This paper considers the problem of controlling the vibration of a lightweight thin-walled rotor with a distributed actuation magnetic bearing (DAMB). A theoretical flexible rotor model is developed that shows how multiharmonic vibration arises due to small noncircularity of the rotor cross section. This model predicts a series of resonance conditions that occur when the rotational frequency matches a subharmonic of a system natural frequency. Rotor noncircularity can be measured offline, and the measurement data used to cancel its effect on the position sensor signals used for feedback control. A drawback of this approach is that noncircularity is difficult to measure exactly and may vary over time due to changing thermal or elastic state of the rotor. Moreover, any additional multiharmonic excitation effects will not be compensated. To overcome these issues, a harmonic vibration control algorithm is applied that adaptively modifies the harmonic components of the actuator control currents to match a target vibration control performance, but without affecting the stabilizing feedback control loops. Experimental results for a short thin-walled rotor with a single DAMB are presented, which show the effectiveness of the techniques in preventing resonance during operation. By combining sensor-based noncircularity compensation with harmonic vibration control, a reduction in vibration levels can be achieved without precise knowledge of the rotor shape and with minimal bearing forces.

References

References
1.
Schweitzer
,
G.
, and
Maslen
,
E. H.
, eds.,
2009
,
Magnetic Bearings, Theory, Design, and Application to Rotating Machinery
,
Springer-Verlag
,
Berlin
.
2.
Schneeberger
,
T.
,
Nussbaumer
,
T.
, and
Kolar
,
J. W.
,
2010
, “
Magnetically Levitated Homopolar Hollow-Shaft Motor
,”
IEEE/ASME Trans. Mechatron.
,
15
(
1
), pp.
97
107
.
3.
Lusty
,
C.
,
Sahinkaya
,
M. N.
, and
Keogh
,
P. S.
,
2016
, “
A Novel Twin-Shaft Rotor Layout With Active Magnetic Couplings for Vibration Control
,”
Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng.
,
230
(
3
), pp.
266
276
.
4.
Cole
,
M. O. T.
, and
Fakkaew
,
W.
,
2018
, “
An Active Magnetic Bearing for Thin-Walled Rotors: Vibrational Dynamics and Stabilizing Control
,”
IEEE/ASME Trans. Mechatron.
,
23
(
6
), pp.
2859
2869
.
5.
Fakkaew
,
W.
,
Cole
,
M. O. T.
,
2018
, “
Vibration Due To Noncircularity of a Rotating Ring Having Discrete Radial Supports—With Application to Thin-Walled Rotor/Magnetic Bearing Systems
,”
J. Sound Vib.
,
423
, pp.
355
372
.
6.
Roche
,
J. M.
,
Palac
,
D. T.
,
Hunter
,
J. E.
,
Myers
,
D. E.
,
Snyder
,
C. A.
,
Kosareo
,
D. N.
,
McCurdy
,
D. R.
, and
Dougherty
,
K. T.
,
2005
, “
Investigation of Exoskeletal Engine Propulsion System Concept
,” NASA Report No. NASA–2005-213369.
7.
Peters
,
D.
,
Kaletsch
,
C.
,
Nordmann
,
R.
, and
Domes
,
B.
, “
Test Rig for a Supercritical Rotor of an Aero Engine
,”
Proceedings of the 12th IFToMM World Congress
,
Besançon, France
,
June 17–21, 2007
.
8.
Genta
,
G.
,
2005
,
Dynamics of Rotating Systems
,
Springer
,
New York
.
9.
Mohamed
,
A. M.
, and
Busch-Vishniac
,
I.
,
1995
, “
Imbalance Compensation and Automation Balancing in Magnetic Bearing Systems Using the Q-Parametrization Theory
,”
IEEE Trans. Control Syst. Technol.
,
3
(
2
), pp.
202
211
.
10.
Lum
,
K.-Y.
,
Coppola
,
V. T.
, and
Bernstein
,
D. S.
,
1996
, “
Adaptive Autocentering Control for an Active Magnetic Bearing Supporting a Rotor With Unknown Mass Imbalance
,”
IEEE Trans. Control Syst. Technol.
,
4
(
5
), pp.
587
597
.
11.
Knospe
,
C.
,
Hope
,
R.
,
Fedigan
,
S.
, and
Williams
,
R.
,
1995
, “
Experiments in the Control of Unbalanced Response Using Magnetic Bearings
,”
Mechatronics
,
5
(
1
), pp.
385
400
.
12.
Herzog
,
R.
,
Buhler
,
P.
,
Gahler
,
C.
, and
Larsonnoeur
,
R.
,
1996
, “
Unbalance Compensation Using Generalized Notch Filters in the Multivariable Feedback of Magnetic Bearings
,”
IEEE Trans. Control Syst. Technol.
,
4
(
5
), pp.
581
586
.
13.
Cui
,
P.
,
Li
,
S.
,
Zhao
,
G.
, and
Peng
,
C.
,
2016
, “
Suppression of Harmonic Current in Active-Passive Magnetically Suspended CMG Using Improved Repetitive Controller
,”
IEEE/ASME Trans. Mechatron.
,
21
(
4
), pp.
2132
2141
.
14.
Nonami
,
K.
, and
Liu
,
Z.
, “
Adaptive Unbalance Vibration Control of Magnetic Bearing System Using Frequency Estimation for Multiple Periodic Disturbances with Noise
,”
Proceedings of IEEE Conference on Control Applications
,
Kohala Coast, HI
,
Aug. 22–27, 1999
.
IEEE
,
Piscataway, NJ
.
15.
Chen
,
Q.
,
Liu
,
G.
, and
Han
,
B.
,
2017
, “
Unbalance Vibration Suppression for AMB System Using Adaptive Notch Filter
,”
Mech. Syst. Signal Process.
,
93
, pp.
136
150
.
16.
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
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
217
(
4
), pp.
393
409
.
17.
Chamroon
,
C.
,
Cole
,
M. O. T.
, and
Wongratanaphisan
,
T.
,
2014
, “
An Active Vibration Control Strategy to Prevent Nonlinearly Coupled Rotor-Stator Whirl Responses in Multimode Rotor-Dynamic Systems
,”
IEEE Trans. Control Syst. Technol.
,
22
(
3
), pp.
1122
1129
.
18.
Wang
,
M.
,
Cole
,
M. O. T.
, and
Keogh
,
P. S.
,
2017
, “
New LMI Based Gain-Scheduled Control for Recovering Contact-Free Operation of a Magnetically Levitated Rotor
,”
Mech. Syst. Signal Process.
,
96
, pp.
104
124
.
19.
Cole
,
M. O. T.
,
Chamroon
,
C.
, and
Keogh
,
P. S.
,
2017
, “
H-Infinity Controller Design for Active Magnetic Bearings Considering Nonlinear Vibrational Rotordynamics
,”
JSME Mech. Eng. J.
,
4
(
5
),
16-00716
.
20.
Chen
,
Q.
,
Liu
,
G.
, and
Zheng
,
S.
,
2015
, “
Suppression of Imbalance Vibration for AMB Controlled Driveline System Using Double-Loop Structure
,”
J. Sound Vib.
,
337
, pp.
1
13
.
21.
Xu
,
X.
, and
Chen
,
S.
,
2015
, “
Field Balancing and Harmonic Vibration Suppression in Rigid AMB-Rotor Systems with Rotor Imbalances and Sensor Runout
,”
Sensors
,
15
(
9
), pp.
21876
21897
.
22.
Jiang
,
K.
,
Zhu
,
C.
,
2011
, “
Multi-Frequency Periodic Vibration Suppressing in Active Magnetic Bearing-Rotor Systems Via Response Matching in Frequency Domain
,”
Mech. Syst. Signal Process.
,
25
, pp.
1417
1429
.
23.
Darbandi
,
S. M.
,
Habibollahi
,
A.
,
Behzad
,
M.
, and
Salarieh
,
H.
,
2016
, “
Sensor Runout Compensation in Active Magnetic Bearings Via an Integral Adaptive Observer
,”
Control Eng. Pract.
,
48
, pp.
111
118
.
24.
Setiawan
,
J. D.
,
Mukherjee
,
R.
, and
Maslen
,
E. H.
,
1999
, “
Adaptive Compensation of Sensor Runout for Magnetic Bearings With Uncertain Parameters: Theory and Experiments
,”
ASME J. Dyn. Syst. Meas. Control
,
123
(
2
), pp.
211
218
.
25.
Siva Srinivas
,
R.
,
Tiwari
,
R.
, and
Kannababu
,
Ch.
,
2018
, “
Application of Active Magnetic Bearings in Flexible Rotordynamic Systems–A State-of-The-Art Review
,”
Mech. Syst. Signal Process.
,
106
, pp.
537
572
.
26.
Cole
,
M. O. T.
,
Keogh
,
P. S.
,
Burrows
,
C. R.
, and
Sahinkaya
,
M. N.
,
2006
, “
Adaptive Control of Rotor Vibration Using Compact Wavelets
,”
ASME J. Vib. Acoust.
,
128
(
5
), pp.
653
665
.
27.
Manchala
,
D. W.
,
Palazzolo
,
A. B.
,
Lin
,
A. K.
,
Kasak
,
A. K.
,
Montague
,
J.
, and
Brown
,
G. V.
,
1997
, “
Constrained Quadratic Programming Active Control of Rotating Mass Imbalance
,”
J. Sound Vib.
,
205
(
5
), pp.
561
580
.
28.
Sahinkaya
,
M.
,
Abulrub
,
A. G.
, and
Burrows
,
C. R.
,
2011
, “
An Adaptive Multi-Objective Controller for Flexible Rotor and Magnetic Bearing Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
133
(
3
), p.
031003
.
29.
Endo
,
M.
,
Hatamura
,
K.
,
Sakata
,
M.
, and
Taniguchi
,
O.
,
1984
, “
Flexural Vibration of a Thin Rotating Ring
,”
J. Sound Vib.
,
92
(
2
), pp.
261
272
.
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