Synchronous vibration in rotor systems having bearings, seals, or other elements with nonlinear stiffness characteristics is prone to amplitude jump when operating close to critical speeds as there may be two or more possible whirl motions for a given unbalance condition. This paper describes research on how active control techniques may eliminate this potentially undesirable behavior. A control scheme based on feedback of rotor-stator interaction forces is considered. Model-based conditions for stability of low amplitude whirl, derived using Lyapunov’s direct method, are used to synthesize controller gains. Subsidiary requirements for existence of a static feedback control law that can achieve stabilization are also explained. An experimental validation is undertaken on a flexible rotor test rig where nonlinear rotor-stator contact interaction can occur across a small radial clearance in one transverse plane. A single radial active magnetic bearing is used to apply control forces in a separate transverse plane. The experiments confirm the conditions under which static feedback of the measured interaction force can prevent degenerate whirl responses such that a low amplitude contact-free orbit is the only possible steady-state response. The gain synthesis method leads to controllers that are physically realizable and can eliminate amplitude jump over a range of running speeds.

References

References
1.
Von Groll
,
G.
, and
Ewins
,
D. J.
, 2000, “
On the Dynamics of Windmilling in Aero-Engines
,”
Proceedings of the Seventh International Conference on Vibrations in Rotating Machinery
, Nottingham, pp.
721
730
.
2.
Johnson
,
D. C.
, 1962, “
Synchronous Whirl of a Vertical Shaft Having Clearance in One Bearing
,”
J. Mech. Eng. Sci.
,
4
(
1
), pp.
85
93
.
3.
Muszynska
,
A.
, and
Goldman
,
P.
, 1993, “
Chaotic Vibrations of Rotor/Bearing/Stator Systems With Looseness or Rubs
,”
Nonlinear Vibrations
,
54
, pp.
187
194
.
4.
Kim
,
Y. B.
, and
Noah
,
S. T.
, 1990, “
Bifurcation Analysis for a Modified Jeffcott Rotor With Bearing Clearances
,”
Nonlinear Dyn.
,
1
, pp.
221
241
.
5.
Yu
,
J. J.
,
Goldman
,
P.
,
Bently
,
D. E.
, and
Muzynska
,
A.
, 2002, “
Rotor/Seal Experimental and Analytical Study of Full Annular Rub
,”
ASME J. Eng. Gas Turbines Power
,
124
(
2
), pp.
340
350
.
6.
Bartha
,
A. R.
, 2000, “
Dry Friction Backward Whirl of Rotors
,” Ph.D. dissertation, ETH, Zurich.
7.
Williams
,
R. J.
, 2004, “
Parametric Characterization of Rub Induced Whirl Instability Using an Instrumented Rotordynamic Test Rig
,”
Proceedings of the Tenth International Conference on Vibrations in Rotating Machinery
, Swansea, Paper C623/012/04, pp.
651
659
.
8.
Childs
,
D. W.
, and
Bhattacharya
,
A.
, 2007, “
Prediction of Dry-Friction Whirl and Whip Between a Rotor and a Stator
,”
ASME J. Vibr. Acoust.
,
129
, pp.
355
362
.
9.
Tamura
,
K.
Shiraki
,
K.
Awa
,
K.
and
Watanabe
,
Y.
, 2002, “
Vibration Behavior of Rotating Shaft Due to Contact with Casing
,”
Proceedings of the Sixth International Conference on Motion and Vibration Control
, Saitama, pp.
1021
1026
.
10.
Villa
,
C.
,
Sinou
,
F.
, and
Thoverez
,
F.
, 2008, “
Stability and Vibration Analysis of a Complex Flexible Rotor Bearing System
,”
Commun. Nonlinear Sci. Numer. Simul.
,
13
, pp.
804
821
.
11.
Ehrich
,
F. F.
, 1988, “
High Order Sub-harmonic Response of High Speed Rotors in Bearing Clearance,” ASME Journal of Vibration, Acoustics
,
Stress and Reliability in Design
,
110
, pp.
9
16
.
12.
Wegener
,
G.
,
Market
R.
, and
Pothmann
,
K.
, 1998, “
Steady-State Analysis of a Multi-Disk or Continuous Rotor With One Retainer Bearing
,”
Proceedings of the Fifth International Conference on Rotor Dynamics
, Darmstadt, pp.
816
828
.
13.
Lawen
,
J. L.
, and
Flowers
,
G. T.
, 1997, “
Synchronous Dynamics of a Coupled Shaft/Bearing/Housing System With Auxiliary Support From a Clearance Bearing: Analysis and Experiment
,”
ASME J. Eng. Gas Turbines Power
,
119
, pp.
431
435
.
14.
Cole
,
M. O. T.
, and
Keogh
,
P. S.
, 2003, “
Rotor Vibration With Auxiliary Bearing Contact in Magnetic Bearing Systems, Part 2: Robust Synchronous Control for Rotor Position Recovery
,”
J. Mech. Eng. Sci.
,
217
(
4
), pp.
393
409
.
15.
Cade
,
I. S.
,
Sahinkaya
,
M. N.
,
Burrows
,
C. R.
, and
Keogh
,
P. S.
, 2009, “
On the Use of Actively Controlled Auxiliary Bearings in Magnetic Bearing Systems
,”
ASME J. Eng. Gas Turbines Power
,
131
(
2
), p.
022507
.
16.
Ginzinger
,
L. B.
, and
Ulbrich
,
H.
, 2008, “
Simulation-Based Controller Design for an Active Auxiliary Bearing
,”
Proceedings of the Eleventh International Symposium on Magnetic Bearings
,
Nara
, Paper No. 532.
17.
Ginzinger
,
L. B.
, 2009, “
Control of a Rubbing Rotor using an Active Auxiliary Bearing
,” Ph.D. dissertation, Technical University Munich.
18.
Cole
,
M. O. T.
, 2009, “
Model-Free Control of Touchdowns Involving Circular Whirl in Rotor-Magnetic Bearing Systems
,”
JSME J. Syst. Des. Dyn.
,
3
(
3
), pp.
584
595
.
19.
Inoue
,
T.
,
Liu
,
J.
,
Ishida
,
Y.
, and
Yoshimura
,
Y.
, 2009, “
Vibration Control and Unbalance Estimation of a Nonlinear Rotor System Using Disturbance Observer
,”
ASME J. Vibr. Acoust.
,
131
, p.
031010
.
20.
Cole
,
M. O. T.
,
, 2008, “
On Frequency Response Based Prediction of Rotor-Stator Circular Rub Behavior
,”
Proceedings of the Eleventh International Conference on Vibrations in Rotating Machinery
,
Exeter
, pp.
215
224
.
21.
Cole
,
M.
, 2008, “
On Stability of Rotordynamic Systems With Rotor-Stator Contact Interaction
,”
Proc. R. Soc. London, Ser. A
,
464
, pp.
3353
3375
.
22.
Balas
,
G.
,
Chiang
,
R.
,
Packard
A.
, and
Safonov
,
M.
, 2011,
Robust Control Toolbox User’s Guide
,
The MathWorks, Inc.
,
Natick, MA
.
23.
Tuan
,
H. D.
, and
Apkarian
,
P.
, 2000, “
Low Nonconvexity-Rank Bilinear Matrix Inequalities: Algorithms and Applications in Robust Controller and Structure Designs
,”
IEEE Trans. Autom. Control
,
45
(
11
), pp.
2111
2117
.
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