Cracked Rotor Research Articles

Research on vibration signal decomposition of cracked rotor-bearing system with double-disk based on CEEMDAN-CWT

In the actual working process, the source of vibration signal is not only the rotor itself, so the detected vibration signal will become complicated. This complex signal makes it difficult to accurately measure the existence of crack. In this paper, a novel method, which includes complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and continuous wavelet transform (CWT), is proposed to analyze the cracked rotor-rolling bearing system. The CEEMDAN-CWT successfully separates the vibration signal of the rotor itself from the original signal and provides results similar to the simulation signal. At the speed below 2000 rpm, the 2X frequency difference between cracked rotor and healthy rotor in CEEMDAN-CWT spectrum is about 1, while the difference of FFT spectrum of original signal is about 0.6, which shows the superiority of the novel method in extracting rotor vibration signals from complex vibration signals.

Numerical and experimental analysis on the whirl orbit with inner loop in cracked rotor system

Cracks in rotor systems are generated because of internal as well as external heavy loading conditions. The external loading conditions could be attributed to thermal gradients (such as in turbomachinery) or other environmental conditions that result in cracks developments. The internal loading conditions can be attributed to cyclic fatigue loading during continuous and recurrent shaft's running which is the most common cause for cracks propagation. The presence of cracks in rotor systems induces nonlinearities into the system which affects its whirl response. Many published literature on cracked rotors have indicated that when the rotational speed is at sub-critical resonance of order 1/n (1/2, 1/3,1/4, etc.…) of the critical rotational speed, the fundamental whirl orbit takes patterns including inner loop/loops of order (n-1) or outer loop/loops of order (n+1) depending on the critical whirling direction. The present study investigates the strong impact of the magnitude of unbalance force on whirling pattern with inner loop in a cracked rotor. Numerical analysis is carried out on the mathematical model of the considered cracked rotor. The unbalance force magnitude is observed to be the main factor affecting the inner loop pattern in the whirl orbit rather than the ½ of the critical resonance speed. Accordingly, the appearance of inner loop in shaft's whirl orbit due to crack propagation in the rotor system is found here to be present before and after passing through resonance speed. This inner loop whirl orbit pattern is not restricted to be associated with ½ of the critical rotational speed as believed in plenty of literature. This kind of whirling is observed to be strongly depending on the unbalance force magnitude rather than the subcritical resonance speed. The experimental results also validate the numerical simulation findings. Therefore, the whirl orbits of the cracked rotor can be categorized into pre-resonance whirl orbit (Pr-WO), resonance whirl orbit (R-WO) and post-resonance whirl orbit (Po-WO) based on the magnitude of the unbalance force. The resultant numerical and experimental findings on the whirl orbit with inner loop can provide a robust insight into the cracked rotor whirl behavior.

Dynamic analysis of slant cracked rotor system considering nonlinear oil film force.

In this paper, considering the combined effects of nonlinear oil film forces and cracks on the rotor-bearing system, the differential equations of motion with 4 degrees of freedom are established by Lagrangian method. Then, the Lundgren-Kutta method is used to solve them and the results of the model are compared with the experimental data. The study demonstrate that the cracked rotor-bearing system is relatively stable at subcritical speeds, mostly in the period-1 motion. But near 1/3 of the critical speed, there is an inner loop in its whirl orbit and a significant increase in the 2x frequency component. When the system speed rises to the region near 1/2 of the critical speed, though the bifurcation motion and a relatively high 2x frequency can be observed, there are no other reliable fault characteristics. The study proves that the rotor crack fault diagnosis method based on the whirl orbits is convincing for slant cracked rotors.

Rotor crack breathing under unbalanced disturbance

Rotor cracks are a type of failure seriously affecting the safe operation of rotating machinery. It has been reported that cracks under the dominant effect of gravity produce a breathing effect and consequently result in an abnormal vibration of the rotor. However, in practice the rotor cannot avoid unbalance disturbances. As the rotational speed of the rotor continues to rise, unbalance replaces the dominant role of gravity and changes the breathing pattern of cracks. Therefore, this work aimed to study the crack breathing process during the acceleration phase of an unbalanced cracked rotor by coupling the strain energy release rate (SERR) technique with the neutral axis (NA) method. It was found that when the unbalance is dominant, the fracture surface remains fixed instead of being uniformly open and closed. That is, during the entire acceleration phase of the rotor, the crack undergoes a process from uniform breathing to breath-hold breathing. The change of breathing mode induces the whirl phenomenon in the cracked rotor, which gradually disappears with increasing unbalance. This whirl phenomenon can be combined with superharmonic resonance characteristics as an assessment tool for crack fault diagnosis. The above findings are helpful in diagnosing rotor cracking faults under unbalanced disturbances.

Dynamic Behavior Analysis of a Rotating Shaft with an Elliptical Breathing Surface Crack

PurposeIn this paper, dynamic behavior of a rotor system with an elliptical breathing crack that simulates the real shape of the crack front is investigated.MethodsA finite element model of the cracked rotor system is developed. The crack breathing mechanism is modelled based on an improved breathing model which considers the inclination of the neutral axis of the cracked element cross-section during shaft rotation. Harmonic balance method is used to solve the equations of motion of the rotor system for steady-state response characteristics. The effect of some parameters such as crack depth, crack shape factor and the spinning speed is investigated.Results and conclusionsThe results show that the unique whirl orbits behavior during passage through the subcritical speeds serve as a key indicator of crack presence in the shaft. The effects of the crack front curvature and the breathing model are revealed. The value of shape factor affects the whirl orbit characteristics such as size of the inner or outer loops and the amount by which the orbits rotate while crossing the subcritical speeds. The presented model considering the real crack front shape may contribute towards improved modelling of cracked rotors and better interpretation of measured vibration response.

A novel method for rotor fault diagnosis based on deep transfer learning with simulated samples

For solving the problem of data without failure samples, a novel transfer unsupervised learning method called classifier constrained domain adaptation network (CCDAN) is proposed for extracting transfer characteristics from simulated samples by theory model for experimental rotor fault diagnosis. Firstly, a dynamical model of Jeffcott rotor with crack fault is established and the achieved vibration responses of the system are used as generated simulation samples. Then, the multilayer convolutional network and multiple-kernel maximum mean discrepancy (MK-MMD) are adopted to extract similar characteristics between source and target domains. Finally, two independent classifiers are designed to constrain the features which have fallen near the decision boundary in network learning, which could effectively increase the accuracy and promote the fault identifying generalization. The proposed CCDAN method is verified through two unsupervised transfer tasks of crack rotor fault datasets. The comprehensive experiment analyses conclude the proposed method can learn the transferable characteristics of rotor crack fault diagnosis and its classification accuracy is superior to the existing intelligent transfer network of fault diagnosis.

Novel energy identification method for shallow cracked rotor system

Many factors like period stress or fatigue may lead to cracks in the rotating shaft which can cause economic losses and accidental risk. Early crack faults will introduce very slight local changes in the whole rotor system. And the monitoring data on rotor systems are disturbed by multiple factors. These problems may make subtle fault information be ignored, resulting in the collection of a possible rotor fault becoming tougher. To overcome such issues, novel energy methods including the vibration energy analysis and the 3D energy model representation are presented to investigate the rotor system with transverse crack. For the rotor system with a shallow crack, the energy response analysis shows the existence of shallow cracks mainly affects the peak response values. Meanwhile, the 3D energy model is used to visualize the fault characteristics. The results show that even shallow cracks can cause special phenomena in the 3D energy model, which can promote the identification of crack faults more accurately. The influence of parameters on rotor vibration energy is studied and the corresponding results are obtained. To validate the theoretical analysis results, relevant experiments are applied. The results show that the experimental results agree with the theoretical analysis. The conclusions achieved in this paper can provide a reference for fault diagnosis of rotor systems in engineering practice.

Numerical and experimental study on quantitative assessment of multiple fault parameters in a warped internally damped rotor with a transverse fatigue crack integrated with an active magnetic bearing

This work aims to apply experimental data in the multi-fault identification algorithm developed for an internally damped warped cracked rotor system integrated with an auxiliary active magnetic bearing (AMB).A quantitative assessment of additive stiffness due to crack, unbalance, and residual bow with their orientations, multiplicative fault due to residual bow and crack, external and internal (rotating) damping, and AMB parameters that affect the dynamics of the system is done. The rotor experiences multiple harmonics in rotation due to the effect of crack and multiplicative bow-crack fault. To overcome the drawback of removal of residual bow at only 1X harmonic in signal processing, the present work addresses the simultaneous estimation of crack, bow, and multiplicative faults. Measurements of vibrational signalsof shaftand control current from PID controller are taken from the rotordynamic test bench. The multi-harmonic full spectrum amplitudes and phases of forward and backward whirl extracted from the measured test data are fed to theidentification algorithm which estimates fault and system uncertain parameters of fatigue cracked rotor system.This technique can effectively identify simultaneous rotor faults with prior knowledge of some characteristics of the rotor system. The novelty of this work is the identification of shaft residual bow with additive stiffness of crack where the additive crack stiffness is the direct indicator of crack and the magnitude of residual bow is of the permanent bend in rotor defining their severity.

The Improved WNOFRFs Feature Extraction Method and Its Application to Quantitative Diagnosis for Cracked Rotor Systems.

During its operation, a rotor system can be exposed to multiple faults, such as rub-impact, misalignment, cracks and unbalancing. When a crack fault occurs on the rotor shaft, the vibration response signals contain some nonlinear components that are considerably tougher to be extracted through some linear diagnosis methods. By combining the Nonlinear Output Frequency Response Functions weighted contribution rate (WNOFRFs) and Kullback–Leibler (KL) divergence, a novel fault diagnosis method of improved WNOFRFs is proposed. In this method, an index, improved optimal WNOFRFs (IOW), is defined to represent the nonlinearity of the faulty rotor system. This method has been tested through the finite element model of a cracked rotor system and then verified experimentally at the shaft crack detection test bench. The results from the simulation and experiment verified that the proposed method is applicable and effective for cracked rotor systems. The IOW indicator shows high sensitivity to crack faults and can comprehensively represent the nonlinear properties of the system. It can also quantitatively detect the crack fault, and the relationship between the values of IOW and the relative depth of the crack is approximately positively proportional. The proposed method can precisely and quantitatively diagnose crack faults in a rotor system.

Dynamic Characteristics Analysis of a Coupled Multi-crack Rotor System

Abstract This paper establishes a coupled model for multi-crack rotor using Timoshenko beam element with six degrees of freedom, and derives the stiffness matrix in the equations of motion accounting for the coupling between multiple cracks (the interaction between cracks). Then the effects of crack orientation angles (the relative angle between cracks, γ) on dynamic characteristics of the coupled multi- crack rotor near 1/3 and 1/2 subcritical speeds are analysed. The coupling between cracks induces more complex nonlinear dynamic characteristics such as large magnitudes of the super-harmonic components, which can be used as the indicators of early crack and for multi-crack identification. This work has a promotive significance for the application of the model-based method in the field of multi-crack detection of actual rotors.

Classification of a cracked-rotor system during start-up using Deep learning based on convolutional neural networks

This article addresses an improvement of a classification procedure on cracked rotors through Deep learning based on convolutional neural networks (CNNs). At first, a cracked rotor-bearing system is modeled by the finite element method (FEM), then throughout its start-up, the related time-domain responses are calculated numerically. In the following, as a pre-processing stage, continuous wavelet transform (CWT) and Short-time Fourier transform (STFT) are applied on the three various health conditions, i.e. without crack, shallow-cracked, and relatively deep-cracked shafts. The plots of CWT’s coefficients and STFT’s in these various classes are used as the input dataset in Deep learning based on CNNs and the three classes are introduced as the output. AlexNet with 25 layers is employed as the network. The results of the testing phase demonstrated that not only this expanded method has a reasonable capacity in the classification of cracked and healthy rotors, but it also can classify cracked rotors with different crack depths with a negligible error.

Impact of non-synchronous whirl on post-resonance backward whirl in vertical cracked rotors

Certain heavy-duty industrial machinery uses vertical rotating shafts. Such rotating systems typically undergo transient operation phases to reach their nominal speeds; recurrent passage through resonance generally occurs during startup and coast down operations. The Non-synchronous whirl between the shaft rotational speed and its whirling in the whirl orbit in the vicinity of the resonance zones, significantly affecting the breathing mechanism of a propagating transverse crack. Therefore, the appearance of Non-synchronous whirl during the passage through resonance rotational speed activates the crack breathing mechanism. To verify this observation, Jeffcott rotor and finite element models with induced breathing cracks are considered here for geometrically symmetrical and asymmetrical vertical rotor configurations. The mathematical models associated with these systems yield linear time-varying equations of motion incorporating the angular acceleration rate. The appearance of a Non-synchronous is found activating the crack breathing mechanism, which immediately excites the post-resonance backward whirl even with small crack depths in the rotor system. Accordingly, the excitation of post-resonance backward whirl can be considered as a strong indicator of an early crack propagation phase in vertical rotors.

Reliable crack detection in a rotor system with uncertainties via advanced simulation models based on kriging and Polynomial Chaos Expansion

In this study the authors propose to take into account the nonlinear effects induced by the presence of a transverse crack to carry out vibratory monitoring and detect transverse cracks in rotating systems subject to model uncertainties. More precisely, we focus more particularly on the global complexity of the nonlinear dynamic behaviour of cracked rotors and the evolution of their harmonic components as a function of the parameters of a transverse breathing crack (its position and depth) when numerous uncertainties are considered. These random uncertainties correspond to random geometric imperfections (two disc thicknesses), random material properties (Young modulus and material density) and boundary conditions uncertainty (two bearing stiffnesses). The objective of the present work is to identify robust indicators capable of determining the presence of a crack and its status even though numerous uncertainties are present.To conduct such a study, an advanced surrogate modelling technique based on kriging and Polynomial Chaos Expansion (PCE) is proposed for the prediction of both the critical speeds and the harmonic components n× during passage through sub-critical resonances. An extensive study to ensure the validation of the surrogate models and a relevant choice of both the parametric and random Design of Experiments (i.e. kriging DoE and PCE DoE) is proposed. The proposed methodology is applied on a flexible rotor with a transverse breathing crack and subjected to random geometric imperfections and fluctuations in material properties of the rotor system.

Negative potential energy content analysis in cracked rotors whirl response

Appearance of transverse cracks in rotor systems mainly affects their stiffness content. The stability of such systems at steady-state running is usually analyzed by using the Floquet’s theory. Accordingly, the instability zones of rotational speeds are dominated by negative stiffness content in the whirl response in the vicinity of critical rotational speeds. Consequently, an effective stiffness measure is introduced here to analyze the effect of the crack and the unbalance force vector orientation on the intensity of negative potential and stiffness content in the whirl response. The effective stiffness expression is obtained from the direct integration of the equations of motion of the considered cracked rotor system. The proposed effective stiffness measure is applied for steady-state and transient operations using the Jeffcott rotor model with open and breathing crack models. The intensity of negative potential and stiffness content in the numerical and experimental whirl responses is found to be critically depending on the propagation level of the crack and the unbalance force vector orientation. Therefore, this can be proposed as a crack detection tool in cracked rotor systems that either exhibit recurrent passage through the critical rotational speeds or steady-state running.

Experimental Comparison of Response for Healthy and Cracked Overhung Rotor System

Online diagnosis of the rotor system has been of great aid for possible detection of crack. In this paper, experimental vibration response of unbalance cracked overhung rotor system with an open crack is compared to the response of a healthy unbalance overhung rotor system for possible indication of the crack presence, due to change in the dynamic response of the cracked rotor system. The experimental modal analysis results have been compared with the finite element results to validate the accuracy of the experimental setup, followed by the comparison of the spectral response for healthy and cracked rotor system. The change in the dynamic behaviour of the cracked rotor system is studied through the waterfall plot and the colour map plot. A noticeable increase of 27.77% in response amplitude for crack overhung rotor system compared to that of healthy overhung rotor system is observed with unbalance provided to disc. The changes seen in both plots can be utilized for the indication of crack presence in the rotor system.

Research of vibration and crack propagation controls on an asymmetrical cracked rotor

To investigate vibration characteristics and delay crack propagations of an asymmetric cracked rotor, the 3D finite element model of the rotor system with a nonlinear contact method is established. Resonance characteristics of the asymmetrical rotor without a crack and within different locations of a crack are investigated systematically. Numerical results show that a crack affects vibration frequencies and the unstable region of the rotor. Meanwhile, an improved proportional integral differential control method with the electromagnetic actuator is used to accomplish the delay crack propagation and the vibration suppression. Based on the mapping model of opening and closing states of a crack, the effects of rotational speeds, an unbalance, and asymmetries of the rotor are discussed in detail. Experimental results show that vibrations and the breathing behavior of cracks in the rotor with the electromagnetic actuator can be suppressed, and the effectiveness of the proposed mapping model of opening and closing states of a crack is verified.

Crack classification in rotor-bearing system by means of wavelet transform and deep learning methods: an experimental investigation

Parallel with significant growth in industry, especially mysteries related to energy engineering, condition monitoring of rotating systems have been experiencing a noticeable increase. One of the prevalent faults in these systems is fatigue crack, so finding reliable procedures in identification of cracks in rotating shafts has become a pressing problem among engineers during recent decades. While a vast majority of cracked rotors can operate for a specific period of time, to prevent catastrophic failures, crack detection and measuring its characteristics (i.e. size and its location) seem to be essential. In the present essay, a hybrid procedure, consisting of Deep Learning and Discrete Wavelet transform (DWT), is applied in detection of a breathing transverse crack and its depth in a rotor-bearing-disk system. DWT with Daubechies 32(db32) as wavelet mother function is applied in signal noise reduction until level 6, also its Relative Wavelet Energy (RWE) and Wavelet entropy (WE) are extracted. A characteristic vector that is a combination of RWE and WE is considered as input to a multi-layer Artificial Neural Network (ANN). In this supervised learning classifier, a multi-layer Perceptron neural network is used; in addition, Rectified Linear Unit (ReLU) function is exerted as activation function in both hidden and output layers. By comparing the results, it can be seen that the applied procedure has strong capacity in identification of crack and its size in the rotor system.

Dynamical analysis of hollow-shaft dual-rotor system with circular cracks

In this paper, we considered a dual-rotor system with crack in shaft. The influence of circular crack in hollow shaft on dynamical response was studied. The equations of motion of 12 elements dual-rotor system model were derived. Harmonic balance method was employed to solve the equations. The critical speed and sub-critical speed responses were investigated. It was found that the circular crack in hollow shaft had greater influence on the first-backward critical speed than the first-forward critical speed. Owing to the influence of crack, the vibration peaks occurred at the 1/2, 1/3 and 1/4 critical speeds of the rotor system, along with a reduction in sub-critical speeds and critical speeds. The deeper crack away from the bearing affected the rotor more significantly. The whirling orbits, the time-domain responses and the spectra were obtained to show the super-harmonic resonance phenomenon in hollow-shaft cracked rotor system.

On post-resonance backward whirl in an overhung rotor with snubbing contact

Rotordynamic systems are central to many aerospace and heavy-duty industrial applications. The vibrational response of such systems is usually associated with forward whirl (FW) and backward whirl (BW) precessions. It is well known in the literature that the BW precession generally precedes the passage through the critical FW resonance precession. Therefore, it can be named as a pre-resonance BW frequency (Pr-BW). However, another kind of BW has been recently observed to be immediately excited after the passage through the critical FW resonance frequency in cracked rotors with anisotropic supports during run-up and coast-down operations. Consequently, this kind of BW can be named as a post-resonance backward whirl (Po-BW) precession. The Pr-BW and Po-BW phenomena are investigated here with an overhung rotor system that exhibits snubbing contact and stiffness anisotropy in the supports. Incorporating the snubbing moment couple into the equations of motion of the considered overhung rotor model yields a piecewise and strongly nonlinear system. Full-spectrum analysis is employed to capture the BW zones of rotational speeds in the whirl response. Wavelet transform spectrum analysis is also employed to determine the frequency content in the Pr-BW and the Po-BW zones. Three cases are considered in this numerical study to explore the effect of the support stiffness isotropy and anisotropy with active and inactive snubbing contact on the Po-BW excitation. For all cases, the Po-BW zones of rotational speeds are found. Moreover, the broadness and recurrence of the Po-BW zones of rotational speeds are more prominent for the cases of active snubbing contact. Even though the Pr-BW and Po-BW zones are excited at different shaft rotational speeds, they are found to possess nearly similar BW frequencies which are less than the FW resonance frequency of the considered system.

Location dependence of breathing mechanism for a slant crack in a shaft

AbstractPeriodic stresses are always imposed on a rotor, and thus, a crack due to fatigue is unavoidable. Machinery must be properly diagnosed to avoid tragic accidents. Vibration detection is the most important tool for such a diagnosis system. It is important to know the vibration characteristics of a cracked rotor in order to develop a monitoring system which can detect a crack in an early stage of propagation. In this study, to explore the crack breathing mechanism, a three‐dimensional finite element model is simulated by using a commercial analysis solver—Abaqus/Standard. A two‐disc rotor system with a slant crack is used under the coupling effect of rotor weight and unbalance force. Unlike crack breathing under rotor weight‐only, a crack opens and closes differently under the effects of unbalance forces. Crack breathing depends on its location along the length of the shaft and individual parameters of the rotor system. A few crack locations are recognised along shaft length where the crack may stay fully closed or open during shaft rotation under certain loading circumstances. These locations also split the shaft into different areas based on the orientation of the unbalance force, crack size and location, where shaft stiffness may be higher or lower. Presented findings indicate that predicting the dynamic response of cracked rotors can be anticipated much accurately. Therefore, the impacts of unbalance forces and individual rotor physical characteristics on crack breathing must be taking into consideration.