A general dynamic model for a large-scale rotor-bearing system with a cracked shaft is introduced. A finite shaft element with a crack is developed using a consistent finite element approach. The model accommodates shafts with tapered portions, multiple disks and anisotropic bearings. The formulation is applicable to rotor-bearing systems with different practical design configurations including intermediate bearings, shaft overhang, and stepped shaft assemblies. A reduced order form of equations of motion is obtained by invoking the actual non-planar (complex) modal transformations. The time-response due to different excitations are calculated, and comparisons are presented to establish the validity and efficiency of the reduced order model. It is hoped that the developed computational scheme offers an efficient and essential core module in establishing other specialized crack detection schemes for rotor-bearing systems.

1.
Wauer
,
J.
,
1990
, “
On the Dynamics of Cracked Rotors: A Literature Survey
,”
Appl. Mech. Rev.
,
43
, No.
1
, pp.
13
17
.
2.
Petroski
,
H. J.
,
1981
, “
Simple Static and Dynamic Models for the Cracked Elastic Beam
,”
Int. J. Fract.
,
17
, pp.
R71–R76
R71–R76
.
3.
Gounaris
,
G.
, and
Dimarogonas
,
A.
,
1988
, “
A Finite Element of a Cracked Prismatic Beam for Structural Analysis
,”
Comput. Struct.
,
28
, No.
3
, pp.
309
313
.
4.
Collins
,
K. R.
,
Plaut
,
R. H.
, and
Wauers
,
J.
,
1991
, “
Detection of Cracks in Rotating Timoshenko Shafts Using Axial Impulses
,”
J. Vibr. Acoust.
,
113
, pp.
74
78
.
5.
Papadopoulos
,
C. A.
, and
Dimarogonas
,
A. D.
,
1988
, “
Coupled Longitudinal and Bending Vibrations of a Cracked Shaft
,”
J. Vibration, Acoustics, Stress and Reliability in Design
,
110
, pp.
1
8
.
6.
Papadopoulos
,
C. A.
, and
Dimarogonas
,
A. D.
,
1992
, “
Coupled Vibration of Cracked Shafts
,”
J. Vibr. Acoust.
,
114
, pp.
461
467
.
7.
Ruotolo
,
R.
,
Surace
,
C.
,
Crespo
,
P.
, and
Storer
,
D.
,
1996
, “
Harmonic Analysis of the Vibrations of a Cantilevered Beam with a Closing Crack
,”
Comput. Struct.
,
61
, No.
6
, pp.
1057
1074
.
8.
Inagaki
,
T.
,
Kanki
,
H.
, and
Shiraki
,
K.
,
1982
, “
Transverse Vibrations of a General Cracked-Rotor Bearing System
,”
ASME J. Mech. Des.
104
, pp.
345
355
.
9.
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. Vibration, Acoustics, Stress and Reliability in Design
,
106
, pp.
139
145
.
10.
Papadapoulos
,
C. A.
, and
Dimarogonas
,
A. D.
,
1987
, “
Coupled Longitudinal and Bending Vibrations of a Rotating Shaft with an Open Crack
,”
J. Sound Vib.
,
117
, No.
1
, pp.
81
93
.
11.
Krawczuk
,
M.
,
1992
, “
Finite Timoshenko—Type Beam Element with a Crack
,”
Engineering Transactions
,
40
, No.
2
, pp.
229
248
.
12.
Stanway
,
R.
, and
Burrows
,
C. R.
,
1981
, “
Active Vibration Control of a Flexible Rotor on Flexibly-Mounted Journal Bearings
,”
J. Dyn. Syst., Meas., Control
,
103
, pp.
383
388
.
13.
Sakata
,
M.
,
Aiba
,
T.
, and
Ohnabe
,
H.
,
1983
, “
Transient Vibration of High-Speed, Lightweight Rotors Due to Sudden Imbalance
,”
J. Eng. Power
,
105
, pp.
480
486
.
14.
Fang, Z. C., and Luo, Z. H., 1989, “Transient Vibration of an Asymmetric Rotor System Through Critical Speed,” ASME Design Engineering Division (Publication) D. E., 18, No. 1, pp. 191–197.
15.
Lee
,
H. P.
,
1995
, “
Dynamic Response of a Rotating Timoshenko Shaft Subject to Axial Forces and Moving Loads
,”
J. Sound Vib.
,
181
, No.
1
, pp.
169
177
.
16.
Mohiuddin
,
M. A.
, and
Khulief
,
Y. A.
,
1994
, “
Modal Characteristics of Rotors Using a Conical Shaft Finite Element
,”
Comput. Methods Appl. Mech. Eng.
,
115
, pp.
125
144
.
17.
Mohiuddin
,
M. A.
, and
Khulief
,
Y. A.
,
1998
, “
Modal Characteristics of Cracked Rotors Using a Conical Shaft Finite Element
,”
Comput. Methods Appl. Mech. Eng.
,
162
, pp.
223
247
.
18.
Likins
,
P. W.
,
1972
, “
Finite Element Appendage Equations for Hybrid Coordinate Dynamic Analysis
,”
Int. J. Solids Struct.
,
8
, pp.
709
731
.
19.
Gunter
,
E. J.
,
Choy
,
K. C.
, and
Allaire
,
P. E.
,
1978
, “
Modal Analysis of Turborotors Using Planar Modes—Theory
,”
J. Franklin Inst.
,
305
(
4
), pp.
221
243
.
20.
Laurenson
,
R. M.
,
1976
, “
Modal Analysis of Rotating Flexible Structures
,”
AIAA J.
,
14
No. (
10
), pp.
1444
1450
.
21.
Meirovitch
,
L.
,
1972
, “
A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems
,”
AIAA J.
,
12
, pp.
1337
1342
.
22.
Sundada
,
W. H.
, and
Dubowsky
,
S.
,
1983
, “
On The Dynamic Analysis and Behavior of Industrial Robotic Manipulators with Elastic Links
,”
ASME J. Mech. Trasm., Autom. Des.
,
105
, pp.
42
51
.
23.
Shabana
,
A. A.
, and
Wehage
,
R.
,
1983
, “
Variable Degree of Freedom Compact Mode Analysis of Inertia Variant Flexible Machine Systems
,”
ASME J. Mech., Transm., Autom. Des.
,
105
(
3
), pp.
370
378
.
24.
Spanos
,
T. J.
, and
Tsuha
,
W. S.
,
1991
, “
Selection of Component Modes for Flexible Multibody Simulations
,”
Journal of Guidance
,
14
No. (
2
), pp.
260
267
.
25.
Khulief
,
Y. A.
,
1992
, “
On The Finite Element Dynamic Analysis of Flexible Mechanisms
,”
Comput. Methods Appl. Mech. Eng.
,
97
, pp.
23
32
.
26.
Kane
,
K.
, and
Torby
,
B. J.
,
1991
, “
The Extended Modal Reduction Method Applied to Rotor Dynamic Problems
,”
J. Vibr. Acoust.
,
113
, pp.
79
84
.
27.
Wilkinson, 1965, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford.
You do not currently have access to this content.