留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

弹性支承-刚性转子系统同步全周碰摩的分岔响应

张华彪 陈予恕 李军

张华彪, 陈予恕, 李军. 弹性支承-刚性转子系统同步全周碰摩的分岔响应[J]. 应用数学和力学, 2012, 33(7): 812-827. doi: 10.3879/j.issn.1000-0887.2012.07.003
引用本文: 张华彪, 陈予恕, 李军. 弹性支承-刚性转子系统同步全周碰摩的分岔响应[J]. 应用数学和力学, 2012, 33(7): 812-827. doi: 10.3879/j.issn.1000-0887.2012.07.003
ZHANG Hua-biao, CHEN Yu-shu, LI Jun. Bifurcation on the Synchronous Full Annular Rub of a Rigid-Rotor Elastic-Support System[J]. Applied Mathematics and Mechanics, 2012, 33(7): 812-827. doi: 10.3879/j.issn.1000-0887.2012.07.003
Citation: ZHANG Hua-biao, CHEN Yu-shu, LI Jun. Bifurcation on the Synchronous Full Annular Rub of a Rigid-Rotor Elastic-Support System[J]. Applied Mathematics and Mechanics, 2012, 33(7): 812-827. doi: 10.3879/j.issn.1000-0887.2012.07.003

弹性支承-刚性转子系统同步全周碰摩的分岔响应

doi: 10.3879/j.issn.1000-0887.2012.07.003
详细信息
    通讯作者:

    张华彪(1984—),男,河北人,博士生(联系人. E-mail:hbzhang5220@foxmail.com).

  • 中图分类号: O322; V235.1

Bifurcation on the Synchronous Full Annular Rub of a Rigid-Rotor Elastic-Support System

  • 摘要: 基于航空发动机转子系统的结构特点,将航空发动机转子系统简化为一个非线性弹性支承的刚性转子系统.根据Lagrange方程建立了弹性支承-刚性不对称转子系统同步全周碰摩的运动方程;采用平均法进行求解,得到了关于系统振幅的分岔方程;根据两状态变量约束分岔理论,分别给出了系统在无碰摩和碰摩阶段参数平面的转迁集和分岔图,讨论了转子偏心、阻尼对系统分岔行为的影响;应用Liapunov稳定性理论分析了系统碰摩周期解的稳定性和失稳方式,给出了系统参数——转速平面上周期解的稳定范围;该文的研究结果对航空发动机转子系统的设计有一定的理论意义.
  • [1] 晏砺堂. 航空燃气轮机振动和减振[M]. 北京: 国防工业出版社, 1991.(YAN Li-tang. Vibration and Vibration Reduction of Aero Gas Turbine[M]. Beijing: National Defense Industrial Press, 1991. (in Chinese))
    [2] 王德友. 旋转机械转静子碰摩振动特性[J]. 航空发动机, 1998, (2): 37-41.(WANG De-you. Rubbing between rotor and stator of rotation machinery[J]. Aero Engine, 1998, (2): 37-41. (in Chinese))
    [3] Ehrich F F. High order subharmonic response of high speed rotors in bearing clearance[J]. Journal of Vibration, Acoustics, Stress, and Reliability in Design, 1988, 110(1): 9-16.
    [4] Li Q H, Lu Q S. Single rub-impacting periodic motions of a rigid constrained rotor system[J]. Communication of Nonlinear Science Numerical Simulation, 2000, 5(4): 158-161.
    [5] 褚福磊, 汤晓瑛, 唐云. 碰摩转子系统的稳定性[J]. 清华大学学报(自然科学版), 2000, 40(4): 119-123.(CHU Fu-lei, TANG Xiao-ying, TANG Yun. Stability of a rub-impact rotor system[J]. Journal of Tsinghua University (Science and Technology), 2000, 40(4):119-123. (in Chinese))
    [6] Kim Y B, Noah S T. Bifurcation analysis for a modified Jeffcott rotor with bearing clearances[J]. Nonlinear Dynamics, 1990, 1(3): 221-241.
    [7] Kim Y B, Noah S T. Quasi-periodic response and stability analysis for a nonlinear Jeffcott rotor[J]. Journal of Sound and Vibration, 1996, 190(2): 239-253.
    [8] Khanlo M H, Ghayour M, Rad Z S. Chaotic vibration analysis of rotating, flexible, continuous shaft-disk system with a rub-impact between the disk and the stator[J]. Communications in Nonlinear Science and Numerical, 2011, 16(1): 566-582.
    [9] Muszynska A, Goldman P. Chaotic responses of unbalanced rotor/bearing/stator systems with looseness or rubs[J]. Chaos, Solitons and Fractals, 1995, 5(9): 1683-1704.
    [10] Chang-Jian C W, Chen C K. Chaos of rub-impact rotor supported by bearings with nonlinear suspension[J]. Tribology International, 2009, 42(3): 426-439.
    [11] Qin W Y, Chen G R, Meng G. Nonlinear responses of a rub-impact overhung rotor[J]. Chaos, Solitons and Fractals, 2004, 19(5): 1161-1172.
    [12] Jiang J, Shang Z Y, Hong L. Characteristics of dry friction backward whirl-A self-excited oscillation in rotor-to-stator contact systems[J]. Science China Technological Sciences, 2010, 53(3): 674-683.
    [13] Wilkes J C, Childs D W, Dyck B J, Phillips S G. The numerical and experimental characteristics of multimode dry-friction whip and whirl[J]. Journal of Engineering for Gas Turbines and Power, 2010, 132(5): 052503.
    [14] Yu J J. On occurrence of reverse full annular rub[J].Journal of Engineering for Gas Turbines and Power, 2012, 134(1): 012505.
    [15] Patel T H, Darpe A K. Coupled bending-torsional vibration analysis of rotor with rub and crack[J].Journal of Sound and Vibration, 2009, 326(3/5): 740-752.
    [16] Luo Y G, Ren Z H, Ma H, Yu T, Wen B C. Stability of periodic motion on the rotor-bearing system with coupling faults of crack and rub-impact[J]. Journal of Mechanical Science and Technology, 2007, 21(6): 860-864.
    [17] Ehehalt U, Markert R, Wegener G. Stability of synchronous forward whirl at rotor-stator-contact[C]ISROMAC-9 Conference, Honolulu, Hawaii, 2002: 1-8.
    [18] Ehehalt U, Markert R. Instability of unbalance excited synchronous forward whirl at rotor-stator-contact[J]. Proceedings of the Applied Mathematics and Mechanics, 2003, 2(1): 60-61.
    [19] Black H F. Interaction of a whirling rotor with a vibrating stator across a clearance annulus[J]. International Journal of Mechanical Engineering Science, 1968, 10(1): 1-12.
    [20] Begg I C. Friction induced rotor whirl—a study in stability[J]. Journal of Engineering for Industry, 1974, 96(2): 450-454.
    [21] Stackley S J. Dynamics of full annular rotor rub[D]. Master’s thesis. USA: Massachusetts Inst. of Tech, 1986.
    [22] Yu J J, Goldman P, Bently D E. Rotor/seal experimental and analytical study on full annular rub[J]. Journal of Engineering Gas Turbine Power, 2002, 124(2): 340-350.
    [23] Muszynska A. Rotordynamics[M]. Florida: CRC Press, 2005.
    [24] Bently D E, Yu J J, Goldman P. Full annular rub in mechanical seals, part Ⅰ: experiment results[C]ISROMAC-8 Conference, Honolulu, Hawaii, 2000: 995-1002.
    [25] Bently D E, Yu J J, Goldman P. Full annular rub in mechanical seals, part Ⅱ: analytical study[C]ISROMAC-8 Conference, Honolulu, Hawaii, 2000: 1003-1010.
    [26] Choi Y S. Investigation on the whirling motion of full annular rotor rub[J]. Journal of Sound and Vibration, 2002, 258(1): 191-198.
    [27] 马建敏, 张文, 郑铁生. 单盘转子碰摩条件分析[J]. 精密制造与自动化, 2003, (S1): 68-70.(MA Jian-min, ZHANG Wen, ZHENG Tie-sheng. Analysis for rub-impact condition of Jeffcott rotor[J]. Grinder Grinding, 2003, (S1):68-70. (in Chinese))
    [28] 马建敏, 张文, 郑铁生. 转子系统参数对碰摩转速的影响[J]. 西南交通大学学报, 2003, 38(5): 537-539.(MA Jian-min, ZHANG Wen, ZHENG Tie-sheng. Influence of rotor system parameters on critical rotation speed for rubbing[J]. Journal of Southwest Jiaotong University, 2003, 38(5): 537-539. (in Chinese))
    [29] Jiang J, Ulbrich H. Stability analysis of full annular rub in rotor-to-stator systems[J]. Proceedings of Applied Mechanics and Mathematics, 2003, 1(2): 88-89.
    [30] Jiang J, Ulbrich H. Stability analysis of sliding whirl in a nonlinear jeffcott rotor with cross-coupling stiffness coefficients[J]. Nonlinear Dynamics, 2001, 24(3): 269-283.
    [31] 许斌, 徐尉南, 张文. 单盘转子的同步全周碰摩及其稳定性分析[J]. 复旦学报(自然科学版), 2006, 45(2): 148-154.(XU Bin, XU Wei-nan, ZHANG Wen. Study of synchronous full annular rub of Jeffcott rotor and its dynamic stability[J]. Journal of Fudan University (Natural Science), 2006, 45(2): 148-154. (in Chinese))
    [32] Zhang G F, Xu W N, Xu B, Zhang W. Analytical study of nonlinear synchronous full annular rub motion of flexible rotor-stator system and its dynamic stability[J]. Nonlinear Dynamics, 2009, 57(4): 579-592.
    [33] 徐尉南, 张文, 许斌. 柔性转子-柔性静子系统的同步全周碰摩分析[J]. 振动与冲击, 2007, 25(2): 1-9.(XU Wei-nan, ZHANG Wen, XU Bin. Analytical study of synchronous full annular rub motion of flexible stator and rotor system[J]. Journal of Vibration and Shock, 2007, 25(2): 1-9. (in Chinese))
    [34] 刘献栋, 李其汉, 杨绍普. 质量偏心旋转机械整圈碰摩的稳定性及其Hopf分叉[J]. 振动工程学报, 1999, 12(1): 40-46.(LIU Xian-dong, LI Qi-han, YANG Shao-pu. The stability and Hopf bifurcation in the annular impact-rub of rotating machinery with imbalance[J]. Journal of Vibration Engineering, 1999, 12(1): 40-46. (in Chinese))
    [35] Groll G V, Ewins D J. The harmonic balance method with arc-length continuation in rotor/stator contact problems[J]. Journal of Sound and Vibration, 2001, 241(2): 223-233.
    [36] Jiang J, Ulbrich H. Stability analysis of full annular rub in rotor-to-stator systems[J]. Proceedings of the Applied Mathematics and Mechanics, 2003, 2(1): 88-89.
    [37] Shang Z Y, Jiang J, Hong L. The influence of the cross-coupling effects on the dynamics of rotor/stator rubbing[C]Proceedings of the Second Conference on Dynamics, Vibration and Control, Chengdu, China, 2009.
    [38] Xie H, Flowers G T, Feng L. Steady state dynamic behavior of a flexible rotor with auxiliary support from a clearance bearing[J]. Journal of Vibration and Acoustics, 1999, 121(1): 78-83.
    [39] Cole M O T. On stability of rotordynamic systems with rotor-stator contact interaction[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008, 464(2100): 3353-3375.
    [40] Keogh P S, Cole M O T. Rotor vibration with auxiliary bearing contact in magnetic bearing systems part Ⅰ: synchronous dynamics[J]. Procee
  • 加载中
计量
  • 文章访问数:  1577
  • HTML全文浏览量:  42
  • PDF下载量:  1113
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-04-20
  • 修回日期:  2012-03-29
  • 刊出日期:  2012-07-15

目录

    /

    返回文章
    返回