高速重载燃气轮机齿轮转子动力学特性研究
|
摘要
随着齿轮传动系统转速不断增加、性能不断提高,对于高速齿轮传动转子系统的动力特性研究越来越成为人们研究的焦点。由于齿轮的啮合作用,使得各转子之间的弯曲振动和扭转振动相互耦合,因而齿轮转子系统的动力学特性不能仅从单个转子来考察,为此必须建立系统的弯扭耦合系统模型来分析其动力学特性。
论文依托国家科技支撑项目计划《高速、重载齿轮传动系统共性关键技术》,以高速重载燃气轮机齿轮传动转子系统为研究对象,结合现有的对简单转子系统动力特性的研究方法,对齿轮转子的动力学特性包括临界转速及不平衡响应进行研究,为燃气轮机齿轮箱的设计提供参考。
论文首先简单介绍了转子振动问题的研究现状和当前面临的主要问题以及国内外对此问题的解决方法。总结了计算转子系统临界转速及振动模态的传递矩阵法,对简单转子系统弯振和扭振分析问题做了细致的研究,列举了几种典型单元的传递矩阵;并对滑动轴承支承转子的动力学特性的计算方法进行了研究。讨论了滑动轴承动力特性及油膜动力特性系数的确定,并就转子振动量的复数表示进行了深入研究,对转子系统的运动形态进行了分析,推导了各向异性支承转子典型单元的传递矩阵。应用整体传递矩阵法的基本理论对多平行轴耦合转子系统进行了建模及分析,推出了其整体传递矩阵。
针对高速、重载燃气轮机齿轮转子系统,讨论并计算其轴承阻尼,刚度,齿轮啮合刚度,啮合阻尼以及齿轮转子系统各相关参数,导出耦合刚度阵,阻尼阵,运用传递矩阵法建立单轴转子的弯振模型及齿轮耦合转子系统的弯扭耦合振动模型,并对其固有特性进行了分析计算。结果表明,由于齿轮的啮合作用,使得转子系统的弯曲振动和扭转振动耦合在一起,并派生出一些新的临界转速及相应模态,因此在系统设计时需特别注意齿轮传动对这些模态的影响。
最后,本文对齿轮转子系统的不平衡量响应进行了分析,结果表明,由于齿轮耦合作用,系统某一转子上的激振力将传递给其他转子,特别是高速轴上的不平衡量将引起转子系统的剧烈振动,因此要注意提高转子尤其是高速转子的动平衡精度,降低不平衡激励,以提高系统的动态品质。
With the increase of rotational speed of gear-rotors and the improvement of its performance, the study of the dynamic characteristic of the gear-rotor system has been becoming a research focus. Because of the gears meshing, bending vibration and torsional vibration of rotors are coupling, so we can’t analyze the dynamic characteristic of rotors system with only one rotor. In order to analyze the dynamic characteristic of gear-rotor system, the lateral-torsional coupling vibration modal must be set up.
Papers rely on the support of national science and technology project“the Common Key Technology of High-speed, Heavy-duty Gear Drive System”, combined with the currently research method of simple rotor dynamic characteristics, to study dynamic characteristic of High-speed, Heavy-duty gas turbine gear-rotor system, which including the critical speed and unbalance response. It has provided reference for the design of gas turbine gear box.
Papers briefly introduced the present research of rotor dynamics, and presented the problem facing in domestic research along with the solutions to that problem have realized. Then we described the transfer matrix method for calculating the critical speed and their vibration modal of the rotor system. The bending and torsional vibration issues of simple rotor were studied separately, many transfer matrixes of several typical units were appended. Furthermore, the method to calculate the characteristic of the rotor which supported by sliding bearing was studied. We discussed the method for calculating the dynamic coefficient of sliding bearing along with its dynamic characteristics, and the plural value of the vibration characteristics was intensively researched, as well as the vibration modal. Then the transfer matrix of rotor supported by sliding bearings was deduced. In succession, the paper gave an overview of basic theory of the whole transmission matrix, with this method the whole transmission matrix of multi-axis parallel coupling rotor system was built.
Basing on the topic of high speed and heavy duty gas turbine gear-rotor system, the bearing damping, stiffness, gear meshing stiffness, meshing damping, the coupling stiffness and the related parameters of gear-rotor system were studied and discussed,. According to the work above, the coupled stiffness and damping matrix were deduced. Then using the transfer matrix method, the bending vibration modal and the lateral-torsional coupling vibration model of gear-rotor system was established. Moreover, its inherent characteristics were analyzed and calculated. The result shows that, because of the gear meshing, making bending vibration of rotor system coupled with the torsional vibration, which derived some new critical speed and the corresponding mode. Therefore, we should pay particular attention to the impact made by gear transmission when designed the system.
Finally, papers analyzed the unbalance response of the gear-rotor system. We can conclude, as the result of the gear coupling effect, when we imposed the exciting force on one rotor, the vibration will be transfer to the others which link together with the running shaft through gear meshing, especially high-speed shaft unbalance will cause intense vibration. Therefore, we should pay attention to improve the precision of dynamic balance of rotor, and reduce the unbalance quantity to improve the dynamic performance of system.
论文依托国家科技支撑项目计划《高速、重载齿轮传动系统共性关键技术》,以高速重载燃气轮机齿轮传动转子系统为研究对象,结合现有的对简单转子系统动力特性的研究方法,对齿轮转子的动力学特性包括临界转速及不平衡响应进行研究,为燃气轮机齿轮箱的设计提供参考。
论文首先简单介绍了转子振动问题的研究现状和当前面临的主要问题以及国内外对此问题的解决方法。总结了计算转子系统临界转速及振动模态的传递矩阵法,对简单转子系统弯振和扭振分析问题做了细致的研究,列举了几种典型单元的传递矩阵;并对滑动轴承支承转子的动力学特性的计算方法进行了研究。讨论了滑动轴承动力特性及油膜动力特性系数的确定,并就转子振动量的复数表示进行了深入研究,对转子系统的运动形态进行了分析,推导了各向异性支承转子典型单元的传递矩阵。应用整体传递矩阵法的基本理论对多平行轴耦合转子系统进行了建模及分析,推出了其整体传递矩阵。
针对高速、重载燃气轮机齿轮转子系统,讨论并计算其轴承阻尼,刚度,齿轮啮合刚度,啮合阻尼以及齿轮转子系统各相关参数,导出耦合刚度阵,阻尼阵,运用传递矩阵法建立单轴转子的弯振模型及齿轮耦合转子系统的弯扭耦合振动模型,并对其固有特性进行了分析计算。结果表明,由于齿轮的啮合作用,使得转子系统的弯曲振动和扭转振动耦合在一起,并派生出一些新的临界转速及相应模态,因此在系统设计时需特别注意齿轮传动对这些模态的影响。
最后,本文对齿轮转子系统的不平衡量响应进行了分析,结果表明,由于齿轮耦合作用,系统某一转子上的激振力将传递给其他转子,特别是高速轴上的不平衡量将引起转子系统的剧烈振动,因此要注意提高转子尤其是高速转子的动平衡精度,降低不平衡激励,以提高系统的动态品质。
With the increase of rotational speed of gear-rotors and the improvement of its performance, the study of the dynamic characteristic of the gear-rotor system has been becoming a research focus. Because of the gears meshing, bending vibration and torsional vibration of rotors are coupling, so we can’t analyze the dynamic characteristic of rotors system with only one rotor. In order to analyze the dynamic characteristic of gear-rotor system, the lateral-torsional coupling vibration modal must be set up.
Papers rely on the support of national science and technology project“the Common Key Technology of High-speed, Heavy-duty Gear Drive System”, combined with the currently research method of simple rotor dynamic characteristics, to study dynamic characteristic of High-speed, Heavy-duty gas turbine gear-rotor system, which including the critical speed and unbalance response. It has provided reference for the design of gas turbine gear box.
Papers briefly introduced the present research of rotor dynamics, and presented the problem facing in domestic research along with the solutions to that problem have realized. Then we described the transfer matrix method for calculating the critical speed and their vibration modal of the rotor system. The bending and torsional vibration issues of simple rotor were studied separately, many transfer matrixes of several typical units were appended. Furthermore, the method to calculate the characteristic of the rotor which supported by sliding bearing was studied. We discussed the method for calculating the dynamic coefficient of sliding bearing along with its dynamic characteristics, and the plural value of the vibration characteristics was intensively researched, as well as the vibration modal. Then the transfer matrix of rotor supported by sliding bearings was deduced. In succession, the paper gave an overview of basic theory of the whole transmission matrix, with this method the whole transmission matrix of multi-axis parallel coupling rotor system was built.
Basing on the topic of high speed and heavy duty gas turbine gear-rotor system, the bearing damping, stiffness, gear meshing stiffness, meshing damping, the coupling stiffness and the related parameters of gear-rotor system were studied and discussed,. According to the work above, the coupled stiffness and damping matrix were deduced. Then using the transfer matrix method, the bending vibration modal and the lateral-torsional coupling vibration model of gear-rotor system was established. Moreover, its inherent characteristics were analyzed and calculated. The result shows that, because of the gear meshing, making bending vibration of rotor system coupled with the torsional vibration, which derived some new critical speed and the corresponding mode. Therefore, we should pay particular attention to the impact made by gear transmission when designed the system.
Finally, papers analyzed the unbalance response of the gear-rotor system. We can conclude, as the result of the gear coupling effect, when we imposed the exciting force on one rotor, the vibration will be transfer to the others which link together with the running shaft through gear meshing, especially high-speed shaft unbalance will cause intense vibration. Therefore, we should pay attention to improve the precision of dynamic balance of rotor, and reduce the unbalance quantity to improve the dynamic performance of system.
引文
[1]刘大易,张宏鹏.燃气轮机的发展前景及其发电技术[J].应用能源技术, 2008, 121(1):5-8.
[2]刘振坤.蔡睿贤院士谈我国燃气轮机的发展[J].燃气轮机技术, 2001, 14(2).
[3] Jeffcott H H. The lateral vibration of loaded shafts in the neighborhood of a whirling speed the effect of want of balance[J]. Phil.mag. , 1919,37.
[4] Rankine W J M. On the centrifugal force of rotating shafts. The Engineer, April. 1869,27.
[5] Prohl M A. A general method for calculating critical speeds of flexible rotors[J]. J. of Appl. Mech. Trans. ASME, 1945, 12(3):142-148.
[6] Myklestad N O. A new method for calculating natural modes of uncoupled bending vibration of airplane wings and other types of beams[J]. J. of Aero. Sci. 1944, 11:153-162.
[7] Horner G C, Pilkey W D. The riccati transfer matrix method[J]. J. of Mech. Des. Trans. ASME, 1978, 100(4):297-302.
[8] Lund J W. Critical speeds, stability and response of a geared train of rotor[J]. ASME Journal of Mechanical Design,1978,100(3):535-538.
[9] Yamada T, Mitsui J. A study on unstable vibration phenomena of a reduction gear system, including the lightly loaded journal bearings, for a marine steam turbine[J]. Bulletin of JSME, 1979, 22(163):98-105.
[10] Ozguven H N, Houser D R. Dynamic analasis of high speed gears by using loaded static transmission error[J]. Journal of Sound and Vibration, 1988, 25(1):71-83.
[11] Kahraman A, Ozguven H N, Houser D R., et al. Dynamic analysis of geared rotors by finite elements[J]. Journal of .Mechanical Design, ASME, 1992, 114(9):507-514.
[12] Kahraman A, Singh R. Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system[J]. Journal of Sound and Vibration, 1991, 146(1):135-156.
[13] Chen C S, Natsiavas S, Nelson H D. Stability analysis and complex dynamics of a gear-pair system supported by a squeeze film damper[J]. ASME Journal of Vibration and Acoustics, 1997, 119(1):85-88.
[14] Raghothama A, Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1999, 226(3): 469-492.
[15] AN-SUNG LEE, JIN-WOONG HA. Prediction of maximum unbalance responses of a gear-coupled two shaft rotor-bearing system[J]. Journal of Sound and vibration, 2004,283(2005):507-523.
[16] LEE A S, HA J W. Prediction of maximum unbalance responses of a gear-coupled two shaft rotor-bearing system[J]. Journal of Sound and vibration, 2005,283:507-523.
[17] Maharathi B B. Dynamic behaviour analysis of linear rotor-bearing systems using the complex transfer matrix technique[J]. International Journal of Acoustics and Vibrations, 2005, 10(3):413-417.
[18] SU J C T, LIE K N. Rotor dynamic instability analysis on hybrid air journal bearings[J]. Tribology International, 2006,39(2006):238-248.
[19] HSIEH S C, Chen J H, LEE A C. A modified transfer matrix method for the coupled lateral and torsional vibrations of asymmetric rotor-bearing systems[J]. Journal of Sound and Vibration, 2008,312(4-5):563-571.
[20] JUN O S, Gadala, Mohamed S. Dynamic behavior analysis of cracked rotor[J]. Journal of Sound and Vibration, 2008, 309(1-2):210-245.
[21] FAN Y S, Wanq S M. Dynamic characteristics of the coupled system of the high pressure rotor and the radial driveshaft of a turbofan engine[C].Advanced Materials Research, v 44-46, p 127-134, 2008, Materials and Product Technologies - 2008 International Conference on Advances in Product Development and Reliability, PDR2008.
[22]顾家柳等.转子动力学[M].北京:国防工业出版社, 1985.
[23]钟一谔,何衍宗,王正,等.转子动力学[M].北京:清华大学出版社, 1987.
[24]闻邦椿,顾家柳,夏松波,等著.高等转子动力学[M].北京:机械工业出版社, 1999.
[25]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.
[26]张辉,朱梓根,晏砺堂.齿轮驱动的转子系统弯扭耦合振动[A].全国第二世界转子动力学学术讨论会文集[C].青岛, 1992.
[27]夏伯乾,虞烈,谢友柏.齿轮-转子-轴承系统弯扭耦合振动模型研究[J].西安交通大学学报, 1997, 31(10):93-99.
[28]夏伯乾,虞烈,谢友柏.齿轮-转子-轴承系统弯扭耦合振动的新模型[J].郑州工业大学学报, 1997, 18(1):1-7.
[29]夏伯乾,虞烈,谢友柏.齿轮耦合对转子-轴承系统稳定性的影响[J].机械科学与技术, 1998, 17(2).
[30]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).
[31]夏伯乾,虞烈,谢友柏. DH型压缩机齿轮-轴承-转子系统动力学分析[J].振动工程学报, 2003,16(2):251-255.
[32]朱勤.多根平行轴齿轮转子系统的弯曲耦合振动分析[J].振动与冲击, 1996, 15(4):41-48.
[33]李明,孙涛,胡海岩.齿轮传动转子-轴承系统动力学的研究进展[J].振动工程学报, 2002,15(3):249-256.
[34]张锁怀,沈允文,丘大谋.齿轮-转子-轴承系统的动力特性试验研究[J].机械科学与技术, 2002, 11(21).
[35]张建云,丘大谋.齿轮刚度及制造误差对多平行轴转子系统动力学性能的影响[J].机械科学与技术. 1996, 15(5):749-754.
[36]柴山,高连勇.多转子系统弯扭耦合振动分析的整体传递矩阵法[J].机械设计, 2005, 22(10):8-11.
[37]宋雪萍,于涛,李国平,等.齿轮轴系弯扭耦合振动特性[J].东北大学学报(自然科学版), 2005, 26(10):990-993.
[38]欧卫林,王三民,袁茹.齿轮耦合复杂转子系统弯扭耦合振动分析的轴单元法[J].航空动力学报, 2005, 20(3):434-439.
[39]庞辉,李育锡,王三民.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]. 2005, 24(7):832-835.
[40]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.
[41]庞辉,方宗德,欧卫林.多平行齿轮耦合转子系统的振动特性分析[J].振动与冲击, 2007, 26(6):21-25.
[42]李润方,王建军.齿轮系统动力学[M].北京:科学出版社, 1997
[43]张志勇等.精通MATLAB6.5版[M].北京:北京航空航天大学出版社, 2003
[44]屈维德.机械振动手册[M].北京:机械工业出版社, 1992
[45]孟光.转子动力学研究的回顾与展望[J].振动工程学报, 2002, 15(1):1-9
[46]苏武会.齿轮耦合多转子系统动力学特性研究[D].西北工业大学, 2007.
[47]机械设计手册编委会.机械设计手册[M].北京:机械工业出版社. 2004.
[48]欧卫林.某航空发动机传动系统的动力学研究及其振动控制[D].西北工业大学, 2005.
[49]庞辉.多转子系统动力特性分析及应用研究.硕士学位论文.西北工业大学. 2005.
[50]蒋书运,陈照波,须根法,等.用整体传递矩阵法计算航空发动机整机临界转速特性[J].哈尔滨工业大学学报. 1998, 3(1):32-35.
[51] Cai Y. Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (A new stiffness function of helical involute tooth pair)[J]. ASME J of Mech. Design,1995, 117(9):460-468.
[52] Wachal J C, Szenasi F R. Field. Vibration of lateral-torsionbal coupling effects on rotor influence in centrifugal compressors. NASA conference publication, No 2147, 1980.
[53] Schwibinger P, Nordmem R. The influence of torsional-lateral-coupling in geared rotor systems on its eigenvalues[A].Modes and Unbalance Vibration,Proc.IMeche[C], 1988, C295/88: 275-287.
[54] Choy F K, Tu Y K, Zakrajsek J J, Townsend D P. Effects of gear box vibration and mass imbalance on the dynamics of multistage gear transmission[J]. ASME Journal of Vibration and Acoustics, Stress and Reliability in Design, 1991, 113:333-344.
[55] Tordion G V, Gabvin R.. Dynamic stability of a two-stage gear train under the influence of variable meshing stiffness[J]. ASME Journal of Engineering for Industry, 1977, (8):785-791.
[56] Raghothama A, Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1999, 226(3): 469-492.
[2]刘振坤.蔡睿贤院士谈我国燃气轮机的发展[J].燃气轮机技术, 2001, 14(2).
[3] Jeffcott H H. The lateral vibration of loaded shafts in the neighborhood of a whirling speed the effect of want of balance[J]. Phil.mag. , 1919,37.
[4] Rankine W J M. On the centrifugal force of rotating shafts. The Engineer, April. 1869,27.
[5] Prohl M A. A general method for calculating critical speeds of flexible rotors[J]. J. of Appl. Mech. Trans. ASME, 1945, 12(3):142-148.
[6] Myklestad N O. A new method for calculating natural modes of uncoupled bending vibration of airplane wings and other types of beams[J]. J. of Aero. Sci. 1944, 11:153-162.
[7] Horner G C, Pilkey W D. The riccati transfer matrix method[J]. J. of Mech. Des. Trans. ASME, 1978, 100(4):297-302.
[8] Lund J W. Critical speeds, stability and response of a geared train of rotor[J]. ASME Journal of Mechanical Design,1978,100(3):535-538.
[9] Yamada T, Mitsui J. A study on unstable vibration phenomena of a reduction gear system, including the lightly loaded journal bearings, for a marine steam turbine[J]. Bulletin of JSME, 1979, 22(163):98-105.
[10] Ozguven H N, Houser D R. Dynamic analasis of high speed gears by using loaded static transmission error[J]. Journal of Sound and Vibration, 1988, 25(1):71-83.
[11] Kahraman A, Ozguven H N, Houser D R., et al. Dynamic analysis of geared rotors by finite elements[J]. Journal of .Mechanical Design, ASME, 1992, 114(9):507-514.
[12] Kahraman A, Singh R. Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system[J]. Journal of Sound and Vibration, 1991, 146(1):135-156.
[13] Chen C S, Natsiavas S, Nelson H D. Stability analysis and complex dynamics of a gear-pair system supported by a squeeze film damper[J]. ASME Journal of Vibration and Acoustics, 1997, 119(1):85-88.
[14] Raghothama A, Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1999, 226(3): 469-492.
[15] AN-SUNG LEE, JIN-WOONG HA. Prediction of maximum unbalance responses of a gear-coupled two shaft rotor-bearing system[J]. Journal of Sound and vibration, 2004,283(2005):507-523.
[16] LEE A S, HA J W. Prediction of maximum unbalance responses of a gear-coupled two shaft rotor-bearing system[J]. Journal of Sound and vibration, 2005,283:507-523.
[17] Maharathi B B. Dynamic behaviour analysis of linear rotor-bearing systems using the complex transfer matrix technique[J]. International Journal of Acoustics and Vibrations, 2005, 10(3):413-417.
[18] SU J C T, LIE K N. Rotor dynamic instability analysis on hybrid air journal bearings[J]. Tribology International, 2006,39(2006):238-248.
[19] HSIEH S C, Chen J H, LEE A C. A modified transfer matrix method for the coupled lateral and torsional vibrations of asymmetric rotor-bearing systems[J]. Journal of Sound and Vibration, 2008,312(4-5):563-571.
[20] JUN O S, Gadala, Mohamed S. Dynamic behavior analysis of cracked rotor[J]. Journal of Sound and Vibration, 2008, 309(1-2):210-245.
[21] FAN Y S, Wanq S M. Dynamic characteristics of the coupled system of the high pressure rotor and the radial driveshaft of a turbofan engine[C].Advanced Materials Research, v 44-46, p 127-134, 2008, Materials and Product Technologies - 2008 International Conference on Advances in Product Development and Reliability, PDR2008.
[22]顾家柳等.转子动力学[M].北京:国防工业出版社, 1985.
[23]钟一谔,何衍宗,王正,等.转子动力学[M].北京:清华大学出版社, 1987.
[24]闻邦椿,顾家柳,夏松波,等著.高等转子动力学[M].北京:机械工业出版社, 1999.
[25]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.
[26]张辉,朱梓根,晏砺堂.齿轮驱动的转子系统弯扭耦合振动[A].全国第二世界转子动力学学术讨论会文集[C].青岛, 1992.
[27]夏伯乾,虞烈,谢友柏.齿轮-转子-轴承系统弯扭耦合振动模型研究[J].西安交通大学学报, 1997, 31(10):93-99.
[28]夏伯乾,虞烈,谢友柏.齿轮-转子-轴承系统弯扭耦合振动的新模型[J].郑州工业大学学报, 1997, 18(1):1-7.
[29]夏伯乾,虞烈,谢友柏.齿轮耦合对转子-轴承系统稳定性的影响[J].机械科学与技术, 1998, 17(2).
[30]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).
[31]夏伯乾,虞烈,谢友柏. DH型压缩机齿轮-轴承-转子系统动力学分析[J].振动工程学报, 2003,16(2):251-255.
[32]朱勤.多根平行轴齿轮转子系统的弯曲耦合振动分析[J].振动与冲击, 1996, 15(4):41-48.
[33]李明,孙涛,胡海岩.齿轮传动转子-轴承系统动力学的研究进展[J].振动工程学报, 2002,15(3):249-256.
[34]张锁怀,沈允文,丘大谋.齿轮-转子-轴承系统的动力特性试验研究[J].机械科学与技术, 2002, 11(21).
[35]张建云,丘大谋.齿轮刚度及制造误差对多平行轴转子系统动力学性能的影响[J].机械科学与技术. 1996, 15(5):749-754.
[36]柴山,高连勇.多转子系统弯扭耦合振动分析的整体传递矩阵法[J].机械设计, 2005, 22(10):8-11.
[37]宋雪萍,于涛,李国平,等.齿轮轴系弯扭耦合振动特性[J].东北大学学报(自然科学版), 2005, 26(10):990-993.
[38]欧卫林,王三民,袁茹.齿轮耦合复杂转子系统弯扭耦合振动分析的轴单元法[J].航空动力学报, 2005, 20(3):434-439.
[39]庞辉,李育锡,王三民.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]. 2005, 24(7):832-835.
[40]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.
[41]庞辉,方宗德,欧卫林.多平行齿轮耦合转子系统的振动特性分析[J].振动与冲击, 2007, 26(6):21-25.
[42]李润方,王建军.齿轮系统动力学[M].北京:科学出版社, 1997
[43]张志勇等.精通MATLAB6.5版[M].北京:北京航空航天大学出版社, 2003
[44]屈维德.机械振动手册[M].北京:机械工业出版社, 1992
[45]孟光.转子动力学研究的回顾与展望[J].振动工程学报, 2002, 15(1):1-9
[46]苏武会.齿轮耦合多转子系统动力学特性研究[D].西北工业大学, 2007.
[47]机械设计手册编委会.机械设计手册[M].北京:机械工业出版社. 2004.
[48]欧卫林.某航空发动机传动系统的动力学研究及其振动控制[D].西北工业大学, 2005.
[49]庞辉.多转子系统动力特性分析及应用研究.硕士学位论文.西北工业大学. 2005.
[50]蒋书运,陈照波,须根法,等.用整体传递矩阵法计算航空发动机整机临界转速特性[J].哈尔滨工业大学学报. 1998, 3(1):32-35.
[51] Cai Y. Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (A new stiffness function of helical involute tooth pair)[J]. ASME J of Mech. Design,1995, 117(9):460-468.
[52] Wachal J C, Szenasi F R. Field. Vibration of lateral-torsionbal coupling effects on rotor influence in centrifugal compressors. NASA conference publication, No 2147, 1980.
[53] Schwibinger P, Nordmem R. The influence of torsional-lateral-coupling in geared rotor systems on its eigenvalues[A].Modes and Unbalance Vibration,Proc.IMeche[C], 1988, C295/88: 275-287.
[54] Choy F K, Tu Y K, Zakrajsek J J, Townsend D P. Effects of gear box vibration and mass imbalance on the dynamics of multistage gear transmission[J]. ASME Journal of Vibration and Acoustics, Stress and Reliability in Design, 1991, 113:333-344.
[55] Tordion G V, Gabvin R.. Dynamic stability of a two-stage gear train under the influence of variable meshing stiffness[J]. ASME Journal of Engineering for Industry, 1977, (8):785-791.
[56] Raghothama A, Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1999, 226(3): 469-492.