Abstract

Different from the crack on the rotating shaft, the crack on the bolt, which is a connecting part of the bolt-disk combined rotor, is a kind of local defect. The local crack on the bolt under high pretension is always in open state, and it increases the overall vibration of the combined rotor significantly in practice. This paper studies the modeling of the crack on the bolt and nonlinear dynamic behaviors of the cracked bolt-disk rotor system. The circumferential bolts with a transverse open crack are treated as several bar elements under the assumption that each bolt has the same original tensile extension length. The cracked correction coefficient is introduced to describe the decreasing amount of bolt's tension due to crack. After this coefficient is obtained according to finite element method, the stiffness matrix of circumferential bolts with crack is built based on total potential energy. The dynamic model consists of a time-independent stiffness matrix for perfect bolts, a time-variant reductive stiffness, and an additional moment. As a result, the crack in bolt reduces rotor's nonlinear stability and leads to greater vibration and fluctuation. In addition, crack depth has much larger influence than crack location on the dynamic behaviors.

References

1.
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
2.
Wauer
,
J.
,
1990
, “
On the Dynamics of Cracked Rotors: A Literature Survey
,”
ASME Appl. Mech. Rev.
,
43
(
1
), pp.
13
17
.10.1115/1.3119157
3.
Papadofoulos
,
C. A.
, and
Dimarogonas
,
A. D.
,
1987
, “
Coupling of Bending and Torsional Vibration of a Cracked Timoshenko Shaft
,”
Ing. Arch.
,
57
, pp.
495
505
.10.1007/BF00534404
4.
Chen
,
C. P.
,
Dai
,
L. M.
, and
Fu
,
Y. M.
,
2007
, “
Nonlinear Response and Dynamic Stability of a Cracked Rotor
,”
Commun. Nonlinear Sci. Numer. Simul.
,
12
(
6
), pp.
1023
1037
.10.1016/j.cnsns.2005.09.004
5.
Bachschmid
,
N.
,
Pennacchi
,
P.
,
Tanzi
,
E.
, and
Vania
,
A.
,
2000
,
Identification of Transverse Crack Position and Depth in Rotor System,”
Meccanica
,
35
, pp.
563
582
.10.1023/A:1010562205385
6.
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
.10.1016/j.ymssp.2007.11.005
7.
Ichimonji
,
M.
, and
Watanabe
,
S.
,
1988
, “
The Dynamics of a Rotor System With a Shaft Having a Slant Crack (a Qualitative Analysis Using a Simple Rotor Model
,”
JSME Int. J. Ser. III
,
31
(
4
), pp.
712
718
.10.1299/jsmec1988.31.712
8.
Prabhakar
,
S.
,
Sekhar
,
A. S.
, and
Mohanty
,
A. R.
,
2002
, “
Transient Lateral Analysis of a Slant-Cracked Rotor Passing Through Its Flexural Critical Speed
,”
Mech. Mach. Theory
,
37
(
9
), pp.
1007
1020
.10.1016/S0094-114X(02)00020-4
9.
Dimentberg
,
F. M.
,
1961
,
Flexural Vibrations of Rotating Shafts
,
Butterworths
,
London, UK
.
10.
Tondl
,
A.
,
1965
,
Some Problems in Rotor Dynamics
,
Chapman & Hall
,
London, UK
.
11.
Chasalevris
,
A. C.
, and
Papadopoulos
,
C. A.
,
2006
, “
Identification of Multiple Cracks in Beams Under Bending
,”
Mech. Syst. Signal Process.
,
20
(
7
), pp.
1631
1673
.10.1016/j.ymssp.2006.03.008
12.
Darpe
,
A. K.
,
Gupta
,
K.
, and
Chawla
,
A.
,
2004
, “
Coupled Bending, Longitudinal and Torsional Vibrations of a Cracked Rotor
,”
J. Sound Vib.
,
269
(
1–2
), pp.
33
60
.10.1016/S0022-460X(03)00003-8
13.
Jun
,
O. S.
,
Eun
,
H. J.
,
Earmme
,
Y. Y.
, and
Lee
,
C. W.
,
1992
, “
Modelling and Vibration Analysis of a Simple Rotor With a Breathing Crack
,”
J. Sound Vib.
,
155
(
2
), pp.
273
290
.10.1016/0022-460X(92)90511-U
14.
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
.10.1016/j.euromechsol.2006.04.002
15.
Simo
,
J. C.
, and
Laursen
,
T. A.
,
1992
, “
An Augmented Lagrangian Treatment of Contact Problems Involving Friction
,”
Comput. Struct.
,
42
(
1
), pp.
97
116
.10.1016/0045-7949(92)90540-G
16.
Wang
,
X.
, and
Yamaguchi
,
A.
,
2002
, “
A. Characteristics of Hydrostatic Bearing/Seal Parts for Water Hydraulic Pumps and Motors, Part 1: Experiment and Theory
,”
Tribol. Int.
,
35
(
7
), pp.
425
433
.10.1016/S0301-679X(02)00023-3
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