复杂转子系统动力学行为研究
|
摘要
大型组装式离心压缩机组包含多根平行转子-轴承系统,通过齿轮箱和联轴器实现动力耦合。随着机组向高速化、轻型化、复杂化方向发展,迫切需要完善系统动力学模型及进行动力学行为研究,为提高机组的稳定性、安全性和可靠性提供理论和工程指导。
本文以大型组装式离心压缩机组转子动力学建模与求解为工程背景,主要围绕紊流工况非线性油膜力及其Jacobi矩阵求解、可倾瓦轴承动力学模型、多平行转子-轴承系统建模及非线性动力求解几个方面,进行动力学建模及相应高效求解算法研究。本文研究工作在理论和应用上取得了一些创新成果,对复杂转子-轴承系统动力特性研究及其工程应用具有积极的意义。
具体地,本文主要研究内容和研究成果可以分为以下几方面：
(1)利用二阶线性椭圆型偏微分方程等价变分不等方程理论,针对紊流工况Reynolds方程,提出了一种联合求解紊流非线性油膜力及其Jacobi矩阵快速算法。考虑到轴承侧端压力不等于零工况,选取权函数和线性插值函数乘积形式作为油膜压力函数,建立有限元离散化的一维变分不等方程。利用修正的追赶法求解油膜压力及其导数,无需迭代自动满足油膜自由边界条件。
(2)考虑到瓦块绕支点摆动和沿几何预载荷方向微幅振动,对于n瓦可倾瓦轴承首次建立了包含2n+2个自由度的可倾瓦轴承完整动力学解析模型。通过建立固结与瓦块的随动坐标系和可倾瓦轴承总体坐标系,全局广义位移向量和力向量可以简练地转换到局部随动坐标系下位移向量和力向量,进而通过求解局部坐标系下的油膜力及其Jacobi矩阵扩充、叠加得到系统的广义油膜力向量及其Jacobi矩阵。对于可倾瓦轴承承受静载荷工况,给出了一种求解静平衡方程的快速算法,可以快速计算得到轴颈和瓦块的静平衡位置同时得到系统的刚度和阻尼系数矩阵。当设定轴颈和瓦块扰动频率,给出了缩聚可倾瓦轴承完整动力特性系数得到八个简化当量刚度系数和阻尼系数的计算方法。
(3)利用有限元方法,建立了比较完善的齿轮啮合多平行转子轴承系统动力学模型。针对转子-轴承系统为局部高维非线性动力系统特点,考虑了广义非线性力影响,提出了一种二次规范降阶方法,通过两次规范降阶把原高维系统转化为与之等价的低维系统,采用配套的打靶法求解低维系统的周期解并通过Floquet定理来判断周期解的稳定性,周期解失稳后采用直接数值积分方法求解系统的长期动力响应。
(4)针对复杂转子系统动力特性的研究,根据本文对轴承—转子系统的求解算法分析,编写了相关的计算程序,对可倾瓦轴承-转子系统和某工程组装式PTA离心压缩机组,进行了线性动力特性分析和非线性动力特性分析,验证了本文模型及算法的有效性及实用性。
Study on Dynamic Behaviour of Complex Rotor Systems
Large assembled centrifugal compressor units are comprised of multi-parallel rotor bearing system, which are dynamic coupled by gear box and coupling. With the development of compressor units towards to high speed, maximization and complication, it's necessary to research the rotor-bearing system dynamic behavior for improving the system stability, security and reliability.
On the background of rotor dynamic modeling and solution of large assembled centrifugal compressor units, this thesis studies on several aspects, such as, the model and algorithm of turbulent nonlinear oil-film forces and their Jacobian matrices, the model of tilting pad journal bearing, the model and nonlinear solution of complicated rotor bearing systems. Some achievements are acquired by current research from theory and practice, and conclusions that are reached are beneficial to study on the behavior of rotor-bearing system and engineering applications.
In detail, there are the following achievements and contents in current research.
(1) Based on the variational inequality of general quasilinear elliptic partial differential equation in free boundary condition, a kind of model with an efficient algorithm is presented to get the nonlinear oil-film force and its Jacobian matrices by solving turbulent Reynolds equation. Considering the condition of bearing side-pressure not equal to zero, the proper oil-film pressure function is chosen in the form of multiplier of weight function and linear interpolation function, and one-dimensional discrete variational inequality of turbulent Reynolds equation is built up. An amendatory direct-method is proposed to solve the oil-film force and its Jacobian matrices. During the process, the operations are restricted within the positive pressure region, and no iteration is involved.
(2) Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model as well as mathematical method which contains 2n+2 degrees of freedom is presented for calculating the dynamical characteristics of tilting pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement and generalized force vector are chosen. The concise transformation of generalized displacement, generalized force and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using Newton-Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration.
(3) The dynamic model of gear-coupled multi parallel rotor is presented using the finite element method. A method of quadratic normal reduction is presented for complex dynamic system with local nonlinearities. The degrees of freedom are reduced and the equivalent system is obtained by quadratic normal reduction and the effects of local nonlinear forces in the modal transformation are considered. Meanwhile the supporting shooting method is proposed to solve the periodic responses and the stability is determined by the Floquet theory. When the response is unstable, the long-term response is obtained by direct numerical integration method.
(4) The relevant program of current algorithm is developed. The linear and nonlinear dynamic behaviors are calculated for the industrial rotor system supported by tilting-pad journal bearing and one industrial assembled PTA centrifugal compressor train. The efficiency and reliability of the model and algorithm in this thesis is proven.
本文以大型组装式离心压缩机组转子动力学建模与求解为工程背景,主要围绕紊流工况非线性油膜力及其Jacobi矩阵求解、可倾瓦轴承动力学模型、多平行转子-轴承系统建模及非线性动力求解几个方面,进行动力学建模及相应高效求解算法研究。本文研究工作在理论和应用上取得了一些创新成果,对复杂转子-轴承系统动力特性研究及其工程应用具有积极的意义。
具体地,本文主要研究内容和研究成果可以分为以下几方面：
(1)利用二阶线性椭圆型偏微分方程等价变分不等方程理论,针对紊流工况Reynolds方程,提出了一种联合求解紊流非线性油膜力及其Jacobi矩阵快速算法。考虑到轴承侧端压力不等于零工况,选取权函数和线性插值函数乘积形式作为油膜压力函数,建立有限元离散化的一维变分不等方程。利用修正的追赶法求解油膜压力及其导数,无需迭代自动满足油膜自由边界条件。
(2)考虑到瓦块绕支点摆动和沿几何预载荷方向微幅振动,对于n瓦可倾瓦轴承首次建立了包含2n+2个自由度的可倾瓦轴承完整动力学解析模型。通过建立固结与瓦块的随动坐标系和可倾瓦轴承总体坐标系,全局广义位移向量和力向量可以简练地转换到局部随动坐标系下位移向量和力向量,进而通过求解局部坐标系下的油膜力及其Jacobi矩阵扩充、叠加得到系统的广义油膜力向量及其Jacobi矩阵。对于可倾瓦轴承承受静载荷工况,给出了一种求解静平衡方程的快速算法,可以快速计算得到轴颈和瓦块的静平衡位置同时得到系统的刚度和阻尼系数矩阵。当设定轴颈和瓦块扰动频率,给出了缩聚可倾瓦轴承完整动力特性系数得到八个简化当量刚度系数和阻尼系数的计算方法。
(3)利用有限元方法,建立了比较完善的齿轮啮合多平行转子轴承系统动力学模型。针对转子-轴承系统为局部高维非线性动力系统特点,考虑了广义非线性力影响,提出了一种二次规范降阶方法,通过两次规范降阶把原高维系统转化为与之等价的低维系统,采用配套的打靶法求解低维系统的周期解并通过Floquet定理来判断周期解的稳定性,周期解失稳后采用直接数值积分方法求解系统的长期动力响应。
(4)针对复杂转子系统动力特性的研究,根据本文对轴承—转子系统的求解算法分析,编写了相关的计算程序,对可倾瓦轴承-转子系统和某工程组装式PTA离心压缩机组,进行了线性动力特性分析和非线性动力特性分析,验证了本文模型及算法的有效性及实用性。
Study on Dynamic Behaviour of Complex Rotor Systems
Large assembled centrifugal compressor units are comprised of multi-parallel rotor bearing system, which are dynamic coupled by gear box and coupling. With the development of compressor units towards to high speed, maximization and complication, it's necessary to research the rotor-bearing system dynamic behavior for improving the system stability, security and reliability.
On the background of rotor dynamic modeling and solution of large assembled centrifugal compressor units, this thesis studies on several aspects, such as, the model and algorithm of turbulent nonlinear oil-film forces and their Jacobian matrices, the model of tilting pad journal bearing, the model and nonlinear solution of complicated rotor bearing systems. Some achievements are acquired by current research from theory and practice, and conclusions that are reached are beneficial to study on the behavior of rotor-bearing system and engineering applications.
In detail, there are the following achievements and contents in current research.
(1) Based on the variational inequality of general quasilinear elliptic partial differential equation in free boundary condition, a kind of model with an efficient algorithm is presented to get the nonlinear oil-film force and its Jacobian matrices by solving turbulent Reynolds equation. Considering the condition of bearing side-pressure not equal to zero, the proper oil-film pressure function is chosen in the form of multiplier of weight function and linear interpolation function, and one-dimensional discrete variational inequality of turbulent Reynolds equation is built up. An amendatory direct-method is proposed to solve the oil-film force and its Jacobian matrices. During the process, the operations are restricted within the positive pressure region, and no iteration is involved.
(2) Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model as well as mathematical method which contains 2n+2 degrees of freedom is presented for calculating the dynamical characteristics of tilting pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement and generalized force vector are chosen. The concise transformation of generalized displacement, generalized force and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using Newton-Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration.
(3) The dynamic model of gear-coupled multi parallel rotor is presented using the finite element method. A method of quadratic normal reduction is presented for complex dynamic system with local nonlinearities. The degrees of freedom are reduced and the equivalent system is obtained by quadratic normal reduction and the effects of local nonlinear forces in the modal transformation are considered. Meanwhile the supporting shooting method is proposed to solve the periodic responses and the stability is determined by the Floquet theory. When the response is unstable, the long-term response is obtained by direct numerical integration method.
(4) The relevant program of current algorithm is developed. The linear and nonlinear dynamic behaviors are calculated for the industrial rotor system supported by tilting-pad journal bearing and one industrial assembled PTA centrifugal compressor train. The efficiency and reliability of the model and algorithm in this thesis is proven.
引文
[1]虞烈,刘恒.轴承-转子系统动力学[M].西安：西安交通大学出版社,2001.
[2]西安交通大学透平压缩机教研室.离心式压缩机原理[M].北京：机械工业出版社,1980.
[3]成正朝,牛大勇.组装式压缩机的特点及发展趋势[J].风机技术,2003,4：3-5.
[4]郑志国,杨树华,孙丽莉.大型PTA工艺气压缩机组国产化技术概述[J]..通用机械,2010,2：26-28.
[5]孟光.转子动力学研究的回顾和展望[J].振动工程学报,2002,15(1)：1-9.
[6]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.振动工程学报,2000,13(4)：497-509.
[7]郑惠萍.大型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.
[8]温诗铸.润滑理论研究的进展与思考[J].摩擦学学报,2007,11：497-503.
[9]董勋.润滑理论[M].上海：上海交通大学出版社,1984.
[10]张直明.滑动轴承的流体动力润滑理论[M].北京：高等教育出版社,1986.
[11]石守红,韩玉强,张锁怀.齿轮耦合的转子-轴承系统的研究现状[J].机械科学与技术,2002,21(5)：703-706.
[12]Childs, D.W. Turbomachinery Rotordynamics:Phenomena, Modeling, and Analysis [M].New York:Johy Wiley & Sons,1993.
[13]张文.转子动力学理论基础[M].北京：科学出版社,1990.
[14]钟一谔,何衍宗,王正,李方泽.转子动力学[M].北京：清华大学出版社,1987.
[15]孙大成.润滑力学讲义[M].北京：中国友谊出版公司,1991.
[16]Tower, B. First Report on Friction Experiments (Friction on Lubricated Bearings)[J].Proceedings of the Institution of Mechanical Engineers,1883, 632-659.
[17]Tower, B. Second Report on Friction Experiments (Experiments on the Oil Pressure in a Bearing) [J].Proceedings of the Institution of Mechanical Engineers, 1885,58-70.
[18]Reynolds, O. On the Theory of the Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil[J].Philosophical Transactions of the Royal Society of London,1886,177:157-234.
[19]Sommerfeld, A.Zur Hydrodynamische Theorie der Schmiermittelreibung [J].Zeitschrift fur Mathemarik and Physik,1904,50:97-155.
[20]Gumbel, L. Monatsblatter Berliner Bezirksver[M]. Berlin:VDI-Verlag,1914.
[21]Swift, H. W. The Stability of Lubricating Films in Journal Bearings [J]. Proceedings of the Institute Civil Engineers, London,1932,233:267-322.
[22]Stieber, W. Das Schwimmlager, Hydrodynamische Theorie des Gleitlagers [M]. Berlin:VDI-Verlag,1933.
[23]Cameron, A., and Wood, W.L. The Full Journal Bearing [J]. Proceedings of the Institution of Mechanical Engineers,1949,161:59-64.
[24]Michell, A.G.M. Progress of Fluid-Film Lubrication [J].Transactions of the ASME,1929,51:153-163.
[25]Ocvirk, F.W., and DuBois, G.B. Analytical Derivation and Experimental Evaluation of Short Bearing Approximations of Full Journal Bearing [R]. Washington:NACA Technical Report 1157,1953.
[26]DuBois, G. B., and Ocvirk, F. W. The Short Bearing Approximation for Plain Journal Bearings [J].Transactions of the ASME,1955,77:1173-1178.
[27]Ng C. W., Pan C. H. T. A linearized turbulent lubrication theory [J]. Trans ASME Ser D,1965,87:675-688.
[28]Dara Childs. Turbomachinery Rotordyanmics [M]. A Wiler-Interscience Publication JOHN WILEY & SONS, INC.
[29]张运清,张直明.一种紊流润滑理论分析新方法-复合型紊流模式理论[J].摩擦学学报.1995,15(3)：271-275.
[30].张新敏等.一种湍流润滑理论分析的工程计算方法[J].润滑与密封,2002,2：4-7.
[31]戴学余,苗旭升等.几种低粘度润滑介质下动静压轴承的性能分析[J].润滑与密封,2004,3：9-13.
[32]朱均,周长新,黄念椿.紊流工况下椭圆轴承性能的研究[J].第二次全国摩擦磨损润滑学术会议论文集,1979.
[33]王晓力,温诗铸,桂长林.动载轴承的非稳态热流体动力润滑[J].清华大学学报,1999,39(8)：30-33.
[34]Christopherson, D.G. A New Mathematical Method for the Solution of Film Lubrication Problems[J].Proceedings of the Institution of Mechanical Engineers,1941,146(3):126-135.
[35]Cryer, C.The Method of Christopherson for Solving Free Boundary Problems for Infinite Journal Bearings by Means of Finite Differences[J].Mathematics of Computation,1971,25:435-443.
[36]Bayada, G..Inequations Variationelles Elliptiques avec Conditions aux Limites Periodiques:Application a la Resolution de I'Euation de Reynolds [D]. Lyon: Universite Lyon I,1972.
[37]Lund, J.W. Spring and Damping Coefficients for the Tilting-Pad Journal Bearing[J].ASLE Transactions,1964,7:342-352.
[38]Hori, Y., and Kato, T. Earthquake-Induced Instability of a Rotor Supported by Oil Film Bearing[J].ASME J. of Vibration, Acoustics, Stress, and Reliability in Design,1990,112(2):160-165.
[39]Earles, L.L., Palazzolo, A.B., and Armentrout R.W. A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings:Part Ⅰ and Ⅱ [J].ASME J.of Tribology,1990,112(2):169-182.
[40]杨建刚,蔡霆.汽轮机轴承动力特性三维流固耦合分析模型[J].中国电机工程学报,2004,24(8)：147-151.
[41]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.
[42]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.
[43]秦平,沈钺,徐华,朱均.考虑进油压力的滑动轴承非线性油膜力数据库[J].摩擦学学报,2004,24(3)：258-261.
[44]焦映厚,陈照波,夏松波,陈明,黄文虎,张志明.转子-非圆轴承系统非线性动力学行为的研究[J]、航空动力学报,2000,15(4)：413-418.
[45]陈照波,焦映厚,夏松波,黄文虎.求解有限长圆柱型滑动轴承中非线性油 膜力的近似解析方法[J].中国电机工程学报,2001,21(增刊)：6-9.
[46]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)：761-768.
[47]Rohde, S.M., and McAllister, 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.
[48]Lewy, H., and Stampacchia, G.On the Regularity of the Solution of a Variational Inequality[J].Communications on Pure and Applied Mathematics,1969, 22:153-188.
[49]Klit, P., and Lund, J.W.Caculation of the Dynamic Coefficients of a Journal Bearing, Using a Variational Approach[J].ASME J.of Tribology,1986,108 (3):421-425.
[50]Bayada, G., and Chambat, M.Nonlinear Variational Formulation for a Cavitation Problem in Lubrication[J].J.of Mathematical Analysis and Applications,1982, 90 (2):286-298.
[51]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.
[52]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,2002,19(3)：90-95.
[53]沈光琰,肖忠会,郑铁生,张文.油叶型轴承-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.
[54]刘大全,肖忠会,张文,郑铁生.滑动轴承非线性油膜力的一位直接解法[J].机械工程学报,2005,41(2)：51-56.
[55]王丽萍,刘大全,张文,郑铁生.求滑动轴承非线性油膜力的加权有限元方法[J].工程力学,2006,23(5)：163-167.
[56]肖忠会,刘大全,张文,郑铁生.发电机组轴承非线性油膜力的快速算法研究[J].中国电机工程学报,2004,24(12)：144-148.
[57]肖忠会,沈光琰,郑铁生,张文.用瑞利-利兹法求解瞬时非稳态滑动轴承油膜力的新算法[J].计算力学学报,2005,22(6)：685-689.
[58]FEDORENKO N D, USENKO V V, MARTSINKOVSKII V S, Tilting pad journal beari-has self-aligning segments which are prevented from moving peripherally by locking screws to give improved load-bearing and damping properties[P], America:SU168266-A1,1992.
[59]Willis W.Gardner, Waukesha, Wis.Tilting pad journal bearing using directed lubrication [P]. America:US005288153A,1994.
[60]Willis W. Gardner, Waukesha, Wis. Journal bearing having vibration damping elements [P]. America:US5739445-A,1998.
[61]Gozdawa R.J. Tilting pad hydrodynamic journal bearing for rotating shaft comprises shell housing with cylindrical bore with at least three bearing pads mounted to pivot [P]. America:US6623164-B1,2000.
[62]Seong Heon Yang. experimental study on the characteristics of pad fluttering in a tilting pad journal bearing[J]. Tribology international,2006,39:686-694.
[63]D.J. Hargreaves, M Fillon. Analysis of a tilting pad journal bearing to avoid pad fluttering [J]. Tribology International,2007,40:607-612.
[64]Seongheon Yang. Prevention fluttering fatigue damage in a tilting pad journal bearing [J]. Tribology International,2009,42(6):816-822.
[65]ILMAR FERREIRA SANTOS. On the adjusting of the dynamic coefficients of tilting-pad journal bearings [J]. Tribology Transactions,1995,38(3):700-706.
[66]Lund, J. W., Spring and damping coefficients for the tilting-pad journal bearing [J].ASLE Trans.,1964,7:342-352.
[67]John C. Nicholas. Lund's tilting pad journal bearing pad assembly method [J]. ASME Trnas. Journal of Vibration and Acoustics,2003,125:448-454.
[68]Orcutt, F. K. The steady-state and dynamic characteristics of the tilting-pad journal bearing in laminar and turbulent flow regimes [J]. ASME J. Lubr. Technol. 1967,89(3),pp:392-404.
[69]Elwell, R. C., Findlay, J. A. Design of pivoted-pad journal bearing [J]. ASME J. Lubr. Technol.1969,91(1):87-103.
[70]Nicholas, J. C., Gunter, E. J., Allaire, P. E. Stiffness and dmaping coefficients for the five pad tilting pad bearing [J]. ASLE Trans.1979,22(2):112-124.
[71]Nicholas, J. C., Gunter, E. J., Barrett, L. E. The influence of tilting pad bearing characteristics on the stability of high speed rotor bearing systems[C]. Topics in fluid film bearing and rotor bearing system design and optimization, an ASME publication.1978:55-78.
[72]Jones, G. J., Martin, F. A. Geometry effects in tilting-pad journal bearings [J]. ASLE Trans.1979,22(3), pp:227-244.
[73]Hashimoto, H., Wada, S., and Marukawa, T. Performance and Characteristics of Large Scale Tilting-pad Journal Bearing [J]. Bull, J.S.M.E.,1985,242(28): 1761-1765.
[74]Lund, J. W. The Influence of Pad Flexibility on the Dynamic Coefficients of a Tilting Pad Journal Bearing [J]. Journal of Tribology,1987,109:65-70.
[75]Kirk, R. G. Evaluation of Pivot Stiffness for Typical Tilting-pad Journal Bearing Designs [J]. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1988,110:165-171.
[76]Dmochowski, W. Dynamic Properties of Tilting-pad Journal Bearings: Experimental and Theoretical Investigation of Frequency Effects due to Pivot Flexibility [J]. Journal of Engineering for Gas Turbines and Power,2007,129: 865-869.
[77]White, M. F., Chan S. H. The subsynchronous dynamic behavior of tilting-pad journal bearings [J]. ASME Journal of Tribology,1992,114:167-173.
[78]Desbordes, H., Fillon, M., etc. Dynamic analysis of tilting-pad journal bearing-Influence of pad deformations [J]. ASME Journal of Tribology,1994, 116:621-628.
[79]张直明.计入支点弹性和阻尼时可倾瓦轴承支撑的转子系统的动力稳定性.机械工程学报[J],1983,19(2),pp：9-21.
[80]Qiuying Chang, Peiran Yang, Yonggang Meng etc. Thermoelastohydrodynamic analysis of the static performance of tilting-pad journal bearings with the Newton-Raphson method [J]. Tribology International.2002,35:225-234.
[81]El-Butch, A. E., Ashour N. M. Transient analysis of misaligned elastic tilting-pad journal bearing [J]. Tribology International.2005,38:41-48.
[82]Noma, M., Mori, A. Study no the structures of fluid flows in the annular space formed by a submerged tilting pad journal bearing [J]. Journal of Visualization. 2006,9(4):457-465.
[83]Shapiro, W., Colsher, R. Dynamic characteristics of fluid film bearings. Proceedings of the sixth turbomachinery symposium[C], Texas A&M University, College Station, Texas.1977, pp:39-53.
[84]Alliare, P. E., Parsell, J. K., Barrett, L. E. A pad perturbation method for the dynamic coefficients of tilting-pad journal bearing [J]. Wear,1981,72(1):29-44.
[85]虞烈.轴承-转子系统的稳定性与振动控制研究[D].西安：西安交通大学,1987.
[86]Rouch, K. E. Dynamics of pivoted-pad journal bearings, including pad translation and rotation effects [J]. ASLE Transaction,1983,26(1):102-109.
[87]Qiao, G., Wang, L. P., and Zheng, T. S. Linear Stability Analysis of a Tilting-pad Journal Bearing System [J]. Journal of Tribology,2007,129:348-353.
[88]王丽萍,乔广,郑铁生.可倾瓦轴承的完整动力分析模型及计算方法[J].机械工程学报,2008,44(1)：75-80.
[89]Yan, Z. Y., Wang, L. P., Qiao, G., Zheng, T. S. An Analytical Model for Complete Dynamical Coefficients of Tilting Pad Journal Bearing [J]. Tribology International,2010,43(1):7-15.
[90]Yan, Z. Y, Lu, Y., Zheng, T. S. An analytical model of tilting-pad journal bearing considering pivot stiffness and damping [J]. ASME Trans, Journal of Tribology, 2011,133(1):011702.1-011702.8.
[91]Tripp, H., Murphy, B. Eccentricity measurements on a tilting-pad bearing [J]. ASLE Transaction,1985,28:217-222.
[92]J. Kostrzewsky, Ron Flack. Accuracy evaluation of experimentally derived dynamic coefficients of fluid film bearings Part Ⅰ:Development of method [J]. Tribol Trans 1990;33(1):105-114.
[93]J. Kostrzewsky, Ron Flack. Accuracy evaluation of experimentally derived dynamic coefficients of fluid film bearings Part Ⅱ:Case studies [J]. Tribol Trans 1990;33(1):115-121.
[94]Brockwell, K. R., Kleinbub, D., Emochowski, W. Measurements of the dynamic operating characteristic of the five shoe tilting pad journal bearing [J]. Tribology Transactions,1990,33:481-492.
[95]Fillon, M., Bligoud, J. C., Frene, J. Experimental study of tilting-pad journal bearings comparison with theoretical thermoelastohydrodynamic results [J]. ASME J. of Lubrication Technology,1992,114:579-588.
[96]Ron Flack, Hunter Cloud, Lloyd Barrett. Influence of journal speed and load on the static operating characteristics of a tilting-pad journal bearing with ball-and-socket pivots [J]. Tribol Trans 2005;48:283-288.
[97]徐华,姜歌东,丛红,谢友柏,王凤才.四瓦可倾瓦径向滑动轴承动力特性的实验研究[J].摩擦学学报,2001,21(5)：225-229.
[98]姜培林,虞烈.可倾瓦径向滑动轴承支撑的转子系统瞬态响应计算[J].计算力学学报[J],1999,16(1)：101-107.
[99]焦映厚,陈照波,刘福利等Jeffcott转子-可倾瓦滑动轴承系统不平衡相应的非线性分析[J].中国电机工程学报,2004,24(12)：227-232.
[100]Renato Brancati, Ernesto Rocca, Riccardo Russot. Non-linear stability analysis of a rigid rotor on tilting pad journal bearings [J]. Tribology International,1996, 29(7):571-578.
[101]Issam Abu-Mahfouz, Maurice L. Adams. Numerical study of some nonlinear dynamics of a rotor supported on a three-pad tilting-pad journal bearing(TPJB) [J]. Transactions of ASME Journal of Vibration and Acoustics, 2005,127:262-272.
[102]Rankine, W. J. M. On the centrifugal force of rotating shafts [J]. Engineer,1869, 27:249-256.
[103]Jeffcott, H. H. The lateral vibration of loaded shafts in the neighbourhood of a whirling speed-The effect of wand of balance [J]. Philosophical Magazine,1919, 6(37):304-314.
[104]Stodola, A. Steam and gas turbines[M]. New York:McGraw-Hill,1927.
[105]Green, R. B. Gyroscopic effects on the critical speeds of flexible rotors [J]. ASME Journal of Applied Mechanics,1948,15:369-376.
[106]Newkirk, B. L. Shaft whipping [J]. General Electric Review,1924,27:169-178.
[107]Newkirk, B. L., Taylor, H. D. Shaft whipping due to oil action in journal bearings [J]. Geneal Electric Review,1925,28:559-568.
[108]Lund J. W. Review of the concept of dynamic coefficients for fluid film journal bearings [J]. ASME Journal of Tribology,1987,109:37-41.
[109]Lund, J. W., and Sternlicht, B. Rotor-bearing dynamics with emphasis on attenuation [J]. ASEM Journal of Basic Engineering,1962,84:491-502.
[110]Lund, J. W. The stability of an elastic rotor in journal bearings with flexible damped supports [J]. ASME Journal of Applied Mechanics,1965,87:911-920.
[111]Gunter, E. J. Dynamic stability of rotor-bearing systems [R]. Wsshington:NASA SP-113,1966.
[112]Childs, D. W. and Moyer, D. S. Vibration characteristic of the HPOTP (High-pressure oxygen turbopump) of the SSME (Space Shuttle Main Engine) [J]. ASME Journal of Engineering for Gas Turbines and Power,1985, 107(1):152-159.
[113]Prohl M. A. A general method of calculating critical speeds of flexible rotors. ASME Trans Journal of Applied Mechanics,1945,67::142-146.
[114]Ruhl, R. L., and Booker, J. F. A finite element model for distributed parameter turborotor system [J]. ASME J. of Engineering for Industry,1972,94(1):126-132.
[115]Nelson, H. D., and McVaugh, J. M. Dynamics of rotor-bearing systems using finite elements [J]. ASME J. of Engineering for Industry,1976,98:593-600.
[116]Nelson, H. D. A finite rotating shaft element using Timoshenko beam theory [J]. ASME J. of Mechanical Design,1980,102(4):793-803.
[117]Rouch K. E. and Kao J. S. A tapered beam finite element for rotor dynamics analysis [J]. Journal of Sound and Vibration,1979,66(1):119-140.
[118]Edney S. L., Fox C. H. J. and Williams E. J. Tapered Timoshenko finite elements for rotor dynamics analysis [J]. Journal of Sound and Vibration,1990, 137(3):463-481.
[119]Bathe K. J. and Wilson E. L. Numerical methods in finite element analysis [D]. Prentice-Hall, INC., Englewood Cliffs, New Jersey,1979.
[120]Mitchell L. D. and Mellen D. M. Torsional-Lateral Coupling in A Geared High Speed Rotor System [D]. ASME,75-DET-75,1975.
[121]Lund J. W. Critical Speeds, Stability and Response of A Geared Train of Rotors [J]. Journal of Mechanical Design,1978,100:535-539.
[122]Lida H. Coupled Torsional-Flexural Vibration of A Shaft in A Geared System of Rotors [J]. Bulletion of JSME,1980,23:2111-2117.
[123]E. Brommundt. and E. Kramer. Instability and Self-excitation Caused by A Gear Coupling in A Simple Rotor System [J]. Forsch Ingenieurwes,2006,70:25-37.
[124]张锁怀,李忆平,丘大谋.用谐波平衡发分析齿轮耦合的转子-轴承系统的动力特性[J].机械工程学报,2000,36(7)：18-23.
[125]张锁怀,李忆平,丘大谋.齿轮耦合的转子-轴承系统非线性动力特性的研究[J].机械工程学报,2001,37(9)：53-57.
[126]李明,胡海岩.完整约束下齿轮啮合转子系统的弯扭耦合振动稳态响应[J].振动工程学报,2003,16(1)：75-80.
[127]宋雪萍,刘树英,闻邦椿.齿轮转子系统的振动特性分析[J].机械科学与技术,2006,25(2)：153-157.
[128]崔亚辉,刘占生,叶建槐等.复杂多级齿轮-转子-轴承系统的动力学建模和数值仿真[J].机械传动,2009,33(6)：44-48.
[129]崔亚辉,刘占生,叶建槐.齿轮-转子耦合系统的动态响应及齿侧间隙对振幅跳跃特性的影响[J].机械工程学报,2009,45(7)：7-15.
[130]蒋庆磊,吴大转,谭善光.齿轮传动多转子耦合系统振动特性研究.振动工程学报[J],2010,23(3)：254-259.
[131]马红.齿轮-轴承-转子系统弯扭耦合振动特性研究[D].西安：西安交通大学,1993.
[132]徐稼轩,郑铁生.结构动力分析的数值方法[M].西安：西安交通大学出版社,1993.
[133]陈玲莉.工程结构动力分析数值方法[M].西安：西安交通大学出版社,2006.
[134]Hurty, W. C. Dynamic Analysis of Structural Systems Using Component Modes [J].AIAA J.,1965,3(4):678-685.
[135]Craig, R. R. and Bampton, M. C. Coupling of Substructures for Dynamic Analysis [J]. AIAA J.,1968,6(7):1313-1319.
[136]Glasgow, D. A. and Nelson, H. D. Stability Analysis of Rotor-Bearing Systems Using Component Mode Synthesis [J]. ASME J. of Mechanical Design,1980, 102(2):352-359.
[137]Nelson, H. D. and Meacham, W. L. Transient Analysis of Rotor-Bearing Systems Using Component Mode Synthesis [R]. Houston:Gas Turbine Conference, ASME Paper 81-GT-110,1982.
[138]Nelson, H. D., Meacham, W. L., Fleming, D. P. and Kascak, A. F. Nonlinear Analysis of Rotor-Bearing Systems Using Component Mode Synthesis [J]. ASME J. of Engineering for Power,1983,105(3):606-614.
[139]Fey, R. H. B. Long Term Structural Dynamics of Mechanical Systems With Local Nonlinearities [J]. ASME J. of Vibration and Acoustics,1996, 118(2):147-153.
[140]Sundarajan, P. and Noah, S. T. An Algorithm for Response and Stability of Large Order Nonlinear Systems-Application to Rotor Systems [J]. J. of Sound and Vibration,1998,214(4):695-723.
[141]张家忠,许庆余,郑铁生.具有局部非线性动力系统系统周期解及稳定性方法[J].力学学报,1998,30(5)：572-579.
[142]Zheng T. and Hasebe, N. Nonlinear Dynamic Behaviors of a Complex Rotor-Bearing System[J]. ASME Journal of Applied Mechanics,2000, 67:485-495.
[143]郑铁生,伍晓红.复杂非线性转子-轴承系统动力特性数值分析[J].力学学报,2001,33(3)：377-389.
[144]Zhipeng Xia, Guang Qiao, Tiesheng Zheng, Wen Zhang. Nonlinear Modeling and Dynamic Analysis of Rotor-Bearing System [J]. Nonlinear Dynamics,2009, 57(4):559-577.
[145]Paardekooper, M.H.C. An Eigenvalue Algorithm for Skew-Symmetric Matrices. Numerical mathematics,1971,17:189-302.
[146]Meirovitch, L.A new Method of Solution of the Eigenvalue Problem for Gyroscopic Systems. AIAA, J.,1974,12(10):1337-1342.
[147]Bauchau, O.A. A Solution of the Eigenproblem for Undamped Gyroscopic Systems with Lanczos Algorithm. International Journal for Numerical Methods in Engineering,1986,23(9):1705-1713.
[148]郑铁生,蔡则彪.非对称矩阵结构固有值分析的广义逆迭代法[J].振动工程学报,1990,3(2)：79-84.
[149]Zheng Zhaochang, Ren Gexue and Williams F.W. The Eigenvalue Problem for Damped Gyroscopic Systems[J]. International Journal of Mechanical Science, 1997,39(6):741-750.
[150]周纪卿,朱因远.非线性振动[M].西安：西安交通大学出版社,1998.
[151]胡海岩.应用非线性动力学[M].北京：航空工业出版社,2000.
[152]Li D X, Xu J X. A method to determine the periodic solution of the non-linear dynamics system [J]. Journal of Sound and Vibration,2004,275:1-16.
[153]Hu Haiyan. Numerical scheme of locating the periodic response of non-smooth non-autonomous systems of high dimension [J]. Computer Methods in Applied Mechanics and Engineering,1995,23(1):53-62.
[154]Hsu, C. S., and Guttalu, R. S. An unraveling algorithm for global analysis of dynamical systems:an application of cell-to-cell mappings [J]. ASME J. of Applied Mechanics,1980,47(4):940-948.
[155]刘恒,陈绍汀.非线性系统全局动态特性分析的PCM法及其在转子系统中的应用[J].应用力学学报,1995,12(3)：7-15.
[156]Tombyses, B., and Aldemir, T. Continuous cell to cell mapping [J]. J. of Sound and Vibration,1997,202(3):395-415.
[157]王明新.偏微分方程基本理论[M].北京：科学技术出版社,2002.
[158]API617. Axial and centrifugal compressors and Expander-compressors for the petroleum chemical and gas industry [S]. America:Chemical and Gas Industry Services,2002.
[2]西安交通大学透平压缩机教研室.离心式压缩机原理[M].北京：机械工业出版社,1980.
[3]成正朝,牛大勇.组装式压缩机的特点及发展趋势[J].风机技术,2003,4：3-5.
[4]郑志国,杨树华,孙丽莉.大型PTA工艺气压缩机组国产化技术概述[J]..通用机械,2010,2：26-28.
[5]孟光.转子动力学研究的回顾和展望[J].振动工程学报,2002,15(1)：1-9.
[6]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.振动工程学报,2000,13(4)：497-509.
[7]郑惠萍.大型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.
[8]温诗铸.润滑理论研究的进展与思考[J].摩擦学学报,2007,11：497-503.
[9]董勋.润滑理论[M].上海：上海交通大学出版社,1984.
[10]张直明.滑动轴承的流体动力润滑理论[M].北京：高等教育出版社,1986.
[11]石守红,韩玉强,张锁怀.齿轮耦合的转子-轴承系统的研究现状[J].机械科学与技术,2002,21(5)：703-706.
[12]Childs, D.W. Turbomachinery Rotordynamics:Phenomena, Modeling, and Analysis [M].New York:Johy Wiley & Sons,1993.
[13]张文.转子动力学理论基础[M].北京：科学出版社,1990.
[14]钟一谔,何衍宗,王正,李方泽.转子动力学[M].北京：清华大学出版社,1987.
[15]孙大成.润滑力学讲义[M].北京：中国友谊出版公司,1991.
[16]Tower, B. First Report on Friction Experiments (Friction on Lubricated Bearings)[J].Proceedings of the Institution of Mechanical Engineers,1883, 632-659.
[17]Tower, B. Second Report on Friction Experiments (Experiments on the Oil Pressure in a Bearing) [J].Proceedings of the Institution of Mechanical Engineers, 1885,58-70.
[18]Reynolds, O. On the Theory of the Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil[J].Philosophical Transactions of the Royal Society of London,1886,177:157-234.
[19]Sommerfeld, A.Zur Hydrodynamische Theorie der Schmiermittelreibung [J].Zeitschrift fur Mathemarik and Physik,1904,50:97-155.
[20]Gumbel, L. Monatsblatter Berliner Bezirksver[M]. Berlin:VDI-Verlag,1914.
[21]Swift, H. W. The Stability of Lubricating Films in Journal Bearings [J]. Proceedings of the Institute Civil Engineers, London,1932,233:267-322.
[22]Stieber, W. Das Schwimmlager, Hydrodynamische Theorie des Gleitlagers [M]. Berlin:VDI-Verlag,1933.
[23]Cameron, A., and Wood, W.L. The Full Journal Bearing [J]. Proceedings of the Institution of Mechanical Engineers,1949,161:59-64.
[24]Michell, A.G.M. Progress of Fluid-Film Lubrication [J].Transactions of the ASME,1929,51:153-163.
[25]Ocvirk, F.W., and DuBois, G.B. Analytical Derivation and Experimental Evaluation of Short Bearing Approximations of Full Journal Bearing [R]. Washington:NACA Technical Report 1157,1953.
[26]DuBois, G. B., and Ocvirk, F. W. The Short Bearing Approximation for Plain Journal Bearings [J].Transactions of the ASME,1955,77:1173-1178.
[27]Ng C. W., Pan C. H. T. A linearized turbulent lubrication theory [J]. Trans ASME Ser D,1965,87:675-688.
[28]Dara Childs. Turbomachinery Rotordyanmics [M]. A Wiler-Interscience Publication JOHN WILEY & SONS, INC.
[29]张运清,张直明.一种紊流润滑理论分析新方法-复合型紊流模式理论[J].摩擦学学报.1995,15(3)：271-275.
[30].张新敏等.一种湍流润滑理论分析的工程计算方法[J].润滑与密封,2002,2：4-7.
[31]戴学余,苗旭升等.几种低粘度润滑介质下动静压轴承的性能分析[J].润滑与密封,2004,3：9-13.
[32]朱均,周长新,黄念椿.紊流工况下椭圆轴承性能的研究[J].第二次全国摩擦磨损润滑学术会议论文集,1979.
[33]王晓力,温诗铸,桂长林.动载轴承的非稳态热流体动力润滑[J].清华大学学报,1999,39(8)：30-33.
[34]Christopherson, D.G. A New Mathematical Method for the Solution of Film Lubrication Problems[J].Proceedings of the Institution of Mechanical Engineers,1941,146(3):126-135.
[35]Cryer, C.The Method of Christopherson for Solving Free Boundary Problems for Infinite Journal Bearings by Means of Finite Differences[J].Mathematics of Computation,1971,25:435-443.
[36]Bayada, G..Inequations Variationelles Elliptiques avec Conditions aux Limites Periodiques:Application a la Resolution de I'Euation de Reynolds [D]. Lyon: Universite Lyon I,1972.
[37]Lund, J.W. Spring and Damping Coefficients for the Tilting-Pad Journal Bearing[J].ASLE Transactions,1964,7:342-352.
[38]Hori, Y., and Kato, T. Earthquake-Induced Instability of a Rotor Supported by Oil Film Bearing[J].ASME J. of Vibration, Acoustics, Stress, and Reliability in Design,1990,112(2):160-165.
[39]Earles, L.L., Palazzolo, A.B., and Armentrout R.W. A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings:Part Ⅰ and Ⅱ [J].ASME J.of Tribology,1990,112(2):169-182.
[40]杨建刚,蔡霆.汽轮机轴承动力特性三维流固耦合分析模型[J].中国电机工程学报,2004,24(8)：147-151.
[41]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.
[42]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.
[43]秦平,沈钺,徐华,朱均.考虑进油压力的滑动轴承非线性油膜力数据库[J].摩擦学学报,2004,24(3)：258-261.
[44]焦映厚,陈照波,夏松波,陈明,黄文虎,张志明.转子-非圆轴承系统非线性动力学行为的研究[J]、航空动力学报,2000,15(4)：413-418.
[45]陈照波,焦映厚,夏松波,黄文虎.求解有限长圆柱型滑动轴承中非线性油 膜力的近似解析方法[J].中国电机工程学报,2001,21(增刊)：6-9.
[46]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)：761-768.
[47]Rohde, S.M., and McAllister, 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.
[48]Lewy, H., and Stampacchia, G.On the Regularity of the Solution of a Variational Inequality[J].Communications on Pure and Applied Mathematics,1969, 22:153-188.
[49]Klit, P., and Lund, J.W.Caculation of the Dynamic Coefficients of a Journal Bearing, Using a Variational Approach[J].ASME J.of Tribology,1986,108 (3):421-425.
[50]Bayada, G., and Chambat, M.Nonlinear Variational Formulation for a Cavitation Problem in Lubrication[J].J.of Mathematical Analysis and Applications,1982, 90 (2):286-298.
[51]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.
[52]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,2002,19(3)：90-95.
[53]沈光琰,肖忠会,郑铁生,张文.油叶型轴承-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.
[54]刘大全,肖忠会,张文,郑铁生.滑动轴承非线性油膜力的一位直接解法[J].机械工程学报,2005,41(2)：51-56.
[55]王丽萍,刘大全,张文,郑铁生.求滑动轴承非线性油膜力的加权有限元方法[J].工程力学,2006,23(5)：163-167.
[56]肖忠会,刘大全,张文,郑铁生.发电机组轴承非线性油膜力的快速算法研究[J].中国电机工程学报,2004,24(12)：144-148.
[57]肖忠会,沈光琰,郑铁生,张文.用瑞利-利兹法求解瞬时非稳态滑动轴承油膜力的新算法[J].计算力学学报,2005,22(6)：685-689.
[58]FEDORENKO N D, USENKO V V, MARTSINKOVSKII V S, Tilting pad journal beari-has self-aligning segments which are prevented from moving peripherally by locking screws to give improved load-bearing and damping properties[P], America:SU168266-A1,1992.
[59]Willis W.Gardner, Waukesha, Wis.Tilting pad journal bearing using directed lubrication [P]. America:US005288153A,1994.
[60]Willis W. Gardner, Waukesha, Wis. Journal bearing having vibration damping elements [P]. America:US5739445-A,1998.
[61]Gozdawa R.J. Tilting pad hydrodynamic journal bearing for rotating shaft comprises shell housing with cylindrical bore with at least three bearing pads mounted to pivot [P]. America:US6623164-B1,2000.
[62]Seong Heon Yang. experimental study on the characteristics of pad fluttering in a tilting pad journal bearing[J]. Tribology international,2006,39:686-694.
[63]D.J. Hargreaves, M Fillon. Analysis of a tilting pad journal bearing to avoid pad fluttering [J]. Tribology International,2007,40:607-612.
[64]Seongheon Yang. Prevention fluttering fatigue damage in a tilting pad journal bearing [J]. Tribology International,2009,42(6):816-822.
[65]ILMAR FERREIRA SANTOS. On the adjusting of the dynamic coefficients of tilting-pad journal bearings [J]. Tribology Transactions,1995,38(3):700-706.
[66]Lund, J. W., Spring and damping coefficients for the tilting-pad journal bearing [J].ASLE Trans.,1964,7:342-352.
[67]John C. Nicholas. Lund's tilting pad journal bearing pad assembly method [J]. ASME Trnas. Journal of Vibration and Acoustics,2003,125:448-454.
[68]Orcutt, F. K. The steady-state and dynamic characteristics of the tilting-pad journal bearing in laminar and turbulent flow regimes [J]. ASME J. Lubr. Technol. 1967,89(3),pp:392-404.
[69]Elwell, R. C., Findlay, J. A. Design of pivoted-pad journal bearing [J]. ASME J. Lubr. Technol.1969,91(1):87-103.
[70]Nicholas, J. C., Gunter, E. J., Allaire, P. E. Stiffness and dmaping coefficients for the five pad tilting pad bearing [J]. ASLE Trans.1979,22(2):112-124.
[71]Nicholas, J. C., Gunter, E. J., Barrett, L. E. The influence of tilting pad bearing characteristics on the stability of high speed rotor bearing systems[C]. Topics in fluid film bearing and rotor bearing system design and optimization, an ASME publication.1978:55-78.
[72]Jones, G. J., Martin, F. A. Geometry effects in tilting-pad journal bearings [J]. ASLE Trans.1979,22(3), pp:227-244.
[73]Hashimoto, H., Wada, S., and Marukawa, T. Performance and Characteristics of Large Scale Tilting-pad Journal Bearing [J]. Bull, J.S.M.E.,1985,242(28): 1761-1765.
[74]Lund, J. W. The Influence of Pad Flexibility on the Dynamic Coefficients of a Tilting Pad Journal Bearing [J]. Journal of Tribology,1987,109:65-70.
[75]Kirk, R. G. Evaluation of Pivot Stiffness for Typical Tilting-pad Journal Bearing Designs [J]. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1988,110:165-171.
[76]Dmochowski, W. Dynamic Properties of Tilting-pad Journal Bearings: Experimental and Theoretical Investigation of Frequency Effects due to Pivot Flexibility [J]. Journal of Engineering for Gas Turbines and Power,2007,129: 865-869.
[77]White, M. F., Chan S. H. The subsynchronous dynamic behavior of tilting-pad journal bearings [J]. ASME Journal of Tribology,1992,114:167-173.
[78]Desbordes, H., Fillon, M., etc. Dynamic analysis of tilting-pad journal bearing-Influence of pad deformations [J]. ASME Journal of Tribology,1994, 116:621-628.
[79]张直明.计入支点弹性和阻尼时可倾瓦轴承支撑的转子系统的动力稳定性.机械工程学报[J],1983,19(2),pp：9-21.
[80]Qiuying Chang, Peiran Yang, Yonggang Meng etc. Thermoelastohydrodynamic analysis of the static performance of tilting-pad journal bearings with the Newton-Raphson method [J]. Tribology International.2002,35:225-234.
[81]El-Butch, A. E., Ashour N. M. Transient analysis of misaligned elastic tilting-pad journal bearing [J]. Tribology International.2005,38:41-48.
[82]Noma, M., Mori, A. Study no the structures of fluid flows in the annular space formed by a submerged tilting pad journal bearing [J]. Journal of Visualization. 2006,9(4):457-465.
[83]Shapiro, W., Colsher, R. Dynamic characteristics of fluid film bearings. Proceedings of the sixth turbomachinery symposium[C], Texas A&M University, College Station, Texas.1977, pp:39-53.
[84]Alliare, P. E., Parsell, J. K., Barrett, L. E. A pad perturbation method for the dynamic coefficients of tilting-pad journal bearing [J]. Wear,1981,72(1):29-44.
[85]虞烈.轴承-转子系统的稳定性与振动控制研究[D].西安：西安交通大学,1987.
[86]Rouch, K. E. Dynamics of pivoted-pad journal bearings, including pad translation and rotation effects [J]. ASLE Transaction,1983,26(1):102-109.
[87]Qiao, G., Wang, L. P., and Zheng, T. S. Linear Stability Analysis of a Tilting-pad Journal Bearing System [J]. Journal of Tribology,2007,129:348-353.
[88]王丽萍,乔广,郑铁生.可倾瓦轴承的完整动力分析模型及计算方法[J].机械工程学报,2008,44(1)：75-80.
[89]Yan, Z. Y., Wang, L. P., Qiao, G., Zheng, T. S. An Analytical Model for Complete Dynamical Coefficients of Tilting Pad Journal Bearing [J]. Tribology International,2010,43(1):7-15.
[90]Yan, Z. Y, Lu, Y., Zheng, T. S. An analytical model of tilting-pad journal bearing considering pivot stiffness and damping [J]. ASME Trans, Journal of Tribology, 2011,133(1):011702.1-011702.8.
[91]Tripp, H., Murphy, B. Eccentricity measurements on a tilting-pad bearing [J]. ASLE Transaction,1985,28:217-222.
[92]J. Kostrzewsky, Ron Flack. Accuracy evaluation of experimentally derived dynamic coefficients of fluid film bearings Part Ⅰ:Development of method [J]. Tribol Trans 1990;33(1):105-114.
[93]J. Kostrzewsky, Ron Flack. Accuracy evaluation of experimentally derived dynamic coefficients of fluid film bearings Part Ⅱ:Case studies [J]. Tribol Trans 1990;33(1):115-121.
[94]Brockwell, K. R., Kleinbub, D., Emochowski, W. Measurements of the dynamic operating characteristic of the five shoe tilting pad journal bearing [J]. Tribology Transactions,1990,33:481-492.
[95]Fillon, M., Bligoud, J. C., Frene, J. Experimental study of tilting-pad journal bearings comparison with theoretical thermoelastohydrodynamic results [J]. ASME J. of Lubrication Technology,1992,114:579-588.
[96]Ron Flack, Hunter Cloud, Lloyd Barrett. Influence of journal speed and load on the static operating characteristics of a tilting-pad journal bearing with ball-and-socket pivots [J]. Tribol Trans 2005;48:283-288.
[97]徐华,姜歌东,丛红,谢友柏,王凤才.四瓦可倾瓦径向滑动轴承动力特性的实验研究[J].摩擦学学报,2001,21(5)：225-229.
[98]姜培林,虞烈.可倾瓦径向滑动轴承支撑的转子系统瞬态响应计算[J].计算力学学报[J],1999,16(1)：101-107.
[99]焦映厚,陈照波,刘福利等Jeffcott转子-可倾瓦滑动轴承系统不平衡相应的非线性分析[J].中国电机工程学报,2004,24(12)：227-232.
[100]Renato Brancati, Ernesto Rocca, Riccardo Russot. Non-linear stability analysis of a rigid rotor on tilting pad journal bearings [J]. Tribology International,1996, 29(7):571-578.
[101]Issam Abu-Mahfouz, Maurice L. Adams. Numerical study of some nonlinear dynamics of a rotor supported on a three-pad tilting-pad journal bearing(TPJB) [J]. Transactions of ASME Journal of Vibration and Acoustics, 2005,127:262-272.
[102]Rankine, W. J. M. On the centrifugal force of rotating shafts [J]. Engineer,1869, 27:249-256.
[103]Jeffcott, H. H. The lateral vibration of loaded shafts in the neighbourhood of a whirling speed-The effect of wand of balance [J]. Philosophical Magazine,1919, 6(37):304-314.
[104]Stodola, A. Steam and gas turbines[M]. New York:McGraw-Hill,1927.
[105]Green, R. B. Gyroscopic effects on the critical speeds of flexible rotors [J]. ASME Journal of Applied Mechanics,1948,15:369-376.
[106]Newkirk, B. L. Shaft whipping [J]. General Electric Review,1924,27:169-178.
[107]Newkirk, B. L., Taylor, H. D. Shaft whipping due to oil action in journal bearings [J]. Geneal Electric Review,1925,28:559-568.
[108]Lund J. W. Review of the concept of dynamic coefficients for fluid film journal bearings [J]. ASME Journal of Tribology,1987,109:37-41.
[109]Lund, J. W., and Sternlicht, B. Rotor-bearing dynamics with emphasis on attenuation [J]. ASEM Journal of Basic Engineering,1962,84:491-502.
[110]Lund, J. W. The stability of an elastic rotor in journal bearings with flexible damped supports [J]. ASME Journal of Applied Mechanics,1965,87:911-920.
[111]Gunter, E. J. Dynamic stability of rotor-bearing systems [R]. Wsshington:NASA SP-113,1966.
[112]Childs, D. W. and Moyer, D. S. Vibration characteristic of the HPOTP (High-pressure oxygen turbopump) of the SSME (Space Shuttle Main Engine) [J]. ASME Journal of Engineering for Gas Turbines and Power,1985, 107(1):152-159.
[113]Prohl M. A. A general method of calculating critical speeds of flexible rotors. ASME Trans Journal of Applied Mechanics,1945,67::142-146.
[114]Ruhl, R. L., and Booker, J. F. A finite element model for distributed parameter turborotor system [J]. ASME J. of Engineering for Industry,1972,94(1):126-132.
[115]Nelson, H. D., and McVaugh, J. M. Dynamics of rotor-bearing systems using finite elements [J]. ASME J. of Engineering for Industry,1976,98:593-600.
[116]Nelson, H. D. A finite rotating shaft element using Timoshenko beam theory [J]. ASME J. of Mechanical Design,1980,102(4):793-803.
[117]Rouch K. E. and Kao J. S. A tapered beam finite element for rotor dynamics analysis [J]. Journal of Sound and Vibration,1979,66(1):119-140.
[118]Edney S. L., Fox C. H. J. and Williams E. J. Tapered Timoshenko finite elements for rotor dynamics analysis [J]. Journal of Sound and Vibration,1990, 137(3):463-481.
[119]Bathe K. J. and Wilson E. L. Numerical methods in finite element analysis [D]. Prentice-Hall, INC., Englewood Cliffs, New Jersey,1979.
[120]Mitchell L. D. and Mellen D. M. Torsional-Lateral Coupling in A Geared High Speed Rotor System [D]. ASME,75-DET-75,1975.
[121]Lund J. W. Critical Speeds, Stability and Response of A Geared Train of Rotors [J]. Journal of Mechanical Design,1978,100:535-539.
[122]Lida H. Coupled Torsional-Flexural Vibration of A Shaft in A Geared System of Rotors [J]. Bulletion of JSME,1980,23:2111-2117.
[123]E. Brommundt. and E. Kramer. Instability and Self-excitation Caused by A Gear Coupling in A Simple Rotor System [J]. Forsch Ingenieurwes,2006,70:25-37.
[124]张锁怀,李忆平,丘大谋.用谐波平衡发分析齿轮耦合的转子-轴承系统的动力特性[J].机械工程学报,2000,36(7)：18-23.
[125]张锁怀,李忆平,丘大谋.齿轮耦合的转子-轴承系统非线性动力特性的研究[J].机械工程学报,2001,37(9)：53-57.
[126]李明,胡海岩.完整约束下齿轮啮合转子系统的弯扭耦合振动稳态响应[J].振动工程学报,2003,16(1)：75-80.
[127]宋雪萍,刘树英,闻邦椿.齿轮转子系统的振动特性分析[J].机械科学与技术,2006,25(2)：153-157.
[128]崔亚辉,刘占生,叶建槐等.复杂多级齿轮-转子-轴承系统的动力学建模和数值仿真[J].机械传动,2009,33(6)：44-48.
[129]崔亚辉,刘占生,叶建槐.齿轮-转子耦合系统的动态响应及齿侧间隙对振幅跳跃特性的影响[J].机械工程学报,2009,45(7)：7-15.
[130]蒋庆磊,吴大转,谭善光.齿轮传动多转子耦合系统振动特性研究.振动工程学报[J],2010,23(3)：254-259.
[131]马红.齿轮-轴承-转子系统弯扭耦合振动特性研究[D].西安：西安交通大学,1993.
[132]徐稼轩,郑铁生.结构动力分析的数值方法[M].西安：西安交通大学出版社,1993.
[133]陈玲莉.工程结构动力分析数值方法[M].西安：西安交通大学出版社,2006.
[134]Hurty, W. C. Dynamic Analysis of Structural Systems Using Component Modes [J].AIAA J.,1965,3(4):678-685.
[135]Craig, R. R. and Bampton, M. C. Coupling of Substructures for Dynamic Analysis [J]. AIAA J.,1968,6(7):1313-1319.
[136]Glasgow, D. A. and Nelson, H. D. Stability Analysis of Rotor-Bearing Systems Using Component Mode Synthesis [J]. ASME J. of Mechanical Design,1980, 102(2):352-359.
[137]Nelson, H. D. and Meacham, W. L. Transient Analysis of Rotor-Bearing Systems Using Component Mode Synthesis [R]. Houston:Gas Turbine Conference, ASME Paper 81-GT-110,1982.
[138]Nelson, H. D., Meacham, W. L., Fleming, D. P. and Kascak, A. F. Nonlinear Analysis of Rotor-Bearing Systems Using Component Mode Synthesis [J]. ASME J. of Engineering for Power,1983,105(3):606-614.
[139]Fey, R. H. B. Long Term Structural Dynamics of Mechanical Systems With Local Nonlinearities [J]. ASME J. of Vibration and Acoustics,1996, 118(2):147-153.
[140]Sundarajan, P. and Noah, S. T. An Algorithm for Response and Stability of Large Order Nonlinear Systems-Application to Rotor Systems [J]. J. of Sound and Vibration,1998,214(4):695-723.
[141]张家忠,许庆余,郑铁生.具有局部非线性动力系统系统周期解及稳定性方法[J].力学学报,1998,30(5)：572-579.
[142]Zheng T. and Hasebe, N. Nonlinear Dynamic Behaviors of a Complex Rotor-Bearing System[J]. ASME Journal of Applied Mechanics,2000, 67:485-495.
[143]郑铁生,伍晓红.复杂非线性转子-轴承系统动力特性数值分析[J].力学学报,2001,33(3)：377-389.
[144]Zhipeng Xia, Guang Qiao, Tiesheng Zheng, Wen Zhang. Nonlinear Modeling and Dynamic Analysis of Rotor-Bearing System [J]. Nonlinear Dynamics,2009, 57(4):559-577.
[145]Paardekooper, M.H.C. An Eigenvalue Algorithm for Skew-Symmetric Matrices. Numerical mathematics,1971,17:189-302.
[146]Meirovitch, L.A new Method of Solution of the Eigenvalue Problem for Gyroscopic Systems. AIAA, J.,1974,12(10):1337-1342.
[147]Bauchau, O.A. A Solution of the Eigenproblem for Undamped Gyroscopic Systems with Lanczos Algorithm. International Journal for Numerical Methods in Engineering,1986,23(9):1705-1713.
[148]郑铁生,蔡则彪.非对称矩阵结构固有值分析的广义逆迭代法[J].振动工程学报,1990,3(2)：79-84.
[149]Zheng Zhaochang, Ren Gexue and Williams F.W. The Eigenvalue Problem for Damped Gyroscopic Systems[J]. International Journal of Mechanical Science, 1997,39(6):741-750.
[150]周纪卿,朱因远.非线性振动[M].西安：西安交通大学出版社,1998.
[151]胡海岩.应用非线性动力学[M].北京：航空工业出版社,2000.
[152]Li D X, Xu J X. A method to determine the periodic solution of the non-linear dynamics system [J]. Journal of Sound and Vibration,2004,275:1-16.
[153]Hu Haiyan. Numerical scheme of locating the periodic response of non-smooth non-autonomous systems of high dimension [J]. Computer Methods in Applied Mechanics and Engineering,1995,23(1):53-62.
[154]Hsu, C. S., and Guttalu, R. S. An unraveling algorithm for global analysis of dynamical systems:an application of cell-to-cell mappings [J]. ASME J. of Applied Mechanics,1980,47(4):940-948.
[155]刘恒,陈绍汀.非线性系统全局动态特性分析的PCM法及其在转子系统中的应用[J].应用力学学报,1995,12(3)：7-15.
[156]Tombyses, B., and Aldemir, T. Continuous cell to cell mapping [J]. J. of Sound and Vibration,1997,202(3):395-415.
[157]王明新.偏微分方程基本理论[M].北京：科学技术出版社,2002.
[158]API617. Axial and centrifugal compressors and Expander-compressors for the petroleum chemical and gas industry [S]. America:Chemical and Gas Industry Services,2002.