高速静压气体轴承—转子系统的特性研究
摘要
静压气体轴承具有运转速度高、精度高、能耗低等优点,在高速精密机床、精密测量仪器、高速转子等设备上具有良好的适用性。当前,随着转子速度的不断提高,一方面高转速带来的动压效应对轴承的动静态特性影响更加突出,雷诺方程无法满足流场精确计算的需求；另一方面高转速导致的诸多非线性因素使转子动力学的线性理论无法满足高速气体轴承-转子系统的研究需求。
本文以提高高速静压气体轴承-转子系统的稳定性为目的,针对静压气体轴承的流场计算、静压气体轴承的动静态特性分析、气体轴承-转子系统特性的耦合研究、系统特性的实验测试等方面开展了系统深入的研究,主要研究内容包括：
分析不同流场数值计算方法对静压气体轴承的适用性。以静压气体止推轴承为研究对象,采用基于雷诺方程的有限差分法及基于N-S方程的有限体积法中的层流模型、湍流模型及二者混合等四种方法对静压气体轴承的流场进行计算。雷诺方程和湍流模型无法满足流场精确计算的需求；选择基于N-S方程的层流模型作为高速静压气体轴承研究中的计算方法。
采用三维流场计算方法研究轴承结构及工况对静压径向气体轴承动静态特性的影响。采用分区划分、局部加密的三维建模方法；通过旋转坐标系与静态网格相结合的方法实现静压气体轴承动态特性的三维计算。计算结果表明：高速状态下,动压效应提高了轴承的主承载能力及刚度,偏心率越大,动压效应越明显；随着转速的增高,主刚度增大,主阻尼减小,交叉刚度和交叉阻尼的变化则因偏心率的不同而不同；随着供气压力的提高,主刚度增大,交叉刚度则在大偏心范围内随供气压力提高而增大,阻尼的变化则因转速和偏心率的不同而不同；高转速、大偏心状态下,受动压效应的影响,环面节流静压气体轴承的主刚度和交叉阻尼大于小孔节流,而交叉刚度和主阻尼则小于小孔节流；随着供气孔个数的增加,主阻尼增大,安装方式对轴承特性的影响可以忽略；切向供气提高了轴承的主阻尼,减小了交叉刚度,有利于提高系统的稳定性,但耗气量较大。
提出一种基于CFD计算结果的静压气体轴承-转子系统特性的耦合研究方法。通过对不同工况下气膜力的CFD计算结果的拟合,得到气膜力随转速和偏心率变化的非线性关系式；将所得的拟合关系式与转子动力学方程进行耦合求解,实现流场精确计算结果与转子动力学方程的耦合,充分考虑动压效应及转子位移对系统特性的影响。气膜力的非线性使系统中不平衡量的改变和响应幅值的增加不是线性变化关系。
设计并搭建高速轴承-转子系统的测试系统,设计新型切向非均匀孔径供气和新型垂直分区非均匀压力供气的静压气体轴承,并对不同轴承结构和工作状态下的系统特性进行测试对比分析。提出一种基于静压气体轴承原理的高速轴承-转子系统非接触式加载方法。所提出的基于CFD计算结果的系统特性的耦合研究方法具有较高的计算精度；与垂直供气相比,切向供气轴承能够减小转子的跳动幅值,定性地证明动态特性理论分析的正确性；新型切向非均匀孔径供气轴承可以有效地提高系统的稳定性；新型垂直分区非均匀压力供气轴承能够减小一阶临界转速附近的跳动幅值,但其后出现了局部增大现象；实验工况下,加载会增加额外的系统振动,且会增大各阶临界转速的跳动幅值；随着供气压力提高,垂直均匀供气轴承-转子系统的一阶临界转速附近的跳动幅值减小,但其后出现了局部增大现象；对于切向供气轴承,供气压力的提高可以提高系统的稳定性。
Aerostatic bearings have been successfully used in high-precision machine tools, high-precision measuring instruments, high-speed rotors and so on because of their advantages such as high-speed, high-precision, and small power dissipation. Now with the increases of rotating speed, several problems arise. On the one hand, the influence of the dynamic effect caused by high rotating speed on the characteristics of them becomes more prominent, the calculation based on Reynolds equation could no longer satisfy the calculation accuracy requirement. On the other hand, the nonlinear factors caused by high rotating speed makes the linear theory of rotor dynamics unable to satisfy the research requirement of high-speed gas bearing-rotor system.
In this paper, the improvement of system stability for high-speed aerostatic bearing-rotor system is taken as the research purpose, the systematic and in-depth research on the calculation of aerostatic bearing flow, the analysis of aerostatic bearing characteristics, the coupled research of the gas bearing-rotor system's characteristics, the experiment of the system. The main research work includes:
The applicability of different calculation methods on aerostatic bearings is analyzed. The thrust aerostatic bearings are chose as a subject, the finite difference method based on Reynolds equation and the finite volume method (FVM) based on N-S equations are both used. For FVM, the laminar model, the turbulent model and the mixture of them are used. The four types of calculation results are compared with experiment results and analyzed. The Reynolds equation and the turbulent model of FVM are not able to satisfy the calculation accuracy requirement. Based on the comparisons of calculation accuracy and efficiency, the laminar model of FVM is chose for the subsequent study. The boundary layer separation, change of the flow state from turbulent to laminar and increase of viscosity are used to explain the pressure recovery after the pressure depression in the flow field.
The static and dynamic characteristics of radial aerostatic bearings of different structure under different working conditions are studied with the three-dimension calculation method. The three-dimension models of radial aerostatic bearings are built, the model is divided into different districts, the calculation grids are refined in some districts. The static girds combined with the rotating coordinate are used for dynamic calculation. The dynamic effect improves the main load capacity and the main stiffness under high-speed working conditions, and the greater the eccentricity, the more obvious dynamic effect pressure. With the increase of rotating speed, the main stiffness increases, the main damping decrease, and the changes of the cross stiffness and the cross damping depend on the eccentricity. With the increase of gas supply pressure, the main stiffness increases, the cross stiffness increases within the bigger eccentricity range, and the changes of the damping depends on the eccentricity and the rotating speed. Under high-speed and big eccentricity working conditions, the influence of dynamic effect on the orifice-compensated aerostatic beaings is greater than that on the orifice-restricted aerostatic beaings, the main stiffness and the cross damping of the orifice-compensated are bigger than them of the orifice-restricted, but the cross stiffness and the main damping of the orifice-compensated are smaller. With the increase of the number of gas supply holes, the main damping increases and the influence of installation types of bearings can be ignored. The tangential gas supply holes can improve the main damping and decrease the cross stiffness with a large gas consumption, which is helpful to the system stability.
The interaction method of aerostatic bearing-rotor system based on the calculation results from CFD is proposed. The nonlinear function of load capacity with rotating speed and eccentricity is obtained through fitting the calculation results under different working conditions. The nonlinear function is used to couple with the rotor dynamic equation, which realizes the coupling between the accurate flow calculation and the rotor dynamic equation. The influence of the dynamic effect and the rotor displacement on the system is fully considered in this method. The results show the relation between the imbalance amount and the response multitude is nonlinear caused by the nonlinear gas film force.
The high-speed bearing-rotor experiment system is built, the new types of aerostatic bearings with tangential nonuniform supply holes and radial nonuniform district supply pressure are designed, the bearing-rotor system with different structure aerostatic bearings are test under different working conditions. One non-contact load exerting method based on the principle of aerostatic beaing is proposed, which can exert dynamic or static load on high-speed rotors. The compassion between experiment and theoretical results shows the proposed fluid-solid interaction method has a high calculation accuracy. Compared with the radial gas supply holes, the tangential gas supply holes can reduce the amplitude of the rotor runout, which certifies the correctness of the theoretical analysis of dynamic characteristics. The new type of aerostatic bearings with tangential nonuniform supply holes can improve the system stability. The new type of aerostatic bearings with radial nonuniform district supply pressure can reduce the amplitude of the rotor runout near the first order critical speed, but after the speed the amplitude increases. Under experiment conditions, the exerted load will increase the vibration of the system, and increase the amplitude of the critical speed. For the aerostatic bearings with radial gas supply holes, the amplitude of the rotor runout near the first order critical speed can be reduced with the increase of supply pressure, but after the speed the amplitude increases. For the aerostatic bearings with radial gas supply holes, the increase of supply pressure can improve the system stability.
本文以提高高速静压气体轴承-转子系统的稳定性为目的,针对静压气体轴承的流场计算、静压气体轴承的动静态特性分析、气体轴承-转子系统特性的耦合研究、系统特性的实验测试等方面开展了系统深入的研究,主要研究内容包括：
分析不同流场数值计算方法对静压气体轴承的适用性。以静压气体止推轴承为研究对象,采用基于雷诺方程的有限差分法及基于N-S方程的有限体积法中的层流模型、湍流模型及二者混合等四种方法对静压气体轴承的流场进行计算。雷诺方程和湍流模型无法满足流场精确计算的需求；选择基于N-S方程的层流模型作为高速静压气体轴承研究中的计算方法。
采用三维流场计算方法研究轴承结构及工况对静压径向气体轴承动静态特性的影响。采用分区划分、局部加密的三维建模方法；通过旋转坐标系与静态网格相结合的方法实现静压气体轴承动态特性的三维计算。计算结果表明：高速状态下,动压效应提高了轴承的主承载能力及刚度,偏心率越大,动压效应越明显；随着转速的增高,主刚度增大,主阻尼减小,交叉刚度和交叉阻尼的变化则因偏心率的不同而不同；随着供气压力的提高,主刚度增大,交叉刚度则在大偏心范围内随供气压力提高而增大,阻尼的变化则因转速和偏心率的不同而不同；高转速、大偏心状态下,受动压效应的影响,环面节流静压气体轴承的主刚度和交叉阻尼大于小孔节流,而交叉刚度和主阻尼则小于小孔节流；随着供气孔个数的增加,主阻尼增大,安装方式对轴承特性的影响可以忽略；切向供气提高了轴承的主阻尼,减小了交叉刚度,有利于提高系统的稳定性,但耗气量较大。
提出一种基于CFD计算结果的静压气体轴承-转子系统特性的耦合研究方法。通过对不同工况下气膜力的CFD计算结果的拟合,得到气膜力随转速和偏心率变化的非线性关系式；将所得的拟合关系式与转子动力学方程进行耦合求解,实现流场精确计算结果与转子动力学方程的耦合,充分考虑动压效应及转子位移对系统特性的影响。气膜力的非线性使系统中不平衡量的改变和响应幅值的增加不是线性变化关系。
设计并搭建高速轴承-转子系统的测试系统,设计新型切向非均匀孔径供气和新型垂直分区非均匀压力供气的静压气体轴承,并对不同轴承结构和工作状态下的系统特性进行测试对比分析。提出一种基于静压气体轴承原理的高速轴承-转子系统非接触式加载方法。所提出的基于CFD计算结果的系统特性的耦合研究方法具有较高的计算精度；与垂直供气相比,切向供气轴承能够减小转子的跳动幅值,定性地证明动态特性理论分析的正确性；新型切向非均匀孔径供气轴承可以有效地提高系统的稳定性；新型垂直分区非均匀压力供气轴承能够减小一阶临界转速附近的跳动幅值,但其后出现了局部增大现象；实验工况下,加载会增加额外的系统振动,且会增大各阶临界转速的跳动幅值；随着供气压力提高,垂直均匀供气轴承-转子系统的一阶临界转速附近的跳动幅值减小,但其后出现了局部增大现象；对于切向供气轴承,供气压力的提高可以提高系统的稳定性。
Aerostatic bearings have been successfully used in high-precision machine tools, high-precision measuring instruments, high-speed rotors and so on because of their advantages such as high-speed, high-precision, and small power dissipation. Now with the increases of rotating speed, several problems arise. On the one hand, the influence of the dynamic effect caused by high rotating speed on the characteristics of them becomes more prominent, the calculation based on Reynolds equation could no longer satisfy the calculation accuracy requirement. On the other hand, the nonlinear factors caused by high rotating speed makes the linear theory of rotor dynamics unable to satisfy the research requirement of high-speed gas bearing-rotor system.
In this paper, the improvement of system stability for high-speed aerostatic bearing-rotor system is taken as the research purpose, the systematic and in-depth research on the calculation of aerostatic bearing flow, the analysis of aerostatic bearing characteristics, the coupled research of the gas bearing-rotor system's characteristics, the experiment of the system. The main research work includes:
The applicability of different calculation methods on aerostatic bearings is analyzed. The thrust aerostatic bearings are chose as a subject, the finite difference method based on Reynolds equation and the finite volume method (FVM) based on N-S equations are both used. For FVM, the laminar model, the turbulent model and the mixture of them are used. The four types of calculation results are compared with experiment results and analyzed. The Reynolds equation and the turbulent model of FVM are not able to satisfy the calculation accuracy requirement. Based on the comparisons of calculation accuracy and efficiency, the laminar model of FVM is chose for the subsequent study. The boundary layer separation, change of the flow state from turbulent to laminar and increase of viscosity are used to explain the pressure recovery after the pressure depression in the flow field.
The static and dynamic characteristics of radial aerostatic bearings of different structure under different working conditions are studied with the three-dimension calculation method. The three-dimension models of radial aerostatic bearings are built, the model is divided into different districts, the calculation grids are refined in some districts. The static girds combined with the rotating coordinate are used for dynamic calculation. The dynamic effect improves the main load capacity and the main stiffness under high-speed working conditions, and the greater the eccentricity, the more obvious dynamic effect pressure. With the increase of rotating speed, the main stiffness increases, the main damping decrease, and the changes of the cross stiffness and the cross damping depend on the eccentricity. With the increase of gas supply pressure, the main stiffness increases, the cross stiffness increases within the bigger eccentricity range, and the changes of the damping depends on the eccentricity and the rotating speed. Under high-speed and big eccentricity working conditions, the influence of dynamic effect on the orifice-compensated aerostatic beaings is greater than that on the orifice-restricted aerostatic beaings, the main stiffness and the cross damping of the orifice-compensated are bigger than them of the orifice-restricted, but the cross stiffness and the main damping of the orifice-compensated are smaller. With the increase of the number of gas supply holes, the main damping increases and the influence of installation types of bearings can be ignored. The tangential gas supply holes can improve the main damping and decrease the cross stiffness with a large gas consumption, which is helpful to the system stability.
The interaction method of aerostatic bearing-rotor system based on the calculation results from CFD is proposed. The nonlinear function of load capacity with rotating speed and eccentricity is obtained through fitting the calculation results under different working conditions. The nonlinear function is used to couple with the rotor dynamic equation, which realizes the coupling between the accurate flow calculation and the rotor dynamic equation. The influence of the dynamic effect and the rotor displacement on the system is fully considered in this method. The results show the relation between the imbalance amount and the response multitude is nonlinear caused by the nonlinear gas film force.
The high-speed bearing-rotor experiment system is built, the new types of aerostatic bearings with tangential nonuniform supply holes and radial nonuniform district supply pressure are designed, the bearing-rotor system with different structure aerostatic bearings are test under different working conditions. One non-contact load exerting method based on the principle of aerostatic beaing is proposed, which can exert dynamic or static load on high-speed rotors. The compassion between experiment and theoretical results shows the proposed fluid-solid interaction method has a high calculation accuracy. Compared with the radial gas supply holes, the tangential gas supply holes can reduce the amplitude of the rotor runout, which certifies the correctness of the theoretical analysis of dynamic characteristics. The new type of aerostatic bearings with tangential nonuniform supply holes can improve the system stability. The new type of aerostatic bearings with radial nonuniform district supply pressure can reduce the amplitude of the rotor runout near the first order critical speed, but after the speed the amplitude increases. Under experiment conditions, the exerted load will increase the vibration of the system, and increase the amplitude of the critical speed. For the aerostatic bearings with radial gas supply holes, the amplitude of the rotor runout near the first order critical speed can be reduced with the increase of supply pressure, but after the speed the amplitude increases. For the aerostatic bearings with radial gas supply holes, the increase of supply pressure can improve the system stability.
引文
[1]十合晋一.气体轴承—设计、制作与应用[M].北京：宇航出版社,1988.
[2]刘暾,刘育华,陈世杰.静压气体润滑[M].哈尔滨：哈尔滨工业大学出版社,1990.
[3]王云飞.气体润滑理论与气体轴承设计[M].北京：机械工业出版社,1999.
[4]李树森,刘暾,张鹏顺.小孔节流方式对气体静压轴承工作刚度影响的分析.润滑与密封[J], 2004,(4)：6-7.
[5]侯予,熊联友,吴刚等.国外多孔质静压气体轴颈轴承理论分析的发展[J].润滑与密封,1998,(1)：62～65
[6]杜金名.多孔质流体静压轴承润滑技术的研究[D].哈尔滨：哈尔滨工业大学,2003.
[7]Information on http://www.precitech.com.
[8]Information on http://www.toshiba-machine.co.jp
[9]姚德良,傅仙罗.圆盘和圆环形压膜轴承的气动力分析[J].应用数学和力学,1981,12(8)：711-718.
[10]党根茂.气体润滑技术[M].南京：东南大学出版社,1990.
[11]Gross William A. Gas Film Lubrication [M]. New York:Wiley,1962.
[12]Constantinescu V. N. Gas Lubrication[M]. New York:ASME,1969.
[13]Powell J. W. John William. Design of Aerostatic Bearings[M]. London:Machinery Publishing Co. Ltd,1970.
[14]Yabe. H, Mori. H, Tanahashi. H. Study on Characteristics of Externally Pressurized Gas Thrust Bearings With Surface-Restriction Compensation-Dynamic Bearing Characteristics [J]. BULL.1982,25(207):1451-1456.
[15]S. H. Nguyen. p-Version Finite Element Analysis of Gas Bearings of Finite Width [J]. Journal of Tribology,1991,113(3):417-420.
[16]M. C. Pandian. A new method for the numerical solution of the Reynolds equation for gas-lubrication slider bearings [J]. Journal of Engineering Mathematics.1985,19(3):3-19.
[17]T. Nakamura, S. Yoshimoto. Static Tilt Characteristics of Aerostatic Rectangular Double-Pad Thrust Bearing with Compound Restrictors [J].Tribology International.1996,29(2):145-152.
[18]温诗铸.静压空气轴承性能的试验分析[M].北京：机械工程学报社,1962.
[19]张言羊.静压式空气轴承的一种近似计算方法[J].西安交通大学学报,1964,(2)：35-44.
[20]齐乃明,刘暾,谭久彬.自主式静压气体轴承实现无穷刚度的条件分析[J].南京理工大学学报,2001,25(2)：147-151.
[21]侯予,熊联友,王瑾等.透平膨胀机新型动压径向气体轴承的试验研究[J].低温工程,1999,(4)：231-235.
[22]陈纯正.中压透平膨胀机橡皮加稳空气轴承稳定性[J].西安交通大学学报,1981,15(4)：13-24.
[23]王林中,侯予,陈纯正.可倾瓦径向气体轴承的静动特性的理论研究[J].润滑与密封,2006,(5)：84-87.
[24]陈汝刚,侯予, 陈纯正.微型气浮轴承高速透平膨胀机的研制[J].西安交通大学学报,2010,44(1)：61-65.
[25]侯予,陈双涛,陈汝刚等.弹性支承箔片动压气体径向轴承的实验研究[J].润滑与密封,2010,35(6)：1-4.
[26]刘立强,熊联友,侯予等.低温透平膨胀机切向供气轴承[J].低温与特气,1998,(1)：40-43.
[27]景岗,杨清好.锯齿形多槽式动静压气体润滑轴承稳态和动态特性的研究[J].华中理工大学学报,1994,22(2)：69-73.
[28]王元勋.主动控制节流无穷静刚度气体润滑轴承研究[D].武汉：华中理工大学,1995.
[29]刘暾,葛卫平,齐乃明等.超精气磁轴承混合轴系的研究[J].中国机械工程；2002,(2)：167-170.
[30]赵宁.磁气混合轴承中弹性箔片径向动压气体轴承的数值分析研究[D].南京航空航天大学,2004.3
[31]刘庆国.超精密气磁轴承轴系动力学及控制方法的研究[D].东北林业大学,2004;5
[32]李树森,孟庆鑫,马兰兰.气磁轴承主轴系统误差补偿技术的研究[J].林业机械与木工设备,2005,33(12)：12-14.
[33]张君安.高刚度空气静压轴承研究[D].西安：西安工业大学,2006.
[34]孙昂,马文琦,王祖温.带有锥形气腔的平面气浮轴承的流场计算分析[J].液压与气动.2008,(1)：14-17.
[35]孙昂,马文琦,王祖温.平面静压气浮轴承超音速流场特性的研究.机械工程学报[J],2010,46(9)：113-119.
[36]于贺春,马文琦,王祖温.基于FLUENT的环面节流静压气体圆盘止推轴承二维流场仿真分析[J].机床与液压,2008,36(10)：109-112.
[37]易家明,徐学兰.多空质静压气体轴承材料的研究[J].轴承,1985,(1)：36-37.
[38]罗继伟,王云飞.多空质静压气体轴承静态性能的有限元分析[J].轴承,1985,(2)：8-12.
[39]杜金名,卢泽生,孙雅洲.影响空气静压多孔质轴承静态性能的有关因素[J].中国机械工程,2003,14(5)：417-420.
[40]杜金名,卢泽生,孙雅洲.气体静压小孔节流与多孔质节流性能的比较[J].润滑与密封,2002,(4)：2-5.
[41]卢泽生,于雪梅.基于分形理论多孔质石墨渗透率的研究[J].机床零部件,2006,(7)：30-31.
[42]卢泽生,于雪梅,孙雅洲.局部多孔质气体静压轴向轴承静态特性的数值求解[J].摩擦学报,2007,27(1)：68-72.
[43]于雪梅,孙雅洲,卢泽生.局部多孔质气体静压止推轴承压力分布的研究[J].润滑与密封,2009,34(11)：53-57.
[44]姚英学,崔大朋,秦冬黎.新型狭缝节流球形静压气体陀螺轴承的动态特性[J].宇航学报,2010,31(8)：2050-2057.
[45]姚英学,杜建军,刘暾等.制造误差对气体静压轴承涡流力矩影响分析方法研究[J].宇航学报,2003,24(2)：124-128.
[46]秦冬黎,姚英学.小孔节流动静压混合气体润滑球轴承的干扰力矩分析[J].润滑与密封,2007,32(4)：131-135.
[47]秦冬黎,姚英学.误差对气体静压球轴承静态承载性能的影响分析[J].哈尔滨轴承,2009,27(3)：44-48.
[48]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.
[49]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)：112-116.
[50]周健斌,孟光,陈杰宇等.气体动压径向短轴承动力学和分岔分析[J].机械强度,2010,32(2)：207-211.
[51]H. M. Talukder, T. B. Stowell. Pneumatic hammer in an externally pressurized orifice-compensated air jounal bearing [J]. Tribology International,2003,36:585-591.
[52]Gross, W. A., and Zachmanaglou, E. C. Perturbation Solutions for Gas-Lubricating Films [J]. ASME, Journal of Basic Engineering,1961,83:139-144.
[53]Ausman, J. S. Linearized ph Stability Theory for Translatory Half-Speed Whirl of Long Self-Acting Gas-Lubricated Journal Bearings [J]. ASME, Journal of Basic Engineering,1963, 83:611-619.
[54]Larson. R, Richardson. H. A Preliminary Study of Whirl Instability for Pressurized Gas Bearings[J]. ASME, Journal of Basic Engineering,1962,84:511-520.
[55]F. F. Ehrich. Subharmonic vibration of rotors in bearing clearance [J]. ASME, Journal of Engineering for Power,1966,88:56-65.
[56]Botman M. Experiments on oil film dampers for turbomaehinery [J]. ASME, Journal of Engineering for Power,1976:(98):393-400.
[57]Holmes AG, Ettles CM, Mayes IW. A Periodic behavior of a rigid shaft in short journal bearings [J]. Int J Numer Method Eng.1978, (12):695-702.
[58]Sykes JEH, Holmes R, The effeet of bearing misalignment on the non-linear vibration of aero-engine rotor-damper assemblies [C]. Proceedings of the Institution of Mechanical Engineers,1990,204(G2):83-99.
[59]Castelli, V., and Elrod, H. G. Solution of the Stability Problem for 360 Degree Self-Acting Gas-Lubricated Bearing [J]. ASME, Journal of Basic Engineering,1961,87:199-212.
[60]EIrod. HG, Mccabe. JT, Chu. TY. Determination of gas-bearing stability by response to a step-jump [J]. ASME, Journal of Lubrication Technology.1967,89 (4):493-498.
[61]M. Malik, C.W. Bert. Differential Quadrature Solutions for Steady-State Incompressible and Compressible lubrication problems [J]. Tribology.1994,116(4):296-302.
[62]K. Czolczyfiski. How to obtain stiffness and damping coefficients of gas bearings [J]. Wear, 1996,201:265-275
[63]P. Sundararajan, S. T. Noah. Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems [J]. ASME, Journal of Vibration and Acoustics,1997,119 (1):9-20.
[64]G. Belforte et al. Theoretical Investigation of Fluid Inertia Effects and Stability of Self-Acting Gas Journal Bearings. ASME, Journal of Tribology 1999,121(10):836-843.
[65]李东升,沈海峰,李群霞.气体静压主轴旋转振动分析[J].润滑与密封,2002,(5)：7-9.
[66]侯予,王瑾,陈纯正.径向小孔静压气体轴承的试验研究[J].润滑与密封.2002,(2)：15-17.
[67]边新孝,李谋渭.静压气体轴承的动刚度和阻尼分析[J].轴承.2004,(12)：1-3.
[68]Kousuke Hikichi et al. Analytical and Experimental Study of Hydroinertia Gas Bearings for Micromachine Gas Turbines[C]. ASME Turbo Expo 2005:Power for Land, Sea, and Air, Reno, Nevada, USA,2005:747-755.
[69]Shuji Tanaka et al. Hydroinertia Gas Bearing System to Achieve 470 m/s Tip Speed of10 mm-Diameter Impellers [J]. ASME, Journal of Tribology,2007,129(7):655-659
[70]Xuehua Zhu, Luis San Andres. Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery [J]. ASME Turbo Expo 2004:Land, Sea and Air, Vienna, Austria,2004:535-561.
[71]Luis San Andres, Dara Childs. Angled Injection—Hydrostatic Bearings Analysis and Comparison to Test Results [J]. Journal of Tribology.1997.119 (1):179-187.
[72]Luis San Andres. Hybrid Flexure Pivot-Tilting Pad Gas Bearings:Analysis and Experimental Validation [J]. Journal of Tribology,2006.128 (7):551-558.
[73]Deborah A. Osborne, Luis San Andres. Experimental Response of Simple Gas Hybrid Bearings for Oil-Free Turbomachinery. ASME, Journal of Engineering for Gas Turbines and Power,2006.128 (7):627-633.
[74]C.-C. Wang, Application of a hybrid method to the nonlinear dynamic analysis of a flexible rotor supported by a spherical gas-lubricated bearing system [J]. Nonlinear Analysis,2008, 108(2):1-19.
[75]Jiun-Shen Wang, Cheng-Chi Wang. Nonlinear dynamic and bifurcation analysis of short aerodynamic journal bearings [J].Tribology,2005,38:740-748.
[76]C.-C. Wang. Nonlinear dynamic behavior and bifurcation analysis of a rigid rotor supported by a relatively short externally pressurized porous gas journal bearing system[J]. Acta Mechanica,2006,183:41-60.
[77]Cheng-Chi Wang, Cheng-Ying Lo, Cha'o-Kuang Chen. Nonlinear Dynamic Analysis of a Flexible Rotor Supported by Externally Pressurized Porous Gas Journal Bearings[J]. ASME, Journal of Tribology,2002,124(7):553-561.
[78]C.-C. Wang. Nonlinear dynamic behavior and bifurcation analysis of a rigid rotor supported by a relatively short externally pressurized porous gas journal bearing system[J]. Acta Mechanica,2006,183:41-60.
[79]Alan H. Epstein. Millimeter-Scale, Mems Gas Turbine Engines[C]. ASME Turbo Expo 2003: Power for Land, Sea, and Air, Atlanta, Georgia, USA,2003:1-27.
[80]L.X.Liu, C.J.Teo, A.H.Epstein et al. Hydrostatic gas journal bearings for micro-turbomachinery [J]. ASME, Journal of Vibration and Acoustics,2005,127:157-164.
[81]F.F.Ehrich, S.A.Jacobson. Development of high-speed gas bearings for high-power density microdevices [J]. ASME, Journal of Engineering for Gas Turbines and Power,2003,125(1): 141-149.
[82]C. J. Teo, Z. S. Spakovszky. Modeling and Experimental Investigation of Micro-hydrostatic Gas Thrust Bearings for Micro-turbomachines [J]. ASME, Journal of Turbomachinery,2006, 128(10):597-605.
[83]D.Kim, S.Lee, M.D.Bryant, F.F.Ling. Hydrodynamic performance of gas microbearings [J]. ASME, Journal of Tribology,2004,126:711-718.
[84]E.S.Piekos, K.S.Breuer. Pseudospectral orbit simulation of nonideal gas-lubricated journal bearings for microfabricated turbomachines [J]. ASME, Journal of Tribology,1999,121 (3): 604-609.
[85]N.Savoulides,N.S.Breuer,S.Jacobson.Low-Order Models for Very Short Hybrid Gas Bearings[J]. ASME, Journal of Tribology,2001,123:368-375.
[86]Cheng-Chi Wang Cha'o-Ku'ang Chen. Bifurcation Analysis of Self-Acting Gas Journal Bearings[J]. ASME, Journal of Tribology,2001,123(10):755-767.
[87]陈策,杨金福,聂超群.动静压混合气体润滑轴承动态稳定性实验研究[J].润滑与密封.2007,32(12)：30-35
[88]陈策.轴承-转子系统非线性动力学行为及其耦合调频技术研究[D].中国科学院工程热物理研究所,2008.
[89]Tondl, A., Bearings with a Tangential Gas Supply. Gas Bearing Symposium, University of Southampton,1967.
[90]熊联友,侯予,吴刚等.轴向缝切向进气径向气体轴承的稳定性研究[J].润滑与密封,1998,(1)：29-33
[91]刘立强,熊联友,侯予等.透平膨胀机新型切向小孔气体轴承稳定性的实验研究[J].低温工程.1999,110(4)：224-227
[92]熊联友,侯予,王瑾等.轴向缝切向进气轴颈轴承稳定性的实验研究[J].润滑与密封,2000,(1)：31-32、68.
[93]侯予,熊联友,王秉琛等.橡胶圈加稳切向小孔供气径向轴承的试验研究[J].润滑与密封,2004,165(5)：39-40、43.
[94]Lund J.W. The stability of an elastic rotor in journal beatings with flexible, damped supports [J]. ASME. Journal of Applied Mechanics,1965,87 (4):911-920.
[95]J. Kerr, The Onset and cessation of half-speed whirl in air-lubricated self-pressurized journal bearings[C]. NEL Report No.273.Glasgow,1966:145-153.
[96]Powell J.W, Tempest M.C. A study of high speed machines with rubber stabilized airbearings [J]. ASME, Journal of Lubrication Technology,1968,90(4):701-708.
[97]Kazimierski, Z, arzecki, K. Stability threshold of flexibly supported hybrid gesjoum al bearing[J]. ASME, Journal of Lubrication Technology,1979, F101:451-457.
[98]侯予,王秉琛,熊联友等.提高小孔供气静压气体径向轴承稳定性方法的探讨[J].润滑与密封.2004,(2)：17-19
[99]陈雪梅,陈世钰.双气膜高速气体静压主轴系统的稳定性研究[J].机电工程技术,1991,(3)：11-15.
[100]Krzysztof Czolczyrlski, Tomasz Kapitaniak, Krzysztof Marynowski. Stability of rotors supported in gas bearings with bushes mounted in air Rings [J]. wear 199 (1996):100-112
[101]K. Czolczynski. Stability of the rotor supported in gas journal bearings with a chamber feeding system [J]. Wear,1997,210:220-236.
[102]L.X.Liu, Z.S.Spakovszky. Effects of Bearing Stiffness Anisotropy on Hydrostatic Micro Gas Journal Bearing Dynamic Behavior [J]. ASME, Journal of Engineering for Gas Turbines and Power,2007,129(1):177-184
[103]Gunter E, Trumper P. The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports [J]. ASME, Journal of Engineering for Industry,1969,91: 1105-1113
[104]Jung-Koo Park, Kyung-Woong Kim. Stability analyses and experiments of spindle system using new type of slot-restricted gas journal bearings [J]. Tribology International,2004,37: 451-462.
[105]H.Sixsmith. Bearings For Rotating Shafts Which Are Lubricated By Gas[P]. USA, Utility Patent Grant,02884282,1959.
[106]龙威,李军,包钢LUENT软件在空气轴承研究领域的应用[J].机床与液压,2006,(16)：151-153.
[107]侯予,赵祥雄,陈双涛等.小孔节流静压止推气体轴承静特性的数值分析[J].润滑与密封,2008,33(9)：2-3,12.
[108]孙昂.高压重载平面止推气体轴承的流场特性研究[D].大连：大连海事大学,2010.
[109]汪礼.常用湍流模型适用性分析及翼型VOF数值模拟[D].武汉,华中科技大学,2007.
[110]V.Viktorov, GBelforte, T.Raparelli. Modeling and Identification of Gas Journal Bearings: Externally Pressurized Gas Bearing Results [J]. ASME, Journal of Tribology,2005,127(7): 548-556.
[111]Jyh-Chyang Renn, Chih-Hung Hsiao. Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings [J]. Tribology International.2004,37:309-315.
[112]蔡大用.数值代数[M].北京：清华大学出版社,1987.
[113]钟英杰,都晋燕,张雪梅.CFD技术及在现代工业中的应用[J].浙江工业大学学报,2003,(3)：284-289.
[114]孟昭智.真空技术手册[M].哈尔滨：黑龙江科技科学出版社,1988.
[115]张恩龙.高速全支撑气体静压电主轴的承载特性研究[D].广州,广东工业大学.2005.
[116]Jeffery M J. Three dimension CFD rotor dynamic analysis of gas labyrinth seals [J].ASME, Journal of Vibration and Acoustics,2003,125:427-826.
[117]Toshio H, Guo Znglin, Gordon K R. Application of fluid dynamics analysis for rotating machinery-part Ⅱ:labyrinth seal analysis[J]. ASME, Journal of Engineering for Gas Turbine and Power,2005,127:820-826.
[118]李雪松,黄典贵.迷宫气封三维非定常流场及转子动特性数值仿真[J].机械工程学报,2003,39(4)：136-140.
[119]刘晓峰,陆颂元.迷宫密封转子动特性三维CFD数值的研究[J].热能动力工程,2006,21(6)：635-639.
[120]李强,刘淑莲,郑水英等.迷宫密封非线性动力特性的数值计算方法[J].浙江大学学报(工学版)：2009,43(3)：500-504.
[121]江帆,黄鹏Fluent高级应用与实例分析[M].北京：清华大学出版社,2008.
[122]张直明,张言养,谢友柏等.滑动轴承的流体动力润滑理论[M].北京：高等教育出版社,1986.
[123]Ding-Wen Yang, Cheng-Hsien Chen, Yuan Kang et al. Influence of orifices on stability of rotor-aerostatic bearing system [J]. Tribology International,2009,42:1206-1219.
[124]孙雅洲,卢泽生,饶河清.基于FLUENT软件的多孔质静压轴承静态特性的仿真与实验研究[J].机床与液压,2007,35(3)：170-172.
[125]王勖成.有限单元法[M].北京：清华大学出版社,2003：162-186
[126]张文.转子动力学基础[M].北京：科学出版社,1990.
[127]吴勃英.数值分析原理[M].北京：科学出版社,2003
[128]裘春航,吕和祥,钟万勰.求解非线性动力学方程的分段直接积分法[J].力学学报.2002,34(3)：36-377
[129]Newmark N M. A Method of Computation for Structural Dynamics[J]. Journal of Engineering Mechanics Division.1959,85(3):67-94
[130]罗敏,刘巨保.用Newmark法求解旋转细长梁的影响因素分析[J].大庆石油学报,2003,27(1)：66-69.
[131]郭泽英,李青宁.基于Newmark法的一种新精细直接积分法[J].陕西理工学院学报,2007,23(2)：65-68.
[132]张强.气体轴承-转子系统动力学特性初步研究[D].南京：南京航空航天大学,2006.
[133]Guido Belforte, Terenziano Raparelli, Vladimir Viktorov et la. An experimental study of high-speed rotor supported by air bearings:test Rig and first experimental results[J]. Tribology International,2006,39:839-845.
[2]刘暾,刘育华,陈世杰.静压气体润滑[M].哈尔滨：哈尔滨工业大学出版社,1990.
[3]王云飞.气体润滑理论与气体轴承设计[M].北京：机械工业出版社,1999.
[4]李树森,刘暾,张鹏顺.小孔节流方式对气体静压轴承工作刚度影响的分析.润滑与密封[J], 2004,(4)：6-7.
[5]侯予,熊联友,吴刚等.国外多孔质静压气体轴颈轴承理论分析的发展[J].润滑与密封,1998,(1)：62～65
[6]杜金名.多孔质流体静压轴承润滑技术的研究[D].哈尔滨：哈尔滨工业大学,2003.
[7]Information on http://www.precitech.com.
[8]Information on http://www.toshiba-machine.co.jp
[9]姚德良,傅仙罗.圆盘和圆环形压膜轴承的气动力分析[J].应用数学和力学,1981,12(8)：711-718.
[10]党根茂.气体润滑技术[M].南京：东南大学出版社,1990.
[11]Gross William A. Gas Film Lubrication [M]. New York:Wiley,1962.
[12]Constantinescu V. N. Gas Lubrication[M]. New York:ASME,1969.
[13]Powell J. W. John William. Design of Aerostatic Bearings[M]. London:Machinery Publishing Co. Ltd,1970.
[14]Yabe. H, Mori. H, Tanahashi. H. Study on Characteristics of Externally Pressurized Gas Thrust Bearings With Surface-Restriction Compensation-Dynamic Bearing Characteristics [J]. BULL.1982,25(207):1451-1456.
[15]S. H. Nguyen. p-Version Finite Element Analysis of Gas Bearings of Finite Width [J]. Journal of Tribology,1991,113(3):417-420.
[16]M. C. Pandian. A new method for the numerical solution of the Reynolds equation for gas-lubrication slider bearings [J]. Journal of Engineering Mathematics.1985,19(3):3-19.
[17]T. Nakamura, S. Yoshimoto. Static Tilt Characteristics of Aerostatic Rectangular Double-Pad Thrust Bearing with Compound Restrictors [J].Tribology International.1996,29(2):145-152.
[18]温诗铸.静压空气轴承性能的试验分析[M].北京：机械工程学报社,1962.
[19]张言羊.静压式空气轴承的一种近似计算方法[J].西安交通大学学报,1964,(2)：35-44.
[20]齐乃明,刘暾,谭久彬.自主式静压气体轴承实现无穷刚度的条件分析[J].南京理工大学学报,2001,25(2)：147-151.
[21]侯予,熊联友,王瑾等.透平膨胀机新型动压径向气体轴承的试验研究[J].低温工程,1999,(4)：231-235.
[22]陈纯正.中压透平膨胀机橡皮加稳空气轴承稳定性[J].西安交通大学学报,1981,15(4)：13-24.
[23]王林中,侯予,陈纯正.可倾瓦径向气体轴承的静动特性的理论研究[J].润滑与密封,2006,(5)：84-87.
[24]陈汝刚,侯予, 陈纯正.微型气浮轴承高速透平膨胀机的研制[J].西安交通大学学报,2010,44(1)：61-65.
[25]侯予,陈双涛,陈汝刚等.弹性支承箔片动压气体径向轴承的实验研究[J].润滑与密封,2010,35(6)：1-4.
[26]刘立强,熊联友,侯予等.低温透平膨胀机切向供气轴承[J].低温与特气,1998,(1)：40-43.
[27]景岗,杨清好.锯齿形多槽式动静压气体润滑轴承稳态和动态特性的研究[J].华中理工大学学报,1994,22(2)：69-73.
[28]王元勋.主动控制节流无穷静刚度气体润滑轴承研究[D].武汉：华中理工大学,1995.
[29]刘暾,葛卫平,齐乃明等.超精气磁轴承混合轴系的研究[J].中国机械工程；2002,(2)：167-170.
[30]赵宁.磁气混合轴承中弹性箔片径向动压气体轴承的数值分析研究[D].南京航空航天大学,2004.3
[31]刘庆国.超精密气磁轴承轴系动力学及控制方法的研究[D].东北林业大学,2004;5
[32]李树森,孟庆鑫,马兰兰.气磁轴承主轴系统误差补偿技术的研究[J].林业机械与木工设备,2005,33(12)：12-14.
[33]张君安.高刚度空气静压轴承研究[D].西安：西安工业大学,2006.
[34]孙昂,马文琦,王祖温.带有锥形气腔的平面气浮轴承的流场计算分析[J].液压与气动.2008,(1)：14-17.
[35]孙昂,马文琦,王祖温.平面静压气浮轴承超音速流场特性的研究.机械工程学报[J],2010,46(9)：113-119.
[36]于贺春,马文琦,王祖温.基于FLUENT的环面节流静压气体圆盘止推轴承二维流场仿真分析[J].机床与液压,2008,36(10)：109-112.
[37]易家明,徐学兰.多空质静压气体轴承材料的研究[J].轴承,1985,(1)：36-37.
[38]罗继伟,王云飞.多空质静压气体轴承静态性能的有限元分析[J].轴承,1985,(2)：8-12.
[39]杜金名,卢泽生,孙雅洲.影响空气静压多孔质轴承静态性能的有关因素[J].中国机械工程,2003,14(5)：417-420.
[40]杜金名,卢泽生,孙雅洲.气体静压小孔节流与多孔质节流性能的比较[J].润滑与密封,2002,(4)：2-5.
[41]卢泽生,于雪梅.基于分形理论多孔质石墨渗透率的研究[J].机床零部件,2006,(7)：30-31.
[42]卢泽生,于雪梅,孙雅洲.局部多孔质气体静压轴向轴承静态特性的数值求解[J].摩擦学报,2007,27(1)：68-72.
[43]于雪梅,孙雅洲,卢泽生.局部多孔质气体静压止推轴承压力分布的研究[J].润滑与密封,2009,34(11)：53-57.
[44]姚英学,崔大朋,秦冬黎.新型狭缝节流球形静压气体陀螺轴承的动态特性[J].宇航学报,2010,31(8)：2050-2057.
[45]姚英学,杜建军,刘暾等.制造误差对气体静压轴承涡流力矩影响分析方法研究[J].宇航学报,2003,24(2)：124-128.
[46]秦冬黎,姚英学.小孔节流动静压混合气体润滑球轴承的干扰力矩分析[J].润滑与密封,2007,32(4)：131-135.
[47]秦冬黎,姚英学.误差对气体静压球轴承静态承载性能的影响分析[J].哈尔滨轴承,2009,27(3)：44-48.
[48]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.
[49]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)：112-116.
[50]周健斌,孟光,陈杰宇等.气体动压径向短轴承动力学和分岔分析[J].机械强度,2010,32(2)：207-211.
[51]H. M. Talukder, T. B. Stowell. Pneumatic hammer in an externally pressurized orifice-compensated air jounal bearing [J]. Tribology International,2003,36:585-591.
[52]Gross, W. A., and Zachmanaglou, E. C. Perturbation Solutions for Gas-Lubricating Films [J]. ASME, Journal of Basic Engineering,1961,83:139-144.
[53]Ausman, J. S. Linearized ph Stability Theory for Translatory Half-Speed Whirl of Long Self-Acting Gas-Lubricated Journal Bearings [J]. ASME, Journal of Basic Engineering,1963, 83:611-619.
[54]Larson. R, Richardson. H. A Preliminary Study of Whirl Instability for Pressurized Gas Bearings[J]. ASME, Journal of Basic Engineering,1962,84:511-520.
[55]F. F. Ehrich. Subharmonic vibration of rotors in bearing clearance [J]. ASME, Journal of Engineering for Power,1966,88:56-65.
[56]Botman M. Experiments on oil film dampers for turbomaehinery [J]. ASME, Journal of Engineering for Power,1976:(98):393-400.
[57]Holmes AG, Ettles CM, Mayes IW. A Periodic behavior of a rigid shaft in short journal bearings [J]. Int J Numer Method Eng.1978, (12):695-702.
[58]Sykes JEH, Holmes R, The effeet of bearing misalignment on the non-linear vibration of aero-engine rotor-damper assemblies [C]. Proceedings of the Institution of Mechanical Engineers,1990,204(G2):83-99.
[59]Castelli, V., and Elrod, H. G. Solution of the Stability Problem for 360 Degree Self-Acting Gas-Lubricated Bearing [J]. ASME, Journal of Basic Engineering,1961,87:199-212.
[60]EIrod. HG, Mccabe. JT, Chu. TY. Determination of gas-bearing stability by response to a step-jump [J]. ASME, Journal of Lubrication Technology.1967,89 (4):493-498.
[61]M. Malik, C.W. Bert. Differential Quadrature Solutions for Steady-State Incompressible and Compressible lubrication problems [J]. Tribology.1994,116(4):296-302.
[62]K. Czolczyfiski. How to obtain stiffness and damping coefficients of gas bearings [J]. Wear, 1996,201:265-275
[63]P. Sundararajan, S. T. Noah. Dynamics of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method—Application to Rotor Systems [J]. ASME, Journal of Vibration and Acoustics,1997,119 (1):9-20.
[64]G. Belforte et al. Theoretical Investigation of Fluid Inertia Effects and Stability of Self-Acting Gas Journal Bearings. ASME, Journal of Tribology 1999,121(10):836-843.
[65]李东升,沈海峰,李群霞.气体静压主轴旋转振动分析[J].润滑与密封,2002,(5)：7-9.
[66]侯予,王瑾,陈纯正.径向小孔静压气体轴承的试验研究[J].润滑与密封.2002,(2)：15-17.
[67]边新孝,李谋渭.静压气体轴承的动刚度和阻尼分析[J].轴承.2004,(12)：1-3.
[68]Kousuke Hikichi et al. Analytical and Experimental Study of Hydroinertia Gas Bearings for Micromachine Gas Turbines[C]. ASME Turbo Expo 2005:Power for Land, Sea, and Air, Reno, Nevada, USA,2005:747-755.
[69]Shuji Tanaka et al. Hydroinertia Gas Bearing System to Achieve 470 m/s Tip Speed of10 mm-Diameter Impellers [J]. ASME, Journal of Tribology,2007,129(7):655-659
[70]Xuehua Zhu, Luis San Andres. Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery [J]. ASME Turbo Expo 2004:Land, Sea and Air, Vienna, Austria,2004:535-561.
[71]Luis San Andres, Dara Childs. Angled Injection—Hydrostatic Bearings Analysis and Comparison to Test Results [J]. Journal of Tribology.1997.119 (1):179-187.
[72]Luis San Andres. Hybrid Flexure Pivot-Tilting Pad Gas Bearings:Analysis and Experimental Validation [J]. Journal of Tribology,2006.128 (7):551-558.
[73]Deborah A. Osborne, Luis San Andres. Experimental Response of Simple Gas Hybrid Bearings for Oil-Free Turbomachinery. ASME, Journal of Engineering for Gas Turbines and Power,2006.128 (7):627-633.
[74]C.-C. Wang, Application of a hybrid method to the nonlinear dynamic analysis of a flexible rotor supported by a spherical gas-lubricated bearing system [J]. Nonlinear Analysis,2008, 108(2):1-19.
[75]Jiun-Shen Wang, Cheng-Chi Wang. Nonlinear dynamic and bifurcation analysis of short aerodynamic journal bearings [J].Tribology,2005,38:740-748.
[76]C.-C. Wang. Nonlinear dynamic behavior and bifurcation analysis of a rigid rotor supported by a relatively short externally pressurized porous gas journal bearing system[J]. Acta Mechanica,2006,183:41-60.
[77]Cheng-Chi Wang, Cheng-Ying Lo, Cha'o-Kuang Chen. Nonlinear Dynamic Analysis of a Flexible Rotor Supported by Externally Pressurized Porous Gas Journal Bearings[J]. ASME, Journal of Tribology,2002,124(7):553-561.
[78]C.-C. Wang. Nonlinear dynamic behavior and bifurcation analysis of a rigid rotor supported by a relatively short externally pressurized porous gas journal bearing system[J]. Acta Mechanica,2006,183:41-60.
[79]Alan H. Epstein. Millimeter-Scale, Mems Gas Turbine Engines[C]. ASME Turbo Expo 2003: Power for Land, Sea, and Air, Atlanta, Georgia, USA,2003:1-27.
[80]L.X.Liu, C.J.Teo, A.H.Epstein et al. Hydrostatic gas journal bearings for micro-turbomachinery [J]. ASME, Journal of Vibration and Acoustics,2005,127:157-164.
[81]F.F.Ehrich, S.A.Jacobson. Development of high-speed gas bearings for high-power density microdevices [J]. ASME, Journal of Engineering for Gas Turbines and Power,2003,125(1): 141-149.
[82]C. J. Teo, Z. S. Spakovszky. Modeling and Experimental Investigation of Micro-hydrostatic Gas Thrust Bearings for Micro-turbomachines [J]. ASME, Journal of Turbomachinery,2006, 128(10):597-605.
[83]D.Kim, S.Lee, M.D.Bryant, F.F.Ling. Hydrodynamic performance of gas microbearings [J]. ASME, Journal of Tribology,2004,126:711-718.
[84]E.S.Piekos, K.S.Breuer. Pseudospectral orbit simulation of nonideal gas-lubricated journal bearings for microfabricated turbomachines [J]. ASME, Journal of Tribology,1999,121 (3): 604-609.
[85]N.Savoulides,N.S.Breuer,S.Jacobson.Low-Order Models for Very Short Hybrid Gas Bearings[J]. ASME, Journal of Tribology,2001,123:368-375.
[86]Cheng-Chi Wang Cha'o-Ku'ang Chen. Bifurcation Analysis of Self-Acting Gas Journal Bearings[J]. ASME, Journal of Tribology,2001,123(10):755-767.
[87]陈策,杨金福,聂超群.动静压混合气体润滑轴承动态稳定性实验研究[J].润滑与密封.2007,32(12)：30-35
[88]陈策.轴承-转子系统非线性动力学行为及其耦合调频技术研究[D].中国科学院工程热物理研究所,2008.
[89]Tondl, A., Bearings with a Tangential Gas Supply. Gas Bearing Symposium, University of Southampton,1967.
[90]熊联友,侯予,吴刚等.轴向缝切向进气径向气体轴承的稳定性研究[J].润滑与密封,1998,(1)：29-33
[91]刘立强,熊联友,侯予等.透平膨胀机新型切向小孔气体轴承稳定性的实验研究[J].低温工程.1999,110(4)：224-227
[92]熊联友,侯予,王瑾等.轴向缝切向进气轴颈轴承稳定性的实验研究[J].润滑与密封,2000,(1)：31-32、68.
[93]侯予,熊联友,王秉琛等.橡胶圈加稳切向小孔供气径向轴承的试验研究[J].润滑与密封,2004,165(5)：39-40、43.
[94]Lund J.W. The stability of an elastic rotor in journal beatings with flexible, damped supports [J]. ASME. Journal of Applied Mechanics,1965,87 (4):911-920.
[95]J. Kerr, The Onset and cessation of half-speed whirl in air-lubricated self-pressurized journal bearings[C]. NEL Report No.273.Glasgow,1966:145-153.
[96]Powell J.W, Tempest M.C. A study of high speed machines with rubber stabilized airbearings [J]. ASME, Journal of Lubrication Technology,1968,90(4):701-708.
[97]Kazimierski, Z, arzecki, K. Stability threshold of flexibly supported hybrid gesjoum al bearing[J]. ASME, Journal of Lubrication Technology,1979, F101:451-457.
[98]侯予,王秉琛,熊联友等.提高小孔供气静压气体径向轴承稳定性方法的探讨[J].润滑与密封.2004,(2)：17-19
[99]陈雪梅,陈世钰.双气膜高速气体静压主轴系统的稳定性研究[J].机电工程技术,1991,(3)：11-15.
[100]Krzysztof Czolczyrlski, Tomasz Kapitaniak, Krzysztof Marynowski. Stability of rotors supported in gas bearings with bushes mounted in air Rings [J]. wear 199 (1996):100-112
[101]K. Czolczynski. Stability of the rotor supported in gas journal bearings with a chamber feeding system [J]. Wear,1997,210:220-236.
[102]L.X.Liu, Z.S.Spakovszky. Effects of Bearing Stiffness Anisotropy on Hydrostatic Micro Gas Journal Bearing Dynamic Behavior [J]. ASME, Journal of Engineering for Gas Turbines and Power,2007,129(1):177-184
[103]Gunter E, Trumper P. The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports [J]. ASME, Journal of Engineering for Industry,1969,91: 1105-1113
[104]Jung-Koo Park, Kyung-Woong Kim. Stability analyses and experiments of spindle system using new type of slot-restricted gas journal bearings [J]. Tribology International,2004,37: 451-462.
[105]H.Sixsmith. Bearings For Rotating Shafts Which Are Lubricated By Gas[P]. USA, Utility Patent Grant,02884282,1959.
[106]龙威,李军,包钢LUENT软件在空气轴承研究领域的应用[J].机床与液压,2006,(16)：151-153.
[107]侯予,赵祥雄,陈双涛等.小孔节流静压止推气体轴承静特性的数值分析[J].润滑与密封,2008,33(9)：2-3,12.
[108]孙昂.高压重载平面止推气体轴承的流场特性研究[D].大连：大连海事大学,2010.
[109]汪礼.常用湍流模型适用性分析及翼型VOF数值模拟[D].武汉,华中科技大学,2007.
[110]V.Viktorov, GBelforte, T.Raparelli. Modeling and Identification of Gas Journal Bearings: Externally Pressurized Gas Bearing Results [J]. ASME, Journal of Tribology,2005,127(7): 548-556.
[111]Jyh-Chyang Renn, Chih-Hung Hsiao. Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings [J]. Tribology International.2004,37:309-315.
[112]蔡大用.数值代数[M].北京：清华大学出版社,1987.
[113]钟英杰,都晋燕,张雪梅.CFD技术及在现代工业中的应用[J].浙江工业大学学报,2003,(3)：284-289.
[114]孟昭智.真空技术手册[M].哈尔滨：黑龙江科技科学出版社,1988.
[115]张恩龙.高速全支撑气体静压电主轴的承载特性研究[D].广州,广东工业大学.2005.
[116]Jeffery M J. Three dimension CFD rotor dynamic analysis of gas labyrinth seals [J].ASME, Journal of Vibration and Acoustics,2003,125:427-826.
[117]Toshio H, Guo Znglin, Gordon K R. Application of fluid dynamics analysis for rotating machinery-part Ⅱ:labyrinth seal analysis[J]. ASME, Journal of Engineering for Gas Turbine and Power,2005,127:820-826.
[118]李雪松,黄典贵.迷宫气封三维非定常流场及转子动特性数值仿真[J].机械工程学报,2003,39(4)：136-140.
[119]刘晓峰,陆颂元.迷宫密封转子动特性三维CFD数值的研究[J].热能动力工程,2006,21(6)：635-639.
[120]李强,刘淑莲,郑水英等.迷宫密封非线性动力特性的数值计算方法[J].浙江大学学报(工学版)：2009,43(3)：500-504.
[121]江帆,黄鹏Fluent高级应用与实例分析[M].北京：清华大学出版社,2008.
[122]张直明,张言养,谢友柏等.滑动轴承的流体动力润滑理论[M].北京：高等教育出版社,1986.
[123]Ding-Wen Yang, Cheng-Hsien Chen, Yuan Kang et al. Influence of orifices on stability of rotor-aerostatic bearing system [J]. Tribology International,2009,42:1206-1219.
[124]孙雅洲,卢泽生,饶河清.基于FLUENT软件的多孔质静压轴承静态特性的仿真与实验研究[J].机床与液压,2007,35(3)：170-172.
[125]王勖成.有限单元法[M].北京：清华大学出版社,2003：162-186
[126]张文.转子动力学基础[M].北京：科学出版社,1990.
[127]吴勃英.数值分析原理[M].北京：科学出版社,2003
[128]裘春航,吕和祥,钟万勰.求解非线性动力学方程的分段直接积分法[J].力学学报.2002,34(3)：36-377
[129]Newmark N M. A Method of Computation for Structural Dynamics[J]. Journal of Engineering Mechanics Division.1959,85(3):67-94
[130]罗敏,刘巨保.用Newmark法求解旋转细长梁的影响因素分析[J].大庆石油学报,2003,27(1)：66-69.
[131]郭泽英,李青宁.基于Newmark法的一种新精细直接积分法[J].陕西理工学院学报,2007,23(2)：65-68.
[132]张强.气体轴承-转子系统动力学特性初步研究[D].南京：南京航空航天大学,2006.
[133]Guido Belforte, Terenziano Raparelli, Vladimir Viktorov et la. An experimental study of high-speed rotor supported by air bearings:test Rig and first experimental results[J]. Tribology International,2006,39:839-845.