The goal of this work is to establish simple condition monitoring principles for diagnosing the depth and location of transverse fatigue cracks in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model, which should account for the crack's depth and location. Two gaping crack models are presented; the first emulates a finite-width notch typically manufactured for experimental purposes, while the second models a gaping fatigue crack. The rotordynamic model used herein is based upon an available overhung rotordynamic test rig that was originally constructed to monitor the dynamics of a mechanical face seal. Four degree-of-freedom, linear equations of motion for both crack models are presented and discussed. Free and forced response analyses are presented, emphasizing results applicable to condition monitoring and, particularly, to diagnosing the crack parameters. The results demonstrate that two identifiers are required to diagnose the crack parameters: the 2X resonance shaft speed and the magnitude of the angular 2X subharmonic resonance. First, a contour plot of the 2X resonance shaft speed versus crack depth and location is generated. The magnitude of the 2X resonance along the desired 2X frequency contour is then obtained, narrowing the possible pairs of crack location and depth to either one or two possibilities. Practical aspects of the suggested diagnostic procedure are discussed, as well as qualitative observations concerning crack detection.

References

References
1.
Green
,
I.
, and
Casey
,
C.
,
2005
, “
Crack Detection in a Rotor Dynamic System by Vibration Monitoring—Part I: Analysis
,”
ASME J. Eng. Gas Turb. Power
,
127
, pp.
425
436
.10.1115/1.1789514
2.
Varney
,
P.
, and
Green
,
I.
,
2012
, “
Crack Detection in a Rotordynamic System by Vibration Monitoring—Part II: Extended Analysis and Experimental Results
,”
ASME J. Eng. Gas Turb. Power
,
134
(
11
), p.
112501
.10.1115/1.4007275
3.
Lee
,
A. S.
, and
Green
,
I.
,
1994
, “
Higher Harmonic Oscillations in a Non-Contacting FMR Mechanical Face Seal Test Rig
,”
ASME J. Vib. Acoust.
,
116
, pp.
161
167
.10.1115/1.2930407
4.
Gasch
,
R.
,
2008
, “
Dynamic Behavior of the Laval Rotor With a Transverse Crack
,”
Mech. Syst. Signal Process.
,
22
, pp.
790
804
.10.1016/j.ymssp.2007.11.023
5.
Green
,
I.
, and
Etsion
,
I.
,
1986
, “
A Kinematic Model for Mechanical Seals With Antirotation Locks or Positive Drive Devices
,”
ASME J. Tribol.
,
108
, pp.
42
45
.10.1115/1.3261141
6.
Green
,
I.
,
2008
, “
On the Kinematic and Kinetics of Mechanical Seals, Rotors, and Wobbling Body
,”
Mechanism Mach. Theory
,
43
, pp.
909
917
.10.1016/j.mechmachtheory.2007.06.004
7.
Lee
,
A. S.
, and
Green
,
I.
,
1994
, “
Rotordynamics of a Mechanical Face Seal Riding on a Flexible Shaft
,”
ASME J. Tribol
,
116
, pp.
345
351
.10.1115/1.2927229
8.
Lee
,
A. S.
, and
Green
,
I.
,
1995
, “
Physical Modeling and Data Analysis of the Dynamic Response of a Flexibly Mounted Rotor Mechanical Seal
,”
ASME J. Tribol.
,
117
, pp.
130
135
.10.1115/1.2830587
9.
Darpe
,
A.
,
Gupta
,
K.
, and
Chawla
,
A.
,
2004
, “
Coupled Bending, Longitudinal, and Torsional Vibrations of a Cracked Rotor
,”
J. Sound Vib.
,
269
(
1
), pp.
33
60
.10.1016/S0022-460X(03)00003-8
10.
Darpe
,
A. K.
,
Gupta
,
K.
, and
Chawla
,
A.
,
2004
, “
Transient Response and Breathing Behavior of a Cracked Jeffcott Rotor
,”
J. Sound Vib.
,
272
, pp.
207
242
.10.1016/S0022-460X(03)00327-4
11.
Papadopoulos
,
C. A.
,
2008
, “
The Strain Energy Release Rate Approach for Modeling Cracks in Rotors: A State-of-the-Art Review
,”
Mech. Syst. Signal Process.
,
22
(4), pp.
763
789
.10.1016/j.ymssp.2007.11.009
12.
Dimarogonas
,
A.
, and
Papadopoulos
,
C. A.
,
1983
, “
Vibration of Cracked Shafts in Bending
,”
J. Sound Vib.
,
91
(
4
), pp.
583
593
.10.1016/0022-460X(83)90834-9
13.
Mayes
,
I. W.
, and
Davies
,
W. G. R.
,
1976
, “
The Vibration Behaviour of a Rotating Shaft System Containing a Transverse Crack
,”
Vibrations in Rotating Machinery
,
IMechE
, London, pp.
53
64
.
14.
Rao
,
J. S.
,
1996
,
Rotor Dynamics
,
3rd ed.
,
New Age International
,
New Delhi
.
15.
Silva
,
J.
, and
Gomez
,
A.
,
1990
, “
Experimental Dynamic Analysis of Cracked Free-Free Beams
,”
Exp. Mech.
,
30
(
1
), pp.
20
25
.10.1007/BF02322697
16.
Grabowski
,
B.
,
1980
, “
The Vibration Behavior of a Turbine Rotor Containing a Transverse Shaft Crack
,”
ASME J. Mech. Design
,
102
, pp.
140
146
.10.1115/1.3254704
17.
Gounaris
,
G. D.
, and
Papadopoulos
,
C. A.
,
2002
, “
Crack Identification in Rotating Shafts by Coupled Response Measurements
,”
Eng. Fract. Mech.
,
69
, pp.
339
352
.10.1016/S0013-7944(01)00076-5
18.
Papadopoulos
,
C. A.
, and
Dimarogonas
,
A. D.
,
1987
, “
Coupled Longitudinal and Bending Vibrations of a Rotating Shaft With an Open Crack
,”
J. Sound Vib.
,
117
(
1
), pp.
81
93
.10.1016/0022-460X(87)90437-8
19.
Quinn
,
D.
,
Mani
,
G.
,
Kasarda
,
E.
,
Bash
,
T.
,
Inman
,
D. J.
, and
Kirk
,
R. G.
,
2005
, “
Damage Detection of a Rotating Cracked Shaft Using an Active Magnetic Bearing as a Force Actuator—Analysis and Experimental Verification
,”
IEEE/ASME Trans. Mechatron.
,
10
(
6
), pp.
640
647
.10.1109/TMECH.2005.859833
20.
Bucher
,
I.
, and
Ewins
,
D. J.
,
2001
, “
Modal Analysis and Testing of Rotating Structures
,”
Philos. Transact. Ser. A Math. Phys. Eng. Sci.
,
359
, pp.
61
96
.10.1098/rsta.2000.0714
21.
Penny
,
J. E. T.
, and
Friswell
,
M. I.
,
2007
, “
The Dynamics of Cracked Rotors
,” IMAC-XXV: A Conference & Exposition on Structural Dynamics, Orlando, FL, February 19–22, Society for Experimental Mechanics, Bethel, CT.
22.
Varney
,
P.
,
2013
, “
Transverse Fatigue Crack Diagnosis in a Rotordynamic System Using Vibration Monitoring
,” Master's thesis, Georgia Institute of Technology, Atlanta, GA.
23.
Casey
,
C.
,
2000
, “
Crack Detection in a Rotordynamic System by Vibration Monitoring
,” Master's thesis, Georgia Institute of Technology, Atlanta, GA.
24.
Budynas
,
R. G.
, and
Nisbett
,
J. K.
,
2008
,
Shigley's Mechanical Engineering Design
,
8th ed.
,
McGraw-Hill
,
New York
.
25.
Dimarogonas
,
A. D.
, and
Paipetis
,
S.
,
1983
,
Analytical Methods in Rotor Dynamics
,
Applied Science Publishers
, London.
26.
Varney
,
P.
, and
Green
,
I.
,
2012
, “
Rotordynamic Analysis Using the Complex Transfer Matrix
,” Proceedings of the ASME International Design Engineering and Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2012), Chicago, IL, August 12–15.
27.
Patel
,
T. H.
,
Zuo
,
M. J.
, and
Darpe
,
A. K.
,
2011
, “
Vibration Response of Coupled Rotor Systems With Crack and Misalignment
,”
IMechE C: J. Mech. Eng. Sci.
,
225
, pp.
700
713
.10.1243/09544062JMES2432
28.
Patel
,
T. H.
, and
Darpe
,
A. K.
,
2008
, “
Vibration Response of a Cracked Rotor in Presence of Rotor-Stator Rub
,”
J. Sound Vib.
,
317
(
3
), pp.
841
865
.10.1016/j.jsv.2008.03.032
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