This paper deals with the long-term dynamic behaviors of a complex rotor-bearing system with multi-degrees-of-freedom and nonclosed form of the bearing forces. Since nonanalytical bearing forces can be available, to increase the numerical accuracy and decrease the CPU time, a new method is presented to calculate the Jacobians of the bearing forces and bearing forces themselves. The algorithm is concise and the computing efforts spent on the Jacobians are very small compared to spend on the bearing forces themselves. In terms of the feature that the nonlinear bearing forces act on the system individually, a new reduction method and corresponding integration technique is proposed to increase the numerical stability and decrease the computing time for the system analysis. The numerical schemes of this study are applied to a rotor system with multi-rigid disks and two elliptical bearing supports. The numerical results reveal very rich and complex nonlinear behavior of the system. [S0021-8936(00)00802-3]

1.
Yamamoto, T. T., 1954, “On critical Speeds of a Shaft,” Mem. Fac. Eng., Nagoya Univ. (Japan), 6, No. 2.
2.
Bently, D., 1974, “Forced Subrotative Speed Dynamic Action of Rotating Machinery,” ASME Paper No. 74-PET-16, Petroleum Mechanical Engineering Conference, Dallas. Texas.
3.
Childs
,
D. W.
,
1982
, “
Fractional-Frequency Rotor Motion due to Nonsymmetric Clearance Effects
,”
ASME J. Eng. Gas Turbines Power
,
104
, pp.
533
541
.
4.
Choi
,
S. K.
, and
Noah
,
S. T.
,
1992
, “
Response and Stability Analysis of Piecewise-Linear Oscillators Under Multi-forcing Frequencies
,”
Nonlinear Dyn.
,
3
, pp.
105
121
.
5.
Yamauchi
,
S.
,
1983
, “
The Nonlinear Vibration of Flexible Rotors, 1st Report, Development of a New Technique
,”
JSME
,
49
, pp.
1862
1868
.
6.
Ehrich
,
F. F.
,
1988
, “
High Order Subharmonic Response of High Speed Rotors in Bearing Clearance
,”
ASME J. Vibr. Acoust.
,
110
, pp.
9
16
.
7.
Childs, D. W., 1984, “Rotordynamic Characteristics of HPOPT (High Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Engine),” Turbomachinery Laboratories Report (Texas A&M Univ.), FDI-84.
8.
Kim
,
Y. B.
, and
Noah
,
S. T.
,
1990
, “
Bifurcation Analysis for a Modified Jaffcott Rotor With Bearing Clearance
,”
Nonlinear Dyn.
,
1
, pp.
221
241
.
9.
Brancati
,
R.
,
Rocca
,
E.
,
Rosso
,
M.
, and
Rosso
,
R.
,
1995
, “
Journal Orbits and Their Stability for Rigid Unbalanced Rotors
,”
ASME J. Tribol.
,
117
, pp.
709
716
.
10.
Della Pietra
,
L.
,
De Rosa
,
E.
, and
Rossi
,
C.
,
1991
, “
Static and Dynamic Behavior of a Rigid Rotor on Journal Bearings
,”
Meccanica
,
26
, pp.
229
245
.
11.
Lund, J. W., and Nielson, H. B., 1980, “Instability Threshold of an Unbalanced Rigid Rotor in Short Journal Bearings,” Second International Conference on Vibration in Rotating Machinery, Cambridge, UK.
12.
Choi
,
S. K.
, and
Noah
,
S. T.
,
1994
, “
Mode-Locking and Chaos in a Jeffcott Rotor With Bearing Clearance
,”
ASME J. Appl. Mech.
,
61
, pp.
131
138
.
13.
Day
,
W. B.
,
1987
, “
Asymptotic Expansions in Nonlinear Rotordynamics
,”
Q. Appl. Mech.
,
44
, pp.
779
792
.
14.
Mclean
,
L. J.
, and
Hahn
,
E. J.
,
1983
, “
Unbalance Behavior of Squeeze Film Damped Multi-Mass Flexible Rotor Bearing System
,”
ASME J. Lubr. Technol.
,
105
, pp.
22
28
.
15.
Shiau
,
T. N.
, and
Jean
,
A. N.
,
1990
, “
Prediction of Steady State Response of Flexible Rotor System With Nonlinear Supports: A New Technique
,”
ASME J. Vibr. Acoust.
,
112
, pp.
501
507
.
16.
Nataraj
,
C.
, and
Nelson
,
H. D.
,
1989
, “
Periodic Solutions in Rotor Dynamic System With Nonlinear Supports: A General Approach
,”
ASME J. Vibr. Acoust.
,
111
, pp.
187
193
.
17.
Nelson
,
H. D.
,
1980
, “
A Finite Rotating Shaft Element Using Timoshenko Beam Theory
,”
ASME J. Mech. Des.
,
102
, pp.
793
803
.
18.
Nelson, H. D., Mechan, W. L., Fleming, D. P., and Kascak, A. F., 1983, “Nonlinear Analysis of Rotor Bearing System Using Component Mode Synthesis,” ASME paper No. 83-GT-303.
19.
Lund, J. W., and Thomson, K. K., 1978, “A Calculation Method and Data for the Dynamic Coefficients of Oil-Lubricated Journal Bearings,” Topics in Fluid Journal Bearing and Rotor Bearing Syst., ASME, New York, pp. 1–28.
20.
Klit
,
P.
, and
Lund
,
J. W.
,
1986
, “
Calculation of the Dynamic Coefficients of a Journal Bearing, Using a Variational Approach
,”
ASME J. Tribol.
,
108
, pp.
421
425
.
21.
Someya, T., 1989, Journal Bearing Data Book, Springer-Verlag, Berlin.
22.
Choy
,
F. K.
,
Braun
,
M. J.
, and
Hu
,
Y.
,
1991
, “
Nonlinear Effects in a Plain Journal Bearing: Part 1—Analytical Study; Part 2—Results
,”
ASME J. Tribol.
,
113
, pp.
555
570
.
23.
Kinderlenhrer, D., and Stanpacchia, G., 1980, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York.
24.
Zheng
,
T.
,
Li
,
L.
, and
Xu
,
Q.
,
1995
, “
An Iterative Method for the Discrete Problems of a Class of Elliptical Variational Inequalities
,”
Chin. J. Appl. Math. Mech.
,
16
, pp.
351
358
(English edition).
25.
Bathe, K., and Wilson, E., 1976, Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.
26.
Parker, T. S., and Chua, L. O. 1989, Practical Numerical Algorithms for Chaotic System, Springer-Verlag, New York.
27.
Seydel, R., 1988, From Equilibrium to Chaos, Practical Bifurcation and Stability Analysis, Elsevier, New York.
28.
Tufilaro, N. B., Abbortt, T., and Jeremiah, R., 1992, An Experimental Approach to Nonlinear Dynamics and Chaos, Addison-Wesley, Reading, MA.
29.
Baker, G. L., and Gollub, J. P., 1990, Chaotic Dynamics: An Introduction, Cambridge University Press, Cambridge, UK.
You do not currently have access to this content.