Turbo generator shafts are often subjected to cyclic torsion resulting in formation of large longitudinal cracks as well as circumferential cracks. The presence of these cracks could greatly impact the shaft resonance frequencies. In this paper, dynamic response of a shaft with longitudinal and circumferential cracks is investigated through a comprehensive analytical study. The longitudinally cracked section of the shaft was modeled as an uncracked shaft with reduced torsional rigidity. Torsional rigidity correction factor (i.e., the ratio of torsional rigidity of the cracked shaft to that of the uncracked shaft) was obtained from finite element analysis and was shown to be only a function of crack depth to the shaft radius. The resonance frequency and frictional energy loss of a shaft with a longitudinal crack were found little affected by the presence of the crack as long as the crack depth was less than 20% of the shaft radius even if the entire shaft is cracked longitudinally. Moreover, we showed that the longitudinal crack location could be more conveniently identified by monitoring the slope of the torsional response along the shaft. The circumferential crack was modeled as a torsional spring with a torsional damping. The torsion spring and damping constants were obtained using fracture mechanics. For a shaft with both a longitudinal crack and a circumferential crack, the resonance frequency was governed by the longitudinal crack when the circumferential crack depth was less than 30% of the shaft radius.

References

References
1.
Dimarogonas
,
A.
, and
Massouros
,
G.
,
1981
, “
Torsional Vibration of a Shaft With a Circumferential Crack
,”
Eng. Fract. Mech.
,
15
(
3
), pp.
439
444
.10.1016/0013-7944(81)90069-2
2.
Dimarogonas
,
A. D.
,
1996
, “
Vibration of Cracked Structures: A State of the Art Review
,”
Eng. Fract. Mech.
,
55
(
5
), pp.
831
857
.10.1016/0013-7944(94)00175-8
3.
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
.10.1016/0022-460X(87)90437-8
4.
Chondros
,
T.
,
2001
, “
The Continuous Crack Flexibility Model for Crack Identification
,”
Fatigue Fract. Eng. Mater. Struct.
,
24
(
10
), pp.
643
650
.10.1046/j.1460-2695.2001.00442.x
5.
Chondros
,
T.
,
2005
, “
Variational Formulation of a Rod Under Torsional Vibration for Crack Identification
,”
Theor. Appl. Fract. Mech.
,
44
(
1
), pp.
95
104
.10.1016/j.tafmec.2005.05.008
6.
Chondros
,
T.
, and
Dimarogonas
,
A.
,
1998
, “
Vibration of a Cracked Cantilever Beam
,”
ASME J. Vib. Acoust.
,
120
(
3
), pp.
742
746
.10.1115/1.2893892
7.
Chondros
,
T.
,
Dimarogonas
,
A.
, and
Yao
,
J.
,
1997
, “
A Consistent Cracked Bar Vibration Theory
,”
J. Sound Vib.
,
200
(
3
), pp.
303
313
.10.1006/jsvi.1996.0718
8.
Chondros
,
T.
,
Dimarogonas
,
A.
, and
Yao
,
J.
,
1998
, “
A Continuous Cracked Beam Vibration Theory
,”
J. Sound Vib.
,
215
(
1
), pp.
17
34
.10.1006/jsvi.1998.1640
9.
Chondros
,
T.
,
Dimarogonas
,
A.
, and
Yao
,
J.
,
1998
, “
Longitudinal Vibration of a Bar With a Breathing Crack
,”
Eng. Fract. Mech.
,
61
(
5
), pp.
503
518
.10.1016/S0013-7944(98)00077-0
10.
Chondros
,
T.
,
Dimarogonas
,
A.
, and
Yao
,
J.
,
1998
, “
Longitudinal Vibration of a Continuous Cracked Bar
,”
Eng. Fract. Mech.
,
61
(
5
), pp.
593
606
.10.1016/S0013-7944(98)00071-X
11.
Chondros
,
T.
, and
Labeas
,
G.
,
2007
, “
Torsional Vibration of a Cracked Rod by Variational Formulation and Numerical Analysis
,”
J. Sound Vib.
,
301
(
3
), pp.
994
1006
.10.1016/j.jsv.2006.11.004
12.
Christides
,
S.
, and
Barr
,
A.
,
1986
, “
Torsional Vibration of Cracked Beams of Non-Circular Cross-Section
,”
Int. J. Mech. Sci.
,
28
(
7
), pp.
473
490
.10.1016/0020-7403(86)90067-6
13.
Dimarogonas
,
A. D.
,
Paipetis
,
S. A.
, and
Chondros
,
T. G.
,
2013
,
Analytical Methods in Rotor Dynamics
,
Springer
,
New York
.
14.
Wauer
,
J.
,
1990
, “
Modelling and Formulation of Equations of Motion for Cracked Rotating Shafts
,”
Int. J. Solids Struct.
,
26
(
8
), pp.
901
914
.10.1016/0020-7683(90)90076-8
15.
Gasch
,
R.
,
1993
, “
A Survey of the Dynamic Behaviour of a Simple Rotating Shaft With a Transverse Crack
,”
J. Sound Vib.
,
160
(
2
), pp.
313
332
.10.1006/jsvi.1993.1026
16.
Bicego
,
V.
,
Lucon
,
E.
,
Rinaldi
,
C.
, and
Crudeli
,
R.
,
1999
, “
Failure Analysis of a Generator Rotor With a Deep Crack Detected During Operation: Fractographic and Fracture Mechanics Approach
,”
Nucl. Eng. Des.
,
188
(
2
), pp.
173
183
.10.1016/S0029-5493(99)00014-X
17.
Barr
,
A.
,
1966
, “
An Extension of the Hu-Washizu Variational Principle in Linear Elasticity for Dynamic Problems
,”
ASME J. Appl. Mech.
,
33
(
2
), p.
465
.10.1115/1.3625076
18.
Sabnavis
,
G.
,
Kirk
,
R. G.
,
Kasarda
,
M.
, and
Quinn
,
D.
,
2004
, “
Cracked Shaft Detection and Diagnostics: A Literature Review
,”
Shock Vib. Dig.
,
36
(
4
), pp.
287
296
.10.1177/0583102404045439
19.
Shih
,
Y.-S.
, and
Chung
,
C.-Y.
,
2013
, “
Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism
,”
ASME J. Vib. Acoust.
,
135
(
6
), p.
061009
.10.1115/1.4024053
20.
Nayeb-Hashemi
,
H.
,
McClintock
,
F.
, and
Ritchie
,
R.
,
1982
, “
Effects of Friction and High Torque on Fatigue Crack Propagation in Mode III
,”
Metall. Trans. A
,
13
(
12
), pp.
2197
2204
.10.1007/BF02648390
21.
Nayeb-Hashemi
,
H.
,
McClintock
,
F.
, and
Ritchie
,
R.
,
1983
, “
Influence of Overloads and Block Loading Sequences on Mode III Fatigue Crack Propagation in A469 Rotor Steel
,”
Eng. Fract. Mech.
,
18
(
4
), pp.
763
783
.10.1016/0013-7944(83)90123-6
22.
Nayeb-Hashemi
,
H.
,
McClintock
,
F.
, and
Ritchie
,
R.
,
1983
, “
Micro-Mechanical Modelling of Mode III Fatigue Crack Growth in Rotor Steels
,”
Int. J. Fract.
,
23
(
3
), pp.
163
185
.10.1007/BF00028821
23.
Nayeb-Hashemi
,
H.
,
Suresh
,
S.
, and
Ritchie
,
R.
,
1983
, “
On the Contrast Between Mode I and Mode III Fatigue Crack Propagation Under Variable-Amplitude Loading Conditions
,”
Mater. Sci. Eng.
,
59
(
1
), pp.
L1
L5
.10.1016/0025-5416(83)90098-8
24.
Ritchie
,
R.
,
McClintock
,
F.
,
Nayeb-Hashemi
,
H.
, and
Ritter
,
M.
,
1982
, “
Mode III Fatigue Crack Propagation in Low Alloy Steel
,”
Metall. Trans. A
,
13
(
1
), pp.
101
110
.10.1007/BF02642420
25.
Vaziri
,
A.
, and
Nayeb-Hashemi
,
H.
,
2005
, “
The Effect of Crack Surface Interaction on the Stress Intensity Factor in Mode III Crack Growth in Round Shafts
,”
Eng. Fract. Mech.
,
72
(
4
), pp.
617
629
.10.1016/j.engfracmech.2004.03.014
26.
Vaziri
,
A.
, and
Nayeb-Hashemi
,
H.
,
2006
, “
A Theoretical Investigation on the Vibrational Characteristics and Torsional Dynamic Response of Circumferentially Cracked Turbo-Generator Shafts
,”
Int. J. Solids Struct.
,
43
(
14
), pp.
4063
4081
.10.1016/j.ijsolstr.2005.05.029
27.
Vaziri
,
A.
, and
Nayeb-Hashemi
,
H.
,
2002
, “
Effects of Local Energy Loss on the Dynamic Response of a Cylindrical Bar With a Penny Shape Crack
,”
ASME
Paper No. IMECE2002-32300.10.1115/IMECE2002-32300
28.
Broberg
,
K. B.
,
1999
,
Cracks and Fracture
,
Academic Press
,
London, UK
.
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