Rotor Crack Research Articles

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.

Typical Fault Modeling and Vibration Characteristics of the Turbocharger Rotor System

To study the typical failure mechanism (rotor unbalance, rotor friction, and rotor crack) and vibration characteristics of the turbocharger rotor system, a rotor system dynamics simulation model was established by an improved four-node aggregate parameter method. The geometric and physical characteristics of the rotor system under three failure states and its dynamics under operation were analyzed. Thus, a typical failure dynamics simulation model of the rotor system was established. On this basis, the output failure simulation signal was extracted using the Hu invariant moment feature extraction method to analyze the system vibration characteristics under each typical failure state of the rotor system. The results show that the model in this paper can effectively reduce the computational volume and computational time, and the errors of numerical simulation were less than 3%. When an unbalance fault occurred in the rotor system, the shaft trajectory was “0” shaped and the response spectrum was dominated by 1X. When the rotor system was frictional, the shaft trajectory was a slightly concave “8” shape, and the response spectrum was dominated by 0.5X. When the rotor system was cracked, the axial trajectory was a “vortex”, and the response spectrum was dominated by 0.5X. Thus, the study of typical failure mechanism and vibration characteristics of a turbocharger rotor system by simulation calculation is effective and has good research prospects, providing an important technical reference for dynamic analysis and fault diagnosis of the rotor system.

Dynamic modeling and vibration analysis of cracked rotor-bearing system based on rigid body element method

Rotor crack occurs frequently in rotating machinery. It is of great significance to study the vibration mechanisms of the cracked rotor-bearing system, which can provide proofs for crack online monitoring. In this paper, a new dynamic model of the cracked rotor-bearing system is developed using the rigid body element (RBE) method, and vibration response analysis is then carried out. The rotor is discretized as a set of RBEs, and each two adjacent RBEs is connected by an elastic joint (EJ). Each EJ is modeled with six imaginary springs (three translational springs and three rotational springs). The breathing crack is modeled through time-varying stiffnesses of imaginary springs, which are obtained using real-time parameters (area, cross-section moment of inertia, and polar moment of inertia) in four processes (crack fully closed, crack partially opened, crack fully opened, and crack partially closed) in a full rotation angle. The interactions of adjacent RBEs are then given based on the force and moment analysis, and the bearing forces are obtained based on two models (i.e., equivalent spring-damper model, and Gupta bearing model). The equations of motions of the cracked rotor-bearing system are developed through Newton-Euler equations and solved by the fourth-order Runge-Kutta-Fehlberg method with a step-changing criterion. The displacement responses are then obtained, and the frequency spectrums of displacement responses and their instantaneous frequencies (IFs) under different rotation speeds are analyzed. Simulation results of the cracked rotor-bearing system are in good agreement with previously published results and experiment results. What’s more, analysis results show that the frequency spectrum of IF can be an indicator for online monitoring of the rotor crack.

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.

Energy harvesting from gravity-induced deformation of rotating shaft for long-term monitoring of rotating machinery

Energy harvesting from rotating machines for self-powered sensor networks has attracted increasing attentions in the last decade. In this work, an energy harvester employing piezoelectric stacks for rotating machinery is proposed, which cannot only harvest kinetic energy from bending deformation of rotating shaft but also has the capability of rotor fault detection. The structure and working concept of the energy harvester are initially presented. Afterward, a theoretical model for the energy harvester is established to clarify its output characteristics. Then, vibration tests under different rotating speeds are carried out with a prototype mounted on a rotor test rig. The effects of electrical connections of piezoelectric stacks, rotor geometry, energy harvester location, and fastener preload on the output performance of energy harvester are evaluated. Finally, the applications of powering a scientific calculator and detecting typical faults of rotor systems including rotor crack and rub impact faults are demonstrated. Apart from fault detection capability, the proposed energy harvester has the advantages of long lifespan and causing little interference with the rotational motion, which overcomes the inherent deficiencies of commonly studied beam-type energy harvesters and manifest the potential of proposed energy harvester for the long-term condition monitoring of rotating machines.

Prediction of Rotor Slot Size Variations in Induction Motor Using Polynomial Chirplet Transform and Regression Algorithms

For constant monitoring of rotor slot in induction motor, average rotor slot variation (ARSV) prediction is proposed. The rotor slots expand due to thermal stress and high intensity magnetic flux. The magnetic flux with high intensity is created in rotor lamination sheet, because of stretching and curving magnetic flux. The surface of rotor slot exhibits thermal stress due to over current which in turn generates heat and transfers the heat into the rotor lamination surface. The magnetic stress-based rotor slot size variation is never monitored or measured before. In the proposed ARSV method, multimodal sensor signals such as Giant magnetoresistance, temperature, current, vibration and voltage acquire magnetic stress and temperature stress of rotor. The acquired signals are analyzed through polynomial chirplet transform to obtain energy band values of signal. The energy band values and microscopic camera image-based rotor slot variation values are used for ARSV prediction. The prediction of ARSV is computed using polynomial regression (PR) method. From experimental results, it is observed that ARSV is greater than 5% from the normal size which leads to extreme damage to the motor through vibration, sparking and harmonics. The prediction accuracy of ARSV is about 94.6% when compared to manual measurement of slots in rotor. Moreover, the prediction of ARSV avoids the major faults, namely eccentricity, overload, under voltage, unbalance voltage, induced rotor slot, rotor crack and rotor burn.

Steady State and Transient Vibration Analysis of an Exponentially Graded Rotor Bearing System Having a Slant Crack

The dynamic behaviour of a slant-cracked exponentially graded (EG) rotor-bearing system has been investigated using the finite element method for flexural vibrations. A two nodded EG rotor element has been developed based on the Timoshenko beam theory. Local flexibility coefficients (LFCs) of a slant-cracked EG shaft element have been derived using fracture mechanics concepts to develop the stiffness matrix of a cracked EG element. The steady-state and transient vibration responses of cracked and uncracked rotor systems have been simulated using the Houbolt time marching method. When a crack is present in the shaft, the subharmonic frequency peaks are centred on operating speed in the steady-state frequency responses, whereas on critical speed in the transient frequency responses at an interval frequency corresponding to the torsional frequency. It has been found that the crack parameters such as crack depth and location, temperature gradients and torsional frequencies have a significant influence on natural frequencies and dynamic responses, which could be implemented for efficient rotor crack detection methodologies.

Rotor crack and bearing fault diagnosis based onVMD-ICA

Abstract The rotor-bearing system is vulnerable to rotor cracks, bearing failures, or even multiple failures at the same time during long-term service, and it is more difficult to diagnose the faults under rotor crack and bearing fault coupling conditions. This paper proposed a signal reconstruction method to classify the rotor crack, the bearing outer ring fault and their coupling faults based on Variational Mode Decomposition (VMD) and Independent Component Analysis (ICA). Firstly, the original vibration signal collected on a rotor-bearing test bench is decomposed with VMD, and several intrinsic mode functions (IMF) are obtained. Then, the correlation kurtosis CK M which introduces the characteristics of periodic correlation function is to evaluate the decomposed IMF component, and screen the rotor crack information component. Finally, the rotor crack information component is input into a virtual channel signal and separated with the original vibration signal with ICA, and then the separated two sets of signals are superimposed to obtain a vibration signal that simultaneously highlights the information of the rotor crack and the bearing outer ring fault. In addition, the time domain signal is directly input into a LightGBM to diagnose different faults. The research results show that this method can simultaneously diagnose the rotor crack, the bearing outer ring fault and the coupling fault.

Unmanned aerial vehicle rotor fault diagnosis based on interval sampling reconstruction of vibration signals and a one-dimensional convolutional neural network deep learning method

With the aim of identifying possible mechanical faults in unmanned aerial vehicle (UAV) rotors during operation, this paper proposes a method based on interval sampling reconstruction of vibration signals and one-dimensional convolutional neural network (1D-CNN) deep learning. Firstly, experiments were designed to collect the vibration acceleration signals of a UAV working at high speed under three states (normal, rotor damage by varying degrees, and rotor crack by different degrees). Then, considering the powerful feature extraction and complex data analysis abilities of 1D-CNN, an effective deep learning model for fault identification is established utilizing 1D-CNN. During analysis, it is found that the recognition rate for minor faults is not ideal, with all weak states being identified as normal, reducing the overall identification accuracy, when using conventional sequential sampling to construct learning sample sets. To this end, in order to make the sample data cover the whole process of data collection as much as possible, a learning sample processing method based on interval sampling reconstruction of the vibration signal is proposed. And it is also verified that the reconstructed sample set can easily reflect the global information of mechanical operation. Finally, according to the comparison of analysis results, the recognition rate of the deep learning model for different degrees of faults is greatly improved, and minor faults could also be accurately identified through this method. The results show that the 1D-CNN deep learning model could diagnose and identify UAV rotor damage faults accurately, by incorporating the proposed method of interval sampling reconstruction.

Identification of Rotor Crack Faults by Vibration Analysis

According to the vibration equation of the cracked rotor, the main vibration characteristics of the cracked rotor are summarized. On this basis, combined with the field diagnosis experience, a practical method of identifying the cracked rotor through vibration analysis is proposed. Furthermore, the proposed method is illustrated by three cases of rotor crack fault identification in the operation of steam turbine and boiler primary air fan. Successful diagnosis avoids the occurrence of potential major accidents.

Simultaneous Fault Detection and Multivariable Adaptive Hybrid Control for Unbalanced Vibrations of Cracked Flexible Rotor Systems

Abstract For the reduction of unbalanced vibrations in a multi-input and multi-output flexible rotor system with electromagnetic actuators (EAs), conventional adaptive feedforward controllers (AFFCs) are very sensitive for changes in rotor spin frequencies. Although frequency updating is used in these controllers, a small variation in the rotor spin frequency can completely reduce their effectiveness. An adaptive notch filter is used in this research for the frequency estimation. By using this external frequency estimation, the performance of the conventional AFFCs can be enhanced. During changes in the rotor spin frequency, fundamental harmonics of the flexible rotor are also excited. Their amplitude is much higher compared to steady-state unbalanced vibrations, which can accelerate the wear and tear of components of EAs. By using feedback controllers, the amplitude of these fundamental harmonics can be reduced significantly. In real rotors with flexible bearing supports, any looseness of bolts and presence of transverse cracks can change system parameters significantly. Multiple harmonics are generated corresponding to even single spinning speed of the rotor. Robust stability as well as performance can be achieved in the presence of uncertainty and rotor crack nonlinearities using feedback controllers designed by mu-synthesis. By using the multiharmonic hybrid control, the higher harmonics can be compensated efficiently in case of a crack in rotor systems. The fast Fourier transform of the control signal can indicate the presence of a transverse crack in an online manner. In this way, active vibration control as well as rotor crack fault detection can be done simultaneously.

An interval fault diagnosis method for rotor cracks

Aiming at the problem that the traditional fault diagnosis methods cannot deal with the uncertain samples, this paper proposes an interval fault diagnosis method and its parameter optimization. First, the interval Gauss function is used to construct the kernel of the proposed interval fault diagnosis method. The weights and offsets of this interval method are calculated by solving the equality equation. Second, with the goal of maximizing the classification accuracy, the Glowworm swarm optimization algorithm is used to select the parameters of this method. Finally, the experimental results of the rotor crack interval fault samples and the University of California Irvine samples show that this method has higher classification accuracy than the traditional interval classification methods.

Detection and localization of fatigue-induced transverse crack in a rotor shaft using principal component analysis

Rotor shafts subjected to severe operating stresses are prone to develop transverse fatigue cracks at the localized stress raisers. Therefore, the ability to identify and locate the incipient fatigue crack is imperative in order to avoid catastrophic failure. The literature on rotor crack detection discussed the importance of monitoring the steady-state 1X, 2X and 3X harmonic response components of rotors. However, the other rotor faults such as misalignment and unbalance, exhibit similar symptoms. Thus, the main aim is to develop new independent fault-related features which measure the driving principle governing the behaviour of various rotor faults. In this article, the application of principal component analysis–based statistical pattern analysis, as a tool for early detection and localization of fatigue-induced transverse crack in a rotor shaft is investigated. To perform this study, accelerated fatigue experiments are conducted on a customized setup. This developed test rig is novel and unique by itself that facilitates generating a fatigue crack in a shaft, under conditions that mimic a real in-service loading environment of industrial rotors. Unlike conventional methods, noise in the acquired vibration and strain data is denoised via classical principal component analysis method. Time- and frequency-domain statistical features extracted from different vibration and strain sensor signals are used for this study. Damage indices such as Hotelling’s T2-statistic and Q-index are used to detect the presence of the crack. It is observed that irrespective of the sensor location, damage index such as Q-statistic of all the sensors is very effective to detect the presence and time of incipient crack. Partial decomposition contributions method is found to be very effective in identifying the location of the crack. This article provides the most significant vibration-based statistical features, which are sensitive to shaft transverse cracks, for different sensor types and their mounting location. Finally, a new fused health indicator which is highly sensitive to the presence of rotor shaft crack is defined and is found successful when applied to a new experimental data.

Weighted contribution rate of nonlinear output frequency response functions and its application to rotor system fault diagnosis

Rotor cracking is a common fault in rotating machinery, that can often be detected based on the vibrations of such machinery. Therefore, many vibration signal based techniques have been developed for rotor fault detection. However, signal based fault diagnosis is often affected by noise and cannot be used to fully quantify the operating conditions of rotors, which are often more relevant to rotor structural characteristics compared to vibration behaviours. Nonlinear output frequency response functions (NOFRFs) represent a nonlinear system frequency analysis approach that was proposed to address challenges associated with applying signal based fault detection. NOFRFs have a wide range of applications in industry, including rotor fault diagnosis. In this study, a novel NOFRFs based criterion called the weighted contribution rate of NOFRFs is proposed to enhance the capability of the NOFRFs based rotor crack detection and quantification. The proposed criterion can amplify the impact of rotor characteristics that are sensitive to rotor cracks, which considerably improves the crack diagnosis performance. The effectiveness and advantages of the proposed rotor damage detection method are verified both experimentally and through simulations, demonstrating its potential applications in the early stages of rotor crack diagnosis.

Dual flexible rotor system with active magnetic bearings for unbalance and coupling misalignment faults analysis

Rotating machines are the backbone of the present industrial world. Early fault detection and conditioning of these machines are primary concern of the researchers associated in this field. There are various faults (assembly error, coupling misalignment, looseness, imbalance, rotor crack, etc.) that cause malfunction of rotating machinery. Imbalance is one of the oldest problem and still challenging to perfectly balance the rotor. Imbalance leads to another inherent fault, i.e., coupling misalignment, especially in dual rotor or rotor train system. Imbalance and misalignment cause excessive vibration in the system that tends to shatter failure of the critical components of rotating machinery. In this article, active magnetic bearings (AMBs) are utilized to suppress the excessive vibration generated due to imbalance and misalignment. To regulate the controlling current of AMB a proportional integral derivative (PID) feedback controller is employed. A quantification technique is suggested to evaluate the tuned AMB characteristics along with imbalance and coupling misalignment dynamic parameters. A finite element method (FEM) modelling with high-frequency reduction scheme is utilized to acquire reduced system equations of motion. There are two advantages of employing condensation scheme, first, it reduces the number of sensors required and second, only linear (practically measurable) degrees of freedom are present in equations of motion derived. A SIMULINK™ code is prepared to solve a reduced linear differential equation. The time series feedback signals (current and displacement) obtained are transformed into a frequency series utilizing Fast Fourier Transformation (FFT) and utilized in developed algorithm. To establish the accuracy and effectiveness of the methodology, the estimated parameters are evaluated under two different frequency bands against measurement and modelling error (5% variation in mass of the disc and bearing characteristic parameters).

Combination algorithm for cracked rotor fault diagnosis based on NOFRFs and HHR

In this paper, a combination algorithm for diagnosing rotor crack fault is presented. Firstly, the nonlinear output frequency response functions (NOFRFs) are used to analyze the severity of crack damage in the rotor system qualitatively. The NOFRFs are obtained by processing the vibration signal through the nonlinear output frequency response functions. Further analysis of the NOFRFs can determine the crack depth qualitatively. Secondly, the position of the crack is then located using the crack position index (CPI) λ based on the higher harmonic response (HHR) and the dynamic compliance matrix. The simulation and experimental results show that the G2(j2wF) in NOFRFs is very sensitive to crack depth, and the crack position index (CPI) λ can determine the shaft segment effectively where the crack is located. The advantage of this combination algorithm is that it can detect the crack faults by measuring the vibration signal of the cracked rotor at two speeds, which makes the measurement process more simplified and reduces the measurement time for real-time monitoring. At each speed only the vibration response of the two nodes need to be measured, which greatly reduces the number of sensor used in the measurement process and reduces the cost of monitoring. The combination algorithm can diagnose cracked rotor faults effectively and has certain application value in the diagnosis of cracked rotor fault.

A parameter-adaptive stochastic resonance based on whale optimization algorithm for weak signal detection for rotating machinery

The parameters of stochastic resonance (SR) system determine its output directly. Inappropriate parameters may lead to an unsatisfactory result even an error. To search the best parameter adaptively, a novel method is proposed in this paper. In the method, the relationships between each parameter are considered. Also, the Kramers rate of noise and some information about the weak signal are considered in our method. In the novel method, what we need to determine artificially is the interval of only one parameter. The others will be searched adaptively and optimally. Therefore, the proposed method is much different with traditional parameter-adaptive SR. The effectiveness and accurateness of our method are proofed by simulation, rotor crack detection and bearing inner diagnosis detection. The results compared with some other methods demonstrate our method can work more effectively. At last, we studied an interesting phenomenon founded in the process of our study and proposed a guide that the upper limitation of the Kramers rate should be equal to the target frequency after compressing when the re-scaling technology was used in SR system. Consequently, this paper makes a great contribution in the application of SR.

Study on Fatigue Degradation Behavior of a Cracked Rotor Subjected to Lateral Vibration

Fatigue crack in a rotary shaft is a common failure observed in rotor systems. Since vibration of the shaft causes alternating fatigue loads, the crack propagates slowly. Meanwhile, the propagating crack may cause nonlinear or unstable vibration of the rotor system. In fact, growth of the crack and vibration of the shaft are coupled with each other. Hence, it is necessary to study the fatigue degradation behavior of the cracked rotor accounting for this coupling effect. In this paper, a coupling model of rotor vibration and crack growth is established through dynamic theory and fracture mechanics, and a sequential iterative procedure is proposed to solve the coupling model. Then, the competing degradation failure mode of the cracked rotor is analyzed with regard to the rapid crack growth failure and the unstable vibration failure. And degradation measures are proposed based on the competing degradation failure criterion. At last, degradation behaviors with the coupling effect of nonlinear vibration behavior and multiple parameters including rotation speed, unbalance eccentricity and orientation angle, and damping are investigated by numerical simulation. The results indicate that nonlinear vibration behavior and multiple parameters have considerable influence on the degradation behaviors, which present complex regularity. The findings are of significance to guide the safety design of the rotor system for long time operation and help to the further research on prognostics and lifetime prediction.

Crack fault diagnosis of rotor systems using wavelet transforms

As the traditional Fourier transformation method cannot process the non-linear and non-stationary vibration signal of the cracking rotor system, the 3-D waterfall spectrum in combination with reassigned wavelet scalogram method is presented to analyze the temporal frequency characteristics of the crack fault. Three different crack depths of rotor crack faults were simulated on a cracking rotor test-bed. The experiment results show that the present method is effective in determining the frequency structure of the signal, especially the twofold frequency component, which can be measured at half of the critical speed. The present method is an effective tool to diagnose cracks in rotor system and the frequency characteristic can be used as references in the diagnosis.