摘要
随着旋转机械得到广泛应用并日益向高性能、大容量方向发展,这促使流体与旋转转子之间的流固耦合作用不断增加,从而这种耦合作用对转子系统的动力特性和稳定性产生影响。
本文以大功率高压多级离心泵为研究对象,围绕影响泵转子系统动力系统性的流体激振与转子系统的耦合作用,重点对多级离心泵级间设置的环压密封力产生机理及其动特性进行理论分析和实验研究。
通过对多级离心泵三维流场计算与模拟,对离心泵的性能进行预测,全面观察多级离心泵的内部流动情况,捕捉到重要的流动现象,并获得主要部件的速度、压力分布,为后续研究中分析流固耦合作用对临界转速的影响提供依据。
建立基于Navier—Stokes方程的密封动力学模型。详细推导计算多级离心泵级间环压密封动特性系数的方法,并通过大量计算实例验证了上述模型及算法,并分析了众多密封参数对密封动力特性的影响。
建立基于有限元方法的大功率多级离心泵转子动力学模型。首先建立转子轴系的有限元模型,介绍线性化的油膜力和密封力模型,给出完善的多级离心泵转子“湿”态动力学分析方法。建立大功率高压多级离心泵转子刚性设计的理论和方法。
在国内首次建立多级转子“湿”效应实验台。对密封力作用下转子系统的振动特征进行试验研究,通过试验结果分析系统密封力对转子系统动力学特性的影响。最后将理论分析的结果与试验结果进行比较。
本文的研究给出了级间密封对多级转子动特性影响的试验结果,初步建立了数值仿真方法体系,为大功率高压离心泵的研制和优化提供了理论基础,具有重要的理论意义和很强的实际应用价值。
As rotating machinery are used widely and become large-capacity, the stabilization and dynamics of rotating rotor were influenced by the increasing in coupled interaction between the fluid and the rotor.
In this paper, the high-power high-pressure multi-stage centrifugal pump is regarded as investigate object. The theoretical analysis and experimental research on the generation mechanism of the ring sealing force set between multi-stage centrifugal and characteristics of ring sealing are studied according as coupled interaction between the fluid and the rotor.
Through three-dimensional flow field simulation of the multi-stage centrifugal pump the performance of centrifugal pump is predicted. Some important flow Phenomena are got. The velocity and pressure distributions within the impellers, guide vanes, et al. are analyzed so that the later calculation on the critical speed can be continued.
Based on Navier-Stokes equations, the seal dynamic model is established. o. Detailed derivation calculate multi-stage centrifugal pump interstage ring pressure seal dynamic coefficients of the method, and large amount of computation is verified by the above model and algorithm, and a number the reaction of sealing parameters on dynamic characteristics of sealing are analyzed.
Based on the finite element method of high-power multi-stage centrifugal pump rotor dynamics model is established. Firstly, the establishment of the rotor shaft of the finite element model, introduced linearized oil-film force and the sealing force model, given the multi-stage centrifugal pump rotor sound "wet" state kinetic analysis. And the rotor rigid design theory and methods of high-power high-pressure multistage centrifugal pump is established.
In the country, a multi-stage rotor "wet" effect bench is established firstly. The sealing force on the vibration characteristics of the rotor system is studied. Through test results, analyzing the influence factor of sealing force to the rotor system dynamics characteristics. Finally, the results of theoretical analysis and experimental results were compared.
In this paper, the study shows the influence of the inter-stage seal on the rotor dynamic characteristics of multi-stage through the test results. A numerical simulation methodology is initially established, which provides a theoretical basis for development and optimization of high-pressure centrifugal pump, and has important theoretical significance and practical value.
引文
[1]虞烈,刘恒.轴承一转子系统动力学[M].西安:西安交通大学出版社,2001.
[2]郑惠萍.大功率旋转机械中非线性因素综述[J].河北科技大学学报,1999,20(3):82-86.
[3]离心式压缩机原理[M].北京:机械工业出版社,1980.
[4]孙国启.大间隙环流中转子系统动力学特性研究[D].西安交通大学.2001.
[5]董勋.润滑理论[M].上海:上海交通大学出版社,1984.
[6]Frenc, J.,Nicolas, D.,Degueurce, B.,Berthe,D.,and Godet, M. Hydrodynamic Lubrication:Bearings and Thrust Bearings[M]. Amsterdam:Elsevier Science,1997.
[7]孙大成.润滑力学讲义[M].北京:中国友谊出版公司,1991.
[8]张直明主编.滑动轴承的流体动力润滑理论[M].北京:高等教育出版社,1986.
[9]钟一愕,何衍宗,王正,李方泽.转子动力学[M].北京:清华大学出版社,1987.
[10]平克斯,斯德因李希特著.西安交通大学轴承研究小组译.流体动力润滑理论[M].北京:机械工业出版社,1980.
[11]张文.转子动力学理论基础[M].北京:科学出版社,1990.
[12]Childs, D. W. Turbomachinery Rotordynamics:Phenomena, Modeling, and Analysis [M].NeWYork:John Wiley&Sons,1993.
[13]Tower, B. First Report on Friction Experiments (Friction on Lubricated Bearings) [J]. Proceedings of the Institution of Mechanical Engineers, 1883,632-659.
[14]Tower, B. Second Report on Friction Experiments (Friction on Oil Pressure in a Bearings) [J]. Proceedings of the Institution of Mechanical Engineers,1885,58-70.
[15]Reynolds,O. On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Oil [J]. Philosophical Transactions of the Royal Society of London,1886,177:157-234.
[16]杨金福,杨昆.滑动轴承非线性动态油膜压力分布特性的研究.动力工程[J].2005,25(4):16-23.
[17]Sommerfold, A. Zur hydrodynamisdhen theoric der Schmiermittelreibunh, Z.math. u. physik,1904(50):97-106.
[18]G. B. Du Bois. Analytical derivation and experimental evalution of short bearing approximation for full journal bearing. NACA Rept.1157-1953.
[19]Gumbel, L. Monatsblatter Berliner Bezirksver [M]. Berlin:VDI-Verlag, 1914.
[20]Swift, H. W. The Stability of Lubricating Films in Journal Bearings [J]. Proceedings of the Institute Civil Engineers, London,1932,233:267-322.
[21]Stieber, W. Das Schwimmlager, Hydrodynamiche Theoriedes Gleitlagers [M].Berlin:VDI-Verlag,1933.
[22]Cameron, A., and Wood, W. L. The Full Journal Bearing [J]. Proceedings of the Institution of Mechanical Engineers,1949,161:59-64.
[23]Kingsbury, A. Trans. ASME,1931:53-59.
[24]Christopher son, D. G. Proc. Institutions of Mech. Eng. (London),1942: 146.
[25]Miche. A. G.M. Trans, ASME,1929:51-153.
[26]Ocvirk,K.W. NACAT,1959:2808
[27]Carre, B. A. The Determination of the Optimum Accelerating Faetor for Successive Over-Relaxation[J]. The Compute r J.,1961,4 (1):73-78.
[28]ChristoPherson, D. G. A New Mathematical Method for the Solution of Film Lubrieation Problems [J]. Proceedings of the Institution of Mechanical Engineers,1941,146 (3):126-135.
[29]Cryer, C. The Method of Christopher son for Solving Free Boundary Problems for Infinite Journal Bearings by Means of Finite Differences [J]. Mathematics of Computation,1971,25:435-443.
[30]Barrett, L. E., Allaire, P. E., andGunter, E. J. The Dynamic Analysis of Journal Bearings Using a Finite Length Correction for Short Bearing Theory [C]. Design Engineering Conference on Fluid Fi lm Bearing and Rotor Bearing System Design and Optimization. Chicago:ASME,1978:29-41.
[31]Blaek, H. F., Brown, R. D. Modal Dynamic Simulation of Flexible Shafts in Hydrodynamic Bearings [C]. Intemational Conference on Vibrations in Rotating Machinery. Cambridge, England:IMechE,1980:109-113.
[32]Myers, C. J. Bifurcation Theory Applied to Oil Whirl in Plain Cylindrical Joumal Bearings [J]. ASME J. of Applied Mechanics,1984,51 (2):244-250.
[33]Braneati, R., Roeea, E., Russo, M, and Russo, R. Journal Orbits and Their Stability for Rigid Unbalanced Rotor[J]. ASME J. of Tribology,1995, 117:709-716.
[34]陈照波,焦映厚,夏松波,黄文虎.求解有限长圆柱型滑动轴似解析方法[J].中国电机工程学报,2001,21(增刊):6-9.
[35]Booker, J. F., and Huebner, K. H. Application of Finite Methods to Lubrication:An Engineering Approach[J]. ASME J. of Lubrication Technology,1972,94 (4):313-323.
[36]Rohde,S. M.,Oh,K. P. Higher Order Finite Element Methods for the Solution of Compressible Porous Bearing Problems [J]. International J. for Numerical Methods in Engineering,1975,9(4):903-911.
[37]Bayada, G. Variational Formulation and Associated Algorithm for the Starved Finite Journal Bearing [J]. ASME J. of Lubrication Technology, 1983,105(3):453-457.
[38]Lund, J. W. Spring and Damping Coefficients for the Tilting-Pad Journal Bearing [J]. ASLE Transactions,1964,7:342-352.
[39]杨建刚,蔡霆,高叠.汽轮机轴承动力特性三维流固祸合分析模型[J].中国电机工程学报,2004,24(8):147—152.
[40]王文,张直明.油叶型轴承非线性油膜力数据库[J].上海工业大学学报,1993,14(4):299—305.
[41]孟志强,徐华,朱均.基于Poincare变换的滑动轴承非线性油膜力数据库方法[J].摩擦学学报,2001,21(3):223—227.
[42]Rohde, S.. M., and Li, D. F. A Generalized Short Bearing Theory [J]. ASME J. of Lubrieation Technology,1980,102 (3):278-252.
[43]Reason, B. R., and Narang, I. P. Rapid Design and Performance Evaluation of steady-State Journal Bearings-A Technique Amenable to Programmable Hand Calculators [J]. ASLE Transactions,1982,25 (4):429-444.
[44]Rohde, S. M., and MeAllister, G. T. A Variational Formulation for a Class of Free Boundary Problems Arising in Hydrodynamic Lubrication [J]. International J. of Engineering Science,1975,13:841-850.
[45]Lewy, H., and Stampacchia, G. On the Regularity of the Solution of a Variational Inequality [J]. Communications on Pure and Appllied Mathematics,1969,22:153-188.
[46]Karamardian, S. The Nonlinear Complementarity Problem with Applications-Part2 [J]. J of Optimization Theory & Applications,1969, 4(3):167-181.
[47]Cimatti, G. On a Problem of the Theory of Lubrication Governed by a Variational Inequality [J]. Applied Mathematics and Optimization,1977, 3:227-242.
[48]Kinderlehrer, D., and StamPacehia, G. An Introduction to Variational Inequalities and their Applications [M]. NewYork:Aeademie Press 1980.
[49]张文,郑铁生,马建敏,郭建萍.油膜轴承瞬态非线性油膜力的力学建模及其表达式[J].自然科学进展,2002,12(3):255—260.
[50]陈龙,郑铁生,张文,马建敏.轴承非线性油膜力的一种变分近似解.应用力学学报[J],2002,19(3):90-95.
[51]沈光玫,肖忠会,郑铁生,张文.油汗卜型轴承—不平衡转子系统的非线性动力学分析[J].航空动力学报,2004,19(5):604-609.
[52]Kraiko, A. N. The Formulation of Problems of Lubrieation Theory for Journal Bearings [J]. J. of Applied Mathematics and Mechanics,2002, 66 (5):757-765.
[53]郑铁生,张文,马建敏,杨树华.滑动轴承非线性油膜力的几个理论问题及应用[J].水动力学研究与进展,2003,18(6):762-768.
[54]Lomakin A A. Calculation of critical speed and securing of dynamic stability of hydraulic high pressure pumps with reference to forces arising in seal gaps [J]. Energomashinostroenie,1958,4(1):1158.
[55]Z.X Lu. Numerical calculation of dynamic coefficients of angular seal ring [J]. Chinese journal of applied mechanics,1995,12(1):81-86.
[56]Black, H. F., Effects of hydraulic forces in annular pressure seals on the vibrations of centrifugal pump rotors [J]. J. M. Een. Sci.,1969, 11(2):206-113.
[57]Black, h. f., Jenssen, D. N., Dynamic hybrid properties of annular pressure seals, proc. J. mech. Engine.,1970,184:92-100.
[58]Childs D W. Dynamic analysis of turbulent annular seals based on hirs' lubrication equation[j]. ASME Journal of lubrication technology, 1983,105:429-436.
[59]Childs D W. Finite-length solutions for rotordynamic coefficients of turbulent annular seals [j]. ASME Journal of lubrication technology, 1983,105:437-445.
[60]Nelson, C. Nguyen, D. Comparison of Hirs'equation with Moody's equation for determining rotordynamic coefficients of annular pressure seals. Journal of Tribology,1987,109:144-148.
[61]Dietzen, F., and Normann, R. calculating rotordynamic coefficients of seals by finite difference techniques. Rotordynamic instability problems in high performance turbomachinery, proceedings of a workshop held at texas A&M university,1988:197-210.
[62]Dietzen, F., and Normann, R. calculating rotordynamic coefficients by finite difference techniques. Journal of tribology,1987
[63]Dietzen, F., and Normann, R. finite difference analysis for the rotordynamic coefficients of turbulent seals in turbopumps. ASME FED-Vol. 48, Symposium on thin fluid films,1987:31-42.
[64]E. A. Baskharone etc. Rotor dynamic effects of the shroud-to-housing leakage flow in centrifugal pumps. Transactions of the ASME,1994,116: 558-563.
[65]Black, H. F. Effects of fluid filled clearance spaces on centrifugal pump and submerged motor vibrations [A]. Proc 8th Turbomach. Symp[C], Texas A&M Univ, College Station, TX,1979.
[66]Black,H. F. Cochrane, E. A. Leakage and hybrid bearing properties of serrated seals in centrifugal pumps [A].6th Intl Conf Fluid Seal ing [C], Munich, Germany,Feb 27-Mar 2,1973.
[67]Black, H. F. Allaire, P. E. Barrett, L E. Inlet flow swirl in short turbulent seal dynamics[A].9th Intl. Conf. Fluid Sealing[C], Leewenhorst, Netherlands, Aprl-3,1981.
[68]Nelson, C. C. Nguyen, D. T. Analysis of eccentric annular flow incompressible seals. Part1:A new solution using fast Fourier transforms for determining hydrodynamic force [J]. ASME J of Tribology,1988,110: 354-360.
[69]Venkataraman B, Palazzolo A B. Thermodynamic analysis of eccentric annular seals using cubic spline interpolations[J]. Tribology Transactions,1997,40(1):183-194
[70]Alexander C R, Childs D w, Yang Z J. Theory versus experiment for the rotordynamic characteristics of a smooth annular gas seal at eccentric positions [J]. ASME J of Tribology,1995,117:148-152
[71]Marquette 0 R, Childs D W, Andres L S. Eccentricity effects on the rotordynamic coefficients of plain annular seals:Theory versus experiment [J]. ASME J of Tribology,1997.119:443-448
[72]Dietzen F J, Nordmann R. Calculating rotordynamic coefficients of seals by finite difference techniques [J]. ASME J ofTribology,1987,109:388 -394
[73]Nordmann R, Dietzen F J, Weiser H P. Calculation rotordynamic coefficients and leakage for annular gas seals by means of finite difference techniques [J]. ASME J ofTribology,1989,110:545-552
[74]Tam L T, Przekwas A J, Muszynska A, et al. Numerical and analytical study of fluid dynamic forces in seals and bearings [J]. ASME J of Vibration, AcoustiCS, Stress and Reliability in Design,1988,110:315-325
[75]Baskharone E A, Hensel S J. A newmodel for leakage prediction in shrouded-impeller turbopurnps [J]. ASME J of Fluids Engineering,1989,111: 118-123
[76]Baskharone E A, Hensel S J, A finite-element perturbation approach to fluid/rotor interaction in turbomachinery elements. Part1: Theory [J]. ASME J of Fluids Engineering,1991,113(3):353-361
[77]Baskharone E A, Hensel S J. A finite-element perturbation approach tofluid/rotor interaction in turbomachinery elements. Part2: Application[J]. ASME J of Fluids Engineering,1991,113 (3):362-367
[78]Baskharone E A, Hensel S J. Moment coefficients of incompressible flowseals with conically whirling rotors [J]. Intl J of Mechanical Sciences,1991,33(2):151-167
[79]Baskharone E A, Hensel S J, Interrelated rotordynamic effects of cylindrical and conical whirl of annular seal rotors [J]. ASME J ofTribology,1991,113(3):470-480
[80]Baskharone E A. Perturbed flow structure in all annular seal due to synchronous whirl[J]. ASME J of Fluids Engineering,1994,116:364-369
[81]Arghir M, Frene J. Inclusion of roughness effects in perturbed Navier-Stocks rotordynamic methods [J]. ASME J ofTribology,1997,119(4):358-360
[82]Nelson C C, Nguyen D T Comparision of Hirs'equation with Moodv, sequation for determining rotordynamic coeffcients of annular pressure seals [J]. ASME J ofTribology,1987,109(1):144-148
[83]Lucas V,Danaila S, Bonneau 0, et al. Roughness influence on turbulent flow through annular seals [J]. ASME J ofTribology,1994,116(2):321-329
[84]Lucas V. Bonneau 0, Frene J. Roughness influence On turbulent flow through annular seals including inertia effects [J]. ASME J of Tribology,1996, 118(2):175-182
[85]Venkataraman B, Palazzolo A B. Thermodynamic analysis of eccentric annular seals using cubic spline interpolations[J]. Tribology Trans, 1997,40(1):183-194
[86]Andres L S, Yang Z, Childs Dw. Thermal effects in cryogenic liquid annular seals. Part2:Numerical solution and results [J]. ASME J of Tribology,1993, 115(2):277-284
[87]Yang Z, Andres L S, Childs DwThermal effects in cryogenic liquid annular seals. Part1:Theory and approximate solution [J]. ASME J of Tribology,1993,115(2):267-276
[88]Iwatsubo T, Yang B S. The effects of elastic deformation on seal dynamic [A]. Proc. Rotating Machinery Dynamics [C],1987 ASME Design Tech Conf,11th Biennial Conf Mech Vib Noise, Boston, MA, Sep 27-30,1987
[89]Venkataraman B, Palazzolo A B. Effects of wall flexibility on the rotordynamic coefficients of turbulent cryogenic annular seals [J]. ASME J of Tribology,1996,118:509-519
[90]Zirkelback N, Andres L S. Bulk - flow model for the transition to turbulence regime in annular pressure seals [J]. Tribology Trans,1996, 39(4):835-842
[91]Andres L S. Analysis of variable fluid properties:Turbulent annular seals [J]. ASME J of Tribology,1991.113:694-702
[92]Simon F, Frene J. Static and dynamic characteristic of turbulent annular eccentric seals:Effect of convergent-tapered geometry and vailable fluid properties [J]. ASME J ofTribology,1989,111:378-385
[93]孙启国,虞烈,谢友柏.间隙环流中同心涡动转子动特性的研究[J].机械强度,2003,25(1):021-024.
[94]张新敏,于慎波,李良,等.锅炉给水泵密封间隙力的数值分析[J].沈阳工业大学学报,1995,17(3).
[95]Ranklne W. On the Centrifugal Force of Rotating Shafts [J]. Engineer,1869,27:249-256.
[96]Jeffcott H H. The Lateral Vibration of Loaded Shafts in the Neighborhood of a Whirling Speed[J]. Philosophical Magzine,1919,7 (6):304-314.
[97]Stodola A. Steam and Gas Turbines[M]. NewYork:McGraw-Hill,1927.
[98]Green R. B. GyroseoPic Effects on the Critieal Speeds of Flexible Rotors[J]. ASME J. of Applied Mechanics,1948,15:369-376.
[99]Newkirk B L. Shaft Whipping[J]. General Electric Review,1924, 27:169-178.
[100]Newkirk B L., and Taylor H D. Shaft Whipping Due to Oil Action in Journal Bearings [J]. General Electric Review,1925,28:559-568.
[101]Lund J. W., and Sternlieht, B. Rotor-Bearing Dynamics with Emphasison Attenuation[J]. ASME J. of Basic Engineering,1962,84:491-502.
[102]Lund J. w. The Stability of an Elastic Rotor in Journal Bearings with Flexible, Damped Supports[J]. ASME J of Applied. Mechanics,1965, 87:911-920.
[103]Gunter E J.Dynamic Stability of ROtor-Bearing systems [R]. Washing-ton:NASASP-113,1966
[104]Chi Ids, D. W. The Space Shuttle Main Engine High-Pressure Fuel Turbopump Rotordynamic Instability Problem[J]. ASMEJ. Of Engineering for Power, 1978,100(1):48-57.
[105]Chi Ids, D.W., and Moyer, D. S. Vibration Characteristic of the HPOTP(High-pressure Oxygen Turbopump) of the SSME (SPaee Shuttle Main Engine) [J].ASME J. of Engineering for Gas Turbines and Power,1985, 107(1):152-159
[106]闻邦椿,顾家柳,夏松波,王正.高等转子动力学—理论、技术与应用[M].北京机械工业出版社,1999.
[107]]黄文虎,武新华,焦映厚,夏松波,陈照波.非线性转子动力学研究综述[J].振动工程学报,2000,13(4):497+509.
[108]孟光.转子动力学研究的回顾与展望[J1.振动工程学报,2002,15(1):1-9.
[109]高叠,张新江,张勇.非线性转子动力学问题研究综述[J1.东南大学学报(自然科学版),2002,32(3):443-452.
[110]Ehrieh, F.F. Some Observation of Chaotic Vibration Phenomena in High Speed Rotordynamics[C]. Twelfth Biennial Conference on Mechanical Vibration and Noise, the ASME Design Technical Conference. Montreal: ASME,1989,18 (5):367-376.
[111]Ishida, Y. Nonlinear Vibrations and Chaos in Rotordynamics[J]. JSME International J., Series C:Dynamics, Control, Robotics, Design and Manufacturing,1994,37 (2):237-245.
[112]Brown, R. D., Addison, P., and Chan, A. H. C. Chaos in the Unbalance Response of journal Bearings[J]. Nonlinear Dynamics,1994,5 (4):421-432.
[113]Brancati, R, Russq, M., and Russo, R. On the Stability of Periodic Motions of an Unbalanced Rigid Rotor on Lubrieated Journal Bearings [J]. Nonlinear Dynamies,1996,10(2):175-185.
[114]Adiletta, G., Guido, A. R., andRossi, C. Chaotic Motions of a Rigid Rotor in short journal Bearings [J]. Nonlinear Dynamics,1996,10(3):251-269.
[115]陈予恕,孟泉.非线性转子一轴承系统的分叉[J].振动工程学报,1993,9(3):266-275.
[116]袁小阳,朱均.滑动轴承—转子系统Hopf分岔分析计算方法[J].航空动力学报,1999,14(2):166-170.
[117]徐小峰,张文.一种非稳态油膜力模型下刚性转子的分岔和混沌特性[J].振动工程学报,2000,13(2):247-253.
[118]Homer G C, Pillkey W D. The Riccati transfer matrix method [J]. Journal of Mechanical Design, Transaction of ASME,1978,100(4),297-302
[119]Myklsetad N O. A new Method for Calculating Natural Modes of Uncoupled Bending Vibrations of Airplane Wings and Other Types of Beams [J]. Journal of Aeronautical Science,1944,11,153-162
[120]Prohl M A. A General Method for Calculating Critical Speeds of Flexible Rotors [J], ASME Journal of Applied Mechanics,1945,12(3),142-148
[121]王正,Riccati传递矩阵法的奇点及其消除方法[J],振动与冲击,1987,(2),74-78
[122]Lund J W, Orcutt F K. Calculation and Experiments on the Unbalance Response of a flexible Rotor[J], ASME Journal of Engineering for Industry,1967,89(4),785-796
[123]Lund J W. Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-film Bearings [J]. ASME Journal of Engineering for Industry, 1974,96(2),509-517
[124]Koening E C. Analysis for calculating lateral vibration characteris-tics of rotating system with any number of flexible supports Part 1-the method of analysis [J].Journal of Applied Mechanics,1961,28,585-590
[125]Bansal P N, Kirk R G. Stability and damped critical speeds of rotor-bearing system[J]. Journalof Engineering for Industry,1975, 97,1325-1332
[126]Inagaki T. Response analysis of a general asymmetric rotor-bearing system[J]. Journal of Mechanical Design,1980,102,147-157
[127]Brian Timothy Murphy. Eigenvalues of Rotating Machinery. Doctoral dissertation, University of Florida,1984
[128]Kang Y. Instability analysis of unsymmetrical rotor-bearing system using the transfer matrix method[J]. Journal of Sound and Vibration, 1997,199(3),381-400
[129]李天维.用传递矩阵法求解复杂转子—支承系统的临界转速[J].力学与实践, 1994,1,8-14
[130]姜培林,虞烈.推力轴承对轴承-转子系统的耦合作用研究[J].应用力学学报,1996,13(4),46-52
[131]庞辉,李育锡等.基于Riccati变换的整体传递矩阵法计算双转子临界转速研究[J].机械科学与技术,2005,24(7),832-834
[132]唐六丁等.双转子-轴承系统动态性能仿真分析[J],机械传动,2006,30(4),55-58.
[133]Xu Hua, Zhu Jun. Influence of the Mechanical Seals on the Dynamic Performance of Rotor-bearing Systems. Front. Mech. Eng. China,2006,1, 96-100
[134]Ruhl R L, Booker,J F. A finite element model for distributed parameter turborotor system[J]. Journal of Engineering for Industry,1972,94(1), 126-134
[135]Ruhl R L and Booker R L. A finite element model for distributed parameter turborotor systems, Transact ions of ASME[J]. Journal of Engineering for Industry,1972,94,128-132
[136]H D Nelson,J M McVaugh. The dynamics of rotor-bearing systems using finite elements[J]. Journal of Engineering for Industry,1976,98, 593-600
[137]E S Zorzi, H D Nelson. Finite element simulation of rotor-bearing systems with internal damping [J]. Journal of Engineering Power ASME, 1977,99,71-76
[138]H D Nelson. A finite rotating shaft element using Timoshenko beam theory [J]. Journal of Mechanical Design ASME,1980,102,793-803
[139]L W Chen, D M Ku. Finite element analysis of natural whirl speeds of rotating shafts[J]. Computers and Structures,1991,40(3),741-747
[140]D M Ku. Finite element analysis of natural whirl speeds for rotor-bearing systems with internal damping[J]. Journal of Mechanical Systems and Signal Processing,1998,12 (5),599-610
[141]Madhumita Kalita. Analysis of whirl speeds for rotor-bearing systems supported on fluid film bearings[J]. Mechanical Systems and Signal Processing,2004,18,1369-1380
[142]M I Friwell. Computing critical speeds for rotating machines with speed dependent bearing properties[J]. Journal of Sound and Vibration,1998, 213(1),139-158
[143]F Oncescu, etc. Investigation of the stability and steady state response of asymmetricrotors using finite element formulation [J]. Journal of Sound and Vibration,2001,245 (2),303-328
[144]B Sudhakara Rao. Analysis of rotors considering distributed bearing stiffness and damping[J]. Computers and Structures,1996,61(5),951-955
[145]M A Mohiuddin, M Bettayeb. Dynamic analysis and reduced order modeling of flexiblerotor-bearing systems [J]. Computers and Structure,1998, 69,349-359
[146]Y Kang,etc. An investigation in stiffness effects on dynamics of rotor-bearing-foundation systems [J]. Journal of Sound and Vibration, 2000,231(2),343-374
[147]K L Cavalca, etc, An investigation on the influence of the supporting structure on the dynamics of the rotor system[J]. Mechanical Systems and Signal Processing,2005,19,157-174
[148]J K Dutt. Stability characteristics of rotating systems with journal bearings on viscoelastic support[J]. Mechanism and Machine Theory, 1996,31 (6),771-779
[149]张文,转子动力学理论基础[M],北京,科学出版社,1990
[150]王培杰,腾弘飞等,非对称复杂转子系统有限元动力分析[J],固体力学学报,1991,12(4),370-676
[151]曹树谦,丁千,陈予恕,滑动轴承的稳态转子系统有限元建模分析[J],汽轮机技术,1999,41(6),347-350
[152]鲁周勋,谢友柏等,200MW汽轮机高压缸中汽流激振对轴系稳定性的影响[J], 动力工程,1994,14(1),1-6
[153]张宏,杜可荣,300MW汽轮机发电机转子-轴承系统稳定性分析[J],华东电力技术,1995,12,14-20
[154]张小龙,何洪庆,涡轮泵转子的临界转速研究-临界转速的有限元法[J],推进技术,2000,21(3),40-42
[155]Gutmark E, and Wygnanski I. The planar turbulent jet[J]. Fluid Mesh.1976,73:456-495
[156]Heskestad G. A Transient Electromagnetic Flowmeter and Calibrtion Facility[J]. Appl. Sci. Res,1965:293-302
[157]Hinze J 0. Turbulent statistics in fully developed channel flow at low Reynolds number. Turbulence,2th edition McGraw-Hill Inc.,1975
[158]张文,不对称截面转子系统的回转失稳[J],振动与动态测试,1983,3,11-16