PSI - Issue 39

Structural Integrity Procedia 00 (2019) 000–000 Available online at www.sciencedirect.com ScienceDirect

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ScienceDirect CP2021 - The 7th International Conference on Crack Paths Preface Sabrina Vantadori a  , Stefano Natali b , Francesco Iacoviello c , José António Correia d , Andrea Carpinteri a , Filippo Berto e a Department of Engineering & Architecture University of Parma, Parma, Italy b Department Chemical Engineering Materials Environment Sapienza University, Rome, Italy c Department of Civil and Mechanical Engineering University of Cassino and Southern Lazio, Cassino, Italy d INEGI & CONSTRUCT, Faculty of Engineering University of Porto, Porto, Portugal e Department of Mechanical and Industrial Engineering Faculty of Engineering, Trondheim, Norway CP2021 - The 7th International Conference on Crack Paths Preface Sabrina Vantadori a  , Stefano Natali b , Francesco Iacoviello c , José António Correia d , Andrea Carpinteri a , Filippo Berto e a Department of Engineering & Architecture University of Parma, Parma, Italy b Department Chemical Engineering Materials Environment Sapienza University, Rome, Italy c Department of Civil and Mechanical Engineering University of Cassino and Southern Lazio, Cassino, Italy d INEGI & CONSTRUCT, Faculty of Engineering University of Porto, Porto, Portugal e Department of Mechanical and Industrial Engineering Faculty of Engineering, Trondheim, Norway Procedia Structural Integrity 39 (2022) 1–2

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of CP 2021 – Guest Editors © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo

Keywords: Preface, Crack Paths.

* Corresponding author. Tel.: +39.0521905962 E-mail address: sabrina.vantadori@unipr.it © 2021 The Authors. Published by ELSEVIER B.V. This is an open ccess article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo

Keywords: Preface, Crack Paths.

* Corresponding author. Tel.: +39.0521905962 E-mail address: sabrina.vantadori@unipr.it

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of CP 2021 – Guest Editors 10.1016/j.prostr.2022.03.065 2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo 2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo

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Author name / Structural Integrity Procedia 00 (2021) 000–000

Sabrina Vantadori et al. / Procedia Structural Integrity 39 (2022) 1–2

1. Preface The 7th International Conference on Crack Paths (CP2021) was organised by the Technical Committee No.3 (TC3) of the European Structural Integrity Society and strongly supported by the Italian Group of Fracture. The CP2021 Conference should have been held at the University La Sapienza in Rome (Italy) but, due to the pandemic situation, we opted for a virtual format edition. The Conference took place from 21st to 24th September, 2021. This Conference followed the Conferences in Parma in 2003 and 2006, Vicenza in 2009, Gaeta in 2012, Ferrara in 2015 and Verona in 2018. It can be stated that it was a successful event. During the Conference, 122 research works coming from 26 different countries were presented, and 7 invited lectures were carried out in a live format by: Donato Firrao (IGF, Italy), David Taylor (Trinity College Dublin, UK), Stavros Kourkoulis (National Technical University of Athens, Greece), José Alexander Araújo (University of Brasília, Brazil), Guozheng Kang (Southwest Jiaotong University, China), Leslie Banks-Sills (Tel Aviv University, Israel), and Guian Qian (Chinese Academy of Sciences, China). The presentations were scheduled in 17 sessions, covering a wide range of topics related to crack path under both static and fatigue loading. Research works covered: experimental determination and theoretical evaluation of crack path (CP); CP of both surface and short cracks; effect of material inhomogeneities, non-proportional cyclic loading, environmental conditions on CP; CP in advanced materials; industrial application of CP concepts and data; and so on. The aim of the Conference was not only to discuss the substantial international progress achieved in the field of crack paths, but also to illustrate how to apply research results to industrial practice. The constructive and vibrant discussions taken at the end of each presentation are a further confirmation of the high scientific quality of the event as well as of the significant level of interactions among the participants. According to the CP Conference tradition, all presentations were video-recorded, and they are now available in the ESIS YouTube channel ( https://www.youtube.com/playlist?list=PLqdhWx9Ll8U7S-ih0-0imydDGSH8Q-RIq ). During the CP2021 Conference, Dr Mahsa Sakha was awarded with the TC3 Young Scientist Award for her presentation entitled “On reliable prediction of fracture path in anisotropic rocks”. This special issue of Procedia Structural Integrity collects ninety papers related to many presentations made during the CP2021 Conference. The number and the quality of the papers is an important sign of the good health of the fracture and fatigue materials / structures community. We hope to meet you soon in presence in the next “Crack Paths” Conference and TC3 activities.

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect StructuralIntegrity Procedia 00 (2019) 000–000

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ScienceDirect

Procedia Structural Integrity 39 (2022) 333–346

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of CP 2021 – Guest Editors Abstract When there is bearing misalignment, shaft bow, mass unbalance, or cracks, rotors are considered faulty. The defect caused by cracks is the most difficult of the four to diagnose since cracks are not apparent. Cracks can’t be identified with displacement gauges, and they can't be fixed with balancing machineries. As a result, a rotor with cracks poses the greatest risk when compared to rotors with any other flaw. Signal-based methods, parametric methods, model-based methods, and modal-based methods are all used to detect cracks. Extensive research has gone into establishing various methodologies and procedures to efficiently model and analyse rotor cracks during the last four decades, resulting in countless technical papers on the subject. For the benefit of the research community, a brief periodic review of such a corpus of work is needed. This paper conducts a chronological review of cracked rotor literature of the last decade, spanning the years 2010 to 2021. On their research, methods, and outcomes, the experimental investigations, mathematical modelling, and computation algorithms are given in condensed form. An attempt has been made to note the potential areas of further research for each piece of literature. © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of CP 2021 – Guest Editors Keywords: Crack identification; Crack localization; Finite element; Wavelet transform; Jeffcot/de Laval rotor; Active magnetic bearing ' y 7th International Conference on Crack Paths A Decadal Review of Various Modelling and Analysis of Cracked Rotors Nabam Teyi a *, Sandeep Singh a a Department of Mechanical Engineering, North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh 791109, India N

* Corresponding author. Tel: +91 8974393401 E-mail address: nbtnerist@gmail.com; nbt@nerist.ac.in

2452-3216© 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of CP 2021 – Guest Editors

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of CP 2021 – Guest Editors 10.1016/j.prostr.2022.03.103

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1. Introduction A rotor is an essential component of nearly all mechanical systems. A rotor unit is a shaft that is supported by bearings and has a flange, a disc, or a gear running down its axis. There could be multiple discs or other items mounted to the shaft. A rotating shaft (a rotor) might be regarded the heart of any machine system because practically all machine systems involve some motion transmission from linear to rotary or vice versa. Rotor behaviour can be found in turbo machines, compressors, heat exchangers, generators, vehicles, turbines, pumps, marine and aircraft engines, and so on. Although these machines are fairly durable and well-designed, shafts in operation are occasionally susceptible to significant flaws that appear without warning. When there is bearing misalignment, shaft bow, mass unbalance, or cracks, such rotor shafts are considered faulty.

Nomenclature AMB Active magnetic bearing ANN Artificial neural network BF Bayesian fusion CMS Component mode synthesis DDC Direct digital controller EL Energy location EMD Empirical mode decomposition FD Fractal dimension FE Finite element FFT Fast Fourier transform

GMA Gaussian multiscale analysis GSM Gapped smoothing method KICA Kernel independent component analysis LCF Low cycle fatigue MAL Modal analysis location MRA Multi resolution analysis ODS Operational deflection shape POM Proper orthogonal modes PSD Power spectral density RBF Radial basis function SCDS Superharmonic characteristic deflection shape SDE Stochastic differential equation SVD Singular value decomposition TOA Time of arrival

WNN Wavelet neural network WPT Wavelet packet transform WT Wavelet transform

1.1. Types of rotor defects Rotor defects due to misalignment: Here the axes are not collinear as shown in Fig. 1. It means that the shaft is not in the exact positional state as it is intended to be due to wrong fixturing, or due to inconsistency in the bearings’ dimensions or positions.

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Fig. 1. Rotor defect due to misalignment.

Rotor defects due to bow: Here the axes of the bearings or bushings that support the shaft are perfectly in alignment, i.e. their axes are collinear, but, the shaft itself is not perfectly straight throughout its length (Fig. 2). Meaning, there is some bending of the shaft somewhere along its length, mostly around the middle portion. This may occur due to wrong manufacturing of the shaft or rough handling of the structure or overloading. Continued operation of such a bowed shaft is dangerous for the machine of which it is part of.

Fig. 2. Rotor defect due to bow. Rotor defects due to mass unbalance: Here the defect is due to mass unbalance due to non uniform distribution of mass of either the shaft material or the disc material or both. This is a common phenomenon in any material in its natural state of being (intrinsic) due to various inconsistencies and complexities in the manufacturing or extraction of the materials. This uneven distribution of mass in materials results in a little shift of the actual centre of mass from the geometric centre of the component. This small distance between the mass centre and the geometric centre is called eccentricity (Fig. 3). Also, during the life of the rotor in its static state there is a natural possibility of accumulation of dust or other substance on some locations on its surface, or chemical reactions on its surface due to environmental situations, which further accentuates mass unevenness. And during the rotor’s dynamic state, there is a natural phenomenon of wear due to friction adding to the mass unevenness.

Fig. 3. Rotor defect due to mass unbalance.

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Rotor defects due to crack(s): Here the defect in rotor is due to presence of crack or cracks either in shaft or in the disc or in both. A crack is a small opening like a slit cut on the rotor’s surface which may occur due to poor manufacturing of the rotor material, or which occurs during the operating period of the component (Fig. 4). Such cracks are so small to the tune of microns that it is impossible to detect its presence visually even just after the rotor is freshly manufactured. Cracks are definitely impossible to be detected visually in a rotating rotor. Presence of cracks in a rotor system is very harmful for its health.

Fig. 4. Rotor defect due to crack. Defect due to cracks is the most complex amongst the four. Cracks are just not visible, neither in the static condition nor the dynamic condition of the rotor. Cracks can neither be detected using displacement gauges nor can these be corrected using balancing machineries. Therefore a rotor with cracks is the riskiest in comparison with rotors with any other defect. Even a freshly manufactured shaft which lets say, is free from any defect, still would have some deflection about its centre due to its own weight. And the longitudinal fibers of the shaft material experience, both tension for certain time, compression at other times, in every single rotation. This is similar to R. R. Moore rotating beam fatigue model. Similar model has been used to study fatigue life of micro arc oxidation coated 6061-T6 Al alloy by Ramakrishna et al. (2017) and Madhavi et al. (2019), and to study high cycle fatigue behaviour of hard turned 300M ultra-high strength steel by Ajaja et al (2019). With continuous rotor spin, the shaft motion may induce a crack. The basic reason of emphasizing cracks in rotors is to avoid unwarranted and uneconomical shutdown of the entire machinery for the crack analysis. Therefore, the required work has to be done in situ. However, difficulties are inherent to analyse any dynamic system. Also the roundness of the shaft and disk in rotor further complicates the study, as any physical reference point in the system is impossible to fix. Therefore, cracks are identified by signal based methods, by parametric methods, by model based methods and by modal based methods. Signal based methods use some sensors and instrumentations for data acquisition and signal processing to obtain solutions. Parametric methods represent the shaft rotor system as a function of mass, damper and spring. Here the mass resists acceleration as in Newtonian force, the damper resists velocity as in viscous force and the spring resists deflection as in spring force, and together, they make up for the dynamic force in the system as a function of time. In model based methods, there is no physical involvement and every effect is represented by a mathematical equation. In modal based methods, the inherent dynamic characteristics of the shaft rotor system in forms of their natural frequencies and mode shapes are used to formulate a process for its behaviour. During the last four decades, significant study has been conducted into the development of various problem solving strategies for the efficient management of rotor cracks, which has resulted in a large number of technical papers on the subject being published. As a result, a succinct periodic review of such a corpus of work is desperately needed. Sabnvavis et al. (2004) presented a review article of the published papers on crack shaft detection and diagnostics from 1990 to 2003, which was published in the The Shock and Vibration Digest. Also, Kushwaha and Patel (2020) conducted an exhaustive study of methodologies and modelling approaches in crack analysis the previous year. Additionally, this research conducts a review of cracked rotor literature from the recent decade, specifically from the years 2010 to 2021, in chronological order.

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1.2. Analysis of cracks Crack detection or identification provides a qualitative indicator of the presence of a fault in the machine, whereas crack classification determines if the fault is a rotor crack or another type of fault. It is possible to determine the location of the crack in the rotor using crack localization; however, it is more difficult to determine the shape and size or severity of a crack using crack assessment. Crack prediction is a method of estimating the remaining useful life of a rotating component. 2. Relevant literatures from 2010 to 2012 Karthikeyan and Tiwari (2010) developed flaw algorithm for detection, localization and sizing of flaw in circular beam on forced response measurement. They experimentally obtained the displacement responses of the flawed beam using transducers and proximity sensors. FE model was developed as well. Flaw model was in good agreement with the experimental results. However, they overestimated the flaw size due to inherent low sensitivity owing to the beam being very thin and relatively long. Based on previous research, Srinivas et al. (2010) projected that spinning machinery would exhibit higher vibration frequencies if it had unbalance and a crack in the shaft. A three-layered networked ANN trained with the Levenberg-Marquardt algorithm and the wavelet transform processed the data. The WT and ANN were used to accomplish three distinct tasks: data collection, feature extraction, and fault detection. Barella et al. (2011) studied a 60 MW thermal power plant rotor turbine failure. After approximately 10 years of operation, the CrMoNiV steel rotor failed. The cause of the crack was discovered not to be corrosion or fretting fatigue but rather a heat gradient during startup and the resulting high stress concentration which was amplified by the indentions. Based on fractography analysis, Momcilovic et al. (2011) investigated a major failure of a 28 MW horizontal hydro turbine shaft in terms of load carrying capacity of critical radius, and concluded that the seal box design resulted in constant flow of river water in the critical radius zone, resulting in corrosion fatigue cracks and major turbine shaft failure. In order to assess the rotor's health, Chana et al. (2011) used an eddy current sensor and Reasoner software to isolate the crack. LCF spin-pit testing was performed on a pre-flawed disc. The QinetiQ eddy current sensor based tip timing device collected time of arrival data to evaluate blade movement induced by disc crack propagation. A probabilistic model of the component's remaining useful life was developed to account for measurement uncertainty. Cheng et al. (2011) found that broad equations of motion for a Jeffcott rotor/de Laval roror with a transverse crack acknowledged the constraints of weight supremacy. The shape of the fracture in the Jeffcott rotor was modelled with fixed and rotating coordinates, and breathing cracks with and without weight dominance. The numerical analysis of a fractured rotor was done at critical speed. This speed was determined by the unbalance orientation angle of a damaged rotor. On the other hand, Dong and Chen (2011) introduced crack identification methods for one unknown crack case and two unknown cracks case for stationary rotors. The FE model used transfer matrix analysis, local flexibility theorem, and contour diagram analysis to locate cracks. Changes in Eigen frequencies of broken rotors were dependent on crack closeness to mode shape nodes, and these changes monotonically increased with crack depth for rotors with low slenderness ratio. Kulesza and Sawicki (2012) suggested a rigid Finite Element (RFE) approach to represent rotating machinery. The RFE model was verified using the Campbell diagram. The breathing mechanism was intuitively explained by modest scalar stochastic differential equations (SDEs) stiffness changes. The eccentricity value and its angular location influenced the damaged rotor’s breathing behaviour. Ricci and Pennacchi (2012) explored system anisotropy and crack position using a model of a genuine hyperstatic rotor with several degrees of freedom. The generator was modelled via FE. For the generator model, they employed linearized stiffness and damping coefficient analysis, and steering function for crack breathing. The Floquet analysis revealed that there was no instability. And the behaviour matched previous reports of significant cracks in generators. A new method for analysing the nonlinear dynamics of Jeffcott rotors/de Laval rotors was proposed by Rubio and Fernández-Sáez (2012). The linearized equations of motion were solved implicitly by Newmark. The nonlinear rotor orbits and resonance curves were studied. The model was efficient and saved time (upto 100 times). However, when the vertical whirl amplitude exceeded the shaft weight static deflection, the simplified quasi-static stiffness matrix approaches failed. Singh and Tiwari (2012) investigated the influence of steps in the shaft on crack detection near and distant from the step. They imitated the rotor system mathematically. Rotor parameter normalised quadratic coefficients were studied. Their programme spotted cracks at

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the step despite noise in forced answers. The key takeaways of the above mentioned literatures from 2010 to 2012 as prospect for further research are presented in Table 1.

Table 1. Analysis of literatures between 2010 to 2012 for work progress Author(s), year Possibility of improvement Karthikeyan and Tiwari, 2010

End conditions (such as cantilever) and flaw models (which take defect thickness into account along with flaw depth) could be changed to test the suggested method. Smaller defects in algorithms may be developed.

Srinivas et al., 2010

May be tried on more applications and seek the success rate percentage for update of the model.

Barella et al., 2011

To be even more precise, steam turbines in use should undergo accurate non destructive testing to check for early stage fatigue cracks. The seal box has to be redesigned to prevent water from entering the shaft-flange transition zone. Non destructive inspection of the transition zone status at a periodical interval should be reformed with increased frequency. There must be a better understanding of the numerous types of faults that can exist in a motor assembly and how to distinguish between them utilising the timing system at the tip. It's important to know the differences between the characteristics of a breathing crack and an open crack on the rotor, because diagnosing a cracked rotor solely based on changes in the critical speed can lead to inaccurate results. It's possible that one can find a solution to this problem.

Momcilovic et al., 2011

Chana et al., 2011

Cheng et al., 2011

Dong and Chen, 2011

Non stationary rotating rotors may be considered for further investigation and model development.

Kulesza and Sawicki, 2012

Amplitudes of combination frequencies and induced coupled axial and torsional vibrations are very low and these may be decently elevated for further study. Results obtained by the present Floquet analysis cannot be assumed as valid for all rotating machines affected by transversal cracks. So here is the further scope for research.

Ricci and Pennacchi, 2012

Rubio and Fernández-Sáez, 2012 Singh and Tiwari, 2012

The technique may be improved to obtain better and more refined results.

More steps and cracks may be included in the model to reproduce real life cases.

3. Relevant literatures from 2013 to 2015 Guo et al. (2013) proposed an early crack detection method for Jeffcott/de Laval rotors with transverse breathing cracks. The cracked rotor's dynamic behaviour at 1/3 and 1/2 sub-critical speeds was studied using empirical EMD and WT spectra. An early detection of the breathing crack might be made by varying the average amplitudes of the 3× and 2× super-harmonic components. Liu and Jiang (2013) studied the properties of normal, transverse, and slant fractured rotors under torsional excitation. They also evaluated broken rotors with transverse and slant cracks for lateral and torsional vibrations, as well as torsional excitation. It affected 1× and coupled frequency, while the slant crack affected 2×. The crack also influenced the torsional responses. Wang et al. (2013) combined KICA with WNN to locate the source of cracks in turbine blades. On-site acoustic emission acquisition equipment was used to examine KICA input parameters. TOA, EL and MAL were evaluated. They accurately identified all crack regions, lowered data transmission and storage costs, and improved source location. With a notch, Zapico-Valle et al. (2013) applied a model-based technique for rotor fracture location and assessment. This was done while a 3-D finite element model generated data for the net. The sensitivity analysis was done for any notch size and position. For notch depths more than 20% of the rotor diameter, the model predicted position and depth, as well as rotor blind areas. Wan et al. (2014) used computer simulation to investigate the impacts of tooth crack propagation on the vibration response of a gear-rotor system with spur gears in order to determine the influence of gear crack damage on gear case vibration. Dynamic modelling helped decipher the diagnostic information in vibration signals. But the theoretical model was not the test bench. There were some discrepancies between simulation and experiment. Castejón et al.

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(2014) used MRA and an ANN to detect rotating machine faults. Three stages of filter analysis were used, as was the Jeffcott/de Laval rotor model. A supervised RBF Network was tested. MRA and RBF formed an automated monitoring system with online diagnosing capacity. Ebrahimi et al. (2014) developed a new continuous model for flexural vibration of open-edged rotors. They compared the first critical speed ratio for a fractured rotor to the exponent degradation rate. An accurate FE cracked rotor model was created to anticipate dynamic behaviour of fractured rotors to avert catastrophic failures. Haji and Oyadiji (2014) proposed a new method for locating cracks in non-rotating rotors using only orthogonal natural frequencies in both horizontal and vertical lateral bending vibration planes. An intact and cracked rotor was FE modelled. On the basis of normalised orthogonal natural frequency curves, a fracture detecting technique was devised. The cracks had sharp, notched peaks while the non-cracks had rounded peaks. These qualities aided in locating and identifying rotor cracks. In order to find cracks, Singh and Tiwari (2014) exploited slope discontinuity in the shaft elastic line. For the purpose of crack identification, an experimental set of shafts, supports, and exciters was used, as well as a shaft equipped with a laser vibrometer for comparison. The MCDLA algorithm, which uses multiple crack detection and localization techniques, was put to the test in an experiment. AL-Shudeifat (2015) studied the backward whirl of a cracked rotor using the open crack model. To solve the time periodic cracked rotor system, the harmonic balance approach used Mathieu's equation and a linear time-periodic system. The method beat Floquet's theory's time-consuming application. Open crack excited the backward whirl speeds. Peng et al. (2015) proposed a method for determining the stability of a rotating cracked rotor system by examining bifurcations at boundary points using comprehensive numerical Eigenvalues. They used a numerical transition matrix and a stability diagram. With high degree of imbalance shaft rotational motion, cracked rotor system could barely retain stable motion around first harmonic and sub harmonic resonance. It was stable for a low degree shaft imbalance. Singh and Tiwari (2015) studied the effects of AMB on a rotor-bearing system with a breathing crack. The SIMULINK model responded. The reference signal’s harmonic was plotted. A crack detection technique was developed using FFT analysis. Because the identification system used data from several spin speeds, it was proven to be resistant against signal noise and modelling mistakes. Söffker et al. (2015) compared model-based and signal based techniques for rotating machinery crack identification. The modern model-based technique was Proportional Integral, while the modern machine learning technique was a revolutionary signal-based approach based on Support Vector Machine and wavelets. In contrast, model-based solutions were more flexible to changes in system load and better able to interact with system physics and modelling parameters. Major remarks from the above mentioned literatures for the period 2013 to 2015 as possibility for future research are presented in Table 2.

Table 2. Analysis of literatures between 2013 to 2015 for work progress Author(s), year Possibility of improvement Guo et al., 2013

There is no consideration given to noise. The EMD method's decomposition procedure for super-harmonic

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components can be influenced by noise if the fractures are minor. The impact of noise on fracture detection needs to be studied further in future research.

Liu and Jiang, 2013

A more robust experimentation on similar line may be performed to obtain more behavioral results.

Wang et al., 2013

Number of training samples may be reduced.

Zapico-Valle et al. 2013

Lower notch depths cause instability in the operation. Additional high modes, more precise modal testing, and a more accurate modal identification system could improve these results. There has to be greater investigation into the factors that influence vibration response, such as meshing friction and backlash, and gear manufacturing faults. The appearance of a crack causes violent excitations near the theoretical critical speed. Use of MRA ascertains that noise doesn’t affect this method. However, scope for improvement exists here. The proposed model is capable of further modifications such as implementing a breathing function to model breathing cracks or considering the gyroscopic effects. It's not a good idea to use a roving disc that's less than 8.0 percent of the shaft mass. Using a roving disc with a mass to area ratio greater than 20.4% increases the risk of the crack spreading and deepening. Possibly some investigation can be done in this area. It is possible to test the algorithm's performance for rotated cracks using a smaller fracture size to see if it detects the rotation.

Wan et al., 2014

Castejón et al., 2014

Ebrahimi et al., 2014

Haji and Oyadiji, 2014

Singh and Tiwari, 2014

AL-Shudeifat, 2015

More parameters may be tested to obtain more varied and more determinant results.

Peng et al., 2015

Fatigued rotor cracks can cause unstable behaviour and bifurcations, especially if the mass eccentricity is unbalanced at a high level while rotating horizontally. This might use some work.

Singh and Tiwari, 2015

Using the finite element method, stiffness in the multi-degree-of-freedom system can be included.

Söffker et al., 2015

More machine learning classifiers like Random Forest (RF) classifier, Logistic Regression (LR) or Naïve Bayes (NB) may be taken up for comparison.

4. Relevant literatures from 2016 to 2018 Ferjaoui et al. (2016) used a nonlinear model to investigate the effects of a transverse crack in a rotor supported by two journal bearings. Bifurcation diagrams and Poincaré maps were employed. Half rotational frequency components in the spectrum and their amplitude rise were regarded markers of rotor cracks. Gómez et al. (2016) used vibration signals to detect cracks in a rotating shaft. WPT energy used the ‘Daubechies 6’ wavelet. Individual level energies trained RBF-ANNs. The faster speed (60 Hz) produced the best outcomes in terms of success rates and cost. The false alarm rate was 1.77 percent and fracture levels exceeding 1 were reliably recognised. A rotating shaft with various crack depths and positions was researched by Gómez et al. (2016). The tests were done in a Rotokit setup at various rotation speeds. WPT was used to evaluate the signals. At the greatest speed tested, the energy of the 3× component of rotation speed was the best indicator of crack (60 Hz). The 3× energy rose for Middle Section and reduced for Side Section. Zhiwen Lu et al. (2016) proposed a proper orthogonal decomposition (POD) based method for multicrack localisation in rotors. They used FD, GSM and ODS. Cracks in the orthogonal modes caused discontinuities in POMs. The FD and GSM localisation results for the rotor with several breaks of differing depths were excellent. Zhiwen Lu et al. (2017) proposed a new crack localisation approach for stepped rotors based SVD in frequency domain. A waterfall plot of vertical response was used, as was a PSD matrix. The method worked well for single or multiple fracture localization in stepped rotors with the right rotating speed and super-harmonic component(s). To study a cracked rotor with an open edge fracture subjected to gravity and imbalance forces, Ebrahimi et al. (2017) developed the method described here. They looked at how the orbit changed with changes in rotor speed. A modified Galerkin approach was used to find each response. These results could be utilised to identify rotor cracks. A Jeffcott/de Laval rotor and an EMD based fracture detection approach were tested experimentally by Guo et al. (2017) They used FFT analysis. During the transit, the cracked rotor was whirled. The super-harmonic component variation in the 1/3

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and 1/2 subcritical zones were found to be a stable feature for crack detection. For a rotor ball bearing system with a transverse crack on the rotor, Upadhyay et al. (2017) employed contact deformation theory. Bifurcation diagrams explored the effect of crack depth and size on rotor ball-bearing system dynamics. The system grew increasingly unstable as the fracture depth increased, yet as the response amplitude increased, the critical rotating speed reduced. S. Singh and Tiwari (2018) investigated AMB-supported flexible rotor systems. The identification techniques were developed using mathematical modelling of the rotor system. The algorithm was tested for robustness in a basic rotor system for measurement noise and bias errors in system parameters. A new method for simulating cracked rotor vibration was described by Spagnol et al. (2018) without assuming weight dominance. a chordal picture of decay was drawn by them. The area moment of inertia and stiffness matrix of the imbalanced broken rotor were studied. The critical speed and peak amplitude of the weight-dominant model moved virtually sinusoidally from 0° to 180°, but the proposed model's critical speed and peak amplitude gradually plateaued when the eccentric mass was placed at angles larger than 90°. The impacts of unbalance on the nonlinear dynamics of the cracked rotor were studied by Wang et al. (2018) using 3D finite element models of the shaft and the breathing crack. The CMS approach was used to minimise model order and boost computing performance. This study examined the effects of distributed unbalance on the crack breathing behaviour and the rotor's dynamic response. Based on bending theory, Xie et al. (2018) suggested an approach for computing the stiffness breathing functions of fractured Jeffcott/de Laval rotors. Time-domain waveforms, phase waterfall graphs, and time–frequency amplitude spectrums were used. The phase waterfall diagram detected high-order frequency components of broken rotors. The radial pattern in phase waterfall plots indicated fractured rotors and may be used for crack monitoring. Salient notes from the above mentioned literatures for the period 2016 to 2018 as option for potential research are presented in Table 3.

Table 3. Analysis of literatures between 2016 to 2018 for work progress. Author(s), year Scope for improvement Ferjaoui et al., 2016

The proposed method could be tried to understand the effect of a slant crack as well.

Gómez et al, 2016

The methodology proposed may be integrated in industrial equipment to study condition monitoring.

342 10

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Gómez et al., 2016

It has applications in condition monitoring under stationary conditions. Research can be undertaken for similar studies in a dynamic system. In order to identify vibration-based damage, measurement technology is largely reliant. The proposed method would be useless if it didn't have accurate vibration data. Here’s where things can be done better. Models with breathing cracks can be made using this method by substituting a breathing function in the equations. It is possible that more trials with smaller cracks be conducted in order to discover the experimentally detectable minimum crack depth using the proposed method. It is also possible to investigate how the initial fracture width affects the cracked rotor system’s dynamic behaviour.

Zhiwen Lu et al., 2016

Ebrahimi et al., 2017

Guo et al., 2017

Upadhyay and Kankar, 2017

Other bearing systems may be studied with the same model.

Zhiwen Lu et al., 2017

Validation of the proposed approach by experiments in laboratory is to be done.

Singh and Tiwari, 2018

Further research is needed to develop and validate this condensation strategy using experiments on a multi disc rotor using AMB.

Spagnol et al., 2018

The procedure may be explored for rotors with multiple cracks.

Wang et al., 2018

There are concerns with this strategy when dealing with extensive cracks because the rotor's dynamic response is no longer much smaller than the static deflection. This could be the subject of some research.

The procedure may be explored for non Jeffcott rotor systems.

Xie at al., 2018

. 5. Relevant literatures from 2019 to 2021

A novel definition of instantaneous whirling speed of axis orbit was defined by Xie et al. (2019). This new feature improved the ability to discern between regular and cracked rotor systems. The steady state vibration response of a cracked system in a Bently KR4 Rotor Test Rig was recorded. Line speed curves for normal and cracked systems were employed here. The relative whirling speed of a fractured rotor system fluctuated between two maxima and minima. The action of the extra stiffness excitation on the normal conversion of kinetic energy to potential energy induced transient change of the relative whirling speed. Hein and Jaanuska (2019) predicted an Euler–Bernoulli cantilever subjected to transverse free vibration using Haar wavelet discrete transform, ANNs and random forests. To evaluate Bayesian regularisation and the Levenberg–Marquardt algorithm, a feed-forward back propagation ANN was used. The data set of eight natural frequency factors provided better crack depth predictions, while the data set of eight Haar wavelet coefficients produced better crack location predictions. Shravankumar and Tiwari (2019) used eddy current proximity probes to investigate a transverse fatigue fracture in a universal tensile machine for fatigue loading. According to the estimates, the rigidity of the intact shaft was lowered by 0.5 percent due to the crack. AL-Shudeifat (2019) examined numerically and experimentally the produced backward whirl in intact and fractured rotor systems. The broken DDC system whirl orbits, the horizontal whirl amplitude time histories, and experimental whirl amplitudes were used. A critical forward whirl speed was reached, and then whirl amplitudes dropped fast, with further low-level transient peaks of forward whirl orbits following closely behind them. There is uncertainty in a fractured hollow-shaft rotor system, hence Fu et al. (2020) created an Uncertain Response Surrogate Function (URSF). The crack signatures for the samples were computed utilising an evolution diagram of the cracked shaft cross-section, URSF based on Chebyshev collocation points, and crack signatures with deterministic parameters. The surrogate function was accurate and resilient, allowing for an effective technique and advice for crack diagnosis in unclear situations. Using the crack-induced local distortions in multiscale SCDSs, Zhiwen Lu et al. (2020) proposed an innovative crack localization approach for stepped rotating rotors based on BF. The GSM, Teager energy operator, and BF were used to construct a new Damage Index Gaussian multiscale analysis. They used a simple rotor bearing system experiment rig, as well as an experimental rotor and sensor setup. The proposed method for single or multiple crack localization in stepped rotors proved effective, accurate, and robust, and it has a lot of practical applications. Torsional oscillation was used in an experiment conducted by Liu and Jiang (2020), who were looking

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for the features of torsional vibration as well as reasons for crack failures in a cracked rotor system. The fundamental frequency and harmonic components of the transverse cracked rotor system had larger amplitudes (particularly for the open crack), while the slant fracture had substantial later-torsional vibration (especially for the breathing crack). According to Ranjan et al. (2021), the Multiple Harmonic Influence Coefficient Method (MHICM), full-spectrum rotor responses and excitation forces are required to establish rotor fault characteristics. Without understanding the rotor system, it is feasible to predict additive fracture stiffness, residual unbalances, or internal damping. Since AMB was a part of the rotor system, it was able to commence multi-harmonic excitation. AL-Shudeifat and Alhammadi (2021) investigated negative potential energy content analysis in cracked rotors whirl response in Jeffcot/de Laval model. The numerical and experimental whirl responses of their investigation showed strong negative stiffness content throughout a wide range of rotational speeds and unbalance force vector angles. As a result, the broken rotor system exhibited large amounts of negative stiffness content, putting it at danger of premature collapse. Pertinent observations from the above mentioned literatures for the period 2019 to 2021 as pointers for probable research are presented in Table 4.

Table 4. Analysis of literatures between 2019 to 2021 for work progress Author(s), year

Scope for improvement

Xie et al., 2019

Fracture flaws can be missed because of the confusion caused by instantaneous-whirl characteristics such as misalignment, oil whirl, or rubbing. The more the diagnostic markers that can be analysed to complement one another, the better the crack diagnosis will be able to be made.

Hein and Jaanuska, 2019

A few other machine learning models may be trained for comparisons.

Shravankumar and Tiwari, 2019

The crack may be modelled using non-linear or stochastic methods, and parameter estimation can be carried

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out.

Al- Shudeifat, 2019

In the future, researchers may look at the backward whirl phenomenon in both undamaged and broken rotor systems. Crack diagnostics methods may be wrong if they are hampered by uncertainty, which can lead to resonance changes. It is possible that a second, more focused study be conducted to find a solution. The method can only be used on cracked rotors, hence the presence of cracks must first be verified using a fracture detection method before the suggested crack localization method be used. More measurement points are needed for better crack localization accuracy, hence sophisticated testing techniques like distributed optical fibre sensing technologies may be used.

Fu et al., 2020

Zhiwen Lu et al., 2020

Liu and Jiang, 2020

The analysis may be extended to circumferential crack cases.

Ranjan et al., 2021

In addition to residual unbalances, the system may identify other multi-harmonic errors such misalignments. AMB can identify different flaws by varying the magnetic stimulation force.

AL-Shudeifat and Alhammadi, 2021

The procedure may be explored for non Jeffcott rotor systems.

6. Conclusion A thorough examination of the crack detection, identification, localization, assessment, and prediction modelling methodologies, experiments, and analysis methods developed over the last decade has been attempted. For readability and to keep the reader’s attention, the review is organised chronologically. The long-term study, which runs from 2010 to 2021, is divided into four three-year segments. According to the study, crack analysis is a dynamic and ever changing field. Many tools, including EMD, WPT, FD, KICA, PSD, GMA, MRA, MAL, SDE, WT, and others, have been used for modelling and analysis. Each year, the work of a select few authors is constantly improved by the addition of new techniques. Over the last decade, apart from several forward modelling and inverse techniques, new algorithms such as the Multicrack Detection and Localization Algorithm (MCDLA), the Multiple Harmonic Influence Coefficient Method (MHICM), and the Uncertain Response Surrogate Function (URSF) have been developed. Traditional FE modelling is still one of the most commonly used modelling approaches for numerical analysis and experiment validation, though ANN is the preferred method for data training. The Jeffcot/de Laval rotor is still a favourite among rotor experts. This review article is written in the hope of providing a concise guide to help researchers just starting out in the field of crack analysis pick the right research objectives, as each table in the document allows for possible work extension. Acknowledgements The authors like to express their gratitude to their affiliated institute for providing the essential assistance in gaining access to journal articles for this review. Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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