Crack Fault Research Articles

Nonlinear Dynamics of a Reduced Cracked Rotor

The transient proper orthogonal decomposition (TPOD) method is applied for order reduction in the rotor system in this paper. A 26-DOFs rotor model with crack is established by the Newton’s second law, and the dynamical behaviors (bifurcation diagram, mplitude frequency curve, etc.) of the crack fault are discussed. The optimal reduced model can be provided by the proper orthogonal mode (POM) energy method, the TPOD method is applied to reduce the original system to a three-DOFs one at a certain speed corresponds to the maximum energy. The efficiency of the TPOD method is verified via comparing with the bifurcation diagram of the original and reduced rotor system. The order reduction method provides qualitative analysis to study the reduced model of the high-dimensional rotor system.

Stability research of multistage gear transmission system with crack fault

The sub-harmonic resonance phenomenon exists in multistage gear transmission system. Collision motion leads the sub-harmonic resonance instability, which brings harm to system stability. So investigating instability conditions of sub-harmonic resonance and effects of fault on stability have important significance on controlling system stability. From the point of view of nonlinear dynamics, dimensionless dynamical equations of multistage gear transmission system which contains a two-stage fixed-axis gear and a one-stage planetary gear are established. The bifurcation diagrams of system are obtained. By the changing of Poincaré section analyze the evolution process of sub-harmonic resonance and instability conditions. The changes of sub-harmonic resonance and system stability are studied under fixed-axis gear tooth crack fault state in different clearance. The study has important significance for operational prediction of system.

Nonlinear response analysis of a rotor system with a transverse breathing crack under interval uncertainties

Parametric uncertainties are present in complex mechanical systems due to various reasons such as material dispersion and wear. This paper investigates the effects of interval uncertain parameters on the dynamic behaviors of a rotor system with a transverse breathing crack in the shaft. The uncertainties are modeled as uncertain-but-bounded interval inputs on the basis that no sufficient prior information is available to define their precise probabilistic distributions. A finite element rotor model is formulated and the harmonic balance method (HBM) is employed to solve the deterministic dynamic problem. Based on the Chebyshev approximation theory, a surrogate model for the uncertain problem is established and then used to determine the bounds of the nonlinear dynamic responses. The accuracy verification is performed by comparing with the scanning method. Simulations are carried out considering different uncertainties with several uncertain degrees. It will provide some references for early crack fault detection and condition monitoring in rotor systems with uncertainties included.

Vibration feature evolution of locomotive with tooth root crack propagation of gear transmission system

Abstract As the prompt development of modern railway transportation towards high-speed and high load-capacity, the high-power locomotive is urgently required. Under this situation, the wheel–rail dynamic interaction is becoming more and more intensified which will deteriorate the vibration condition of the key elements of locomotive, such as the gear transmissions. Once gear failures are present, such as gear tooth crack or breakage, it is likely to threaten the operation safety of the locomotive. Thus, deep insight into the fault features of the locomotive gear transmission is urgently necessary for prevention of the induced disastrous consequences. This paper is concentrated on the fault vibration feature extraction of a locomotive in presence of gear tooth root crack under the complicated dynamic excitations from both the gear transmissions and the nonlinear wheel–rail interactions. The locomotive–track coupled dynamics model considering the dynamic effect of the mechanical power transmission path is employed, and the time-varying mesh stiffness of the gear pair with tooth root crack fault and the rail geometric irregularities are then incorporated into the dynamics model to obtain the vibration responses. Then, angular synchronous average technique is proposed to enhance the fault vibration features, and the statistical indicators extracted in frequency domain are developed to reveal the evolution law for the crack propagation scenarios along crack depth or tooth width. The analyzed results indicate that the angular synchronous average technique could effectively reveal the fault vibration feature, and the M8A in the selected statistical indicators is most sensitive to the tooth crack propagation in frequency domain.

Optimal demodulation subband selection for sun gear crack fault diagnosis in planetary gearbox

Envelope analysis (EA) is one of the most usually used demodulation methods for fault diagnosis of gearboxes, the main problem for EA is to find a frequency subband that contains more fault-related components. However, modulation phenomenon can be observed for both healthy and damaged situations in planetary gearboxes. And most of the traditional EA techniques cannot distinguish the fault-related modulation components from fault-unrelated modulation components, which may leads to a degradation of the fault diagnosis method for planetary gearbox. In order to overcome the problem of finding the subband that contains the most fault-related modulation components, this paper proposed a new optimal demodulation subband selection method (ODSSM) for fault diagnosis of planetary gearbox. With the proposed method, the fault-related degree of each subband is evaluated based on a new index that measuring the ratio of fault-related modulation components to fault-unrelated modulation components in envelope spectrum. The index then is employed to find the optimal demodulation subband in the entire frequency range based on genetic algorithm (GA). Finally, fault diagnosis results can be obtained based on EA method. For validation, the proposed method and other two methods are utilized to detect the sun gear crack fault in planetary gearbox. The results show that the proposed method can detect the gear fault in both simulation signals and experiment signals, and achieves improved demodulation performance than the other two methods.

Gear fault diagnosis using transmission error and ensemble empirical mode decomposition

Abstract Classification of spall and crack faults of gear teeth is studied by applying the ensemble empirical mode decomposition (EEMD) to the transmission error (TE) measured by the encoders of the input and output shafts. Finite element models of the gears with the two faults are built, and TE’s are obtained by simulation of the faulty gears under loaded contact to identify the different characteristics. A simple test bed for a pair of spur gears is prepared to illustrate the approach, in which the TE’s are measured for the gears with seeded spall and crack, respectively. EEMD is applied to extract fault features under the noise from the measured TE. The differences of the spall and crack are clearly identified by the selected features of the intrinsic mode functions based on the class separability criterion. The k-nearest neighbor method is applied for the classification of the faults and normal gears using the features. The proposed method is advantageous over the existing practices in the sense that the TE signal measures the gear faults more directly with less noise, enabling successful diagnosis.

Fractional-order modeling and dynamic analyses of a bending-torsional coupling generator rotor shaft system with multiple faults

ABSTRACT Unexpected vibrations induced by the crack fault and other unbalance factors in rotor system seriously affect the health and reliability of the generator. Here, to explore the vibration performances, a bending-torsional coupling model of the generator rotor shaft system is established, in which electromagnetic malfunction (unbalanced magnetic pull) and mechanical failures (fractional-order damping, crack and contact-rubbing) are considered. Then, the simulation is done by a modified Adams-Bashforth-Moulton algorithm. Based on the simulation, the correctness of the new coupling model is verified by comparing with previous model and experimental data. At the same time, the new coupling model is analyzed to obtain the dynamic evolutions of the generator rotor shaft system with the changes of crack depth ratio, the fractional order of damping, rotational speed ratio and mass eccentricity of rotor. In addition to this, some critical values and ranges are proposed. Finally, these results can efficiently provide a theoretical reference for the design of generator rotor system and be applied to forecasting and diagnosing vibration faults in generator rotor shaft system.

Crack Fault Classification for Planetary Gearbox Based on Feature Selection Technique and K-means Clustering Method

During the condition monitoring of a planetary gearbox, features are extracted from raw data for a fault diagnosis. However, different features have different sensitivity for identifying different fault types, and thus, the selection of a sensitive feature subset from an entire feature set and retaining as much of the class discriminatory information as possible has a directly effect on the accuracy of the classification results. In this paper, an improved hybrid feature selection technique (IHFST) that combines a distance evaluation technique (DET), Pearson’s correlation analysis, and an ad hoc technique is proposed. In IHFST, a temporary feature subset without irrelevant features is first selected according to the distance evaluation criterion of DET, and the Pearson’s correlation analysis and ad hoc technique are then employed to find and remove redundant features in the temporary feature subset, respectively, and hence, a sensitive feature subset without irrelevant or redundant features is selected from the entire feature set. Further, the k-means clustering method is applied to classify the different kinds of health conditions. The effectiveness of the proposed method was validated through several experiments carried out on a planetary gearbox with incipient cracks seeded in the tooth root of the sun gear, planet gear, and ring gear. The results show that the proposed method can successfully distinguish the different health conditions of a planetary gearbox, and achieves a better classification performance than other methods. This study proposes a sensitive feature subset selection method that achieves an obvious improvement in terms of the accuracy of the fault classification.

A Study on Coupling Faults’ Characteristics of Fixed‐Axis Gear Crack and Planetary Gear Wear

To identify the fault frequency characteristics of the gear transmission system under coupling fault of fixed‐axis gear crack and planetary gear wear, dimensionless dynamical equations of gear transmission system were established. Bifurcations in normal condition and coupling fault condition were contrasted. The affected excitation frequency range was found. Fault frequency characteristics in sensitive interval caused by the coupling fault of fixed‐axis gear crack and planetary gear wear were analyzed. Simulation analysis shows that the crack fault in fixed‐axis gear brings up peaks in doubling of 1~10 for fault frequency, the wear fault in planetary gear increases the amplitude of meshing frequency and its double and triple, and the coupling of both shows two kinds of fault features around the planetary gear meshing frequency.

The operation modal analysis of the structure crack fault diagnosis based on pseudo-successive data

In order to monitor the crack propagation of the structure in the working state for a long time, an operation modal analysis method based on pseudo-successive data is proposed. The vibration response signals of the cantilever beam under white noise excitation are collected and the modal parameters are extracted by the time-frequency operation modal analysis method based on the complex Morlet wavelet. In comparison with the experimental modal analysis results of hammering method, it is revealed that the error of the time-frequency operation modal analysis method is less than 10 %. By setting cracks of different lengths on the cantilever beam, the vibration response signals are extracted, and the modal parameters are extracted by the operation modal analysis method separately. By comparing those modal parameters above, it is found that the natural frequencies of the second, the fourth and the sixth orders decrease with the increase of the crack depth, and the changes of natural frequencies show the monotonicity. So, it can be used as an index for quantitative identification of crack damage. The pseudo continuous data monitoring signals of crack propagation can be constructed by means of “first discrete, then continuous”. The modal parameters changes of the whole crack propagation can be observed in one time plane by means of the operation modal analysis method. Therefore, the effective monitoring and diagnosis of the structure can be completed in case of excessive data of long-time vibration monitoring signals.

Effects of Crack Faults on the Dynamics of Piezoelectric Cantilever-Based MEMS Sensor

The presence of cracks on the surface of MEMS microelectromechanical system (MEMS) devices affects their functional parameter, such as resonance frequency. Overtime, these cracks may cause the devices’ failure. Therefore, it is important to identify the symptoms of the cracks presence so that the affected devices can be removed/bin-out before delivering to the customers thus avoiding failure during applications of these devices. In this paper, we present a predictive and quantitative fault modeling approach using the linear time invariant (LTI) technique for a piezoelectric cantilever-based sensor. The analytical fault model is developed by correlating single edge, double edge, and surface cracks with the resonance frequency of the cantilever. The Simulink is utilized to design the LTI-based faulty device by integrating the dynamic equations associated to actuation and sensing mechanisms of the device under study. The model is validated by comparing it with the finite element method model containing the same design parameters, using the COMSOL Multiphysics. We observed that the presence of cracks at any location on the surface of the device stimulates the amplitude that causes decrease in its resonance frequency. The increase in the amplitude of vibration due to the presence of cracks is electrically sensed by the piezoresistive mechanism. Finally, the fault detection methodology is presented by using the Stateflow technique. We found that the proposed techniques can be significant to study the faulty behavior of the MEMS devices.

An optimized rail crack detection algorithm based on population status

To improve efficiency and accuracy of wavelet packet decomposition method modified by simple genetic algorithm (SGA), a novel genetic algorithm, which is based on variance of population and population entropy, is proposed. And then wavelet packet decomposition method is optimized by this algorithm to detect rail cracks. In the optimized method, internal state of population and population diversity are linked up with evolutionary operations to adjust crossover-mutation operators of genetic algorithm. Further, a mathematical model describing fault signal is established, and its parameters are optimized to effectively extract information. The proposed algorithm was tested by test functions and simulated fault signals of rail cracks. The results about simulated fault signals show that convergence probability of proposed algorithm — at best — is 45% higher than that of SGA and 28% higher than that of improved adaptive genetic algorithm (IAGA), and accuracy of crack fault detection reaches above 92%. Meanwhile, the proposed algorithm isn’t prone to stagnation and has fast convergence speed and high accuracy of fault detection. This research not only improves performance of SGA, but also provides a new detection method for fault diagnosis of wheel-rail noise.

Experimental Dynamic Analysis of a Breathing Cracked Rotor

Crack fault diagnostics plays a critical role for rotating machinery in the traditional and Industry 4.0 factory. In this paper, an experiment is set up to study the dynamic response of a rotor with a breathing crack as it passes through its 1/2, 1/3, 1/4 and 1/5 subcritical speeds. A cracked shaft is made by applying fatigue loads through a three-point bending apparatus and then placed in a rotor testbed. The vibration signals of the testbed during the coasting-up process are collected. Whirl orbit evolution at these subcritical speed zones is analyzed. The Fourier spectra obtained by FFT are used to investigate the internal frequencies corresponding to the typical orbit characteristics. The results show that the appearance of the inner loops and orientation change of whirl orbits in the experiment are agreed well with the theoretical results obtained previously. The presence of higher frequencies 2X, 3X, 4X and 5X in Fourier spectra reveals the causes of subharmonic resonances at these subcritical speed zones. The experimental investigation is more systematic and thorough than previously reported in the literature. The unique dynamic behavior of the orbits and frequency spectra are feasible features for practical crack diagnosis. This paper provides a critical technology support for the self-aware health management of rotating machinery in the Industry 4.0 factory.

Fault Diagnosis System Research of Large-scale Linear Vibrating Screen

The paper takes side panel cracks of large-scale Linear vibrating screen as research object and designs the hardware and upper computer diagnosis interface of fault diagnosis system. The side panel vibration signals have been de-noised and the wavelet packet energy feature has been extracted in Matlab with wavelet analysis theory. Meanwhile, the fault characteristic is sent to genetic neural network for identification. The practical manufacturing application shows that this kind of side panel crack fault diagnosis system of large-scale vibrating screen based on wavelet analysis has high fault recognition ability, classification precision and speed.

Fault feature analysis of cracked gear based on LOD and analytical-FE method

Abstract At present, there are two main ideas for gear fault diagnosis. One is the model-based gear dynamic analysis; the other is signal-based gear vibration diagnosis. In this paper, a method for fault feature analysis of gear crack is presented, which combines the advantages of dynamic modeling and signal processing. Firstly, a new time-frequency analysis method called local oscillatory-characteristic decomposition (LOD) is proposed, which has the attractive feature of extracting fault characteristic efficiently and accurately. Secondly, an analytical-finite element (analytical-FE) method which is called assist-stress intensity factor (assist-SIF) gear contact model, is put forward to calculate the time-varying mesh stiffness (TVMS) under different crack states. Based on the dynamic model of the gear system with 6 degrees of freedom, the dynamic simulation response was obtained for different tooth crack depths. For the dynamic model, the corresponding relation between the characteristic parameters and the degree of the tooth crack is established under a specific condition. On the basis of the methods mentioned above, a novel gear tooth root crack diagnosis method which combines the LOD with the analytical-FE is proposed. Furthermore, empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) are contrasted with the LOD by gear crack fault vibration signals. The analysis results indicate that the proposed method performs effectively and feasibility for the tooth crack stiffness calculation and the gear tooth crack fault diagnosis.

Multi-faults decoupling on turbo-expander using differential-based ensemble empirical mode decomposition

This paper dedicates on the multi-faults decoupling of turbo-expander rotor system using Differential-based Ensemble Empirical Mode Decomposition (DEEMD). DEEMD is an improved version of DEMD to resolve the imperfection of mode mixing. The nonlinear behaviors of the turbo-expander considering temperature gradient with crack, rub-impact and pedestal looseness faults are investigated respectively, so that the baseline for the multi-faults decoupling can be established. DEEMD is then utilized on the vibration signals of the rotor system with coupling faults acquired by numerical simulation, and the results indicate that DEEMD can successfully decouple the coupling faults, which is more efficient than EEMD. DEEMD is also applied on the vibration signal of the misalignment coupling with rub-impact fault obtained during the adjustment of the experimental system. The conclusion shows that DEEMD can decompose the practical multi-faults signal and the industrial prospect of DEEMD is verified as well.

Deep Learning in Visual Computing and Signal Processing

Deep learning is a subfield of machine learning, which aims to learn a hierarchy of features from input data. Nowadays, researchers have intensively investigated deep learning algorithms for solving challenging problems in many areas such as image classification, speech recognition, signal processing, and natural language processing. In this study, we not only review typical deep learning algorithms in computer vision and signal processing but also provide detailed information on how to apply deep learning to specific areas such as road crack detection, fault diagnosis, and human activity detection. Besides, this study also discusses the challenges of designing and training deep neural networks.

A novel fault diagnosis approach of gearbox using an embedded sensor fixed gear body

The vibration signals measured from the surface of a gearbox are complex, nonlinear and non-stationary. This paper presents a novel test approach for tooth root crack fault diagnosis of a spur gearbox using an embedded piezoelectric accelerometer. This enhances the ability to extract useful fault information and provide early fault detection in gear transmission systems. The proposed method uses two piezoelectric accelerometers embedded symmetrically on the gear body, which effectively shortens the transmission path of the vibration signals stimulated by a gear fault. The proposed approach is tested by analyzing experimental data from a healthy gear system and systems with cracked gear faults. In order to extract the weak fault information from the experimental data, minimum entropy deconvolution (MED) is first used to eliminate noise from the vibration signals, and then the cyclic autocorrelation function is used to extract the frequency components. The results suggest that the proposed approach can effectively detect 2 mm and 4 mm crack faults, while traditional methods can only detect 4 mm crack faults.

Fault mode analysis and detection for gear tooth crack during its propagating process based on dynamic simulation method

Gearbox is one of the most important parts of rotating machinery, therefore, it is vital to carry out health monitoring for gearboxes. However, it is still an unsolved problem to disclose the impact of gear tooth crack fault on gear system vibration features during the crack propagating process, besides effective crack fault mode detection methods are lacked. In this study, an analytical model is proposed to calculate the time varying mesh stiffness of the meshing gear pair, and in this model the tooth bending stiffness, shear stiffness, axial compressive stiffness, Hertzian contact stiffness and fillet-foundation stiffness are taken into consideration. Afterwards, the vibration mechanism and effects of different levels of gear tooth crack on the gear system dynamics are investigated based on a 6 DOF dynamic model. Then, the crack fault vibration mode is studied, and a parametrical-Laplace wavelet method is presented to describe the crack fault mode. Furthermore, based on the maximum correlation coefficient (MCC) criterion, the optimized Laplace wavelet base is determined, which is then designed as a health indicator to detect the crack fault. The results show that the proposed method is effective in fault diagnosis of severe tooth crack as well as the early stage tooth crack.

Dynamic analysis on rotor-bearing system with coupling faults of crack and rub-impact

Rub-impact and fatigue crack are two important rotor faults. Based on the crack theory, an improved switching crack model is presented. Dynamic characteristics of a rotor-bearing system with imbalance, rub-impact and transverse crack are attempted. Various nonlinear dynamic phenomena are analyzed using numerical method. The results reveal that unstable form of the rotor system with coupling faults is extremely complex as the rotating speed increases and there are some low frequencies with large amplitude. The influence of crack depth and angle on the dynamic behavior of a cracked rotor is important insomuch as the quasi-periodical and chaotic motions in system response will occur along with different parameters. It is indicated that this study can contribute to a further understanding of the nonlinear dynamics of such a rotor system with coupling faults of crack and rub-impact.