Abstract behavior of a cracked rotor. Important achievements

AbstractFatigue crack is animportant rotor fault, which can lead to catastrophic failure if undetected properlyand in time. Study and Investigation of dynamics of cracked shafts arecontinuing since last four decades. Some review papers were also publishedduring this period. The aim of this paper is to present a review on recentstudies and investigations done on cracked rotor. It is not the intention ofthe authors to provide all literatures related with the cracked rotor.

However,the main emphasis is to provide all the methodologies adopted by variousresearchers to investigate a cracked rotor. The paper incorporates a candidcommentary on various methodologies.  1. IntroductionRotorshaft is considered as one of the important part of various rotating machines.

Due to manufacturing defect or cyclic loading, fatigue crack frequently appearsin rotating shaft. Fatigue crack is considered as one of the main reasons forcatastrophic failures in rotating shaft.  Presenceof fatigue cracks fault may interrupt smooth, effective and efficient operation and performance of the machines. This problem has attractedthe attention of researchers. Through numbers of researches methodologyinvestigation of dynamics of cracked rotor has been done, and work is stillcontinuing in this area. The numbers of review papers were presented from timeto time on this subject. The study and investigation in the last few decades oncracked rotors are presented in a review paper by Wauer 1; Gasch 2 haspresented a survey on simple rotor, Dimarogonas 3 has presented a review, andmore recently presented by Sabnavis et al.

4. Various methods like Wavelettransform, Finite element method, Nonlinear dynamics, Hilbert-Huang transform,and so forth, have been applied to study the dynamic behavior of a crackedrotor. Important achievements have been made during these years; the knowledgeof the dynamical behavior of cracked shafts has helped in predicting presenceof crack in a rotor. But there is demand for more powerful rotor nowadays.Hence more accurate and reliable technique is required to predict thegeneration and propagation of a crack in a rotating shaft. This paper proposescandid comment on various approaches. 2.

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Reviewof Different Modeling Approaches Applied to Investigate Cracked Rotor Modelling and analysisof cracked rotor is continuing since last four decades. Number of modelingtechniques is used by various researchers. These approaches will be presentedin the next subsections.

2.1 HHT (Hilbert-HuangTransform): Hilbert-Huang transform fordetection and monitoring of crack in transient response of a cracked rotorpresented by Guo and Peng 5. This method is particularly useful foridentifying very small crack depths. Hilbert-Huang transform has good potentialfor nonlinear and non stationary data analysis, especially fortime-frequency-energy representations.  2.

2 Breathing Mechanism: The crack breathing inrotors is simulated using two well-known models by Patel and Darpe 8. One isthe switching/hinge crack model, in which the stiffness of the rotor switchesfrom one corresponding to the closed crack to the stiffness corresponding tothe fully open crack state. The other model is the response dependent breathingcrack model presented by Jun et al. 9. 2.

3 Wavelet Transform and Wavelet Finite Element Approach: Wavelets method may be used todetect the damage location and depth by considering modal frequencies, modalshape, and modal damp, and so forth. Zheng et al. 10 applied the wavelettransform technique for bifurcation and chaos study. 2.

4 Investigationthrough Finite Element Approach: Three dimensional (3D) FEA has attracted theresearchers as an investigative tool for the study of crack breathingmechanism. Due to ease in simulation, many researchers applied finite elementtechnique for analysis of crack in a rotating shaft. Papadopoulos andDimarogonas 20 have analyzed for the local crack compliance for asix-degree-of-freedom crack beam segment.2.5 Analysis throughNonlinear Dynamics of Cracked Rotor: Muller et al. 34 investigated nonlinear dynamicsof a cracked rotating shaft using changing stiffness coefficient.

Bovsunovskii 35 has done the numerical study of forced and decayingvibrations of a system simulating a body with a closing crack under the actionof various modes of a nonlinear restoring force and linear viscous friction. Inhis study, he determined the natural frequency of transverse and longitudinalvibration of a cracked beam with an open and close crack. 3. ConclusionsAfter an exhaustivesurvey of literature, the potential researchers in this field have various toolsand methodologies to be applied to detect and proper identification of a crack.

The methodologies have some specific advantages over the other. Now, there is achoice before the dynamics people to adopt proper techniques. The paper may beconcluded as follows.

 (i) Crack breathingmechanism plays an important role in analysis of dynamic behavior of a crackedrotor. This breathing phenomenon must be modeled accurately to detect the crackin a rotor. (ii) Wavelet transformmethod was used by various researchers to predict the generation andpropagation of a crack in rotating shaft. This propagation mechanism may bemodeled so that the early failure of the rotor shaft may be detected. (iii) Finite elementmethod is a better choice and applied by various researchers to analyze thedynamic behavior of a shaft having different kind of cracks, for example,transverse crack, two cracks, slant crack, and so forth.

The crack element mustbe accurately discretized to depict the real behavior of a cracked rotor. (iv) Wavelet along withfinite element method is also a good choice to have advantages of bothtechniques. Recently wavelet along with genetic algorithm analysis is alsofinding place in the various Literature.