业大学，2012.
[44]黄国平，王跃，梁德旺.用于微型涡轮机的节流孔式静压气浮轴承实验[J].航空动力学报,2008,23(3):541-546.
[45] Fang JC, Zheng SQ, Han BC. AMB Vibration Control for Structural Resonance of Double-gimbalControl Moment Gyro with High-speed Magnetically Suspended Rotor[J]. IEEE/ASME TransMechatronics,2013,18(1):632-639.
[46] Xie GX, Luo JB, Liu SH, Zhang CH, Lu XC. Micro-bubble Phenomenon in NanoscaleWater-based Lubricating Film Induced by External Electric Field[J]. TribologyLetters,2008,29:169-176.
[47]刘宇,刘正林,吴铸新,周建辉.基于MATLAB的轴向开槽水润滑径向轴承性能分析[J].润滑与密封,2009,34(4):71-73
[48] Bird GA. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. New York, NY:OxfordScience Publications,1994.
[49]黄海,孟光,赵三星.二阶滑移边界对微型气浮轴承稳定性能的影响[J].力学学报,2006,5:668-673.
[50]黄海,孟光.考虑二阶滑移流效应的微型气浮轴承-转子稳定性分析及其动态响应[J].振动与冲击,2008,27(5):310-311
[51]黄海,孟光,赵三星.滑移边界对微型气浮轴承稳态性能的影响[J].机械工程学报,2006,42(增刊):21-25.
[52]黄海.微型轴承－转子系统动力特性的研究[D].上海:上海交通大学,2007.
[53] Lee YB, Kwaka HD, Kima CH, Lee NS. Numerical Prediction of Slip Flow Effect onGas-lubricated Journal Bearings for MEMS/MST-based Micro-Rotating Machinery[J]. TribologyInternational,2004,38:89-96.
[54] Fukui S, Kaneko R. Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized BoltzmanEquation: First Report-Derivation of Generalized Lubrication Equation Including Thermal CreepFlow[J]. ASME Journal of Tribology,1988,10:253-62.
[55] Fukui S, Kaneko R. A Database for Interpolation of Poiseuille Flows Rates for High KnudsenNumber Lubrication Problems[J].ASME Journal of Tribology1990;112:78-83.
[56] Maxwell J. C. Illustrations of the Dynamical Theory of Gases II[J]. Philosophical Magazine,1860,20:21-32
[57] Maxwell J. C. Illustrations of the Dynamical Theory of Gases III[J]. Philosophical Magazine,1860,20:33-37
[58] Maxwell J. C. On the Dynamical Theory of Gases[J]. Phil. Traps. Rod., Soc. London,1867,157:49-88
[59] Zhou WD, Liu B, Yu SK, et al. A Generalized Heat Transfer Model for Thin Film Bearings atHead-disk interface[J]. Applied Physics Letters,2008,92(4):043109-1-3.
[60]刘韧.微发动机气体动静压混合润滑推力轴承-转子系统动力学研究[D].北京:北京理工大学,2012.
[61] Zhang HJ, Zhu CS, Yang Q. Characteristics of Micro Gas Journal Bearings Based on EffectiveViscosity[J]. ASME Journal of Turbomachinery,2009,131(4):041707-1-5.
[62] Zhang HJ, ZhuCS, Yang Q. Effect of Effective Viscosity on Characteristics of Microscale GasJournal Bearings.4th IEEE International Conference on Nano/Micro Engineered and MolecularSystems, NEMS2009[C], Shenzhen, China,2009:121-125.
[63] Zhang HJ, ZhuCS, Tang M. Effects of Rarefaction on the Characteristics of Micro Gas JournalBearings[J]. Journal of Zhejiang University: Science A,2010,11:43-49.
[64]张海军,祝长生,杨琴.有效黏度效应对气体径向微轴承性能的影响[J].中国电机工程学报,2009,29(29):84-88.
[65] Ayon, AA, Braff, R, Lin, CC, Sawin, HH, Schmidt, MA. Characterization of a Time MultiplexedInductively Coupled Plasma Etcher[J]. J Electrochem Soc,1999,146(1):339-349.
[66] Piekos ES, Breuer KS. Manufacturing Effects in Microfabricated Gas Bearings: Axially varyingclearance[J]. Journal of Tribology-Transactions of the Asme,2002,124:815-821.
[67] Teo CJ. MEMS Turbomachinery Rotordynamics: Moldeling, Design and Testing[D]. PhD thesis,Department of Aeronautics and Astronautics, Massachusetts Institute of Technology,2006
[68] Teo CJ, Spakovszky ZS. Analysis of Tilting Effects and Geometric Nonuniformities inMicro-hydrostatic Gas Thrust Bearings[J]. ASME J Turbomach,2006,128:606-615.
[69]张文明,孟光,陈迪.微型旋转机械轴承研究进展[J].振动与冲击,2008,27(5):27-31.
[70] Meng G, Zhang WM, Huang H, Li HG, Chen D. Micro-Rotor Dynamics forMicro-Electro-Mechanical Systems (MEMS). Chaos, Solitons and Fractals[J].2009,40(2):538-562.
[71]张文明.微转子系统动力特性的研究[D].上海:上海交通大学,2006.
[72] Piekos ES, Orr DJ, et al. Design and Analysis of Microfabricated High Speed Gas JournalBearings[J]. American Institute of Aeronautics and Astronautics Paper,97-1966:1-11.
[73] Piekos ES, Breuer KS. Pseudospectral Orbit Simulation of Nonideal Gas-Lubricated JournalBearings for Microfabricated Turbomachines[J].ASME J Tribol,1999,121:604-609.
[74] Liu R, Wang XL, Zhang XQ. Effects of Gas Rarefaction on Dynamic Characteristics of MicroSpiral-grooved Thrust Bearing[J]. ASME J Tribol,2012,134(2):022201.1-022201.7.
[75]刘韧,王晓力.微气体螺旋槽推力轴承润滑数值模拟[J].机械工程学报,2010,(46)21:113-117.
[76] Liu R, Wang XL. Dynamic Characteristics Analysis of Micro Air Spiral Grooved ThrustBearing-Rotor System. IEEE-NEMS2011,2011IEEE International Conference on Nano/MicroEngineered and Molecular Systems [C], Kaohsiung, Taiwan,2011:719-723.
[77]刘韧,王晓力.基于有限体积法的螺旋槽气体推力轴承润滑计算[J].北京理工大学学报,2010,30(12):1400-1404.
[78]刘韧,王晓力,魏学玉.微气体螺旋槽推力轴承动力学特性系数研究[J].中国机械工程,
[79] Liu R, Wang XL. On Micro Gas Thrust Bearing for Micro System. Chinese Gas LubricationInstitution, CMES2010, Fifteenth Chinese Gas Lubrication Conference [C], Shenzhen, China,2010:383-386.
[80]刘韧,王晓力.微气体螺旋槽推力轴承润滑计算及系统性能预测.2009年第九届中国摩擦学会议
[C],北京,中国,2009:232-234.
[81]戚社苗,耿海鹏,虞烈.动压气体轴承的动态刚度和动态阻尼系数[J].机械工程学报,2007,43(5):91-98.
[82]戚社苗,耿海鹏,虞烈.扰动频率对动压气体轴承动态刚度和阻尼系数的影响[J].西安交通大学学报,2006,40(3):270-274.
[83]张瑞乾,张锡圣.径向气体/液体轴承动力特性系数的统一求法[J].北京航空航天大学学报,1994,20(4):474-481.
[84] Lund JW. The Stability of an Elastic Rotor in Journal Bearings with Flexible, Damed Supports[J].Journal of Applied Mechanics,1965, December:911-920.
[85] Lund JW. Caculation of Stiffness and Damping Properties of Gas Bearings[J].Journal ofLubrication Technology,1968,October:793-803.
[86] Miller, BA, Green, I. Numerical Formulation for the Dynamic Analysis of Spiral-grooved Gas FaceSeals[J]. ASME J Tribol,2001,123(2):395-403.
[87] Kim D, Lee S, Bryant, MD, Ling FF. Hydrodynamic Performance of Gas Microbearings[J].Journal of Tribology,2004,126(4):711-718.
[88] Kim D. Design and Fabrication of Sub-Millimeter Scale Gas Bearings with Tungsten-ContainingDiamond Like Carbon Coatings. Ph.D. thesis, Mechanical Engineering, University of Texas atAustin, Austin.
[89] Zhou JB, Meng G, Chen, JY, Zhang, WM. Bifurcation Analysis of Ultrashort Self-acting GasJournal Bearings for MEMS[J]. IEEE Trans Ind Electron,2009,56(8):3188-3194.
[90]周健斌,孟光,张文明.微机电系统径向气体轴承特性研究[J].振动与冲击,2007,26(9):30-33
[91]周健斌,孟光,陈杰宇,张文明.微型气体动压径向短轴承一转子系统动态特性研究[J].振动与冲击,2008,27(s):113-116.
[92]周健斌.微型转子轴承系统动力学问题研究[D].上海:上海交通大学,2009.
[93] Wang CC, Chen CK. Bifurcation Analysis of Self-Acting Gas Journal Bearings[J].Journal ofTribology,2001,123:755-767.
[94] Wang CC. Bifurcation Analysis of an Aerodynamic Journal Bearing System Considering the Effectof Stationary Herringbone Grooves[J].Chaos, Solitons and Fractals,2007,33:1532-1545.
[95] Wang CC, Yau HT, Kuan CF, Yan JJ. Application of Hybrid Method to the Quasi-PeriodicAnalysis of Micro Gas Journal Bearing System.2008IEEE International Symposium onKnowledge Acquisition and Modeling Workshop Proceedings[C], KAM2008, Wuhan, China,2008:79-82.
[96] Wang CC, Yau HT, Yeh YL, Jang MJ, LinJF. Influence of the Bearing Number on Micro GasBearing System.20094th IEEE International Conference on Nano/Micro Engineered andMolecular Systems (IEEE-NEMS2009)[C], Piscataway, NJ, USA,2009:975-979.
[97] Wang CC. Application of a Hybrid Numerical Method to the Nonlinear Dynamic Analysis of aMicro Gas Bearing System[J].Nonlinear Dynamics,2010,59:695-710.
[98] Wang CC. Application of a Hybrid Method to the Bifurcation Analysis of a Relative Short GasJournal Bearing System with Herringbone Grooves[J].Industrial Lubrication andTribology,2011,63(5):307-319.
[99] Wang CC, Yau HT. Application of a Hybrid Numerical Method to The Bifurcation Analysis of aRigid Rotor Supported by a Spherical Gas Journal Bearing System[J].Nonlinear Dynamics,2008,51:515-528.
[100] Wang CC. Application of a Hybrid Method to the Nonlinear Dynamic Analysis of a FlexibleRotor Supported by a Spherical Gas-lubricated Bearing System[J].Nonlinear AnalysisTheory,Methods&Applications,2009,70:2035-2053.
[101] Teo CJ, Spakovszky ZS. Modeling and Experimental Investigation of Micro-Hydrostatic GasThrust Bearings for Micro-Turbomachines[J]. ASME J Turbomach,2006,128:597-605.
[102] Liu LX, Teo CJ, Epstein AH, Spakovszky ZS. Hydrostatic Gas Journal Bearings forMicro-Turbomachinery[J]. Journal of Vibration and Acoustics,2005,127:157-164.
[103] Liu LX, Spakovszky ZS. Effects of Bearing Stiffness Anisotropy on Hydrostatic Micro GasJournal Bearing Dynamic Behavior[J]. Journal of Engineering for Gas Turbines and Power,2007,129:177-184.
[104] Teo CJ, Liu LX, et al. High-Speed Operation of a Gas-Bearing Supported MEMS-AirTurbine[J]. Journal of Tribology,2009,131:032001(9pp).
[105] Tanaka1S, Isomura K, Togo S, Esashi M. Turbo Test Rig with Hydroinertia Air Bearings for aPalmtop Gas Turbine[J]. J Micromech Microeng,2004,14:1449-1454.
[106] Boltzmann L. Weitere Studien Uber Das Warmegleichgenicht Unfer GasmolekulerStizurzgsberiehte der Akaderrcie der Wissenschaften Wien,1872,66:275-370
[107] Burgdorfer A.. The Influence of the Molecular Mean Free Path on The Performance ofHydrodynamic Gas Lubricated Bearings[J]. ASME Journal of Basic Engineering,1959,(81):94-100.
[108] Hsia YT, Domoto GA. An Experimental Investigation Of Molecular Rarefaction Effects In GasLubricated Bearings At Ultralow Clearances[J]. ASME Journal Of Lubrication Technology,1983,(105):120-130.
[109] Ehrich FF, Jacobson SA, Development of High-Speed Gas Bearings For High-Power DensityMicrodevices[J]. Journal of Engineering for Gas Turbines and Power,2003,125:141-148.
[110]杨小兵，王传敏，孙金池.工艺参数对Si深槽刻蚀的影响[J]. MEMS器件与技术,2009,46(7):424-427.
[111] Boufnichel M, Aachboun S, Grangeon F, Lefaucheux P, Ranson P. Profile Control of HighAspect Ratio Trenches of Silicon. I. Effect of Process Parameters on Local Bowing[J]. J Vac SciTechnol B,2002,20(4);1508-1513.
[112] Boufnichel M, Aachboun S, Lefaucheux P, Ranson P. Profile Control of High Aspect RatioTrenches of Silicon. II. Study of the Mechanisms Responsible for Local Bowing Formation andElimination of this Effect[J].Journal of Vacuum Science and Technology B,2003,21:267-273.
[113]胡焕林，张永胜，王旭迪.深高宽比微结构的干法刻蚀[J].真空,2004，41(5):32-34.
[114] Shan XC, et al. High-aspect-Ratio Fabrications of Micro Journal Air Bearings for Micro GasTurbine Engine[J]. Device and Process Technologies for MEMS, Microelectronics, and PhotonicsIII,2004(5276):428-433.
[115] Li J, Zhang QX, Asundi A, Liu AQ. MEMS Deep RIE Fabrication Process and DeviceCharacterization[C]. in Microsystems Engineering: Metrology and Inspection III, June23,2003-June25,2003, Munich, Germany,2003:80-86.
[116]温诗铸，黄平．摩擦学原理[M].北京:清华大学出版社，2008,22-25.
[117]黄平．摩擦学教程[M].北京:高等教育出版社，2008,378-379.
[118]池长青.气体动静压轴承的动力学及热力学[M].北京：北京航空航天大学出版社，2008.
[2] Thompson M, Whalen S. Design, Fabrication, and Testing of a Micro Heat Engine[J]. AIAA2002-5729.
[3] London AP, Epstein AH, Kerrebrock JL. A high Pressure Bipropellant Micro-Rocket Engine.36thAIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit[C],16-19July2000Huntsville,Alabama
[4] Thompson M, Whalen S. Design, Fabrication, and Testing of a Micro Heat Engine. AIAA2002-5729.
[5] Skinner J, Olson A, Bahr D, Richards C, Richards. A Piezoelectric Membrane Generator forMEMS Power. NanoTech2002-"At the Edge of Revolution"9-12September2002, Houston,Texas, AIAA2002-5745:1-7.
[6] Larangot B, Rossi1C, Camps1T, Berthold A, et. al. Solid Propellant Micro-Rockets-towards aNew Type of Power MEMS. NanoTech2002-"At the Edge of Revolution"9-12September2002,Houston, Texas, AIAA2002-5756.
[7] Lysherski SE. MEMS and NEMS: Systems, Devices, and Structures. CRC Press, Boca Raton,FL,2002.
[8]王琪民．微型机械导论[M].合肥:中国科技大学出版社，2003.3,
[9]刘广玉，樊尚春，周浩敏．微机械电子系统及其应用[M].北京:北京航空航天大学出版社，2003.2,
[10] Fujita H. Microactuators and Micromachines. In: Proceedings of IEEE[C], August1998,86(8):1721-1732.
[11] Carol Livermore, Anthony RF, Theodore L, Stephen DU, et al. A High-Power MEMS ElectricInduction Motor[J]. Journal of Micro-electro-mechanical Systems,2004,13(3):465-471.
[12] Senturia SD. Simulation and Design of Microsystems: a10-year perspective[J].Sensors andActuators A,1998,67:1-7.
[13] Epstein AH. Micro-Engines Scholar Lecture[J]. ASME Journal of Turbo-machinery,2004,5(2):204-211.
[14] Epstein AH. Millimeter-Scale Micro-Electro-Mechanical Systems Gas Turbine Engines[J]. Journalof Engineering for Gas Turbines and Power,2004,126(4):205-226.
[15] Lin CC. Development of a Microfabricated Turbine-Driven Air Bearing Rig[D]. Cambridge:Massachusetts Institute of Technology,1999.
[16] Epstein AH, Senturia SD. Power MEMS and Micro Engines. IEEE,1997lnfernational Conferenceon Solid-state Sensors and Actuators Chicago[C], June16-19,1997.
[17] Epstein AH, Senturia SD. Macro Power From Micro Machinery[J].Science,1997,276(5316):1211.
[18] Shan XC, Zhang QD, Sun YF, Wang ZF. Design, Fabrication and Characterization of an Air-drivenMicro Turbine Device[C]. Institute of Physics Publishing Journal of Physics: Conference Series,2006,34:316-321.
[19] Shan XC, Zhang QD, Sun YF, Maeda R. Studies on a Micro Turbine Device with Both Journal-andThrust-air Bearings[J]. Microsyst Technol,2007,13:1501-1508.
[20] Zhang QD, Shan XC, Guo GX, Wong S. Performance Analysis of Air Bearing in a MicroSystem[J]. Materials Science and Engineering A,2006,423:225-229.
[21] Zhang QD, Shan XC. Dynamic Characteristics of Micro Air Bearings for Microsystems[J].Microsyst Technol,2008,14:229-234.
[22] Zhang QD, Shan XC. Micro Air Bearing for a Microturbine[J]. IEEE Sens J,2008,8(5):435-440.
[23] Tanaka S, Hikichi K, Togo S, et al．World’s Smallest Gas Turbine Establishing Brayton Cycle[C].The7th international workshop on micro and nanothchnology for power generation and energyconversion application,2007:359-362．
[24] Kousuke I, Shuji T, et.at. Development of Micromachine Gas Turbine for Portable PowerGeneration[J]. JSME International Journal Series B,2004,47(3):459-464.
[25] Kousuke I, Shinichi T, Kousuke H, Satoshi G, Shuji T.Analytical and Experimental Study ofHydroinertia Gas Bearings For Micromachine Gas Turbines[C]. Proceedings of the ASME TurboExpo, Power for Land, Sea and Air,2005:1-9.
[26] Kousuke I, Shuji T, ShinIchi, T, Togo, S, Esashi M. Development of High-Speed Micro-GasBearings for Three-dimensional Micro-turbo Machines[J]. Journal of Micromechanics andMicroengineering,2005,15(9):S222-227.
[27] Isomura K, Murayama M, Teramoto S, Hikichi K, Endo Y, Togo S. Experimental Verification ofthe Feasibility of a100W Class Micro-Scale Gas Turbine at an Impeller Diameter of10mm [J].Journal of Micromechanics and Microengineering,2006,16(9):254-561.
[28] Peirs J, Reynaerts D, Verplaetsen F. A Microturbine For Electric Power Generation[J]. Sensors andActuators,A113(2004):86-93.
[29] Peirs J, Reynaerts D, Verplaetsen FA. Development of an Axial Microturbine for a Portable GasTurbine Generato[J]. Journal of Micromechanics and Microengineering,2003,13: S190-195．
[30] Almasi A. New Application of Micro-Turbine:Nuclear Emergency Cooling[J]. Proc IMechE PartA:J Power and Energy,2012.226(8):1076-1080.
[31]李军伟,钟北京,王建华,魏志军,王宁飞.空气槽对微型Swiss-Roll燃烧器工作特性的影响.北京理工大学学报,2010,30(2):140-144.
[32]李军伟,钟北京.微细直管燃烧器的散热损失研究[J].中国电机工程学报,2007,27(20):59-64.
[33]张永生,周俊虎,杨卫娟,刘茂省,岑可法.微燃烧稳定性分析和微细管道燃烧实验研究[J].浙江大学学报(工学版),2006,40(7):1178-1182.
[34]周俊虎,刘茂省,杨卫娟,张永生,周志军,岑可法.微燃烧发动机应用于微型飞行器的性能分析[J].燃烧科学与技术,2006,12(3):193-197.
[35]胡国新,王明磊.微细通道内可燃气体预混燃烧实验与微型发动机燃烧方案[J].热能动力工程,2003,18(4):352-355.
[36]梁德旺,黄国平.厘米级微型涡轮喷气发动机主要研究进展[J].燃气涡轮试验与研究,2004,17(2):9-13.
[37]黄国平,梁德旺,何志强.大型飞机辅助动力装置与微型涡轮发动机技术特点对比[J].航空动力学报,2008,23(2):383-388
[38]戚峰.微尺度射流、平板边界层及叶栅流动实验研究[D].南京:南京航空航天大学,2006.
[39]唐振寰.微型发动机整机振动分析[D].南京：南京航空航天大学,2009.
[40]徐进良,胡建军,曹海亮.微燃烧透平发电系统的研制及性能测试[J].中国机械工程,2008,19(12):1399-1405.
[41]周杨,刘火星,邹正平.微小型发动机涡轮气动设计研究[J].推进技术,2010,1:64-69.
[42]郑东亚,杜发荣,丁水汀,韩树军,张奇.微小型涡喷发动机转子涡动控制方法研究[J].推进技术,2010,31(1):52-55.
[43]曾昭奇.一种微型燃气涡轮发动机及其组合微细电加工技术研究[D].哈尔滨:哈尔滨工业大学，2012.
[44]黄国平，王跃，梁德旺.用于微型涡轮机的节流孔式静压气浮轴承实验[J].航空动力学报,2008,23(3):541-546.
[45] Fang JC, Zheng SQ, Han BC. AMB Vibration Control for Structural Resonance of Double-gimbalControl Moment Gyro with High-speed Magnetically Suspended Rotor[J]. IEEE/ASME TransMechatronics,2013,18(1):632-639.
[46] Xie GX, Luo JB, Liu SH, Zhang CH, Lu XC. Micro-bubble Phenomenon in NanoscaleWater-based Lubricating Film Induced by External Electric Field[J]. TribologyLetters,2008,29:169-176.
[47]刘宇,刘正林,吴铸新,周建辉.基于MATLAB的轴向开槽水润滑径向轴承性能分析[J].润滑与密封,2009,34(4):71-73
[48] Bird GA. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. New York, NY:OxfordScience Publications,1994.
[49]黄海,孟光,赵三星.二阶滑移边界对微型气浮轴承稳定性能的影响[J].力学学报,2006,5:668-673.
[50]黄海,孟光.考虑二阶滑移流效应的微型气浮轴承-转子稳定性分析及其动态响应[J].振动与冲击,2008,27(5):310-311
[51]黄海,孟光,赵三星.滑移边界对微型气浮轴承稳态性能的影响[J].机械工程学报,2006,42(增刊):21-25.
[52]黄海.微型轴承－转子系统动力特性的研究[D].上海:上海交通大学,2007.
[53] Lee YB, Kwaka HD, Kima CH, Lee NS. Numerical Prediction of Slip Flow Effect onGas-lubricated Journal Bearings for MEMS/MST-based Micro-Rotating Machinery[J]. TribologyInternational,2004,38:89-96.
[54] Fukui S, Kaneko R. Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized BoltzmanEquation: First Report-Derivation of Generalized Lubrication Equation Including Thermal CreepFlow[J]. ASME Journal of Tribology,1988,10:253-62.
[55] Fukui S, Kaneko R. A Database for Interpolation of Poiseuille Flows Rates for High KnudsenNumber Lubrication Problems[J].ASME Journal of Tribology1990;112:78-83.
[56] Maxwell J. C. Illustrations of the Dynamical Theory of Gases II[J]. Philosophical Magazine,1860,20:21-32
[57] Maxwell J. C. Illustrations of the Dynamical Theory of Gases III[J]. Philosophical Magazine,1860,20:33-37
[58] Maxwell J. C. On the Dynamical Theory of Gases[J]. Phil. Traps. Rod., Soc. London,1867,157:49-88
[59] Zhou WD, Liu B, Yu SK, et al. A Generalized Heat Transfer Model for Thin Film Bearings atHead-disk interface[J]. Applied Physics Letters,2008,92(4):043109-1-3.
[60]刘韧.微发动机气体动静压混合润滑推力轴承-转子系统动力学研究[D].北京:北京理工大学,2012.
[61] Zhang HJ, Zhu CS, Yang Q. Characteristics of Micro Gas Journal Bearings Based on EffectiveViscosity[J]. ASME Journal of Turbomachinery,2009,131(4):041707-1-5.
[62] Zhang HJ, ZhuCS, Yang Q. Effect of Effective Viscosity on Characteristics of Microscale GasJournal Bearings.4th IEEE International Conference on Nano/Micro Engineered and MolecularSystems, NEMS2009[C], Shenzhen, China,2009:121-125.
[63] Zhang HJ, ZhuCS, Tang M. Effects of Rarefaction on the Characteristics of Micro Gas JournalBearings[J]. Journal of Zhejiang University: Science A,2010,11:43-49.
[64]张海军,祝长生,杨琴.有效黏度效应对气体径向微轴承性能的影响[J].中国电机工程学报,2009,29(29):84-88.
[65] Ayon, AA, Braff, R, Lin, CC, Sawin, HH, Schmidt, MA. Characterization of a Time MultiplexedInductively Coupled Plasma Etcher[J]. J Electrochem Soc,1999,146(1):339-349.
[66] Piekos ES, Breuer KS. Manufacturing Effects in Microfabricated Gas Bearings: Axially varyingclearance[J]. Journal of Tribology-Transactions of the Asme,2002,124:815-821.
[67] Teo CJ. MEMS Turbomachinery Rotordynamics: Moldeling, Design and Testing[D]. PhD thesis,Department of Aeronautics and Astronautics, Massachusetts Institute of Technology,2006
[68] Teo CJ, Spakovszky ZS. Analysis of Tilting Effects and Geometric Nonuniformities inMicro-hydrostatic Gas Thrust Bearings[J]. ASME J Turbomach,2006,128:606-615.
[69]张文明,孟光,陈迪.微型旋转机械轴承研究进展[J].振动与冲击,2008,27(5):27-31.
[70] Meng G, Zhang WM, Huang H, Li HG, Chen D. Micro-Rotor Dynamics forMicro-Electro-Mechanical Systems (MEMS). Chaos, Solitons and Fractals[J].2009,40(2):538-562.
[71]张文明.微转子系统动力特性的研究[D].上海:上海交通大学,2006.
[72] Piekos ES, Orr DJ, et al. Design and Analysis of Microfabricated High Speed Gas JournalBearings[J]. American Institute of Aeronautics and Astronautics Paper,97-1966:1-11.
[73] Piekos ES, Breuer KS. Pseudospectral Orbit Simulation of Nonideal Gas-Lubricated JournalBearings for Microfabricated Turbomachines[J].ASME J Tribol,1999,121:604-609.
[74] Liu R, Wang XL, Zhang XQ. Effects of Gas Rarefaction on Dynamic Characteristics of MicroSpiral-grooved Thrust Bearing[J]. ASME J Tribol,2012,134(2):022201.1-022201.7.
[75]刘韧,王晓力.微气体螺旋槽推力轴承润滑数值模拟[J].机械工程学报,2010,(46)21:113-117.
[76] Liu R, Wang XL. Dynamic Characteristics Analysis of Micro Air Spiral Grooved ThrustBearing-Rotor System. IEEE-NEMS2011,2011IEEE International Conference on Nano/MicroEngineered and Molecular Systems [C], Kaohsiung, Taiwan,2011:719-723.
[77]刘韧,王晓力.基于有限体积法的螺旋槽气体推力轴承润滑计算[J].北京理工大学学报,2010,30(12):1400-1404.
[78]刘韧,王晓力,魏学玉.微气体螺旋槽推力轴承动力学特性系数研究[J].中国机械工程,
[79] Liu R, Wang XL. On Micro Gas Thrust Bearing for Micro System. Chinese Gas LubricationInstitution, CMES2010, Fifteenth Chinese Gas Lubrication Conference [C], Shenzhen, China,2010:383-386.
[80]刘韧,王晓力.微气体螺旋槽推力轴承润滑计算及系统性能预测.2009年第九届中国摩擦学会议
[C],北京,中国,2009:232-234.
[81]戚社苗,耿海鹏,虞烈.动压气体轴承的动态刚度和动态阻尼系数[J].机械工程学报,2007,43(5):91-98.
[82]戚社苗,耿海鹏,虞烈.扰动频率对动压气体轴承动态刚度和阻尼系数的影响[J].西安交通大学学报,2006,40(3):270-274.
[83]张瑞乾,张锡圣.径向气体/液体轴承动力特性系数的统一求法[J].北京航空航天大学学报,1994,20(4):474-481.
[84] Lund JW. The Stability of an Elastic Rotor in Journal Bearings with Flexible, Damed Supports[J].Journal of Applied Mechanics,1965, December:911-920.
[85] Lund JW. Caculation of Stiffness and Damping Properties of Gas Bearings[J].Journal ofLubrication Technology,1968,October:793-803.
[86] Miller, BA, Green, I. Numerical Formulation for the Dynamic Analysis of Spiral-grooved Gas FaceSeals[J]. ASME J Tribol,2001,123(2):395-403.
[87] Kim D, Lee S, Bryant, MD, Ling FF. Hydrodynamic Performance of Gas Microbearings[J].Journal of Tribology,2004,126(4):711-718.
[88] Kim D. Design and Fabrication of Sub-Millimeter Scale Gas Bearings with Tungsten-ContainingDiamond Like Carbon Coatings. Ph.D. thesis, Mechanical Engineering, University of Texas atAustin, Austin.
[89] Zhou JB, Meng G, Chen, JY, Zhang, WM. Bifurcation Analysis of Ultrashort Self-acting GasJournal Bearings for MEMS[J]. IEEE Trans Ind Electron,2009,56(8):3188-3194.
[90]周健斌,孟光,张文明.微机电系统径向气体轴承特性研究[J].振动与冲击,2007,26(9):30-33
[91]周健斌,孟光,陈杰宇,张文明.微型气体动压径向短轴承一转子系统动态特性研究[J].振动与冲击,2008,27(s):113-116.
[92]周健斌.微型转子轴承系统动力学问题研究[D].上海:上海交通大学,2009.
[93] Wang CC, Chen CK. Bifurcation Analysis of Self-Acting Gas Journal Bearings[J].Journal ofTribology,2001,123:755-767.
[94] Wang CC. Bifurcation Analysis of an Aerodynamic Journal Bearing System Considering the Effectof Stationary Herringbone Grooves[J].Chaos, Solitons and Fractals,2007,33:1532-1545.
[95] Wang CC, Yau HT, Kuan CF, Yan JJ. Application of Hybrid Method to the Quasi-PeriodicAnalysis of Micro Gas Journal Bearing System.2008IEEE International Symposium onKnowledge Acquisition and Modeling Workshop Proceedings[C], KAM2008, Wuhan, China,2008:79-82.
[96] Wang CC, Yau HT, Yeh YL, Jang MJ, LinJF. Influence of the Bearing Number on Micro GasBearing System.20094th IEEE International Conference on Nano/Micro Engineered andMolecular Systems (IEEE-NEMS2009)[C], Piscataway, NJ, USA,2009:975-979.
[97] Wang CC. Application of a Hybrid Numerical Method to the Nonlinear Dynamic Analysis of aMicro Gas Bearing System[J].Nonlinear Dynamics,2010,59:695-710.
[98] Wang CC. Application of a Hybrid Method to the Bifurcation Analysis of a Relative Short GasJournal Bearing System with Herringbone Grooves[J].Industrial Lubrication andTribology,2011,63(5):307-319.
[99] Wang CC, Yau HT. Application of a Hybrid Numerical Method to The Bifurcation Analysis of aRigid Rotor Supported by a Spherical Gas Journal Bearing System[J].Nonlinear Dynamics,2008,51:515-528.
[100] Wang CC. Application of a Hybrid Method to the Nonlinear Dynamic Analysis of a FlexibleRotor Supported by a Spherical Gas-lubricated Bearing System[J].Nonlinear AnalysisTheory,Methods&Applications,2009,70:2035-2053.
[101] Teo CJ, Spakovszky ZS. Modeling and Experimental Investigation of Micro-Hydrostatic GasThrust Bearings for Micro-Turbomachines[J]. ASME J Turbomach,2006,128:597-605.
[102] Liu LX, Teo CJ, Epstein AH, Spakovszky ZS. Hydrostatic Gas Journal Bearings forMicro-Turbomachinery[J]. Journal of Vibration and Acoustics,2005,127:157-164.
[103] Liu LX, Spakovszky ZS. Effects of Bearing Stiffness Anisotropy on Hydrostatic Micro GasJournal Bearing Dynamic Behavior[J]. Journal of Engineering for Gas Turbines and Power,2007,129:177-184.
[104] Teo CJ, Liu LX, et al. High-Speed Operation of a Gas-Bearing Supported MEMS-AirTurbine[J]. Journal of Tribology,2009,131:032001(9pp).
[105] Tanaka1S, Isomura K, Togo S, Esashi M. Turbo Test Rig with Hydroinertia Air Bearings for aPalmtop Gas Turbine[J]. J Micromech Microeng,2004,14:1449-1454.
[106] Boltzmann L. Weitere Studien Uber Das Warmegleichgenicht Unfer GasmolekulerStizurzgsberiehte der Akaderrcie der Wissenschaften Wien,1872,66:275-370
[107] Burgdorfer A.. The Influence of the Molecular Mean Free Path on The Performance ofHydrodynamic Gas Lubricated Bearings[J]. ASME Journal of Basic Engineering,1959,(81):94-100.
[108] Hsia YT, Domoto GA. An Experimental Investigation Of Molecular Rarefaction Effects In GasLubricated Bearings At Ultralow Clearances[J]. ASME Journal Of Lubrication Technology,1983,(105):120-130.
[109] Ehrich FF, Jacobson SA, Development of High-Speed Gas Bearings For High-Power DensityMicrodevices[J]. Journal of Engineering for Gas Turbines and Power,2003,125:141-148.
[110]杨小兵，王传敏，孙金池.工艺参数对Si深槽刻蚀的影响[J]. MEMS器件与技术,2009,46(7):424-427.
[111] Boufnichel M, Aachboun S, Grangeon F, Lefaucheux P, Ranson P. Profile Control of HighAspect Ratio Trenches of Silicon. I. Effect of Process Parameters on Local Bowing[J]. J Vac SciTechnol B,2002,20(4);1508-1513.
[112] Boufnichel M, Aachboun S, Lefaucheux P, Ranson P. Profile Control of High Aspect RatioTrenches of Silicon. II. Study of the Mechanisms Responsible for Local Bowing Formation andElimination of this Effect[J].Journal of Vacuum Science and Technology B,2003,21:267-273.
[113]胡焕林，张永胜，王旭迪.深高宽比微结构的干法刻蚀[J].真空,2004，41(5):32-34.
[114] Shan XC, et al. High-aspect-Ratio Fabrications of Micro Journal Air Bearings for Micro GasTurbine Engine[J]. Device and Process Technologies for MEMS, Microelectronics, and PhotonicsIII,2004(5276):428-433.
[115] Li J, Zhang QX, Asundi A, Liu AQ. MEMS Deep RIE Fabrication Process and DeviceCharacterization[C]. in Microsystems Engineering: Metrology and Inspection III, June23,2003-June25,2003, Munich, Germany,2003:80-86.
[116]温诗铸，黄平．摩擦学原理[M].北京:清华大学出版社，2008,22-25.
[117]黄平．摩擦学教程[M].北京:高等教育出版社，2008,378-379.
[118]池长青.气体动静压轴承的动力学及热力学[M].北京：北京航空航天大学出版社，2008.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |