A method is presented for predicting the occurrence of a hysteresis phenomenon, which is observed in experimental results dealing with the instability of rotor-bearing systems. The method is based on the Hopf bifurcation theory. It is shown that the existence of a hysteresis phenomenon is dependent upon the system’s operating parameters. To this end, the effect of oil viscosity on the hysteresis phenomenon and its implications on the rotor-bearing instability are investigated. The results of a series of experiments illustrating the effectiveness of the prediction of the hysteresis phenomenon using the Hopf bifurcation theory are also presented.
Issue Section:
Research Papers
1.
Newkirk
, B. L.
, and Taylor
, H. D.
, 1925, “Shaft Whipping Due to Oil Action in Journal Bearing
,” Gen. Electr. Rev.
0095-9480, 28
, pp. 559
–568
.2.
Adams
, M. L.
, Adams
, M. L.
, and Guo
, J. S.
, 1996, “Simulations and Experiments of the Non-linear Hysteresis Loop for Rotor-Bearing Instability
,” C500/001/96, IMechE Conference Transactions 1996-6
, Sixth International Conference on Vibration in Rotating Machinery, Oxford, UK, September, pp. 309
–319
.3.
Pinkus
, O.
, 1956, “Experimental Investigation of Resonant Whip
,” Trans. ASME
0097-6822, 78
, pp. 975
–983
.4.
Hori
, Y.
, 1959, “A Theory of Oil Whip
,” ASME J. Appl. Mech.
0021-8936, 26
, pp. 189
–198
5.
Hori
, Y.
, 1988, “Anti-earthquake Considerations in Rotordynamics
,” C318/88, Proceedings of the ImechE Fourth International Conference on Vibration in Rotating Machinery
, Edinburgh, September, pp. 1
–8
.6.
Guo
, J. S.
, 1995, “Characteristics of the Nonlinear Hysteresis Loop for Rotor-Bearing Instability
,” Ph.D. thesis, Department of Mechanical and Aerospace Engineering, Case Western Reserve University.7.
Horattas
, G. A.
, 1996, “Experimental Investigation of Dynamic Nonlinearities in Rotating Machinery
,” Ph.D. thesis, Department of Mechanical and Aerospace Engineering, Case Western Reserve University.8.
Horattas
, G. A.
, Adams
, M. L.
, Abdel Magied
, M. F.
, and Loparo
, K. A.
, 1997, “Experimental Investigation of Dynamic Nonlinearities in Rotating Machinery
,” Proceedings of ASME DETC’ 1997
, 1997 ASME Design Engineering Technical Conferences, September 14–17, Sacramento, California.9.
Muszynska
, A.
, 1998, “Transition to Fluid-Induced Stability Boundaries Self-Excited Vibrations of a Rotor and Instability Threshold ‘Hysteresis’
,” Proceedings of ISROMAC-7
, The 7th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, February, Honolulu, HI, pp. 775
–784
.10.
Myers.
C. J.
, 1984, “Bifurcation Theory Applied to Oil Whirl in Plain Cylindrical Journal Bearings
,” ASME J. Appl. Mech.
0021-8936, 51
, pp. 244
–250
.11.
Hollis
, P.
, and Taylor
, D. L.
, 1986, “Hopf Bifurcation to Stability Boundaries in Fluid Film Bearings
,” ASME J. Tribol.
0742-4787, 108
, pp. 184
–189
.12.
Sundararajan
, P.
, and Noah
, S. T.
, 1995, “Local and Global Effects of Nonlinearities in Rotating Machinery—Application to Journal Bearing Supported Rotor Systems
,” Turbomachinery Research Consortium Report, Texas A&M University.13.
Noah
, S. T.
, 1995, “Significance of Considering Nonlinear Effects in Predicting the Dynamic Behavior of Rotating Machinery
,” J. Vib. Control
1077-5463, 1
, pp. 431
–458
.14.
Deepak
, J. C.
, and Noah
, S. T.
, 1998, “Experimental Verification of Subcritical Whirl Bifurcation of a Rotor Supported on a Fluid Film Bearing
”, ASME J. Tribol.
0742-4787, 120
, pp. 605
–609
.15.
Hassard
, B. D.
, Kazarinoff
, N. D.
, and Wan
, Y. H.
, 1981, Theory and Applications of Hopf Bifurcation
, London Mathematical Society Lecture Notes 41
, Cambridge University Press
, Cambridge, UK.16.
Chauvin
, D.
, 2003, “An Experimental Investigation of Whirl Instability Including Effects of Lubricant Temperature in Plain Circular Journal Bearings
,” M.S. thesis, Department of Mechanical Engineering, Louisiana State University.17.
Lund
, J. W.
, 1974, “Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-Film Bearings
”, J. Eng. Ind.
0022-0817, 96
(2
), pp. 509
–517
.18.
Bhat
, R. B.
, Rao
, J. S.
, and Sankar
, T. S.
, 1982, “Optimum Journal Bearing Parameters for Minimum Rotor Unbalance Response in Synchronous Whirl
,” ASME J. Mech. Des.
0161-8458, 104
, pp. 339
–344
.19.
Khonsari
, M. M.
, and Chang
, Y. J.
, 1993, “Stability Boundary of Non-linear Orbits within Cleareance Circle of Journal Bearings
,” ASME J. Vibr. Acoust.
0739-3717, 115
, pp. 303
–307
.20.
Khonsari
, M. M.
, and Booser
, E. R.
, 2001, Applied Tribology: Bearing Design and Lubrication
, John Wiley & Sons
, New York.21.
Khonsari
, M. M.
, 1987, “A Review of Thermal Effects in Hydrodynamic Bearings. Part II: Journal Bearings
,” ASLE Trans.
0569-8197, 30
(1
), pp. 26
–33
.22.
Khonsari
, M.
, Jang
, J.
, and Fillon
, M.
, 1996, “On the Generalization of Thermohydrodynamic Analysis for Journal Bearings
,” ASME J. Tribol.
0742-4787, 118
, pp. 571
-579
.23.
Chang
, Y. J.
, 1991, “The Effect of Supply Temperature and Shaft Flexibility on the Shaft of Journal Bearings
,” M.S. thesis, Department of Mechanical Engineering, University of Pittsburgh.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.
