Modeling And Analysis of A Jeffcott Rotor As A Continuous Cantilever Beam And An Unbalanced Disk System

Abstract

The paper presents simulations of a continuous cantilever beam and an unbalanced disk system by extending classical Jeffcott rotor approach to a model that gives the first three (or more) modes of the flexible beam. Normal modes of a constrained structure method are used to develop the equations of motion including gyroscopic effects. Centrifugal force created by the unbalanced mass of the disk is considered as a constraint for the flexible beam. The first three modes of the flexible beam having an unbalanced disk are taken into

consideration, which cannot be found through the classical Jeffcott rotor modeling. Hence, the model computes the first three natural frequencies of the rotor, and presents a very good correspondence with the first natural frequency obtained by the Jeffcott model. The change in the natural frequencies with respect to the disk mass to shaft mass ratio and the disk diameter to shaft length ratio are computed and presented. Instability problem due to inertial effects is encountered if these two ratios are kept high; which cannot be predicted by the classical Jeffcott rotor model.

Key words: Jeffcott rotor, rotor whirl, modal vibration.

Keywords

• Jeffcott rotor, rotor whirl, modal vibration.

References

1. Nelson, F.C., “A brief history of early rotor dynamics”, Sound and Vibration, 37 (6): 8-11, (2003).
2. Nelson, F.C., “Rotor dynamics without equations”, International Journal of COMADEM, 10 (3): 2- 10, (2007).
3. Rao, J.S., “History of Rotating Machinery Dynamics”, Springer Science + Business Media, New York, NY, (2011).
4. Rao , J. S., “Rotor Dynamics”, John Wiley and Sons, (1983). [5] Vance, J. M., “Rotordynamics of
5. Turbomachinery”, John Wiley and Sons, New
6. York, NY, (1988). [6] Kramer, E., “Dynamics of Rotors and
7. Foundations”, Springer –Verlag, (1993).
8. Genta, G., “Dynamics of Rotating Systems”, Springer Science+Business Media, New York, NY, (2005).

9. Vance, J., Zeidan, F., Murphy, B., “Machinery Vibration and Rotordynamics”, John Wiley and Sons, New Jersey, (2010).
10. Genta, G., “Whirling of unsymmetrical rotors: A finite element approach based on complex co- ordinates”, Journal of Sound and Vibration, 124 (1): 27-53, (1988).
11. Kessler, C. L., “Complex modal analysis of rotating machinery”, PhD thesis, University of Cincinnati, (1999).
12. Campos, J., Crawford, M., Longoria, R., “Rotordynamic Modeling Using Bond Graphs: Modeling the Jeffcott Rotor”, IEEE Transaction on Magnetics, 41 (1):274-280 (2005).
13. Khanlo, H.M., Ghayour, M., Ziaei-Rad, S., “Chaotic vibration analysis of rotating, flexible, continuous shaft-disk system with a rub-impact between the disk and the stator”, Commun Nonlinear Sci Numer Simulat, 16: 566-582, (2011).
14. Thomson, W.T., “Theory of Vibration with Applications”, Prentice Hall, Englewood Cliffs, NJ, (1981).
15. Rao, S.S., “Mechanical Vibrations”, Prentice Hall, New Jersey, (2005).