In the current study, the authors examine the torsional vibrations of a rotor enclosed within a stator subjected to dry friction. Through the experiments, it is demonstrated that forward whirling of the rotor occurs while in contact with the stator, backward whirling occurs with contact, as well as impacting motions, which are characterized by nonsynchronous whirling with rotor-stator collisions. While undergoing these motions, the torsional oscillations are excited by stick-slip interactions. Experimental data are presented to show the presence of a stable torsional mode dominated motion while subjected to stick-slip forces during dry-friction whirling. In this motion state, the torsional oscillation response occurs at a combination of frequencies including drive and whirl frequencies. A finite dimensional model is constructed and simulations carried out by using this model are able to capture the system dynamics, including the torsional responses observed during dry-friction whirling. Numerical results obtained by using this model are consistent with experimental observations. The findings of this study are relevant to whirling motions experienced by rotating, long flexible structures, such as drill strings used in oil-well explorations.

References

1.
Black
,
H.
,
1967
, “
Synchronous Whirling of a Shaft Within a Radially Flexible Annulus Having Small Radial Clearance
,”
Proc. Inst. Mech. Eng.
,
181
(
1
), pp.
65
73
.10.1243/PIME_CONF_1966_181_012_02
2.
Black
,
H.
,
1968
, “
Interaction of a Whirling Rotor With a Vibrating Stator Across a Clearance Annulus
,”
J. Mech. Eng. Sci.
,
10
(
1
), pp.
1
12
.10.1243/JMES_JOUR_1968_010_003_02
3.
Feng
,
Z.
, and
Zhang
,
X.
,
2002
, “
Rubbing Phenomena in Rotor-Stator Contact
,”
Chaos, Solitons Fractals
,
14
(
2
), pp.
257
267
.10.1016/S0960-0779(01)00231-4
4.
Yamamoto
,
T.
, and
Ishida
,
Y.
,
2001
,
Linear and Nonlinear Rotordynamics: A Modern Treatment With Applications
,
Wiley-Interscience
,
New York
.
5.
Muszynska
,
A.
,
1986
, “
Whirl and Whip—Rotor/Bearing Stability Problems
,”
J. Sound Vib.
,
110
(
3
), pp.
443
462
.10.1016/S0022-460X(86)80146-8
6.
Liao
,
C.
,
Balachandran
,
B.
,
Karkoub
,
M.
, and
Abdel-Magid
,
Y.
,
2011
, “
Drill-String Dynamics: Reduced-Order Models and Experimental Studies
,”
ASME J. Vib. Acoust.
,
133
(
4
), p.
041008
.10.1115/1.4003406
7.
Liao
,
C.
,
Vlajic
,
N.
,
Karki
,
H.
, and
Balachandran
,
B.
,
2012
, “
Parametric Studies on Drill-String Motions
,”
Int. J. Mech. Sci.
,
54
(
1
), pp.
260
268
.10.1016/j.ijmecsci.2011.11.005
8.
Vlajic
,
N.
,
Liao
,
C.
,
Karki
,
H.
, and
Balachandran
,
B.
,
2011
, “
Stick-Slip and Whirl Motions of Drill Strings: Numerical and Experimental Studies
,”
ASME
Paper No. DETC2011-47949.10.1115/DETC2011-47949
9.
Leine
,
R.
,
van Campen
,
D.
, and
Keultjes
,
W.
,
2002
, “
Stick-Slip Whirl Interaction in Drillstring Dynamics
,”
ASME J. Vib. Acoust.
,
124
(
2
), pp.
209
220
.10.1115/1.1452745
10.
Li
,
G.
, and
Paidoussis
,
M.
,
1994
, “
Impact Phenomena of Rotor-Casing Dynamical Systems
,”
Nonlinear Dyn.
,
5
, pp.
53
70
.10.1007/BF00045080
11.
Kreuzer
,
E.
, and
Struck
,
H.
,
2005
, “
Active Damping of Spatio-Temporal Dynamics of Drill-Strings
,”
IUTAM Symposium on Chaotic Dynamics and Control of Systems in Processes in Mechanics
, Vol. 122, Springer, Berlin/Heidelberg, pp.
407
417
.10.1007/1-4020-3268-4_38
12.
Christoforou
,
A.
, and
Yigit
,
A.
,
1997
, “
Dynamic Modelling of Rotating Drillstrings With Borehole Interactions
,”
J. Sound Vib.
,
206
(
2
), pp.
243
260
.10.1006/jsvi.1997.1091
13.
Jansen
,
J.
,
1993
, “
Nonlinear Dynamics of Oilwell Drillstrings
,” Ph.D. thesis, Delft University of Technology, Delft, Netherlands.
14.
Melakhessou
,
H.
,
Berlioz
,
A.
, and
Ferraris
,
G.
,
2003
, “
A Nonlinear Well-Drillstring Interaction Model
,”
ASME J. Vib. Acoust.
,
125
(
1
), pp.
46
52
.10.1115/1.1523071
15.
Mihajlovic
,
N.
,
van Veggel
,
A.
,
van de Wouw
,
N.
, and
Nijmeijer
,
H.
,
2004
, “
Analysis of Friction-Induced Limit Cycling in an Experimental Drill-String System
,”
J. Dyn. Syst., Meas., Control
,
126
(
4
), pp.
709
720
.10.1115/1.1850535
16.
Mihajlovic
,
N.
,
van de Wouw
,
N.
,
Rosielle
,
P.
, and
Nijmeijer
,
H.
,
2007
, “
Interaction Between Torsional and Lateral Vibrations in Flexible Rotor Systems With Discontinuous Friction
,”
Nonlinear Dyn.
,
50
(
3
), pp.
679
699
.10.1007/s11071-006-9172-3
17.
Edwards
,
S.
,
Lees
,
A.
, and
Friswell
,
M.
,
1999
, “
The Influence of Torsion on Rotor/Stator Contact in Rotating Machinery
,”
J. Sound Vib.
,
225
(
4
), pp.
767
778
.10.1006/jsvi.1999.2302
18.
Diangui
,
H.
,
2000
, “
Experiment on the Characteristics of Torsional Vibration of Rotor-to-Stator Rub in Turbomachinery
,”
Tribol. Int.
,
33
, pp.
75
79
.10.1016/S0301-679X(00)00029-3
19.
Nayfeh
,
A.
, and
Balachandran
,
B.
,
1995
,
Applied Nonlinear Dynamics
,
Wiley
,
New York
.
20.
Rosenstein
,
M.
,
Collins
,
J.
, and
Luca
,
C. D.
,
1993
, “
A Practical Method for Calculating Largest Lyapunov Exponents From Small Data Sets
,”
Physica D
,
65
, pp.
117
134
.10.1016/0167-2789(93)90009-P
21.
Khulief
,
Y.
,
Al-Sulaiman
,
F.
, and
Bashmal
,
S.
,
2007
, “
Vibration Analysis of Drillstrings With Self-Excited Stick-Slip Oscillations
,”
J. Sound Vib.
,
299
(
3
), pp.
540
558
.10.1016/j.jsv.2006.06.065
22.
Piovan
,
M.
, and
Sampaio
,
R.
,
2006
, “
Nonlinear Model for Coupled Vibrations of Drill-Strings
,”
Mecanica Computacional
,
25
, pp.
1751
1765
.
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