The combined effect of a crack with unbalanced force vector orientation in cracked rotor-bearing-disk systems on the values and locations of critical whirl amplitudes is numerically and experimentally investigated here for starting up operations. The time-periodic equations of motion of the cracked system are formulated according to the finite element (FE) time-varying stiffness matrix. The whirl response during the passage through the critical whirl speed zone is obtained via numerical simulation for different angles of the unbalance force vector. It is found that the variations in the angle of unbalance force vector with respect to the crack opening direction significantly alters the peak values of the critical whirl amplitudes and their corresponding critical whirl speeds. Consequently, the critical speeds of the cracked rotor are found to be either shifted to higher or lower values depending on the unbalance force vector orientation. In addition, the peak whirl amplitudes are found to exhibit significant elevation in some zones of unbalance force angles whereas significant reduction is observed in the remaining zones compared with the crack-free case. One of the important findings is that there exists a specific value of the unbalance force angle at which the critical whirl vibration is nearly eliminated in the cracked system compared with the crack-free case. These all significant numerical and experimental observations can be employed for crack damage detection in rotor systems.

References

References
1.
Ishida
,
Y.
,
2008
, “
Cracked Rotors: Industrial Machine Case Histories and Nonlinear Effects Shown by Simple Jeffcott Rotor
,”
Mech. Syst. Signal Process.
,
22
(
4
), pp.
805
817
.
2.
Bently
,
D.
, and
Muszynska
,
A.
,
1986
, “
Early Detection of Shaft Cracks on Fluid-Handling Machines
,” ASME International Symposium on Fluid Machinery Trouble Shooting, 1986 Winter Annual Meeting, Anaheim, CA, Dec., pp.
53
58
.
3.
Sabnavis
,
G.
,
Kirk
,
R. G.
,
Kasarda
,
M.
, and
Quinn
,
D.
,
2004
, “
Cracked Shaft Detection and Diagnostics: A Literature Review
,”
Shock Vib. Dig.
,
36
(
4
), p.
28
7.
4.
Puskar
,
A.
, and
Golovin
,
S.
,
1985
,
Fatigue in Materials: Cumulative Damage Processes
,
Elsevier Science Publishers
,
Amsterdam, The Netherlands
, p.
316
.
5.
Dimarogonas
,
A. D.
,
Paipetis
,
S. A.
, and
Chondros
,
T. G.
,
2013
,
Analytical Methods in Rotor Dynamics
,
Springer Science & Business Media
,
Berlin
.
6.
Al-Shudeifat
,
M. A.
, and
Butcher
,
E. A.
,
2011
, “
New Breathing Functions for the Transverse Breathing Crack of the Cracked Rotor System: Approach for Critical and Subcritical Harmonic Analysis
,”
J. Sound Vib.
,
330
(
3
), pp.
526
544
.
7.
Sinou
,
J. J.
,
2008
, “
Detection of Cracks in Rotor Based on the 2x and 3x Super-Harmonic Frequency Components and the Crack-Unbalance Interactions
,”
Commun. Nonlinear Sci. Numer. Simul.
,
13
(
9
), pp.
2024
2040
.
8.
Sinou
,
J. J.
,
2007
, “
Effects of a Crack on the Stability of a Non-Linear Rotor System
,”
Int. J. Non-Linear Mech.
,
42
(
7
), pp.
959
972
.
9.
Sinou
,
J. J.
, and
Lees
,
A. W.
,
2007
, “
A Non-Linear Study of a Cracked Rotor
,”
Eur. J. Mech. A/Solids
,
26
(
1
), pp.
152
170
.
10.
AL-Shudeifat
,
M. A.
,
2013
, “
On the Finite Element Modeling of the Asymmetric Cracked Rotor
,”
J. Sound Vib.
,
332
(
11
), pp.
2795
2807
.
11.
Al-Shudeifat
,
M. A.
, and
Butcher
,
E. A.
,
2010
, “
On the Modeling of Open and Breathing Cracks of a Cracked Rotor System
,”
ASME
Paper No. DETC2010-28289.
12.
Jun
,
O. S.
, and
Gadala
,
M. S.
,
2008
, “
Dynamic Behavior Analysis of Cracked Rotor
,”
J. Sound Vib.
,
309
(
1–2
), pp.
210
245
.
13.
Cao
,
J.
,
Xue
,
S.
,
Lin
,
J.
, and
Chen
,
Y.
,
2013
, “
Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping
,”
ASME J. Comput. Nonlinear Dyn.
,
8
(
3
), p.
031008
.
14.
Varney
,
P.
, and
Green
,
I.
,
2012
, “
Crack Detection in a Rotor Dynamic System by Vibration Monitoring—Part II: Extended Analysis and Experimental Results
,”
ASME J. Eng. Gas Turbines Power
,
134
(
11
), p.
112501
.
15.
Kulesza
,
Z.
, and
Sawicki
,
J. T.
,
2011
, “
Auxiliary State Variables for Rotor Crack Detection
,”
J. Vib. Control
,
17
(
6
), pp.
857
872
.
16.
Al-Shudeifat
,
M. A.
,
Butcher
,
E. A.
, and
Stern
,
C. R.
,
2010
, “
General Harmonic Balance Solution of a Cracked Rotor-Bearing-Disk System for Harmonic and Sub-Harmonic Analysis: Analytical and Experimental Approach
,”
Int. J. Eng. Sci.
,
48
(
10
), pp.
921
935
.
17.
Penny
,
J. E.
,
Friswell
,
M. I.
, and
Zhou
,
C.
,
2006
, “
Condition Monitoring of Rotating Machinery Using Active Magnetic Bearings
,”
International Symposium on Mechatronics and its Applications
, pp.
3497
3506
.
18.
Kulesza
,
Z.
, and
Sawicki
,
J. T.
,
2012
, “
Rigid Finite Element Model of a Cracked Rotor
,”
J. Sound Vib.
,
331
(
18
), pp.
4145
4169
.
19.
Saavedra
,
P. N.
, and
Cuitino
,
L. A.
,
2002
, “
Vibration Analysis of Rotor for Crack Identification
,”
Modal Anal.
,
8
(
1
), pp.
51
67
.
20.
Guo
,
D.
,
Chu
,
F. L.
, and
He
,
Y. Y.
,
2003
, “
Vibration Analysis of Rotor With Transverse Surface Cracks
,”
ASME
Paper No. GT2003-38041.
21.
Sekhar
,
A.
,
1999
, “
Vibration Characteristics of a Cracked Rotor With Two Open Cracks
,”
J. Sound Vib.
,
223
(
4
), pp.
497
512
.
22.
Mohiuddin
,
M.
, and
Khulief
,
Y.
,
2002
, “
Dynamic Response Analysis of Rotor-Bearing Systems With Cracked Shaft
,”
ASME J. Mech. Des.
,
124
(
4
), pp.
690
696
.
23.
Sekhar
,
A.
, and
Prabhu
,
B. S.
,
1994
, “
Transient Analysis of a Cracked Rotor Passing Through Critical Speed
,”
J. Sound Vib.
,
173
(
3
), pp.
415
421
.
24.
Dong
,
G. M.
,
Chen
,
J.
, and
Zou
,
J.
,
2004
, “
Parameter Identification of a Rotor With an Open Crack
,”
Eur. J. Mech. A/Solids
,
23
(
2
), pp.
325
333
.
25.
Mumoz
,
Q. R.
,
Ramirez
,
S. J.
, and
Kubiak
,
S. J.
,
1997
, “
Rotor Modal Analysis for a Rotor Crack Detection
,”
Proc. SPIE
,
3089
, pp.
877
879
.http://semimac.org/wp-content/uploads/2016/01/sem.org-IMAC-XV-15th-Int-15-22-5-Rotor-Modal-Analysis-Rotor-Crack-Detection.pdf
26.
Dong
,
G. M.
, and
Chen
,
J.
,
2009
, “
Crack Identification in a Rotor With an Open Crack
,”
J. Mech. Sci. Technol.
,
23
(
11
), pp.
2964
2972
.
27.
Collins
,
K.
,
Plaut
,
R.
, and
Wauer
,
J.
,
1991
, “
Detection of Cracks in Rotating Timoshenko Shafts Using Axial Impulses
,”
ASME J. Vib. Acoust.
,
113
(
1
), pp.
74
78
.
28.
Gounaris
,
G. D.
, and
Papadopoulos
,
C. A.
,
2002
, “
Crack Identification in Rotating Shafts by Coupled Response Measurements
,”
Eng. Fract. Mech.
,
69
(
3
), pp.
339
352
.
29.
Kulesza
,
Z.
,
2014
, “
Dynamic Behavior of Cracked Rotor Subjected to Multisine Excitation
,”
J. Sound Vib.
,
333
(
5
), pp.
1369
1378
.
30.
Babu
,
T. R.
,
Srikanth
,
S.
, and
Sekhar
,
A.
,
2008
, “
Hilbert–Huang Transform for Detection and Monitoring of Crack in a Transient Rotor
,”
Mech. Syst. Signal Process.
,
22
(
4
), pp.
905
914
.
31.
Guo
,
D.
, and
Peng
,
Z. K.
,
2007
, “
Vibration Analysis of a Cracked Rotor Using Hilbert–Huang Transform
,”
Mech. Syst. Signal Process.
,
21
(
8
), pp.
3030
3041
.
32.
Kumar
,
V. S.
,
Harikrishna
,
C.
,
Sai
,
C. K.
, and
Nagaraju
,
C.
,
2015
, “
Dynamic Analysis of a Cracked Rotor-an Experimental and Finite Element Investigation
,”
Mater. Today: Proc.
,
2
(
4–5
), pp.
2131
2136
.
33.
Seibold
,
S.
, and
Weinert
,
K.
,
1996
, “
A Time Domain Method for the Localization of Cracks in Rotors
,”
J. Sound Vib.
,
195
(
1
), pp.
57
73
.
34.
Kumar
,
C.
, and
Rastogi
,
V.
,
2009
, “
A Brief Review on Dynamics of a Cracked Rotor
,”
Int. J. Rotating Mach.
,
2009
, p.
758108
.
35.
Gounaris
,
G.
,
Papadopoulos
,
C.
, and
Dimarogonas
,
A.
,
1996
, “
Crack Identification in Beams by Coupled Response Measurements
,”
Comput. Struct.
,
58
(
2
), pp.
299
305
.
36.
Dimarogonas
,
A.
,
1996
, “
Vibration of Cracked Structures: A State of the Art Review
,”
Eng. Fract. Mech.
,
55
(
5
), pp.
831
857
.
37.
Wauer
,
J.
,
1990
, “
On the Dynamics of Cracked Rotors: A Literature Survey
,”
ASME Appl. Mech. Rev.
,
43
(
1
), pp.
13
17
.
38.
Varney
,
P. A.
,
2013
, “
Transverse Fatigue Crack Diagnosis in a Rotordynamic System Using Vibration Monitoring
,”
Ph.D. thesis
, Georgia Institute of Technology, Atlanta, GA.https://smartech.gatech.edu/handle/1853/47655
39.
Darpe
,
A. K.
,
2007
, “
A Novel Way to Detect Transverse Surface Crack in a Rotating Shaft
,”
J. Sound Vib.
,
305
(
1–2
), pp.
151
171
.
40.
Chasalevris
,
A.
, and
Papadopoulos
,
C.
,
2008
, “
Coupled Horizontal and Vertical Bending Vibrations of a Stationary Shaft With Two Cracks
,”
J. Sound Vib.
,
309
(
3–5
), pp.
507
528
.
41.
Papadopoulos
,
C.
, and
Dimarogonas
,
A.
,
1987
, “
Coupled Longitudinal and Bending Vibrations of a Rotating Shaft With an Open Crack
,”
J. Sound Vib.
,
117
(
1
), pp.
81
93
.
42.
Giannopoulos
,
G. I.
,
Georgantzinos
,
S. K.
, and
Anifantis
,
N. K.
,
2015
, “
Coupled Vibration Response of a Shaft With a Breathing Crack
,”
J. Sound Vib.
,
336
, pp.
191
206
.
43.
Guo
,
C.
,
Al-Shudeifat
,
M. A.
,
Yan
,
J.
,
Bergman
,
L. A.
,
McFarland
,
D. M.
, and
Butcher
,
E. A.
,
2013
, “
Stability Analysis for Transverse Breathing Cracks in Rotor Systems
,”
Eur. J. Mech. A/Solids
,
42
, pp.
27
34
.
44.
AL-Shudeifat
,
M. A.
,
2015
, “
Stability Analysis and Backward Whirl Investigation of Cracked Rotors With Time-Varying Stiffness
,”
J. Sound Vib.
,
348
, pp.
365
380
.
45.
Swanson
,
E.
,
Powell
,
C. D.
, and
Weissman
,
S.
,
2005
, “
A Practical Review of Rotating Machinery Critical Speeds and Modes
,”
Sound Vib.
,
39
(
5
), pp.
16
17
.http://sandv.com/downloads/0505swan.pdf
46.
Gomez-Mancilla
,
J.
,
Sinou
,
J. J.
,
Nosov
,
V. R.
,
Thouverez
,
F.
, and
Zambrano
,
A.
,
2004
, “
The Influence of Crack-Imbalance Orientation and Orbital Evolution for an Extended Cracked Jeffcott Rotor
,”
C. R. Mech.
,
332
(
12
), pp.
955
962
.
47.
Wang
,
S.
,
Zi
,
Y.
,
Qian
,
S.
,
Zi
,
B.
, and
Bi
,
C.
,
2018
, “
Effects of Unbalance on the Nonlinear Dynamics of Rotors With Transverse Cracks
,”
Nonlinear Dyn.
,
91
(4), pp.
2755
2772
.
48.
Mobarak
,
H. M.
,
Wu
,
H.
,
Spagnol
,
J. P.
, and
Xiao
,
K.
,
2018
, “
New Crack Breathing Mechanism Under the Influence of Unbalance Force
,”
Arch. Appl. Mech.
,
88
(
3
), pp.
341
372
.
49.
Al Hosani
,
H.
,
AL-Shudeifat
,
M. A.
,
Saeed
,
A. S.
, and
Balawi
,
S.
,
2017
, “
Effect of Unbalance Force Direction on a Cracked Rotor Whirl Response
,”
ASME
Paper No. DETC2017-68261.
50.
Giannopoulos
,
G. I.
,
2017
, “
Crack Identification in Graphene Using Eigenfrequencies
,”
Int. J. Appl. Mech.
,
9
(
01
), p.
1750009
.
You do not currently have access to this content.