Investigating Nonlinear Vibration Behavior of Rotors with Asymmetry Shaft Considering Misalignment
Subject Areas : Mechanical Engineering
A.A
Jafari
1
(Department of Mechanical Engineering, KNT University, Tehran, Iran)
P
Jamshidi
2
(Department of Mechanical Engineering, KNT University, Tehran, Iran)
Keywords: Misalignment, Nonlinear vibration, Rotor dynamics, Asymmetric shaft,
Abstract :
In this paper, the nonlinear vibration behavior of a rotor with asymmetric shaft considering misalignment is studied. The system consists of a rectangular shaft and a disk which is connected to a motor through a flexible coupling. In order to consider higher order deformations, nonlinear Bernoulli beam is used for modeling the shaft. Gibbons’ equations are utilized to apply misaligned coupling forces. The equations of motion of the system are derived using the Lagrangian method and then discretized by the Rayleigh-Ritz method. In order to solve nonlinear equations and hence obtaining nonlinear responses, multiple scales method is used. The vibration behavior of the system near the resonance frequencies is studied by taking into account various parameters including unbalance forces and the effect of the asymmetry of cross section of the shaft. The analytical results are consistent with those of numerical method with a good accuracy. In addition, the effects of variations of the system parameters on the rotor vibration behavior have been shown graphically. In the end, the changes in the various parameters of the system and their effects on the rotor vibration response are discussed.
[1] Tondl A., 1965, Some Problems of Rotor Dynamics, Publishing House of the Czechoslovak Academy of Sciences, Prague.
[2] Badlani M., Kleinhenz W., 1978, The effect of rotary inertia and shear deformation on the parametric stability of unsymmetric shafts, Mechanism and Mashine Theory 13: 543-553.
[3] Sheu H.-C., Chen L.-W., 2000, A lumped mass model for parametric instability analysis of cantilever shaft-disk systems, Journal of Sound and Vibration 234: 331-348.
[4] Pei Y.-C., 2009, Stability boundaries of a spinning rotor with parametrically excited gyroscopic system, European Journal of Mechanics - A/Solids 28: 891-896.
[5] Shahgholi M., Khadem S.E., 2012, Primary and parametric resonances of asymmetrical rotating shafts with stretching nonlinearity, Mechanism and Machine Theory 51: 131-144.
[6] Jafari A.A., Jamshidi P., 2015, Investigating the stability of rotors with asymmetry cross sections using perturbation method, The 5th International Conference on Acoustics and Vibrations.
[7] Gibbons C., 1976, Coupling misalignment forces, Proceedings 5th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, Texas.
[8] Sekhar A., Prabu B., 1995, Effects of coupling misalignment on vibrations of rotating machinery, Journal of Sound and Vibration 185(4): 655-671.
[9] Al-Hussain K.M., Redmond I., 2002, Dynamic response of two rotors connected by rigid mechanical coupling with parallel misalignment, Journal of Sound and Vibration 249(3): 483-498.
[10] Al-Hussain K.M., 2003, Dynamic stability of two rigid rotors connected by a flexible coupling with angular misalignment, Journal of Sound and Vibration 266(2): 217-234
[11] Lees A. W., 2007, Misalignment in rigidly coupled rotors, Journal of Sound and Vibration 305: 261-271.
[12] Patel T.H., Darpe A.K., 2009, Experimental investigations on vibration response of misaligned rotors, Mechanical Systems and Signal Processing 23(7): 2236-2252.
[13] Patel T.H., Darpe A.K., 2009, Vibration response of misaligned rotors, Journal of Sound and Vibration 325(3): 609-628
[14] Pennacchi P., Vania A. , Chatterton S., 2012, Nonlinear effect caused by coupling misalignment in rotors equipped with journal bearing, Mechanical and Systems and Signal Processing 30: 306-322.
[15] Ma H., Wang X., Niu N., Wen B., 2015, Oil-film instability simulation in an overhung rotor system with flexible coupling misalignment, Archive of Applied Mechanics 85: 893-907.
[16] Feng S., Geng H., Qi S., Yu L., 2012, Vibration of a misaligned rotor system with asymmetric shaft stiffness, Advanced Materials Research 503-504: 813-818.
[17] Lalanne M., Ferraris G., 1998, Rotordynamics Prediction in Engineering, John Wiley & Sons.
[18] Kr.Jalan A., Mohanty A.R., 2009, Modal based fault diagnosis of a rotor-bearing system for misalignment and unbalance under steady-state condition, Journal of Sound and Vibration 327: 604-622.
[19] Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillations, Wiley, New York.