This paper demonstrates nonlinear theoretical analysis of a flexible rotor system supported by a full-circular journal bearing focusing on the bifurcation phenomenon in the vicinity of the stability limit (bifurcation point). A third-order polynomial approximation model is used for the representation of the oil film force of the journal bearing. The reduced-order model, with modes concerning the bifurcation, is deduced using the center manifold theory. The dynamical equation in the normal form relating the bifurcation which leads to the oil whirl is obtained using the normal form theory. The influences of various parameters are investigated based on the analysis of a deduced dynamical equation in the normal form. Furthermore, the validity of the derived analytical observation is confirmed by comparing it with the numerically obtained frequency response result.

References

1.
Childs
,
D.
,
Moes
,
H.
, and
van Leeuwen
,
H.
,
1977
, “
Journal Bearing Impedance Descriptions for Rotordynamic Applications
,”
ASME J. Lubr. Technol.
,
99
(
2
), pp.
198
210
.
2.
Gasch
,
R.
, and
Pfutzner
,
H.
,
1975
,
Rotordynamik: Eine Einfuhrung
,
Springer-Verlag
,
Berlin
.
3.
Hori
,
Y.
, and
Kato
,
T.
,
1989
, “
Seismic Effect on the Stability of a Rotor Supported by Oil Film Bearings
,”
Trans. Jpn. Soc. Mech. Eng., Ser. C
,
55
(
511
), pp.
611
617
(in Japanese).
4.
Zhao
,
S. X.
,
Dai
,
X. D.
,
Meng
,
G.
, and
Zhu
,
J.
,
2005
, “
An Experimental Study of Nonlinear Oil-Film Forces of a Journal Bearing
,”
J. Sound Vib.
,
287
(
4
), pp.
827
843
.
5.
Meruane
,
V.
, and
Pascual
,
R.
,
2008
, “
Identification of Nonlinear Dynamic Coefficients in Plain Journal Bearing
,”
Tribol. Int.
,
41
(
8
), pp.
743
754
.
6.
Muszynska
,
A.
,
1986
, “
Whirl and Whip-Rotor/Bearing Stability Problems
,”
J. Sound Vib.
,
110
(
3
), pp.
443
462
.
7.
Chouchane
,
M.
, and
Amamou
,
A.
,
2011
, “
Bifurcation of Limit Cycles in Fluid Film Bearings
,”
Int. J. Nonlinear Mech.
,
46
(
9
), pp.
1258
1264
.
8.
Wang
,
J. K.
, and
Khonsari
,
M. M.
,
2006
, “
On the Hysteresis Phenomenon Associated With Instability of Rotor-Bearing Systems
,”
ASME J. Tribol.
,
128
(
1
), pp.
188
196
.
9.
Wang
,
J. K.
, and
Khonsari
,
M. M.
,
2006
, “
Prediction of the Stability Envelope of Rotor-Bearing System
,”
ASME J. Vib. Acoust.
,
128
(
2
), pp.
197
202
.
10.
Wang
,
J. K.
, and
Khonsari
,
M. M.
,
2006
, “
Bifurcation Analysis of a Flexible Rotor Supported by Two Fluid-Film Journal Bearing
,”
ASME J. Tribol.
,
128
(
3
), pp.
594
603
.
11.
Hassard
,
B. D.
,
Kazarinoff
,
N. D.
, and
Wan
,
Y. H.
,
1981
,
Theory and Applications of Hopf Bifurcation
(London Mathematical Society Lecture Notes, Vol.
41
),
Cambridge University Press
,
New York
.
12.
Carr
,
J.
,
1982
,
Applications of Centre Manifold Theory
, Springer-Verlag, Berlin.
13.
Yabuno
,
K.
,
2004
,
Introduction to Nonlinear Analysis for Engineers
, Saiensu-sha Co. Ltd., Tokyo, Japan (in Japanese).
14.
Mori
,
T.
,
1968
, “
Oil Whip in the Journal Bearing
,”
J. Jpn. Soc. Lubr. Eng.
,
13
(
6
), pp.
287
298
(in Japanese).
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