During touchdowns of active magnetic bearings (AMB), the violent collision between rotors and touchdown bearings (TDB) can cause damages to both parts. Orbit response recognition provides a way for the AMB controller to automatically switch the control algorithm to actively suppress the rotor–TDB vibration and promptly relevitate the rotor during touchdowns. A novel method based on Hilbert transform (HT) is proposed to recognize the orbit responses (pendulum vibration, combined rub and bouncing, and full rub) in touchdowns. In this method, the rotor suspension status is monitored by the AMB controller in real-time. When touchdown is detected, the rotor displacement signal during the sampling period is intercepted, and the instantaneous frequency (IF) is calculated by HT. Then, the local variance of IF during the sampling period is calculated, and it is compared with the threshold value. Combined rub and bouncing can be identified for it has the largest local variance. Finally, the mean value of IF during the sampling period is calculated and is compared with the other threshold value. Pendulum vibration can be identified for it has a lower and fixed mean value, while full rub has a larger value. The principle of the recognition method is demonstrated by the simulated results of a thermo-dynamic model. The results reveal that the method is feasible in recognizing the orbit responses and can be implemented in the AMB controller to help switch the control algorithms automatically in case of touchdowns.

References

References
1.
Schweitzer
,
G.
, and
Maslen
,
E. H.
,
2012
,
Magnetic Bearings: Theory, Design, and Application to Rotating Machinery
,
Springer
,
Berlin
, Chap. 13.
2.
Fumagalli
,
M. A.
,
1997
, “
Modelling and Measurement Analysis of the Contact Interaction Between a High Speed Rotor and Its Stator
,”
Ph.D. thesis
, Swiss Institute of Technology, Zurich, Switzerland.https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/143592/eth-22592-02.pdf
3.
Schweitzer
,
G.
,
2011
, “
Applications and Research Topics for Active Magnetic Bearings
,”
IUTAM Symposium on Emerging Trends in Rotor Dynamics
, New Delhi, India, Mar. 23–26, pp.
263
273
.http://www.mcgs.ch/web-content/Delhi_IUTAM_Symp.pdf
4.
Siebke
,
P.
, and
Golbach
,
H.
,
2014
, “
A Novel Rolling Element Back-Up Bearing for a 9 t Rotor Application
,”
14th International Symposium on Magnetic Bearings
(
ISMB
), Linz, Austria, Aug. 11–14, pp.
454
458
.
5.
Sun
,
G.
,
2003
, “
A High Fidelity Ball Bearing and Damper Model Including Thermal Effects for Magnetic Suspension Auxiliary Service and Blade Loss Simulation
,” Ph.D. thesis, Texas A&M University, College Station, TX.
6.
Fumagalli
,
M.
,
Varadi
,
P.
, and
Schweitzer
,
G.
,
1994
, “
Impact Dynamics of High Speed Rotors in Retainer Bearings and Measurement Concepts
,”
Fourth International Symposium on Magnetic Bearings (ISMB)
, Zurich, Switzerland, Aug. 24–26, pp.
239
244
.
7.
Fumagalli
,
M.
, and
Schweitzer
,
G.
,
1996
, “
Motion of a Rotor in Retainer Bearings
,”
Fifth International Symposium on Magnetic Bearings
, Kanazawa, Japan, Aug. 28–30, pp.
509
514
.
8.
Yang
,
G.
,
Shi
,
Z.
, and
Mo
,
N.
,
2014
, “
Technical Design and Engineering Prototype Experiment of Active Magnetic Bearing for Helium Blower of HTR-PM
,”
Ann. Nucl. Energy
,
71
, pp.
103
110
.
9.
Caprio
,
M. T.
,
Murphy
,
B. T.
, and
Herbst
,
J. D.
,
2004
, “
Spin Commissioning and Drop Tests of a 130 kW-hr Composite Flywheel
,”
The Nineth International Symposium on Magnetic Bearings
(
ISMB
), Lexington, Kentucky, Aug. 3–6.https://repositories.lib.utexas.edu/bitstream/handle/2152/30671/PR_365.pdf?sequence=1
10.
Takahashi
,
N.
,
2013
, “
Reviews of Magnetic Bearing Development in Japan
,”
J. Syst. Des. Dyn.
,
7
(
2
), pp.
111
126
.
11.
Ishii
,
T.
, and
Kirk
,
R. G.
,
1996
, “
Transient Response Technique Applied to Active Magnetic Bearing Machinery During Rotor Drop
,”
ASME J. Vib. Acoust.
,
118
(
2
), pp.
154
163
.
12.
Kirk
,
R. G.
, and
Ishii
,
T.
,
1993
, “
Transient Rotor Drop Analysis of Rotor Following Magnetic Bearing Power Outage
,”
MAG` 93: Magnetic Bearings, Magnetic Drives, and Dry Gas Seals Conference and Exhibition
, Alexandria, VA, July 29–30, pp.
53
61
.
13.
Kaü
rkkaüinen
,
A.
,
Helfert
,
M.
,
Aeschlimann
,
B.
, and
Mikkola
,
A.
,
2008
, “
Dynamic Analysis of Rotor System With Misaligned Retainer Bearings
,”
ASME J. Tribol.
,
130
(
2
), p.
021102
.
14.
Kärkkäinen
,
A.
,
2007
, “
Dynamic Simulations of Rotors During Drop on Retainer Bearings
,”
Ph. D. thesis
, Lappeenranta University of Technology, Lappeenranta, Finland.http://www.doria.fi/handle/10024/31108
15.
Cole
,
M. O. T.
,
Keogh
,
P. S.
, and
Burrows
,
C. R.
,
2001
, “
The Dynamic Behavior of a Rolling Element Auxiliary Bearing Following Rotor Impact
,”
ASME J. Tribol.
,
124
(
2
), pp.
406
413
.
16.
Zeng
,
S.
,
2002
, “
Motion of AMB Rotor in Backup Bearings
,”
ASME J. Vib. Acoust.
,
124
(
3
), pp.
460
464
.
17.
Zeng
,
S.
,
Zhang
,
J. Q.
, and
Wang
,
H. N.
,
2006
, “
Transient Response of Active Magnetic Bearing Rotor During Rotor Drop on Backup Bearings
,”
ARCHIVE Proc. Inst. Mech. Eng. Part C
,
220
(
6
), pp.
785
794
.
18.
Bartha
,
A. R.
,
2000
, “
Dry Friction Backward Whirl of Rotors
,”
Ph.D. thesis
, Swiss Federal Institute of Technology, Zurich, Switzerland.https://www.research-collection.ethz.ch/handle/20.500.11850/145085
19.
Bartha
,
A. R.
,
2000
, “
Dry Friction Backward Whirl of Rotors: Theory, Experiments, Results and Recommendations
,”
Seventh International Symposium on Magnetic Bearings
(
ISMB
), Zurich, Switzerland, Aug. 23–25, pp.
231
238
.
20.
Wilkes
,
J.
,
Moore
,
J.
,
Ransom
,
D.
, and
Vannini
,
G.
,
2013
, “
An Improved Catcher Bearing Model and an Explanation of the Forward Whirl/Whip Phenomenon Observed in Active Magnetic Bearing Transient Drop Experiments
,”
ASME J. Eng. Gas Turbines Power
,
136
(
4
), p.
042504
.
21.
Jarroux
,
C.
,
Dufour
,
R.
,
Mahfoud
,
J.
,
Defoy
,
B.
,
Alban
,
T.
, and
Delgado
,
A.
,
2016
, “
On the Drop of a Rotor-AMB System Onto Touch-Down Bearing
,”
Vibrations in Rotating Machinery Conference (VIRM)
, Manchester, UK, Sept. 13–15, pp.
671
681
.
22.
Jarroux
,
C.
,
Dufour
,
R.
,
Mahfoud
,
J.
,
Defoy
,
B.
,
Alban
,
T.
, and
Delgado
,
A.
,
2016
, “
Non-Linear Models for Rotor-AMB System Drop
,”
Third International Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD)
, Marrakech, Morocco, May 23–25, Paper No.
05005
.
23.
Zhong
,
W.
,
Palazzolo
,
A.
, and
Kang
,
X.
,
2016
, “
Multi-Objective Optimization Design of Nonlinear Magnetic Bearing Rotordynamic System
,”
ASME J. Vib. Acoust.
,
139
(
1
), p.
011011
.
24.
Hawkins
,
L.
,
Filatov
,
A.
, and
Imani
,
S.
,
2007
, “
Test Results and Analytical Predictions for Rotor Drop Testing of an Active Magnetic Bearing Expander/Generator
,”
ASME J. Eng. Gas Turbines Power
,
129
(
2
), pp.
522
529
.
25.
Sun
,
G.
,
Palazzolo
,
A. B.
,
Provenza
,
A.
, and
Montague
,
G.
,
2004
, “
Detailed Ball Bearing Model for Magnetic Suspension Auxiliary Service
,”
J. Vib. Sound
,
269
(
3–5
), pp.
933
963
.
26.
Keogh
,
P. S.
, and
Cole
,
M. O. T.
,
2003
, “
Rotor Vibration With Auxiliary Bearing Contact in Magnetic Bearing Systems Part 1: Synchronous Dynamics
,”
Proc. Inst. Mech. Eng., Part C
,
217
(
4
), pp.
377
392
.
27.
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
,
217
(
4
), pp.
393
409
.
28.
Cole
,
M. O. T.
, and
Keogh
,
P. S.
,
2003
, “
Asynchronous Periodic Contact Modes for Rotor Vibration Within An Annular Clearance
,”
Proc. Inst. Mech. Eng., Part C
,
217
(
10
), pp.
1101
1115
.
29.
Larsonneur
,
R.
, and
Bühler
,
P.
,
2008
, “
Recovery of Impact in a Magnetic Bearing Device
,” Patent No.
WO2008154757 A1
.https://www.google.com/patents/WO2008154757A1?cl=de
30.
ISO
,
2012
, “
Mechanical Vibration—Vibration of Rotating Machinery Equipped With Active Magnetic Bearings—Part 4: Technical Guidelines
,” International Organization for Standardization, Geneva, Switzerland, Standard No.
ISO 14839-4
.https://www.iso.org/standard/50442.html
31.
Liu
,
T.
,
Zhang
,
W.
, and
Yan
,
S.
,
2015
, “
A Novel Image Enhancement Algorithm Based on Stationary Wavelet Transform for Infrared Thermography to the De-Bonding Defect in Solid Rocket Motors
,”
Mech. Syst. Signal Process.
,
62–63
, pp.
366
380
.
32.
Taner
,
M. T.
,
Koehler
,
F.
, and
Sheriff
,
R. E.
,
1979
, “
Complex Seismic Trace Analysis
,”
Geophysics
,
44
(
6
), pp.
1041
1063
.
33.
Huang
,
N. E.
,
Shen
,
Z.
,
Long
,
S. R.
,
Wu
,
M. C.
,
Shih
,
H. H.
,
Zheng
,
Q.
, and
Liu
,
H. H.
,
1998
, “
The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis
,”
Proc. R. Soc. London A
,
454
(
1971
), pp.
903
995
.
34.
Lyu
,
M. D.
,
Wang
,
Z. X.
,
Liu
,
T.
,
Jia
,
X. H.
, and
Wang
,
Y. M.
,
2016
, “
Frequency Analysis of the Orbit Responses of Active Magnetic Bearings in Touchdown Using Hilbert Transform
,”
Int. J. Struct. Stab. Dyn.
,
17
(
8
), p.
1750086.
35.
Cizek
,
V.
,
1970
, “
Discrete Hilbert transform
,”
IEEE Transactions on Audio and Electroacoustics
,
18
(
4
), pp.
340
343
.
36.
Kak
,
S. C.
,
1970
, “
The Discrete Hilbert Transform
,”
Proc. IEEE
,
58
(
4
), pp.
585
586
.
37.
Kak
,
S. C.
,
1973
, “
Hilbert Transformation for Discrete Data
,”
Int. J. Electron.
,
34
(
2
), pp.
177
183
.
38.
Gold
,
B.
,
Oppenheim
,
A. V.
, and
Rader
,
C. M.
,
1969
, “
Theory and Implementation of the Discrete Hilbert Transform
,”
The Symposium on Computer Processing in Communications
, New York, Apr., p.
235
.http://www.rle.mit.edu/dspg/documents/HilbertComplete.pdf
39.
Harris
,
T. A.
, and
Kotzalas
,
M. N.
,
2007
,
Rolling Bearing Analysis, Fifth Edition
,
Taylor & Francis
,
New York
.
40.
Hunt
,
K. H.
, and
Crossley
,
F. R. E.
,
1975
, “
Coefficient of Restitution Interpreted as Damping in Vibroimpact
,”
ASME J. Appl. Mech.
,
42
(
2
), pp.
440
445
.
41.
Yu
,
C.
,
Jin
,
C.
,
Yu
,
X.
, and
Xu
,
L. X.
,
2015
, “
Dynamic Analysis of Active Magnetic Bearing Rotor Dropping on Auto-Eliminating Clearance Auxiliary Bearing Devices
,”
ASME J. Eng. Gas Turbines Power
,
137
(
6
), p.
062502
.
42.
Lee
,
J. G.
, and
Palazzolo
,
A.
,
2012
, “
Catcher Bearing Life Prediction Using a Rainflow Counting Approach
,”
ASME J. Tribol.
,
134
(
3
), p.
031101
.
43.
Zhao
,
Y.
,
Yang
,
G.
,
Shi
,
Z.
, and
Zhao
,
L.
,
2016
, “
Thermal Analysis and Simulation of Auxiliary Bearings and Its Application in the High Temperature Reactor-10
,”
ASME J. Tribol.
,
138
(
1
), p.
011102
.
44.
Sun
,
G.
,
2006
, “
Auxiliary Bearing Life Prediction Using Hertzian Contact Bearing Model
,”
ASME J. Vib. Acoust.
,
128
(
2
), pp.
203
209
.
45.
Sun
,
G.
,
2006
, “
Rotor Drop and Following Thermal Growth Simulations Using Detailed Auxiliary Bearing and Damper Models
,”
J. Sound Vib.
,
289
(
1
), pp.
334
359
.
46.
Jorgensen
,
B. R.
, and
Shin
,
Y. C.
,
1997
, “
Dynamics of Machine Tool Spindle/Bearing Systems Under Thermal Growth
,”
ASME J. Tribol.
,
119
(
4
), pp.
875
882
.
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