A transverse shaft crack is a serious malfunction that can occur due to cyclic loading, creep, stress corrosion, and other mechanisms to which rotating machines are subjected. Though studied for many years, the problems of early crack detection and warning are still in the limelight of many researchers. This is due to the fact that the crack has subtle influence on the dynamic response of the machine and still there are no widely accepted, reliable methods of its early detection. This paper presents a new approach to these problems. The method utilizes the coupling mechanism between the bending and torsional vibrations of the cracked, nonrotating shaft. By applying an external lateral force of constant amplitude, a small shaft deflection is induced. Simultaneously, a harmonic torque is applied to the shaft inducing its torsional vibrations. By changing the angular position of the lateral force application, the position of the deflection also changes opening or closing of the crack. This changes the way the bending and torsional vibrations are being coupled. By studying the coupled lateral vibration response for each angular position of the lateral force one can assess the possible presence of the crack. The approach is demonstrated with a numerical model of a rotor. The model is based on the rigid finite element method (RFE), which has previously been successfully applied for the dynamic analysis of many complicated, mechanical structures. The RFE method is extended and adopted for the modeling of the cracked shafts. An original concept of crack modeling utilizing the RFE method is presented. The crack is modeled as a set of spring-damping elements (SDEs) of variable stiffness connecting two sections of the shaft. By calculating the axial deformations of the SDEs, the opening/closing mechanism of the crack is introduced. The results of numerical analysis demonstrate the potential of the suggested approach for effective shaft crack detection.

References

References
1.
Bently
,
D. E.
, and
Muszynska
,
A.
, 1986, “
Detection of Rotor Cracks
,” Proceedings of Texas A&M University 15th Turbomachinery Symposium and Short Courses, Corpus Christi, TX, pp.
129
139
.
2.
Saavedra
,
P. N.
, and
Cuitino
,
L. A.
, 2002, “
Vibration Analysis of Rotor for Crack Identification
,”
J. Vib. Control
,
8
(
1
), pp.
51
67
.
3.
Bachschmid
,
N.
,
Pennacchi
,
P.
, and
Tanzi
,
E.
, 2010,
Cracked Rotors: A Survey on Static and Dynamic Behaviour Including Modelling and Diagnosing
,
Springer
,
Berlin
.
4.
Bachschmid
,
N.
,
Pennacchi
,
P.
,
Tanzi
,
E.
, and
Vania
,
A.
, 2000, “
Identification of Transverse Crack Position and Depth in Rotor Systems
,”
Meccanica
,
35
, pp.
563
582
.
5.
Söffker
,
D.
,
Bajkowski
,
J.
, and
Müller
,
P. C.
, 1993, “
Detection of Cracks in Turborotors—A New Observer-Based Method
,”
ASME J. Dyn. Syst. Measure. Control
,
3
, pp.
518
524
.
6.
Kulesza
,
Z.
, and
Sawicki
,
J. T.
, 2010, “
Auxiliary State Variables for Rotor Crack Detection
,”
J. Vib. Control
,
17
(
6
), pp.
857
872
.
7.
Loparo
,
K. A.
,
Adams
,
M. L.
,
Lin
,
W.
,
Abdel-Magied
,
M. F.
, and
Afshari
,
N.
, 2000, “
Fault Detection and Diagnosis of Rotating Machinery
,”
IEEE Trans. Ind. Electron.
,
47
(
5
), pp.
1005
1014
.
8.
He
,
Y.
,
Guo
,
D.
, and
Chu
,
F.
, 2001, “
Using Genetic Algorithms to Detect and Configure Shaft Crack for Rotor-Bearing System
,”
Comput. Methods Appl. Mech. Eng.
,
190
, pp.
5895
5906
.
9.
Litak
,
G.
, and
Sawicki
,
J. T.
, 2009, “
Intermittent Behaviour of a Cracked Rotor in the Resonance Region
,”
Chaos Solitions Fractals
,
42
, pp.
1495
1501
.
10.
Xiang
,
J.
,
Zhong
,
Y.
,
Chen
,
X.
, and
He
,
Z.
, 2008, “
Crack Detection in a Shaft by Combination of Wavelet-Based Elements and Genetic Algorithm
,”
Int. J. Solids Struct.
,
45
, pp.
4782
4795
.
11.
Guo
,
D.
, and
Peng
,
Z. K.
, 2007, “
Vibration Analysis of a Cracked Rotor Using Hilbert-Huang Transform
,”
Mech. Syst. Signal Process.
,
21
, pp.
3030
3041
.
12.
Plaut
,
R. H.
, 1995, “
Parametric, External and Combination Resonances in Coupled Flexural and Torsional Oscillations of an Unbalanced Rotating Shaft
,”
J. Sound Vib.
,
183
(
5
), pp.
889
897
.
13.
Ishida
,
Y.
, and
Inoue
,
T.
, 2006, “
Detection of a Rotor Crack Using a Harmonic Excitation and Nonlinear Vibration Analysis
,”
ASME J. Vib. Acoust.
,
128
, pp.
741
749
.
14.
Sawicki
,
J. T.
,
Friswell
,
M. I.
,
Kulesza
,
Z.
,
Wroblewski
,
A.
, and
Lekki
,
J. D.
, 2011, “
Detecting Cracked Rotors Using Auxiliary Harmonic Excitation
,”
J. Sound Vib.
,
330
, pp.
1365
1381
.
15.
Sawicki
,
J. T.
,
Storozhev
,
D. L.
, and
Lekki
,
J. D.
, 2011, “
Exploration of NDE Properties of AMB Supported Rotors for Structural Damage Detection
,”
ASME J. Eng. Gas Turbines Power
,
133
(10)
, p.
102501
.
16.
Sawicki
,
J. T.
, and
Baaklini
,
G. Y.
, 2004, “
Coupled Lateral and Torsional Vibrations of a Cracked Rotor
,” Proceedings of ASME Turbo Expo 2004, Power for Land, Sea, and Air. June 14–17, Vienna, Austria.
17.
Darpe
,
K.
,
Gupta
,
K.
, and
Chawla
,
A.
, 2004, “
Coupled Bending, Longitudinal and Torsional Vibrations of a Cracked Rotor
,”
J. Sound Vib.
,
269
, pp.
33
60
.
18.
Kruszewski
,
J.
,
Sawiak
,
S.
, and
Wittbrodt
,
E.
, 1999, “
The Rigid Finite Element Method in Dynamics of Structures
,” WNT, Warsaw, Poland (in Polish).
19.
Wittbrodt
,
E.
,
Adamiec-Wójcik
,
I.
, and
Wojciech
,
S.
, 2006,
Dynamics of Flexible Multibody Systems: Rigid Finite Element Method
,
Springer
,
Berlin
.
20.
Grabowski
,
B
., 1984, “
The Vibrational Behaviour of a Rotating Shaft Containing a Transverse Crack
,”
Dynamics of Rotors—Stability System Identification (CISM Courses and Lectures, Vol. 273)
,
O.
Mahrenholtz
, ed.,
Springer
,
New York
.
21.
Gasch
,
R. A.
, 1993, “
A Survey of the Dynamic Behaviour of a Simple Rotating Shaft With a Transverse Crack
,”
J. Sound Vib.
,
160
(
2
), pp.
313
332
.
22.
Mayes
,
I. W.
, and
Davies
,
W. G. R.
, 1984, “
Analysis of the Response of a Multi-Rotor-Bearing System Containing a Transverse Crack in a Rotor
,”
J. Vib. Acoust. Stress Reliability Design
,
83 84 DET
, pp.
139
145
.
23.
Nelson
,
H. D.
, and
McVaugh
,
J. M.
, 1976, “
The Dynamics of Rotor Bearing Systems Using Finite Elements
,”
ASME J. Eng. Ind.
,
98
, pp.
593
600
.
24.
Wu
,
X.
,
Sawicki
,
J. T.
,
Friswell
,
M. I.
, and
Baaklini
,
G. Y.
, 2005, “
Finite Element Analysis of Coupled Lateral and Torsional Vibrations of a Rotor With Multiple Cracks
,” Proceedings of GT2005 ASME Turbo Expo 2005: Power for Land, Sea and Air, June 6-9, Reno, NV. Paper No. GT2005-68839, pp.
841
850
.
25.
Dimarogonas
,
D.
, and
Paipetis
,
S. A.
, 1983,
Analytical Methods in Rotor Dynamics
,
Applied Science Publishers
,
London
.
26.
Sihler
,
C
., 2005, “
A Novel Torsional Exciter for Modal Vibration Testing of Large Rotating Machinery
,”
Mech. Syst. Signal Process.
,
20
, pp.
1725
1740
.
27.
Gaddis
,
T. W.
,
Nelson
,
K. I.
, and
Thomas
,
G. W.
, 1996, “
Vibration Testing on Rotating Machine Components
,” US Patent 5,553,501, United Technologies Corporation.
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