Keywords: rotor-bearing system, breathing crack, crack identification, continuous systems, coupling.

The coupling due to crack initially used in [1,2] has been widely used for rotor crack identification during last two decades as in [3,4,5] with one of the very recent works in [6] to introduce the continuous wavelet transform in order to investigate the coupling effects of the crack while breathing. In present work a rotor bearing system is constructed obtained from continuous rotor equations of motion as in [7,8] and finite fluid film bearings, combined in a novel way so as to compose a strongly non-linear dynamical system. The crack breathing model, that follows the well known strain energy release rate (SERR) method, has been recently developed in [9] and is used in this work to simulate the crack effect.

Using horizontal external excitation with constant frequency the coupling phenomenon in the vertical bending vibrations is introduced for specific time moments while crack is open, but is disappeared in time moments that the crack is closed. This coupling variance in time is extracted using a continuous wavelet transform in the time histories of steady state operation, yielding very sensitive results. This sensitivity is a benefit of analyzing the subtraction of time histories before and after crack development as in [10]. The proposed method combined with the current non-linear system is developed considering that many other defects can produce similar coupling behaviour introduced by the model, thus the main effort was to separate the crack coupling effects from other coupling mechanisms while in operation.

1

C.A. Papadopoulos, A.D. Dimarogonas, "Coupling of Bending and Torsional Vibration of a Cracked Timoshenko Shaft", Ingenieur-Archiv, 57, 257-266, 1987. doi:10.1007/BF00534404

2

C.A. Papadopoulos, A.D. Dimarogonas, "Coupled longitudinal and bending Vibrations of a cracked shaft", Journal of Vibration, Acoustics, Stress and Reliability in Design, 110, 1-8, 1987. doi:10.1016/0022-460X(87)90437-8

3

W.M. Ostachowicz, M. Krawczuk, "Coupled torsional and bending vibrations of a rotor with an open crack", Archives of Applied Mechanics, 62, 191-201, 1992.

4

A.K. Darpe, A. Chawla, K. Gupta, "Analysis of the response of a cracked Jeffcott rotor to axial excitation", Journal of Sound and Vibration, 249, 429-445, 2002. doi:10.1006/jsvi.2001.3870

5

G.D. Gounaris, C.A. Papadopoulos, "Crack identification in rotating shafts by coupled response measurements", Engineering Fracture Mechanics, 69, 339-352, 2002. doi:10.1016/S0013-7944(01)00076-5

6

A.K. Darpe, "A novel way to detect transverse surface crack in a rotating shaft", Journal of Sound and Vibration, 305, 151-171, 2007. doi:10.1016/j.jsv.2007.03.070

7

T. Yamamoto, Y. Ishida, "Linear and non linear rotor dynamics", Wiley series in non linear science, John Wiley & Sons, Inc, 2001.

8

C.W. Lee, "Vibration Analysis of Rotors", Kluwer Academic Publishers, The Netherlands, 1993.

9

A.C. Chasalevris, C.A. Papadopoulos, "Coupled horizontal and vertical bending vibrations of a stationary shaft with two cracks", Journal of Sound and Vibration, 309, 507-528, 2008. doi:10.1016/j.jsv.2007.07.039

10

I. Imam, S.H. Azzaro, R.J. Bankert, J. Scheibel, "Development of an on-line rotor crack detection and monitoring System", Journal of Vibration, Acoustics, Stress and Reliability in Design 111, 241-250, 1989.

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