Vibration Analysis of Rotor for Crack Identification

Abstract

A theoretical and experimental dynamic analysis of a rotor-bearing system with a transversely cracked shaft is presented. To model the system for FEM analysis, a finite element for a cracked cylindrical shaft is developed. The additional flexibility due to the crack is evaluated from the linear fracture mechanics, using a breathing crack model derived in a rigorous way. A simplified opening/closing crack model is proposed to reduce the computational effort. The resulting parametrically excited system is nonlinear, and the equations of motion are solved using Hilbert, Hughes, and Taylor integration method (HHT) implemented in Matlab platform, where the stationary vibration caused by gravity and unbalance is analyzed. The results show that for half the first critical speed, the super-harmonic 2 ×Ω and the typical orbit provide good indices for crack detection in rotating shafts.

Keywords

Crack cracked shaft stiffness variation breathing crack

Get full access to this article

View all access options for this article.

References

Bentley, D. E. , and Muszynska, A. , 1986, “Detection of rotor cracks,” 15th Turbomachinery Symposium, Texas.

Change, L. , Bernasconi, O. , and Xenophontides, N. , 1989, “A generalized approach to the dynamics of crack shafts,” ASME Journal of Vibration, Acoustics, Stress and Reliability in Design 111, 257-263.

Cuitiño, L. A., 2000, Dynamic Behavior of Cracked Beams and Shafts, Master's thesis, Department of Mechanical Engineering, Faculty of Engineering, University of Concepción, Concepción, Chile.

Dimarogonas, A. D. and Paipetis, S. A. , 1983, Analytical Methods in Rotor Dynamic, Applied Science, London.

Dirr, B. O. and Schmalhorst, B. K. , 1988, “Crack depth analysis of a rotating shaft by vibration measurements,” ASME Journal of Vibration, Acoustics, Stress and Reliability in Design 110, 158-164.

Gash, R. , 1993, “A survey of the dynamic behavior of a simple rotor shaft with a transverse crack,” Journal of Sound and Vibration 62(2), 313-332.

Go, C. G. and Lin, Y. S. , 1994, “Infinitely small element for dynamic problems of cracked beam,” Engineering Fracture Mechanics 48(4), 475-482.

Huang, S. C. , Huanh, Y. M. , and Shieh, S. M. , 1993, “Vibration and stability of a rotating shaft containing a transverse crack,” Journal of Sound and Vibration 162(2), 387-401.

Iman, I. , Azzaro, S. H. , Bankert, R. J. , and Scheibel, I. , 1989, “Development of an on-line rotor crack detection and monitoring system,” Journal of Sound and Vibration 111, 241-250.

10.

Inagaki, T. , Kanki, H. , and Shiraki, K. , 1982, “Transverse vibration of a general cracked rotor bearing system,” ASME Journal of Mechanical Design 104, 345-355.

11.

Jun, O.S. and Eun, H. J. , 1992, “Modeling and vibration analysis of a simple rotor with a breathing crack,” Journal of Sound and Vibration 155(2), 273-290.

12.

Lee, C. , Yun, J. , and Eun, O. S , 1992, “Modeling of a simple rotor with a switching crack and it experimental verification,” Journal of Sound and Acoustics 114, 217-225.

13.

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 Journal of Vibration, Acoustics, Stress and Reliability in Design 106, 139-145.

14.

Nelson, H. D. and Nataraj, C. , 1986, “The dynamic of a rotor system with a cracked shaft,” ASME Journal of Vibration, Acoustics, Stress and Reliability in Design 108, 189-196.

15.

Ostachowicz, W. M. and Krawczuk, M. , 1990, “Vibration analysis of a cracked beam,” Computer & Structures 36(2), 245-250.

16.

Papadopoulos, C. A. and Dimarogonas, A. D. , 1987, “Coupled longitudinal and bending vibrations of a rotating shaft with an open crack,” Journal of Sound and Vibration 117(1), 81-93.

17.

Papadopoulos, C. A. and Dimarogonas, A. D. , 1988, “Stability of cracked rotors in the coupled vibration mode,” ASME Journal of Vibration, Acoustics, Stress and Reliability in Design 110, 356-359.

18.

Saavedra, P. , Baquedano, D. , and San Juan, L. , 1996, “Modelo numérico para el estudio dinámico de un rotor con eje agrietado,” Revista Internacional de [ILLEGIBLE][ILLEGIBLE] para [ILLEGIBLE][ILLEGIBLE] en Ingenieria 12(2), 125-146.

19.

Sekhar, A. S. and Balaji, P. , 1997, “Dynamic analysis of a rotor system considering a slant crack in the shaft,” Journal of Sound and Vibration 208(3), 457-474.

20.

Sekhar, A. S. and Prabhu, B. S. , 1992

“Crack detection and vibration characteristics of cracked shafts,”

Journal of Sound and Vibration 157(2), 375-381.