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

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

doi: 10.3879/j.issn.1000-0887.2012.07.003
  • Received Date: 2011-04-20
  • Rev Recd Date: 2012-03-29
  • Publish Date: 2012-07-15
  • Aero engine rotor system was simplified to be an unsymmetrical-rigid-rotor with nonlinear-elasticsupport based on its characteristics. Governing equations of the rubbing system obtained from Lagrange equation were solved by averaging method to find the bifurcation equations. Then, according to the two-dimensional constraint bifurcation theory, transition sets and bifurcation diagrams of the system with and without rubbing were given to study the influence of system’s eccentric and damping on the bifurcation behaviors, respectively. Finally, according to Liapunov stability theory, the stability region of steady-state rubbing solution and the boundary of static bifurcation and Hopf bifurcation were determined to discuss the influence of system parameters on the evolution of system’s motion. The research results may provide some references for the design of aero rotor systems.
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  • [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
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