Planar dynamics of a rotor supported by long hydrodynamic journal bearing is investigated theoretically. An analytical model of the long journal bearing system is numerically integrated for analysis of fixed point and periodic oscillations. The nonlinearities in the system arise due to a nonlinear fluid film force acting on the journal. The influences of three dimensionless parameters, viz. bearing parameter, unbalance, and rotor speed, on the dynamic behavior of the rotor bearing system is studied and compared with the short journal bearing. For the same bearing parameter, short bearing has large operating speed compared to a long bearing. The results are presented in the form of a bifurcation diagram and Poincaré map of the oscillations based on numerical computation. The considered unbalanced system shows periodic, multiperiodic, and quasi-periodic motion in different speed range. Jumping phenomenon is also observed for a high value of bearing parameter with unbalance.

References

1.
Newkirk
,
B.
,
1924
, “
Shaft Whipping
,”
Gen. Electr. Rev.
,
27
(
3
), pp.
169
178
.
2.
Newkirk
,
B. L.
, and
Taylor
,
H. D.
,
1925
, “
Shaft Whipping Due to Oil Action in Journal Bearings
,”
Gen. Electr. Rev.
,
28
(
8
), pp.
559
568
.https://dyrobes.com/wp-content/uploads/2012/12/Shaft-Whipping-Action-Due-to-Oil-Action-in-Journal-Bearings-Newkirk-Taylor-1925.pdf
3.
Hori
,
Y.
,
1959
, “
A Theory of Oil Whip
,”
Trans. ASME J. Appl. Mech.
,
26
(2), pp.
189
198
.
4.
Holmes
,
R.
,
1960
, “
The Vibration of a Rigid Shaft on Short Sleeve Bearings
,”
J. Mech. Eng. Sci.
,
2
(
4
), pp.
337
341
.
5.
Reddi
,
M.
, and
Trumpler
,
P.
,
1962
, “
Stability of the High-Speed Journal Bearing Under Steady Load
,”
ASME J. Eng. Ind.
,
84
(
3
), pp.
351
358
.
6.
Jw
,
L.
, and
Saibel
,
E.
,
1967
, “
Oil Whip Whirl Orbits of a Rotor in Sleeve Bearings
,”
ASME J. Eng. Ind.
,
89
(
4
), pp.
813
823
.
7.
Myers
,
C.
,
1984
, “
Bifurcation Theory Applied to Oil Whirl in Plain Cylindrical Journal Bearings
,”
ASME J. Appl. Mech.
,
51
(
2
), pp.
244
250
.
8.
Gardner
,
M.
,
Myers
,
C.
,
Savage
,
M.
, and
Taylor
,
C.
,
1985
, “
Analysis of Limit-Cycle Response in Fluid-Film Journal Bearings Using the Method of Multiple Scales
,”
Q. J. Mech. Appl. Math.
,
38
(
1
), pp.
27
45
.
9.
Butcher
,
E. A.
,
Dabiri
,
A.
, and
Nazari
,
M.
,
2015
, “
Transition Curve Analysis of Linear Fractional Periodic Time-Delayed Systems Via Explicit Harmonic Balance Method
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
4
), p.
041005
.
10.
Hollis
,
P.
, and
Taylor
,
D.
,
1986
, “
Hopf Bifurcation to Limit Cycles in Fluid Film Bearings
,”
ASME J. Tribol.
,
108
(
2
), pp.
184
189
.
11.
Adiletta
,
G.
,
Guido
,
A.
, and
Rossi
,
C.
,
1996
, “
Chaotic Motions of a Rigid Rotor in Short Journal Bearings
,”
Nonlinear Dyn.
,
10
(
3
), pp.
251
269
.
12.
Adiletta
,
G.
,
Guido
,
A.
, and
Rossi
,
C.
,
1997
, “
Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings—Part I: Theoretical Analysis
,”
Nonlinear Dyn.
,
14
(
1
), pp.
57
87
.
13.
Adiletta
,
G.
,
Guido
,
A.
, and
Rossi
,
C.
,
1997
, “
Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings—Part II: Experimental Analysis
,”
Nonlinear Dyn.
,
14
(
2
), pp.
157
189
.
14.
Dabiri
,
A.
,
Nazari
,
M.
, and
Butcher
,
E. A.
,
2016
, “
Chaos Analysis and Control in Fractional Order Systems Using Fractional Chebyshev Collocation Method
,”
ASME
Paper No. IMECE2016-67909.
15.
Huang
,
C.
,
Cao
,
J.
, and
Xiao
,
M.
,
2016
, “
Hybrid Control on Bifurcation for a Delayed Fractional Gene Regulatory Network
,”
Chaos, Solitons Fractals
,
87
, pp.
19
29
.
16.
Xiao
,
M.
,
Zheng
,
W. X.
,
Jiang
,
G.
, and
Cao
,
J.
,
2017
, “
Stability and Bifurcation of Delayed Fractional-Order Dual Congestion Control Algorithms
,”
IEEE Trans. Autom. Control
,
62
(
9
), pp.
4819
4826
.
17.
Brouwers
,
H.
,
van Campen
,
D.
, and
de Kraker
,
A.
,
1990
, “
Limit Cycle Predictions of a Nonlinear Journal-Bearing System
,”
ASME J. Eng. Ind.
,
112
(2), pp.
168
171
.
18.
Boyaci
,
A.
,
Hetzler
,
H.
,
Seemann
,
W.
,
Proppe
,
C.
, and
Wauer
,
J.
,
2009
, “
Analytical Bifurcation Analysis of a Rotor Supported by Floating Ring Bearings
,”
Nonlinear Dyn.
,
57
(
4
), pp.
497
507
.
19.
Amamou
,
A.
, and
Chouchane
,
M.
,
2014
, “
Nonlinear Stability Analysis of Long Hydrodynamic Journal Bearings Using Numerical Continuation
,”
Mech. Mach. Theory
,
72
, pp.
17
24
.
20.
Govaerts
,
W. J.
,
2000
,
Numerical Methods for Bifurcations of Dynamical Equilibria
, Society for Industrial and Applied Mathematics, Philadelphia, PA.
21.
Krauskopf, B., Osinga, H. M., and Galan-Vioque,
J.
, eds.,
2007
,
Numerical Continuation Methods for Dynamical Systems
(Path Following and Boundary Value Problems), Springer, Dordrecht, The Netherlands.
22.
Kuznetsov
,
Y. A.
,
2013
,
Elements of Applied Bifurcation Theory
, Vol.
112
, Springer-Verlag, New York.
23.
Govaerts
,
W.
,
Kuznetsov
,
Y. A.
, and
Dhooge
,
A.
,
2005
, “
Numerical Continuation of Bifurcations of Limit Cycles in Matlab
,”
SIAM J. Sci. Comput.
,
27
(
1
), pp.
231
252
.
24.
Chouchane
,
M.
, and
Amamou
,
A.
,
2011
, “
Bifurcation of Limit Cycles in Fluid Film Bearings
,”
Int. J. Non-Linear Mech.
,
46
(
9
), pp.
1258
1264
.
25.
Sghir
,
R.
, and
Chouchane
,
M.
,
2015
, “
Prediction of the Nonlinear Hysteresis Loop for Fluid-Film Bearings by Numerical Continuation
,”
Proc. Inst. Mech. Eng. Part C
,
229
(
4
), pp.
651
662
.
26.
Ferjaoui
,
N.
,
Naimi
,
S.
, and
Chouchane
,
M.
,
2016
, “
Bifurcation Analysis of a Flexible Balanced Cracked Rotor–Bearing System
,”
C. R. Méc.
,
344
(
9
), pp.
661
671
.
27.
Frene
,
J.
,
Nicolas
,
D.
,
Degueurce
,
B.
,
Berthe
,
D.
, and
Godet
,
M.
,
1997
,
Hydrodynamic Lubrication: Bearings and Thrust Bearings
, Vol.
33
,
Elsevier
, Amsterdam, The Netherlands.
28.
Brindley
,
J.
,
Savage
,
M.
, and
Taylor
,
C.
,
1990
, “
The Nonlinear Dynamics of Journal Bearings
,”
Philos. Trans. R. Soc. London A
,
332
(
1624
), pp.
107
119
.
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