Abstract behavior of a cracked rotor. Important achievements


Fatigue crack is an
important rotor fault, which can lead to catastrophic failure if undetected properly
and in time. Study and Investigation of dynamics of cracked shafts are
continuing since last four decades. Some review papers were also published
during this period. The aim of this paper is to present a review on recent
studies and investigations done on cracked rotor. It is not the intention of
the authors to provide all literatures related with the cracked rotor. However,
the main emphasis is to provide all the methodologies adopted by various
researchers to investigate a cracked rotor. The paper incorporates a candid
commentary on various methodologies.

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1. Introduction

shaft is considered as one of the important part of various rotating machines.
Due to manufacturing defect or cyclic loading, fatigue crack frequently appears
in rotating shaft. Fatigue crack is considered as one of the main reasons for
catastrophic failures in rotating shaft.  Presence
of fatigue cracks fault may interrupt smooth, effective and efficient operation and performance of the machines. This problem has attracted
the attention of researchers. Through numbers of researches methodology
investigation of dynamics of cracked rotor has been done, and work is still
continuing in this area. The numbers of review papers were presented from time
to time on this subject. The study and investigation in the last few decades on
cracked rotors are presented in a review paper by Wauer 1; Gasch 2 has
presented a survey on simple rotor, Dimarogonas 3 has presented a review, and
more recently presented by Sabnavis et al. 4. Various methods like Wavelet
transform, Finite element method, Nonlinear dynamics, Hilbert-Huang transform,
and so forth, have been applied to study the dynamic behavior of a cracked
rotor. Important achievements have been made during these years; the knowledge
of the dynamical behavior of cracked shafts has helped in predicting presence
of crack in a rotor. But there is demand for more powerful rotor nowadays.
Hence more accurate and reliable technique is required to predict the
generation and propagation of a crack in a rotating shaft. This paper proposes
candid comment on various approaches.


2. Review
of Different Modeling Approaches Applied to Investigate Cracked Rotor


Modelling and analysis
of cracked rotor is continuing since last four decades. Number of modeling
techniques is used by various researchers. These approaches will be presented
in the next subsections.

2.1 HHT (Hilbert-Huang
Transform): Hilbert-Huang transform for
detection and monitoring of crack in transient response of a cracked rotor
presented by Guo and Peng 5. This method is particularly useful for
identifying very small crack depths. Hilbert-Huang transform has good potential
for nonlinear and non stationary data analysis, especially for
time-frequency-energy representations.


2.2 Breathing Mechanism: The crack breathing in
rotors is simulated using two well-known models by Patel and Darpe 8. One is
the switching/hinge crack model, in which the stiffness of the rotor switches
from one corresponding to the closed crack to the stiffness corresponding to
the fully open crack state. The other model is the response dependent breathing
crack model presented by Jun et al. 9.


2.3 Wavelet Transform and Wavelet Finite Element Approach: Wavelets method may be used to
detect the damage location and depth by considering modal frequencies, modal
shape, and modal damp, and so forth. Zheng et al. 10 applied the wavelet
transform technique for bifurcation and chaos study.


2.4 Investigation
through Finite Element Approach: Three dimensional (3D) FEA has attracted the
researchers as an investigative tool for the study of crack breathing
mechanism. Due to ease in simulation, many researchers applied finite element
technique for analysis of crack in a rotating shaft. Papadopoulos and
Dimarogonas 20 have analyzed for the local crack compliance for a
six-degree-of-freedom crack beam segment.

2.5 Analysis through
Nonlinear Dynamics of Cracked Rotor: Muller et al. 34 investigated nonlinear dynamics
of a cracked rotating shaft using changing stiffness coefficient.
Bovsunovskii 35 has done the numerical study of forced and decaying
vibrations of a system simulating a body with a closing crack under the action
of various modes of a nonlinear restoring force and linear viscous friction. In
his study, he determined the natural frequency of transverse and longitudinal
vibration of a cracked beam with an open and close crack.


3. Conclusions

After an exhaustive
survey of literature, the potential researchers in this field have various tools
and methodologies to be applied to detect and proper identification of a crack.
The methodologies have some specific advantages over the other. Now, there is a
choice before the dynamics people to adopt proper techniques. The paper may be
concluded as follows.


(i) Crack breathing
mechanism plays an important role in analysis of dynamic behavior of a cracked
rotor. This breathing phenomenon must be modeled accurately to detect the crack
in a rotor.


(ii) Wavelet transform
method was used by various researchers to predict the generation and
propagation of a crack in rotating shaft. This propagation mechanism may be
modeled so that the early failure of the rotor shaft may be detected.


(iii) Finite element
method is a better choice and applied by various researchers to analyze the
dynamic behavior of a shaft having different kind of cracks, for example,
transverse crack, two cracks, slant crack, and so forth. The crack element must
be accurately discretized to depict the real behavior of a cracked rotor.


(iv) Wavelet along with
finite element method is also a good choice to have advantages of both
techniques. Recently wavelet along with genetic algorithm analysis is also
finding place in the various Literature.