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TECHNICAL PAPERS

Subharmonic and Chaotic Motions of a Hybrid Squeeze-Film Damper-Mounted Rigid Rotor With Active Control

[+] Author and Article Information
Chieh-Li Chen, Her-Terng Yau

Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan

Yunhua Li

Institute of Automatic Control, Beijing University of Aeronautics and Astronautics, Beijing

J. Vib. Acoust 124(2), 198-208 (Mar 26, 2002) (11 pages) doi:10.1115/1.1448318 History: Received October 01, 2000; Received August 01, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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References

Holmes,  A. G., Ettles,  C. M., and Mayes,  I. W., 1978, “Aperiodic Behavior of a Rigid Shaft in Short Journal Bearings,” Int. J. Numer. Methods Eng., 12, pp. 695–702.
Nikolajsent,  J. I., and Holmes,  R., 1979, “Investigation of Squeeze-Film Isolators for the Vibration Control of a Flexible Rotor,” ASME J. Mech. Des. 21, pp. 247–252.
Sykes,  J. E. H., and Holmes,  R., 1990, “The Effect of Bearing Misalignment on the Non-Linear Vibration of Aero-Engine Rotor-Damper Assemblies,” Proceedings Institution of Mechanical Engineers, 204, pp. 83–99.
Kim,  Y. B., and Noah,  S. T., 1990, “Bifurcation Analysis of a Modified Jeffcot Rotor with Bearing Clearances,” Nonlinear Dyn., 1, pp. 221–241.
Ehrich,  F. F., 1991, “Some Observations of Chaotic Vibration Phenomena in High-Speed Rotordynamics,” ASME J. Vibr. Acoust., 113, pp. 50–57.
Zhao,  J. Y., Linnett,  I. W., and Mclean,  L. J., 1994, “Subharmonic and Quasi-Periodic Motion of an Eccentric Squeeze Film Damper-Mounted Rigid Rotor,” ASME J. Vibr. Acoust., 116, pp. 357–363.
Brown,  R. D., Addison,  P., and Chan,  A. H. C., 1994, “Chaos in the Unbalance Response of Journal Bearings,” Nonlinear Dyn., 5, pp. 421–432.
Adiletta,  G., Guido,  A. R., and Rossi,  C., 1996, “Chaotic Motions of a Rigid Rotor in Short Journal Bearings,” Nonlinear Dyn., 10, pp. 251–269.
Adiletta,  G., Guido,  A. R., and Rossi,  C., 1997, “Nonlinear Dynamics of a Rigid Unbalanced Rotor in Short Bearings. Part I: Theoretical Analysis,” Nonlinear Dyn., 14, pp. 57–87.
Adiletta,  G., Guido,  A. R., and Rossi,  C., 1997, “Nonlinear Dynamics of a Rigid Unbalanced Rotor in Short Bearings. Part II: Experimental Analysis,” Nonlinear Dyn., 14, pp. 157–189.
Sundararajan,  P., and Noah,  S. T., 1997, “Dynamics of Forced Nonlinear Systems Using Shooting/Arc-length Continuation Method—Application to Rotor Systems,” ASME J. Vibr. Acoust., 119, pp. 9–20.
Chen,  C. L., and Yau,  H. T., 1998, “Chaos in the Imbalance Response of a Flexible Rotor Supported by Oil Film Bearings with Non-Linear Suspension,” Nonlinear Dyn., 16, pp. 71–90.
Wolf,  A., Swift,  J. B., Swinney,  H. L., and Vastano,  J. A., 1985, “Determining Lyapunov Exponents From A Time Series,” Physica D, 16D, pp. 285–317.
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Vance, J. M. 1988, Rotordynamics of Turbomachinery, John Wiley & Sons, Inc., New York.
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Figures

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Cross section of a rigid rotor supported by a HSFD with active control
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The pressure distribution of HSFD in axis direction
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The pressure distribution of HSFD in rotational direction (−a≤z≤a)
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Bifurcation diagram of X(nT) (a) and Y(nT) (b) versus rotor speed s (case 1)
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Subharmonic motion at s=2.6 (case 1): (a) rotor trajectory (b) Poincaré map (c) (d) displacement power in X and Y directions (case 1)
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Pressure distribution in the static pressure chamber at s=2.6 (case 1)
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Bifurcation diagram of X(nT) (a) and Y(nT) (b) versus rotor speed s (case 2)
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The local bifurcation diagram of X(nT) (a) and Y(nT) (b) in the range of 2.5<s<2.85
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The trajectory of rotor at s=2.7, 2.8, 2.82, 4.0(9.1(a)–9.4(a)); Poincaré section projected onto the X(nT)-Y(nT) plane (9.1(b)–9.4(b)); displacement power in X and Y directions (9.1(c)–9.4(c) and 9.1(d)–9.4(d))  
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Aperiodic motion of bearing center at s=3.0: (a) rotor trajectory (b) (c) displacements power spectrum (d) (e) time series of rotor trajectory (f) (g) (h) Poincare’ maps
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Pressure distribution in the static pressure chamber at s=3.0 (case 2)
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The maximum Lyapunov exponent plotted as a function of the number of drive cycles at s=3.0 (case 2)
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Variation c(r) with embedding dimension at s=3.0 (case 2) (a) and variation of correlation dimension with embedding dimension (b)
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Bifurcation diagram of X(nT) (a) and Y(nT) (b) versus rotor speed s with kp=75000 (case 2)
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Synchronous motion of rotor trajectory at s=3.0 with kp=75000 (a) rotor trajectory (b) (c) time series of rotor trajectory (d) (e) (f) (g) pressure distributions in the static pressure chambers
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The structure of elect-hydraulic controllable orifice with actuator (chamber 2)

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