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TECHNICAL PAPERS

Stability and Stability Degree of a Cracked Flexible Rotor Supported on Journal Bearings

[+] Author and Article Information
G. Meng

Institute of Mechatronics Engineering, Foshan University, Guangdong, P. R. of China

R. Gasch

Institute of Aeronautics and Astronautics, Technical University, Berlin, Germany

J. Vib. Acoust 122(2), 116-125 (Dec 01, 1999) (10 pages) doi:10.1115/1.568448 History: Received May 01, 1992; Revised December 01, 1999
Copyright © 2000 by ASME
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References

Jack, A. R., and Patterson, A. N., 1976, “Cracking in 500 MW LP Rotor Shafts,” 1st Mechanical Engineering Conference (The Influence of the Environment on Fatigue).
Gasch, R., 1976, “Dynamic Behavior of a Simple Rotor with a Cross Sectional Crack,” Conf. on Vibrations in Rotating Machinery, IMechE, London, pp. 123–128.
Mayes,  I. W., and Davies,  W. G. R., 1984, “Analysis of the Response of a Multi-Rotor-Bearing System Containing a Transverse Crack in a Rotor,” ASME J. Vibra. Acoust. Stress Reliab. Des., 106, pp. 139–145.
Nelson,  H. D., and Nataraj,  C., 1986, “The Dynamics of a Rotor System with a Cracked Shaft,” ASME J. Vibra. Acoust. Stress Reliab. Des., 108, pp. 189–196.
Collins,  K. R., Plaut,  R. H., and Wauer,  J., 1991, “Detection of Crack in Rotating Timoshenko Shafts Using Axial Impulses,” ASME J. Vibr. Acoust., 113, pp. 74–78.
Gasch, R., et al., 1988, “Dynamic Behavior of the Laval Rotor with a Cracked Hollow Shaft—A Comparison of Crack Model,” IMechE Conf. of Vibrations in Rotating Machinery, Sept., UK, C314/88.
Bernasconi,  O., 1986, “Solution for Torsional Vibrations of Stepped Shafts Using Singularity Functions,” Int. J. Mech. Sci., 28, pp. 31–39.
Muszynska, A., 1982, “Shaft Crack Detection,” Proc. 7th Machinery Dynamics Seminar, Edmonton, Canada.
Papadopoulos,  C. A., and Dimarogonas,  A. D., 1987, “Coupled Longitudinal and Bending Vibrations of a Rotating Shaft with an Open Crack,” J. Sound Vib., 117, pp. 81–93.
Imam,  I., , 1989, “Development of an On-Line Rotor Crack Detection and Monitoring System,” ASME J. Vibra. Acoust. Stress Reliab. Des., 111, July, pp. 241–250.
Dimarogonas, A. D., and Paipetis, S. A., 1983, Analytical Methods in Rotor Dynamics, Applied Science, London.
Wauer,  J., 1990, “On the Dynamics of Cracked Rotors: a Literature Survey,” Appl. Mech. Rev., 43, No. 1, pp. 13–17.
Tamura, A., et al., 1988, “Unstable Vibration of a Rotor with a Transverse Crack,” IMechE Conf. of Vibrations in Rotating Machinery, Sept., UK, C322/88.
Gasch, R., 1992, “A Survey of the Dynamic Behavior of a Simple Rotating Shaft with a Transverse Crack,” J. Vibr. Shock, No. 4, Oct.
Someya, T., 1989, Journal—Bearing Databook, Springer-Verlag, New York.
Vance, J. M., 1988, Rotordynamics of Turbomachinery, Wiley, New York.
Caesari, L., 1970, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, 3rd ed., Springer-Verlag, Germany.
Fridemann,  P., , 1977, “Efficient Numerical Treatment of Periodic Systems with Application to Stability Problems,” Int. J. Numer. Methods Eng., 11, pp. 1117–1136.

Figures

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Schematic diagram of a cracked flexible rotor supported on journal bearings
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Influence of gravity parameter on the diagram of stability degree, without crack case (ΔKξ=0.0,ΔKη=0.0,De=0.01,So=2.0,α=0.2)
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Lobes bearing, influence of gravity parameter and fixed Sommerfeld number on the diagram of stability degree, without crack case (ΔKξ=0.0,ΔKη=0.0,De=0.01,α=0.2)
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Position of crack ridge zones, influence of mass ratio for large gravity parameter (4-lobes bearing, ΔKξ=0.7,ΔKη=0.0,De=0.01,So=0.1,Wg=5.0)
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Position of crack ridge zones, influence of mass ratio for small gravity parameter (tilting pad bearing, ΔKξ=0.5,ΔKη=0.0,De=0.01,So=0.1,Wg=0.001)
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Position of crack ridge zones, influence of stiffness ratio (tilting pad bearing, ΔKη=0.0,De=0.01,So=0.1,α=0.2,Wg=0.001)
Grahic Jump Location
Influence of gravity parameter on the diagram of stability degree (ΔKξ=0.7,ΔKη=0.0,De=0.01,So=2.0,α=0.2)
Grahic Jump Location
4-Lobes bearing, influence of fixed Sommerfeld number and gravity parameter on the diagram of stability degree (ΔKξ=0.5,ΔKη=0.0,De=0.01,α=0.2)
Grahic Jump Location
Tilting pad bearing, influence of stiffness change ratio and gravity parameter on the diagram of stability degree (ΔKη=0.0,De=0.01,So=2.0,α=0.2)

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