In situ Modelling of Lateral-Torsional Vibration of a Rotor-Stator with Multiple Parametric Excitations
This paper presents a 4-DOF nonlinear model of a
cracked de Laval rotor-stator system derived based on Energy
Principles. The model has been used to simulate coupled torsionallateral
response of the faulty system with multiple parametric
excitations; rotor-stator-rub, a breathing transverse crack, eccentric
mass and an axial force. Nonlinearity of a “breathing” crack is
incorporated in the model using a simple hinge mechanism suitable
for a shallow crack. Response of the system while passing via its
critical speed with intermittent rotor-stator rub is analyzed. Effects of
eccentricity with phase and acceleration are investigated. Features of
crack, rub and eccentricity in vibration response are explored for
condition monitoring. The presence of a crack and rub are observable
in the power spectrum despite excitations by an axial force and rotor
unbalance. Obtained results are consistent with existing literature and
could be adopted into rotor condition monitoring strategies.
[1] T.H. Patel, and A.K. Darpe, Coupled bending torsional vibration analysis
of rotor with rub and crack, Journal of Sound and Vibration Vol.326,
2009, pp 740–752.
[2] F. CHU, and W. LU, Determination of the rubbing location in a multidisc
rotor system by means of dynamic stiffness identification. Journal of
sound and vibration, 2001. 235-246.
[3] G. Litak, and J. T. Sawicki, Intermittent behaviour of a cracked rotor in
the resonance region, Chaos, Solutions and Fractals, 2009, 42, 1495-
1501.
[4] R. Gasch, A Survey of the Dynamic Behaviour of a Simple Rotating
Shaft with Transverse Crack, Journal of Sound and Vibration, 1993,
160(2): 313-332
[5] J.T. Sawicki, A. K. Sen, and L. Grzegorz, Multiresolution Wavelet
Analysis of the Dynamics of a Cracked Rotor International Journal of
Rotating Machinery, 2009.
[6] R.F. Beatty, Differentiating Rotor response due to radial rubbing, Journal
of Vibration, Acoustics, Stress ,and Reliability in Design Vol107, 1985,
pp151–160.
[7] B. O. Al-bedoor, Transient torsional and lateral vibrations of unbalanced
rotors with rotor-to-stator rubbing. Journal of Sound and vibration
229(3), 2000, 627-645.
[8] J.T. Sawicki, J. Padovan, and R. Al-Khatib, The Dynamics of Rotor with
Rubbing. International Journal of Rotating Machinery 1999, Vol. 5, No.
4, 1998, pp. 295-304.
[9] J.T. Sawicki, X. Wu, G. Y. Baaklini, and A. L. Gyekenyesi, “Vibrationbased
crack diagnosis in rotating shafts during acceleration through
resonance,” in Nondestructive Evaluation and Health Monitoring of
Aerospace Materials and Composites II, vol. 5046 of Proceedings of
SPIE, 2003, pp. 1–10, San Diego, Calif, USA.
[10] Y. B. Kim, and S.T. Noah, Bifurcation analysis for modified Jeffcott
rotor with bearing clearances, Nonlinear Dynamics Vol. 1, 1990, pp 221-
241.
[11] F. CHU, and W. LU, Stiffening effect of the rotor during the rotor-tostator
rub in a rotating machine, Journal of Sound and Vibration
Vol.308, 2007, pp 758–766.
[12] R. Sukkar, and A.S. Yigit, Analysis of fully coupled torsional and lateral
vibrations of unbalanced rotors subject to axial loads. Kuwait
J.Sci.Eng.35 (2B), 2008, pp. 143-170.
[13] I. Mayes, W. Davies, The vibration behavior of a rotating shaft system
containing a transverse crack. Vibration in rotating machinery, Inst.
Mech, E, 1976, p.53-65.
[14] A.S. Sekhar, Crack identification in a rotor system: a model- based
approach. Journal of sound and vibration 270, 2004, 887-920.
[15] A.S. Yigit, and A.P. Christoforou, Coupled Torsional and Bending
Vibrations of Actively Controlled Drillstings. Journal of Sound and
Vibration, 2000, 234: 67-83.
[16] A.K.Darpe, Dynamics of cracked rotor. PhD Thesis, IIT Delhi, 2000.
[1] T.H. Patel, and A.K. Darpe, Coupled bending torsional vibration analysis
of rotor with rub and crack, Journal of Sound and Vibration Vol.326,
2009, pp 740–752.
[2] F. CHU, and W. LU, Determination of the rubbing location in a multidisc
rotor system by means of dynamic stiffness identification. Journal of
sound and vibration, 2001. 235-246.
[3] G. Litak, and J. T. Sawicki, Intermittent behaviour of a cracked rotor in
the resonance region, Chaos, Solutions and Fractals, 2009, 42, 1495-
1501.
[4] R. Gasch, A Survey of the Dynamic Behaviour of a Simple Rotating
Shaft with Transverse Crack, Journal of Sound and Vibration, 1993,
160(2): 313-332
[5] J.T. Sawicki, A. K. Sen, and L. Grzegorz, Multiresolution Wavelet
Analysis of the Dynamics of a Cracked Rotor International Journal of
Rotating Machinery, 2009.
[6] R.F. Beatty, Differentiating Rotor response due to radial rubbing, Journal
of Vibration, Acoustics, Stress ,and Reliability in Design Vol107, 1985,
pp151–160.
[7] B. O. Al-bedoor, Transient torsional and lateral vibrations of unbalanced
rotors with rotor-to-stator rubbing. Journal of Sound and vibration
229(3), 2000, 627-645.
[8] J.T. Sawicki, J. Padovan, and R. Al-Khatib, The Dynamics of Rotor with
Rubbing. International Journal of Rotating Machinery 1999, Vol. 5, No.
4, 1998, pp. 295-304.
[9] J.T. Sawicki, X. Wu, G. Y. Baaklini, and A. L. Gyekenyesi, “Vibrationbased
crack diagnosis in rotating shafts during acceleration through
resonance,” in Nondestructive Evaluation and Health Monitoring of
Aerospace Materials and Composites II, vol. 5046 of Proceedings of
SPIE, 2003, pp. 1–10, San Diego, Calif, USA.
[10] Y. B. Kim, and S.T. Noah, Bifurcation analysis for modified Jeffcott
rotor with bearing clearances, Nonlinear Dynamics Vol. 1, 1990, pp 221-
241.
[11] F. CHU, and W. LU, Stiffening effect of the rotor during the rotor-tostator
rub in a rotating machine, Journal of Sound and Vibration
Vol.308, 2007, pp 758–766.
[12] R. Sukkar, and A.S. Yigit, Analysis of fully coupled torsional and lateral
vibrations of unbalanced rotors subject to axial loads. Kuwait
J.Sci.Eng.35 (2B), 2008, pp. 143-170.
[13] I. Mayes, W. Davies, The vibration behavior of a rotating shaft system
containing a transverse crack. Vibration in rotating machinery, Inst.
Mech, E, 1976, p.53-65.
[14] A.S. Sekhar, Crack identification in a rotor system: a model- based
approach. Journal of sound and vibration 270, 2004, 887-920.
[15] A.S. Yigit, and A.P. Christoforou, Coupled Torsional and Bending
Vibrations of Actively Controlled Drillstings. Journal of Sound and
Vibration, 2000, 234: 67-83.
[16] A.K.Darpe, Dynamics of cracked rotor. PhD Thesis, IIT Delhi, 2000.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:68322", author = "B. X. Tchomeni and A. A. Alugongo and L. M. Masu", title = "In situ Modelling of Lateral-Torsional Vibration of a Rotor-Stator with Multiple Parametric Excitations", abstract = "This paper presents a 4-DOF nonlinear model of a
cracked de Laval rotor-stator system derived based on Energy
Principles. The model has been used to simulate coupled torsionallateral
response of the faulty system with multiple parametric
excitations; rotor-stator-rub, a breathing transverse crack, eccentric
mass and an axial force. Nonlinearity of a “breathing” crack is
incorporated in the model using a simple hinge mechanism suitable
for a shallow crack. Response of the system while passing via its
critical speed with intermittent rotor-stator rub is analyzed. Effects of
eccentricity with phase and acceleration are investigated. Features of
crack, rub and eccentricity in vibration response are explored for
condition monitoring. The presence of a crack and rub are observable
in the power spectrum despite excitations by an axial force and rotor
unbalance. Obtained results are consistent with existing literature and
could be adopted into rotor condition monitoring strategies.
", keywords = "Axial force, Crack, Nonlinear, Rotor-Stator, Rub.", volume = "8", number = "11", pages = "1855-7", }
