Dynamic Stability Analysis of Periodically Time-Varying Rotor System with a Transverse Crack
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Abstract
Fatigue cracks may appear in horizontal rotating machinery due to periodic stresses imposed to its shaft. The investigation of stability behavior of cracked rotors can lead to proper diagnosis of machinery and to prevent possible accidents caused by the rotor failure. In this study, the dynamic stability of a rotor with a transverse crack is investigated. Models of both open and breathing cracks are developed and then used in the model of a cracked Jeffcot (de Laval) rotor. The stability of rotor motion equations represented by differential equations with periodic coefficients is investigated using Floquet theory. While both crack models show instability regions around the first un-damped frequency, sub-harmonic regions are predicted by the breathing crack models. Compared to perturbation methods frequently used to determine the stability regions, the transition matrix approach used in this study can be applied to complex models of rotors and consequently may help in the identification of cracks in rotating machinery.
- Y. Ishida, “Cracked Rotors: Industrial Machine Case Histories and Nonlinear Effects Shown by Simple Jeffcott Rotor,” Mechanical Systems and Signal Processing, Vol. 22, No. 4, 2008, pp. 805-817. doi:10.1016/j.ymssp.2007.11.005
- J. Wauer, “On the Dynamics of Cracked Rotors: A Literature Survey,” Applied Mechanical Reviews, Vol. 43, 1990, pp. 13-17. http://dx.doi.org/10.1115/1.3119157
- A. D. Dimarogonas, “Vibration of Cracked Structures: A State of the Art Review,” Engineering Fracture Mechanics, Vol. 55, No. 5, 1996, pp. 831-857. doi:10.1016/0013-7944(94)00175-8
- A. H. Nayfeh and D. T. Mook, “Nonlinear Oscillations,” John Wiley & Sons, New York, 1975.
- J. Dugundji and J. W. Wendell, “Some Analysis Methods for Rotating Systems with Periodic Coefficients,” American Institute of Aeronautics and Astronautics Journal, Vol. 21, No. 6, 1982, pp. 890-897. doi: 10.2514/3.8167
- A. D. Dimaragonas and S. A. Paipetis, “Rotor Dynamics,” Elsevier, London, 1983.
- H. Tada, P. C. Paris and G. R. Irwin, “The Stress Analysis of Cracks Handbook,” Del. Research Corporation, Hellertown, 1973.
- O. S. Jun, H. J. Eun, Y. Y. Earmme and C.-W. Lee, “Modeling and Vibration Analysis of a Simple Rotor with a Breathing Crack,” Journal of Sound and Vibration, Vol. 155, No. 2, 1992, pp. 273-290. doi:10.1016/0022-460X(92)90511-U
- C. D. Untaroiu, “Contributions on Dynamic Stability of Rotors,” PhD. Dissertation, “Politehnica” University, Bucharest, 1999.
- O. S. Jun and M. S. Gadala, “Dynamic Behavior Analysis of Cracked Rotor,” Journal of Sound and Vibration, Vol. 309, No. 1-2, 2008, pp. 210-245. doi:10.1016/j.jsv.2007.06.065
- M. Lalanne and G. Ferraris, “Rotordynamics Prediction in Engineering,” John Wiley & Sons, New York, 1998,.
- R. Gasch, “Dynamic Behaviour of the Laval Rotor with a Transverse Crack,” Mechanical Systems and Signal Processing, Vol. 22, No. 4, 2008, pp. 790-804. doi:10.1016/j.ymssp.2007.11.023
- M. He, P. E. Allaire and P. Sheth, “ComboRotor 1.0 Beta User’s Manual,” ROMAC Report No. 521, University of Virginia, Charlottesville, 2007.
- C. D. Untaroiu and A. Untaroiu, “Constrained Design Optimization of Rotor-Tilting Pad Bearings Systems,” Journal of Engineering for Gas Turbines and Power/ ASME Transactions, Vol. 132, No. 12, 2010, Article ID: 122502, pp. 1-7. doi:10.1115/1.4001811