Vibration Analysis of a Multi-disk, Bearing and Mass Unbalance Rotor Using Assumed Modes Method

Authors

1 Department of Mechanical Engineering, University of Yazd, Yazd, Iran

2 Department of Mechanical Engineering, Malek Ashtar University of Technology, Esfahan, Iran

Abstract

In this paper, a simple and efficient method for modeling and solving the equations of a rotor with any number of disks, bearings and mass unbalances is presented using the assumed modes method. This model consists of a continuous shaft, arbitrary number of mass unbalances in any axial location and phase angle, and any number of rigid disks and bearings. This arrangement is extensively used in diverse applications. In this study, final governing differential equations are not derived because the assumed modes method is directly inserted to solving process. Some examples in both cases of free and forced vibration are performed. The results show the accuracy of this modeling and the ability of it to predicting the vibration behavior of the rotor in a complex combination of shaft, disk and bearing. This study also shows that the present approach can give the results as accurate as the most popular approach, i.e. the Finite Element Method.

Keywords

References

[1]   Musznynska, M., “Rotordynamics”, CRC Press, Taylor & Francis Group, LLC, 2005, pp. 1-30.
[2]    Katz, R., “The Dynamic Response of a Rotating Shaft Subject to an Axially Moving and Rotating Load”, Journal of Sound and Vibration, Vol. 246, No. 5, 2001, pp. 757-775.
[3]   Chasalevris, A. C., “Vibration Analysis of Nonlinear-Dynamic Rotor-Bearing Systems and Defect Detection”. PhD Dissertation, University of Patras, 2009.
[4]   Jun, O. S., Kim, J. O., “Free Bending Vibration of a Multi-Step Rotor”, Journal of Sound and Vibration, Vol. 224, No. 4, 1999, pp. 625-642.
[5]   Shabaneh, N. H., Jean, W. Zu., “Dynamic Analysis of Rotor-Shaft Systems with Viscoelastically Supported Bearings”, Mechanism and Machine Theory, Vol. 35, 2000, pp. 1313-1330.
[6]   Kalita, M.,  Kakoty, S. K., “Analysis of Whirl Speeds for Rotor-Bearing Systems Supported on Fluid Film Bearing”, Mechanical Systems and Signal Processing, Vol. 18, 2004, pp. 1369-1380.
[7]   Khanlo, H. M., Ghayour, M., and Ziaei-Rad, S., “Chaotic Vibration Analysis of Rotating, Flexible, Continuous Shaft-Disc System with a Rub-Impact Between the Disc and the Stator”, Commun Nonlinear Sci Numer Simulat, Vol. 16, 2011, pp. 566-582.
[8]   Tiwari, R., “A Brief History and State of the Art of Rotordynamics”, Department of Mechanical Engineering, Indian Institute of Technology Guwahati, 2008, pp. 7-30.
[9]   Lee, W., Jei, Y. G., “Modal Analysis of Continuous Rotor-Bearing Systems”, Journal of Sound and Vibration, Vol. 126, No. 2, 1988, pp. 345-361.
[10]     Oncescu, F., Lakis, A. A., and Ostiguy, G., “Investigation of the Stability and Steady State Response of Asymmetric Rotors, Using Finite Element Formulation”, Journal of Sound and Vibration, Vol. 245, No. 2, 2001, pp. 303-328.
[11]     Xiang, J., Chen, D., Chen, X., and He, Zh., “A Novel Wavelet-Based Finite Element Method for the Analysis of Rotor-Bearing Systems”, Finite Elements in Analysis and Design, Vol. 45, 2009, pp. 908-916.
[12]     Shad, M. R., “Modelling and Analysis of Nonlinear Dynamic Behavior of Rotors”, PhD Dissertation, University of Toulouse, 2011.
[13]     Atepor, L., “Vibration Analysis and Intelligent Control of Flexible Rotor Systems Using Smart Materials”, PhD Dissertation, University of Glasgow, 2008.
[14]     Choi, L., Park, J. M., “Finite Element Analysis of Rotor Bearing Systems Using a Modal Transformation Matrix”, Journal of Sound and Vibration, Vol. 111, No. 3, 1986, pp. 441-456.
[15]     Rao, S., “Vibration of Continuous Systems”, John Wiley & Sons, 2007, pp. 661-673.
[16]     Srikrishnanivas, S., “Rotor Dynamic Analysis of RM12 Jet Engine Rotor Using Ansys”, Master’s Degree Thesis, Blekinge Institute of Technology, Karlskrona, Sweden, 2012.
[17]     Das, A. S., and Dutt, J. K., “Reduced Model of a Rotor-Shaft System Using Modified SEREP”, Mechanics Re-search Communications, Vol. 35, 2008, pp. 398-407.
 
 

Files

Share

How to cite

Statistics