带内环槽的螺旋槽干式气体端面密封的性能研究
|
摘要
在石油和石化行业中,干式气体端面密封(DGS)在高速旋转机械(如离心压缩机)上应用日趋广泛,并正逐渐扩展到泵及反应釜等中低速回转设备上。但是由于DGS在启动时不易开启,低速低压下难以建立稳定的气膜,同时也缺少完善的中低速设计理论和方法,因此制约了DGS的推广应用。所以,研究并完善中低速条件下DGS的设计理论,改善DGS在低速低压条件下和启动时的工作性能,具有重要意义。
首先,针对光滑面螺旋槽干式气体端面密封(S-DGS)建立了端面气膜压力控制方程组,采用有限单元法进行求解,计算了密封性能参数,并与相关文献进行了比较,验证了有限元程序的可靠性。在此基础上,研究比较了收敛型槽深S-DGS与普通等槽深S-DGS的密封性能,结果表明,在低速低压条件下,收敛型槽深S-DGS的密封性能没有明显优势。其次,建立了带内环槽S-DGS端面气膜压力控制方程,并采用有限单元法求解,研究了低速低压条件下密封性能随端面微槽几何参数变化的规律,以获得较大气膜刚度或开启力以及较小泄漏量为几何结构优化原则,对微槽几何参数进行了优化。最后,基于流体润滑理论,考虑端面气膜滑移流,建立并采用有限单元法求解了带内环槽S-DGS的端面膜压控制方程,系统研究了低速低压条件下滑移流对该种密封性能的影响。结果表明,当0.05≤Kn＜1时,滑移流对密封性能产生明显影响。在此基础上,以获得较大气膜刚度和较小泄漏量为端面几何参数优化准则,对考虑滑移流条件下带内环槽S-DGS密封端面几何结构参数进行了优化。研究结果为改善S-DGS的开启特性,提高S-DGS的低速低压工作能力,以及带内环槽S-DGS的实际设计与应用提供了较全面的理论依据。
Dry gas face seals (DGSs) have been successfully applied to rotating equipments with high speed such as compressors and gradually under slow speed conditions. But it's difficult to form a stable gas film between the two faces when starting up and at slow speeds and low pressures, which restricts the application widely. Therefore it's very important to perfect the basic theories of design and to improve start-up performances of DGSs at low and moderate speeds.
Firstly, the finit element method (FEM) was used to solve the governing equations for compressible gases for a spiral-groove dry gas seal (S-DGS) with smooth surfaces. Comparisons of the sealing performances with a typical S-DGS proved the validity of the calculation. It is also found that a S-DGS with some converged groove depth has no advantages over the typical S-DGS under slow speed and low pressure conditions. Secondly, a mathematic model was built to analyze the sealing performances for a S-DGS with an inner annular groove connected to the spiral groove on the face and the micro-groove structure parameters were optimized based on the rule of getting larger film stiffness or opening force while maintaining lower leakage. Lastly, based on theory of lubrication, a model for gas film pressure considering slip flow was developed and the effects of slip flow on sealing performances were systematically studied at slow speeds and low pressures. It is suggested that when Knudsen number is larger than or equals 0.05 and less than 1.0, the effects of the slip flow on sealing performances are significant. Based on the same optimization rule, the principle for optimized face geometry parameters of such a DGS was presented, which provides theory guidance for improving start-up performances at slow speeds and low pressures and practical application and design.
首先,针对光滑面螺旋槽干式气体端面密封(S-DGS)建立了端面气膜压力控制方程组,采用有限单元法进行求解,计算了密封性能参数,并与相关文献进行了比较,验证了有限元程序的可靠性。在此基础上,研究比较了收敛型槽深S-DGS与普通等槽深S-DGS的密封性能,结果表明,在低速低压条件下,收敛型槽深S-DGS的密封性能没有明显优势。其次,建立了带内环槽S-DGS端面气膜压力控制方程,并采用有限单元法求解,研究了低速低压条件下密封性能随端面微槽几何参数变化的规律,以获得较大气膜刚度或开启力以及较小泄漏量为几何结构优化原则,对微槽几何参数进行了优化。最后,基于流体润滑理论,考虑端面气膜滑移流,建立并采用有限单元法求解了带内环槽S-DGS的端面膜压控制方程,系统研究了低速低压条件下滑移流对该种密封性能的影响。结果表明,当0.05≤Kn＜1时,滑移流对密封性能产生明显影响。在此基础上,以获得较大气膜刚度和较小泄漏量为端面几何参数优化准则,对考虑滑移流条件下带内环槽S-DGS密封端面几何结构参数进行了优化。研究结果为改善S-DGS的开启特性,提高S-DGS的低速低压工作能力,以及带内环槽S-DGS的实际设计与应用提供了较全面的理论依据。
Dry gas face seals (DGSs) have been successfully applied to rotating equipments with high speed such as compressors and gradually under slow speed conditions. But it's difficult to form a stable gas film between the two faces when starting up and at slow speeds and low pressures, which restricts the application widely. Therefore it's very important to perfect the basic theories of design and to improve start-up performances of DGSs at low and moderate speeds.
Firstly, the finit element method (FEM) was used to solve the governing equations for compressible gases for a spiral-groove dry gas seal (S-DGS) with smooth surfaces. Comparisons of the sealing performances with a typical S-DGS proved the validity of the calculation. It is also found that a S-DGS with some converged groove depth has no advantages over the typical S-DGS under slow speed and low pressure conditions. Secondly, a mathematic model was built to analyze the sealing performances for a S-DGS with an inner annular groove connected to the spiral groove on the face and the micro-groove structure parameters were optimized based on the rule of getting larger film stiffness or opening force while maintaining lower leakage. Lastly, based on theory of lubrication, a model for gas film pressure considering slip flow was developed and the effects of slip flow on sealing performances were systematically studied at slow speeds and low pressures. It is suggested that when Knudsen number is larger than or equals 0.05 and less than 1.0, the effects of the slip flow on sealing performances are significant. Based on the same optimization rule, the principle for optimized face geometry parameters of such a DGS was presented, which provides theory guidance for improving start-up performances at slow speeds and low pressures and practical application and design.
引文
[1]Whipple R T E Herringbone-pattern thrust bearings[J].T/M29,Harwell,Berkshire,England:Atomic Energy Research Establishment,1951.
[2]Mclanoski S B,Pan C H T.The static and dynamic characteristic of the spiral-grooved thrust bearing[J].ASME J.Basic Eng,1965,87:547-558.
[3]Muijderman E A.Spiral groove bearings[J].Philips Technical Library,Springer-Verlag,New-York,1966.
[4]Constantinescu V N,Galetuse S.On extending the narrow spiral-groove theory to configurations of interest in seals[J].Trans.of ASME,Journal of Tribology,1992,114(3):563-566.
[5]Gardner J F.Combined hydrostatic and hydrodynamic principles applied to non-contacting face seals[A].Proc.of 4~(th) Inter.Conf.on Fluid Sealing[C].1970,350-360.
[6]Gabriel R P.Fundamentals of spiral groove noncontacting face seals[J].Lubr.Eng.,1979,35(7):367-375.
[7]Shapiro W,Walowit J,Jones H F.Analysis of spiral-groove face seals for liquid oxygen[J].ASLE Trans.,1984,27(3):177-188.
[8]Tadashi Sawada.具有净轴向流量的稀薄气体粘性密封的性能[A].四川密封技术研究所等编译.第十届国际流体密封会议论文集[C].重庆:科学技术文献出版社重庆分社,1987,275-285.
[9]Chang-Ho Kim.Analysis for rotordynamic coefficients of helically-grooved turbulent annular seals[J],Trans.of ASME,J.of Tribology,1987,109(1):136-143.
[10]Yuchi Sato.Performance characteristics of shrouded rayleigh-step and spiral groove viscous pumps[J],Trans.of ASME,J.of Tribology,1992,114(4):499-506.
[11]James D D,Potter A F.Numerical analysis of the gas-lubricated spiral-groove thrust bearing-compressor [J].ASME J.of Lubr.Tech.,1967,89(4):439-444.
[12]Zuk J,Renkel H E.Numerical Solutions for the flow and pressure fields in an idealized spiral grooved pumping seal[A].Proc.of 4~(th) Inter.Conf.on Fluid Sealing[C],1970,290-301.
[13]Smalley A J.The narrow groove theory of spiral groove gas bearings:development and application of a generalized formulation for numerical solution[J].ASME J.of Lubr.Tech.,1972,94(1):86-92.
[14]Murata S,Miyake Y,Kawabata N.Exact two-dimensional analysis of circular disk spiral groove bearing(Part Ⅰ)[J].ASME J.of Lubr.Tech.,1979,101(4):424-430.
[15]Murata S,Miyake Y,Kawabata N.Exact two-dimensional analysis of circular disk spiral groove beating(Part Ⅱ)[J].ASME J.of Lubr.Tech.,1979,101(4):431-436.
[16]Walowit J A,Pinkus O.Analysis of face seals with shrouded pockets[J].ASME J.of Lubr.Tech.,1982,104(2):262-270.
[17]Ikeuchi K,Mori H,Nishida T.A face seal with circumferential pumping grooves and rayleigh-steps[J].ASME J.of Tribology,1988,110(2):313-319.
[18]Lipschitz A,Basu P,Johnson R P.A bi-directional gas thrust bearing[J].Tribology Trans.,1991,34(1):9-16.
[19]Kowalski C A,Basu P.Reverse rotation capability of spiral-groove gas face seals[J].Tribology Trans.,1995,38(3):549-556.
[20]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社,1988.
[21]Reddi M M,Chu T Y.Finite element solution of the steady-state compressible lubrication problem[J].ASME J.of Lubr.Tech.,1970,92(3):495-503.
[22]Basu P.Analysis of a radial groove gas face seal[J].Tribology Trans.,1992,35(1):11-20.
[23]Satomi T,Lin G.Design optimization of spirally grooved thrust air bearings for polygon mirror laser scanners[J].JSME Inter.,Series C,1993,36(3):348-354.
[24]Bonneau D,Huitric J,Tournerie B.Finite element analysis of grooved gas thrust bearings and grooved gas face seals[J].ASME J.of Tribology,1993,115(7):348-354.
[25]Henandez P,Boudet R.Modeling of the behavior of dynamical Gas seals:calculation with a finite element method implicitly assuring the continuity of flow[J].Proc.Inst.Mech.Eng.,Part J:J.of Eng.Tribology,1995,209(3):195-201.
[26]Zirkelback N L,Andres L S.Effect of frequency excitation on force coefficient of spiral groove gas seals[J].ASME J.of Tribology,1999,121(4):853-863.
[27]蔡文新,朱报桢.螺旋槽气体密封的研究[J].流体机械,1994,22(9):2-7.
[28]彭建,左孝桐,顾永泉.螺旋槽干气密封的优化设计[J].流体机械,1995,23(3):24-27.
[29]彭建,左孝桐,王福.不同槽型气体端面密封研究[J].流体机械,1996,24(11):8-12.
[30]胡丹梅,吴宗祥.直线槽端面气体密封的分析计算[J].流体机械,1996,24(9):16-22.
[31]杨梦辰,张瑞乾,李翔,等.平面螺旋槽气体止推轴承的研究[J].机械设计,1998,15(2):9-11.
[32]党建军,秋卫平,钱志博.有限元法在机械密封设计中的应用研究[J].航空计算技术,2000,30(1):6-8.
[33]刘雨川,徐万孚,陈国林,等.端面气膜密封的高性能端面结构[J].航空学报,2000,21(2):187-190.
[34]刘雨川,徐万孚,王之栎,等.气膜端面密封角向摆动自振稳定性[J].机械工程学报,2002,38(4): 1-6.
[35]林培峰,张秋翔,蔡纪宁,等.螺旋槽干气密封的有限元分析[J].北京化工大学学报,2002,29(3):57-63.
[36]李涛子,张秋翔,蔡纪宁,等.T型槽干气密封稳态特性的有限元分析[J].北京化工大学学报,2003,30(2):58-62.
[37]冯向忠.泵用干式气体端面密封的理论研究[D].东营:中国石油大学(华东),2004.
[38]蒋小文,顾伯勤.螺旋槽干气密封端面间气膜特性[J].化工学报,2005,56(8):1419-1425.
[39]尹晓妮,彭旭东.干式气体端面密封性能的有限元分析中形函数的选择[J].润滑与密封,2006,31(3):13-18.
[40]陈小宁,郝木明.螺旋槽气体润滑机械密封温度场有限元分析[J].机械设计与制造,2007,(5):16-18.
[41]冯向忠,彭旭东.螺旋槽干式气体端面密封性能的数值分析[J].润滑与封,2004,29(6):41-43.
[42]彭旭东,冯向忠,胡丹梅,等.非接触式气体润滑密封变形的数值分析[J].摩擦学学报,2004,24(6):536-539.
[43]汤臣杭,杨惠霞,王玉明.单向双列螺旋槽干气密封流场数值模拟[J].润滑与密封,2007,32(1):145-148.
[44]Gabriel R P.Fundamentals of spiral groove noncontacting face seals[J].Lubrication Engineering,1994,50(3):215-224.
[45]Shellef R A,Johnson R P.Abi-directional gas face seal[J].Tribology Transactions,1992,35(1):53-58.
[46]Salant R F.Homiller S J.The effects of shallow groove patterns on mechanical seal leakage[J].Tribology Transactions,1992,35(1):142-148.
[47]Zirkelback N.Parametric study of spiral groove gas face seals[J].Tribology Transactions,2000,43(2):337-343.
[48]胡丹梅,郝木明,杨惠霞.非接触式气体端面密封低速性能试验研究[J].流体机械,1998,26(9):3-6.
[49]赵惠清,蔡嵘,国巨发.深槽浅槽机械密封的对比分析[J].北京化工大学学报,1999,26(2):37-39.
[50]冯向忠,彭旭东.螺旋槽干式气体端面密封的刚度和泄漏量研究[J].石油大学学报(自然科学版),2005,29(2):83-92.
[51]丁雪兴,程香平,张伟政,等.螺旋槽干气密封槽形参数的协调优化[J].力学与实践,2007,29(3):26-30.
[52]Sedy J.Face Seal with Angled and Annular Groove[P].世界专利:WO 95/06832.1995-03-09.
[53]Kulkarni S B.Double Gas Barrier Seal[P].世界专利:WO 95/21343.1995-08-10.
[54]王玉明.双环带螺旋槽端面密封[P].中国专利:96108614.9.1996-06-22.
[55]王玉明.可双向旋转的双列双叶螺旋槽端面密封[P].中国专利:98103575.2.1999-02-03.
[56]王玉明.螺旋槽端面密封[P].中国专利:98120372.1999-04-28.
[57]Burgdorfer A.The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated beatings[J].ASME J of Basic Eng.,1959,81(2):94-100.
[58]Hsia Y T,Domoto G A.An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances[J].J.of Lubr.Tech.1983,105(1):120-130.
[59]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].J.of Tribology,1988,110(2):253-261.
[60]Mitsuya Y.Modified reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient[J].ASME J.of Tribology,1993,115(2):289-294.
[61]Chi-Chuan Hwang,Rong-Fong Fung,Rong-Fu Yang etal.A new modified reynolds equation for ultrathin film gas lubrication[J].IEEE Trans.on Magnet.,1996,32(2):344-347.
[62]Pecht G G,Netzel J P.Design and application of non-contacting gas lubricated seals for slow speed services[J].Lubr.Eng.,1999,55(7):20-25.
[63]Ching-Shung Chen.Gas flow in micro-channels using a boundary-layer approach[J].Inter.J.of Computer applications in Tech.,2000,13(6):316-323.
[64]Ruan B.Finite element analysis of the spiral groove gas face at the slow speed and the low pressure condition-slip flow consideration[J].Tribology Trans.,2000,43(3):411-418.
[65]赵汉中.微细圆管中气体流动的稀薄效应和可压缩效应[J].华中科技大学学报,2001,29(10):96-98.
[66]赵越,宋鹏云,李伟,等.螺旋槽气体润滑机械密封低速运转特性-理论研究[J].润滑与密封,2005,30(5):70-73.
[67]许鹏先,潘琦,申改章.基于滑移边界的干气密封的数值模拟[J].润滑与密封,2007,32(5):98-101.
[68]尹晓妮,彭旭东.考虑滑移流条件下干式气体端面密封的有限元分析[J].润滑与密封,2006,31(4):55-59.
[69]顾永泉.机械端面密封[M],第一版.东营:石油大学出版社,1994.
[70]Harp S R,Salant R E.Analysis of mechanical seal behavior during transient operation[A].Proc.Of the 1997 Joint ASME/STLE/IMechE World Tribology Conf.[C].London,UK,Sept.8-12,1997.
[71]章本照.流体力学中的有限元方法[M].北京:机械工业出版社,1986.
[72]李开泰,黄艾香,黄庆怀.有限元方法及其应用(Ⅰ)[M].西安:西安交通大学出版社,1984.
[73]何光渝.FORTRAN 77算法手册[M].北京:科学出版社,1993.
[74]刘雨川.端面气膜密封特性研究[D].北京:北京航空航天大学,1999.
[75]Shen C,Jiang J Z.Finite length microchannel flow in transitional regine[J].Acta Aerodynamica Sinica,2008,26(2):257-262.
[2]Mclanoski S B,Pan C H T.The static and dynamic characteristic of the spiral-grooved thrust bearing[J].ASME J.Basic Eng,1965,87:547-558.
[3]Muijderman E A.Spiral groove bearings[J].Philips Technical Library,Springer-Verlag,New-York,1966.
[4]Constantinescu V N,Galetuse S.On extending the narrow spiral-groove theory to configurations of interest in seals[J].Trans.of ASME,Journal of Tribology,1992,114(3):563-566.
[5]Gardner J F.Combined hydrostatic and hydrodynamic principles applied to non-contacting face seals[A].Proc.of 4~(th) Inter.Conf.on Fluid Sealing[C].1970,350-360.
[6]Gabriel R P.Fundamentals of spiral groove noncontacting face seals[J].Lubr.Eng.,1979,35(7):367-375.
[7]Shapiro W,Walowit J,Jones H F.Analysis of spiral-groove face seals for liquid oxygen[J].ASLE Trans.,1984,27(3):177-188.
[8]Tadashi Sawada.具有净轴向流量的稀薄气体粘性密封的性能[A].四川密封技术研究所等编译.第十届国际流体密封会议论文集[C].重庆:科学技术文献出版社重庆分社,1987,275-285.
[9]Chang-Ho Kim.Analysis for rotordynamic coefficients of helically-grooved turbulent annular seals[J],Trans.of ASME,J.of Tribology,1987,109(1):136-143.
[10]Yuchi Sato.Performance characteristics of shrouded rayleigh-step and spiral groove viscous pumps[J],Trans.of ASME,J.of Tribology,1992,114(4):499-506.
[11]James D D,Potter A F.Numerical analysis of the gas-lubricated spiral-groove thrust bearing-compressor [J].ASME J.of Lubr.Tech.,1967,89(4):439-444.
[12]Zuk J,Renkel H E.Numerical Solutions for the flow and pressure fields in an idealized spiral grooved pumping seal[A].Proc.of 4~(th) Inter.Conf.on Fluid Sealing[C],1970,290-301.
[13]Smalley A J.The narrow groove theory of spiral groove gas bearings:development and application of a generalized formulation for numerical solution[J].ASME J.of Lubr.Tech.,1972,94(1):86-92.
[14]Murata S,Miyake Y,Kawabata N.Exact two-dimensional analysis of circular disk spiral groove bearing(Part Ⅰ)[J].ASME J.of Lubr.Tech.,1979,101(4):424-430.
[15]Murata S,Miyake Y,Kawabata N.Exact two-dimensional analysis of circular disk spiral groove beating(Part Ⅱ)[J].ASME J.of Lubr.Tech.,1979,101(4):431-436.
[16]Walowit J A,Pinkus O.Analysis of face seals with shrouded pockets[J].ASME J.of Lubr.Tech.,1982,104(2):262-270.
[17]Ikeuchi K,Mori H,Nishida T.A face seal with circumferential pumping grooves and rayleigh-steps[J].ASME J.of Tribology,1988,110(2):313-319.
[18]Lipschitz A,Basu P,Johnson R P.A bi-directional gas thrust bearing[J].Tribology Trans.,1991,34(1):9-16.
[19]Kowalski C A,Basu P.Reverse rotation capability of spiral-groove gas face seals[J].Tribology Trans.,1995,38(3):549-556.
[20]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社,1988.
[21]Reddi M M,Chu T Y.Finite element solution of the steady-state compressible lubrication problem[J].ASME J.of Lubr.Tech.,1970,92(3):495-503.
[22]Basu P.Analysis of a radial groove gas face seal[J].Tribology Trans.,1992,35(1):11-20.
[23]Satomi T,Lin G.Design optimization of spirally grooved thrust air bearings for polygon mirror laser scanners[J].JSME Inter.,Series C,1993,36(3):348-354.
[24]Bonneau D,Huitric J,Tournerie B.Finite element analysis of grooved gas thrust bearings and grooved gas face seals[J].ASME J.of Tribology,1993,115(7):348-354.
[25]Henandez P,Boudet R.Modeling of the behavior of dynamical Gas seals:calculation with a finite element method implicitly assuring the continuity of flow[J].Proc.Inst.Mech.Eng.,Part J:J.of Eng.Tribology,1995,209(3):195-201.
[26]Zirkelback N L,Andres L S.Effect of frequency excitation on force coefficient of spiral groove gas seals[J].ASME J.of Tribology,1999,121(4):853-863.
[27]蔡文新,朱报桢.螺旋槽气体密封的研究[J].流体机械,1994,22(9):2-7.
[28]彭建,左孝桐,顾永泉.螺旋槽干气密封的优化设计[J].流体机械,1995,23(3):24-27.
[29]彭建,左孝桐,王福.不同槽型气体端面密封研究[J].流体机械,1996,24(11):8-12.
[30]胡丹梅,吴宗祥.直线槽端面气体密封的分析计算[J].流体机械,1996,24(9):16-22.
[31]杨梦辰,张瑞乾,李翔,等.平面螺旋槽气体止推轴承的研究[J].机械设计,1998,15(2):9-11.
[32]党建军,秋卫平,钱志博.有限元法在机械密封设计中的应用研究[J].航空计算技术,2000,30(1):6-8.
[33]刘雨川,徐万孚,陈国林,等.端面气膜密封的高性能端面结构[J].航空学报,2000,21(2):187-190.
[34]刘雨川,徐万孚,王之栎,等.气膜端面密封角向摆动自振稳定性[J].机械工程学报,2002,38(4): 1-6.
[35]林培峰,张秋翔,蔡纪宁,等.螺旋槽干气密封的有限元分析[J].北京化工大学学报,2002,29(3):57-63.
[36]李涛子,张秋翔,蔡纪宁,等.T型槽干气密封稳态特性的有限元分析[J].北京化工大学学报,2003,30(2):58-62.
[37]冯向忠.泵用干式气体端面密封的理论研究[D].东营:中国石油大学(华东),2004.
[38]蒋小文,顾伯勤.螺旋槽干气密封端面间气膜特性[J].化工学报,2005,56(8):1419-1425.
[39]尹晓妮,彭旭东.干式气体端面密封性能的有限元分析中形函数的选择[J].润滑与密封,2006,31(3):13-18.
[40]陈小宁,郝木明.螺旋槽气体润滑机械密封温度场有限元分析[J].机械设计与制造,2007,(5):16-18.
[41]冯向忠,彭旭东.螺旋槽干式气体端面密封性能的数值分析[J].润滑与封,2004,29(6):41-43.
[42]彭旭东,冯向忠,胡丹梅,等.非接触式气体润滑密封变形的数值分析[J].摩擦学学报,2004,24(6):536-539.
[43]汤臣杭,杨惠霞,王玉明.单向双列螺旋槽干气密封流场数值模拟[J].润滑与密封,2007,32(1):145-148.
[44]Gabriel R P.Fundamentals of spiral groove noncontacting face seals[J].Lubrication Engineering,1994,50(3):215-224.
[45]Shellef R A,Johnson R P.Abi-directional gas face seal[J].Tribology Transactions,1992,35(1):53-58.
[46]Salant R F.Homiller S J.The effects of shallow groove patterns on mechanical seal leakage[J].Tribology Transactions,1992,35(1):142-148.
[47]Zirkelback N.Parametric study of spiral groove gas face seals[J].Tribology Transactions,2000,43(2):337-343.
[48]胡丹梅,郝木明,杨惠霞.非接触式气体端面密封低速性能试验研究[J].流体机械,1998,26(9):3-6.
[49]赵惠清,蔡嵘,国巨发.深槽浅槽机械密封的对比分析[J].北京化工大学学报,1999,26(2):37-39.
[50]冯向忠,彭旭东.螺旋槽干式气体端面密封的刚度和泄漏量研究[J].石油大学学报(自然科学版),2005,29(2):83-92.
[51]丁雪兴,程香平,张伟政,等.螺旋槽干气密封槽形参数的协调优化[J].力学与实践,2007,29(3):26-30.
[52]Sedy J.Face Seal with Angled and Annular Groove[P].世界专利:WO 95/06832.1995-03-09.
[53]Kulkarni S B.Double Gas Barrier Seal[P].世界专利:WO 95/21343.1995-08-10.
[54]王玉明.双环带螺旋槽端面密封[P].中国专利:96108614.9.1996-06-22.
[55]王玉明.可双向旋转的双列双叶螺旋槽端面密封[P].中国专利:98103575.2.1999-02-03.
[56]王玉明.螺旋槽端面密封[P].中国专利:98120372.1999-04-28.
[57]Burgdorfer A.The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated beatings[J].ASME J of Basic Eng.,1959,81(2):94-100.
[58]Hsia Y T,Domoto G A.An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances[J].J.of Lubr.Tech.1983,105(1):120-130.
[59]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].J.of Tribology,1988,110(2):253-261.
[60]Mitsuya Y.Modified reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient[J].ASME J.of Tribology,1993,115(2):289-294.
[61]Chi-Chuan Hwang,Rong-Fong Fung,Rong-Fu Yang etal.A new modified reynolds equation for ultrathin film gas lubrication[J].IEEE Trans.on Magnet.,1996,32(2):344-347.
[62]Pecht G G,Netzel J P.Design and application of non-contacting gas lubricated seals for slow speed services[J].Lubr.Eng.,1999,55(7):20-25.
[63]Ching-Shung Chen.Gas flow in micro-channels using a boundary-layer approach[J].Inter.J.of Computer applications in Tech.,2000,13(6):316-323.
[64]Ruan B.Finite element analysis of the spiral groove gas face at the slow speed and the low pressure condition-slip flow consideration[J].Tribology Trans.,2000,43(3):411-418.
[65]赵汉中.微细圆管中气体流动的稀薄效应和可压缩效应[J].华中科技大学学报,2001,29(10):96-98.
[66]赵越,宋鹏云,李伟,等.螺旋槽气体润滑机械密封低速运转特性-理论研究[J].润滑与密封,2005,30(5):70-73.
[67]许鹏先,潘琦,申改章.基于滑移边界的干气密封的数值模拟[J].润滑与密封,2007,32(5):98-101.
[68]尹晓妮,彭旭东.考虑滑移流条件下干式气体端面密封的有限元分析[J].润滑与密封,2006,31(4):55-59.
[69]顾永泉.机械端面密封[M],第一版.东营:石油大学出版社,1994.
[70]Harp S R,Salant R E.Analysis of mechanical seal behavior during transient operation[A].Proc.Of the 1997 Joint ASME/STLE/IMechE World Tribology Conf.[C].London,UK,Sept.8-12,1997.
[71]章本照.流体力学中的有限元方法[M].北京:机械工业出版社,1986.
[72]李开泰,黄艾香,黄庆怀.有限元方法及其应用(Ⅰ)[M].西安:西安交通大学出版社,1984.
[73]何光渝.FORTRAN 77算法手册[M].北京:科学出版社,1993.
[74]刘雨川.端面气膜密封特性研究[D].北京:北京航空航天大学,1999.
[75]Shen C,Jiang J Z.Finite length microchannel flow in transitional regine[J].Acta Aerodynamica Sinica,2008,26(2):257-262.