Simulating gear and bearing interactions in the presence of faults: Part II: Simulation of the vibrations produced by extended bearing faults

This paper presents a combined dynamic model for gears and bearings, in which an extended fault in the inner/outer race of rolling element bearings can be studied in the presence of gear interaction. A combined gear/bearing model has been made to obtain a better understanding of the interaction of the two components. The essentials of the gear/bearing model and the results of simulating the vibration of localized faults in rolling element bearings in a gearbox environment have been discussed and illustrated in the first part of this paper (part I). The simulation model has now been modified to model extended faults of the type that do not necessarily produce high frequency impact responses, but do modulate the gearmesh signals. The paper compares the simulated and actual signals from the gear/bearing test rig for inner and outer race extended faults, and in particular demonstrates that they react similarly to existing diagnostic techniques.     

Experimental studies on the effects of reduction in gear tooth stiffness and lubricant film thickness in a spur geared system

Gears are one of the most common mechanisms for transmitting power and motion and their usage can be found in numerous applications. Studies on gear teeth contacts have been considered as one of the most complicated applications in tribology. Depending on the application, the speed and load conditions of teeth may change triggering several types of failures on teeth surface such as wear, scuffing, micro-pitting and pitting. The above-mentioned faults influence changes in vibration and acoustic signals, due to changes in operating conditions such as increase in temperature and decrease in lubricant film thickness and specific film thickness. These abnormal changes result in cumulative effects on localised or distributed faults on load bearing surfaces of gears. Such damages cause reduction in tooth stiffness and severity of damage can be assessed by evaluating the same using vibration-based signals.This paper presents the results of experimental investigations carried out to assess wear in spur gears of back-to-back gearbox under accelerated test conditions. The studies considered the estimation of operating conditions such as film thickness and their effects on the fault growth on teeth surface. Modal testing experiments have been carried out on the same gear starting from healthy to worn out conditions to quantify wear damage. The results provide a good understanding of dependent roles of gearbox operating conditions and vibration parameters as measures for effective assessment of wear in spur gears.     

基于形态差值滤波和差分熵的滚动轴承故障诊断

针对滚动轴承内外圈的早期故障,提出了一种新的诊断方法,该方法融合了数学形态学对非线性信号的滤波和信息熵理论在信号表征方面的优越性。首先,利用数学形态差值滤波器对实测的轴承内外圈轻重损伤的故障信号进行消噪处理,充分突出了有用的故障特征信息;然后,利用差分熵提取该信号中的突变特征信息,对其进行不确定性和复杂性度量;最后,根据突变点的冲击时间间隔和内外圈故障周期性冲击的时间间隔一致的思想来完成对滚动轴承的故障诊断。通过对仿真信号和滚动轴承实测内外圈两种故障程度的振动信号的诊断分析,证明该方法能够很好地识别轴承内外圈早期故障的类型,且具有很高的准确率。     

Defect diagnostics of roller bearing using instantaneous frequency normalization under fluctuant rotating speed

We investigated the feasibility of utilizing the normalized characteristic frequencies for diagnosing the defective roller bearings in case of fluctuant rotating speeds. The time-frequency distributions of the envelope signals of the vibration data were constructed through the Empirical mode decomposition (EMD) as well as the instantaneous frequency calculation. The bearing defect-related frequencies were then normalized with respect to the instantaneous rotation frequency of the shaft so that the factor of the rotating speed fluctuation was removed; thus the characteristic frequencies of bearing malfunctions could be observed in terms of constant values. The magnitude distributions of the marginal envelope spectra at the corresponding normalized bearing defect-related frequencies were extracted as the feature vectors. The Support vector machine (SVM) was used to classify the extracted feature vectors of different bearing fault classes. A test rig of roller bearing system was performed to illustrate the different bearing faults, including different levels of inner race defect, outer race defect and roller defect. The analysis results demonstrate the capability and effectiveness of the proposed approach for accurately identifying the bearing defects in case of fluctuant rotating speed.     

Detection and diagnosis of bearing and cutting tool faults using hidden Markov models

Over the last few decades, the research for new fault detection and diagnosis techniques in machining processes and rotating machinery has attracted increasing interest worldwide. This development was mainly stimulated by the rapid advance in industrial technologies and the increase in complexity of machining and machinery systems. In this study, the discrete hidden Markov model (HMM) is applied to detect and diagnose mechanical faults. The technique is tested and validated successfully using two scenarios: tool wear/fracture and bearing faults. In the first case the model correctly detected the state of the tool (i.e., sharp, worn, or broken) whereas in the second application, the model classified the severity of the fault seeded in two different engine bearings. The success rate obtained in our tests for fault severity classification was above 95%. In addition to the fault severity, a location index was developed to determine the fault location. This index has been applied to determine the location (inner race, ball, or outer race) of a bearing fault with an average success rate of 96%. The training time required to develop the HMMs was less than 5 s in both the monitoring cases.     

Transient modeling and parameter identification based on wavelet and correlation filtering for rotating machine fault diagnosis

At constant rotating speed, localized faults in rotating machine tend to result in periodic shocks and thus arouse periodic transients in the vibration signal. The transient feature analysis has always been a crucial problem for localized fault detection, and the key aim for transient feature analysis is to identify the model and its parameters (frequency, damping ratio and time index) of the transient, and the time interval, i.e. period, between transients. Based on wavelet and correlation filtering, a technique incorporating transient modeling and parameter identification is proposed for rotating machine fault feature detection. With the proposed method, both parameters of a single transient and the period between transients can be identified from the vibration signal, and localized faults can be detected based on the parameters, especially the period. First, a simulation signal is used to test the performance of the proposed method. Then the method is applied to the vibration signals of different types of bearings with localized faults in the outer race, the inner race and the rolling element, respectively, and all the results show that the period between transients, representing the localized fault characteristic, is successfully detected. The method is also utilized in gearbox fault diagnosis and the effectiveness is verified through identifying the parameters of the transient model and the period. Moreover, it can be drawn that for bearing fault detection, the single-side wavelet model is more suitable than double-side one, while the double-side model for gearbox fault detection. This research proposed an effective method of localized fault detection for rotating machine fault diagnosis through transient modeling and parameter detection.     

An automated procedure for detection and identification of ball bearing damage using multivariate statistics and pattern recognition

This paper suggests an automated approach for fault detection and classification in roller bearings, which is based on pattern recognition and principal components analysis of the measured vibration signals. The signals recorded are pre-processed applying a wavelet transform in order to extract the appropriate high frequency (detailed) area needed for ball bearing fault detection. This is followed by a pattern recognition (PR) procedure used to recognise between signals coming from healthy bearings and those generated from different bearing faults. Four categories of signals are considered, namely no fault signals (from a healthy bearing), inner race fault, outer race fault and rolling element fault signals. The PR procedure uses the first six principal components extracted from the signals after a proper principal component analysis (PCA). In this work a modified PCA is suggested, which is much more appropriate for categorical data. The combination of the modified PCA and the PR method ensures that the fault is automatically detected and classified to one of the considered fault categories. The method suggested does not require the knowledge/determination of the specific fault frequencies and/or any expert analysis: once the signal filtering is done and the PC's are found the PR method automatically gives the answer if there is a fault present and its type.     

Application of higher order spectral features and support vector machines for bearing faults classification

Condition monitoring and fault diagnosis of rolling element bearings timely and accurately are very important to ensure the reliability of rotating machinery. This paper presents a novel pattern classification approach for bearings diagnostics, which combines the higher order spectra analysis features and support vector machine classifier. The use of non-linear features motivated by the higher order spectra has been reported to be a promising approach to analyze the non-linear and non-Gaussian characteristics of the mechanical vibration signals. The vibration bi-spectrum (third order spectrum) patterns are extracted as the feature vectors presenting different bearing faults. The extracted bi-spectrum features are subjected to principal component analysis for dimensionality reduction. These principal components were fed to support vector machine to distinguish four kinds of bearing faults covering different levels of severity for each fault type, which were measured in the experimental test bench running under different working conditions. In order to find the optimal parameters for the multi-class support vector machine model, a grid-search method in combination with 10-fold cross-validation has been used. Based on the correct classification of bearing patterns in the test set, in each fold the performance measures are computed. The average of these performance measures is computed to report the overall performance of the support vector machine classifier. In addition, in fault detection problems, the performance of a detection algorithm usually depends on the trade-off between robustness and sensitivity. The sensitivity and robustness of the proposed method are explored by running a series of experiments. A receiver operating characteristic (ROC) curve made the results more convincing. The results indicated that the proposed method can reliably identify different fault patterns of rolling element bearings based on vibration signals.     

Blind vibration component separation and nonlinear feature extraction applied to the nonstationary vibration signals for the gearbox multi-fault diagnosis

Fault diagnosis of gearboxes, especially the gears and bearings, is of great importance to the long-term safe operation. An unexpected damage on the gearbox may break the whole transmission line down. It is therefore crucial for engineers and researchers to monitor the health condition of the gearbox in a timely manner to eliminate the impending faults. However, useful fault detection information is often submerged in heavy background noise. Thereby, a new fault detection method for gearboxes using the blind source separation (BSS) and nonlinear feature extraction techniques is presented in this paper. The nonstationary vibration signals were analyzed to reveal the operation state of the gearbox. The kernel independent component analysis (KICA) algorithm was used hereby as the BSS approach for the mixed observation signals of the gearbox vibration to discover the characteristic vibration source associated with the gearbox faults. Then the wavelet packet transform (WPT) and empirical mode decomposition (EMD) nonlinear analysis methods were employed to deal with the nonstationary vibrations to extract the original fault feature vector. Moreover, the locally linear embedding (LLE) algorithm was performed as the nonlinear feature reduction technique to attain distinct features from the feature vector. Lastly, the fuzzy k-nearest neighbor (FKNN) was applied to the fault pattern identification of the gearbox. Two case studies were carried out to evaluate the effectiveness of the proposed diagnostic approach. One is for the gear fault diagnosis, and the other is to diagnose the rolling bearing faults of the gearbox. The nonstationary vibration data was acquired from the gear and rolling bearing fault test-beds, respectively. The experimental test results show that sensitive fault features can be extracted after the KICA processing, and the proposed diagnostic system is effective for the multi-fault diagnosis of the gears and rolling bearings. In addition, the proposed method can achieve higher performance than that without KICA processing with respect to the classification rate.     

Detection of signal transients based on wavelet and statistics for machine fault diagnosis

This paper presents a transient detection method that combines continuous wavelet transform (CWT) and Kolmogorov–Smirnov (K–S) test for machine fault diagnosis. According to this method, the CWT represents the signal in the time-scale plane, and the proposed “step-by-step detection” based on K–S test identifies the transient coefficients. Simulation study shows that the transient feature can be effectively identified in the time-scale plane with the K–S test. Moreover, the transients can be further transformed back into the time domain through the inverse CWT. The proposed method is then utilized in the gearbox vibration transient detection for fault diagnosis, and the results show that the transient features both expressed in the time-scale plane and re-constructed in the time domain characterize the gearbox condition and fault severity development more clearly than the original time domain signal. The proposed method is also applied to the vibration signals of cone bearings with the localized fault in the inner race, outer race and the rolling elements, respectively. The detected transients indicate not only the existence of the bearing faults, but also the information about the fault severity to a certain degree.     

Feature selection using Decision Tree and classification through Proximal Support Vector Machine for fault diagnostics of roller bearing

Roller bearing is one of the most widely used rotary elements in a rotary machine. The roller bearing's nature of vibration reveals its condition and the features that show the nature, are to be extracted through some indirect means. Statistical parameters like kurtosis, standard deviation, maximum value, etc. form a set of features, which are widely used in fault diagnostics. Often the problem is, finding out good features that discriminate the different fault conditions of the bearing. Selection of good features is an important phase in pattern recognition and requires detailed domain knowledge. This paper illustrates the use of a Decision Tree that identifies the best features from a given set of samples for the purpose of classification. It uses Proximal Support Vector Machine (PSVM), which has the capability to efficiently classify the faults using statistical features. The vibration signal from a piezoelectric transducer is captured for the following conditions: good bearing, bearing with inner race fault, bearing with outer race fault, and inner and outer race fault. The statistical features are extracted therefrom and classified successfully using PSVM and SVM. The results of PSVM and SVM are compared.     

基于小波分析的重载卡车变速箱装配品质在线检测方法研究

为确定某型变速箱装配品质,从变速箱内部结构出发,简要介绍了变速箱常见装配故障,从理论上分析了变速箱在各挡位情况下各齿轮和轴承等零件的常见故障特征频率,并搭建声压信号采集平台,采集变速箱不同挡位运转时产生的声压信号,利用小波阈值去噪法对采集的原始声压信号进行去噪,并运用小波分析对去噪后的声压信号进行分解,对相应的频段信号...     

动车组转向架轴承局部损伤振动特性分析

针对动车组转向架轴承,根据轴承故障产生机理建立了轴承故障动力学工程模型。模型充分考虑了车轴弯曲刚度、轴承间隙及滚动体和滚道间的非线性接触力等因素,并包含内圈、外圈以及滚动体故障轴承动力学模型,使用龙格库塔数值积分方法进行了动力学仿真分析。针对实际轴承搭建实验台,对不同故障类型及不同程度故障进行了实际测试。仿真分析与实验结果吻合度较高,最大误差不超过5%,证明了该动力学模型的有效性。     

Enhanced detection of rolling element bearing fault based on stochastic resonance

Early bearing faults can generate a series of weak impacts. All the influence factors in measurement may degrade the vibration signal. Currently, bearing fault enhanced detection method based on stochastic resonance(SR) is implemented by expensive computation and demands high sampling rate, which requires high quality software and hardware for fault diagnosis. In order to extract bearing characteristic frequencies component, SR normalized scale transform procedures are presented and a circuit module is designed based on parameter-tuning bistable SR. In the simulation test, discrete and analog sinusoidal signals under heavy noise are enhanced by SR normalized scale transform and circuit module respectively. Two bearing fault enhanced detection strategies are proposed. One is realized by pure computation with normalized scale transform for sampled vibration signal, and the other is carried out by designed SR hardware with circuit module for analog vibration signal directly. The first strategy is flexible for discrete signal processing, and the second strategy demands much lower sampling frequency and less computational cost. The application results of the two strategies on bearing inner race fault detection of a test rig show that the local signal to noise ratio of the characteristic components obtained by the proposed methods are enhanced by about 50% compared with the band pass envelope analysis for the bearing with weaker fault. In addition, helicopter transmission bearing fault detection validates the effectiveness of the enhanced detection strategy with hardware. The combination of SR normalized scale transform and circuit module can meet the need of different application fields or conditions, thus providing a practical scheme for enhanced detection of bearing fault.     

滚动轴承外圈多点故障特征分析

滚动轴承发生多点故障时会产生复杂的振动特征,影响轴承故障诊断的准确性。针对滚动轴承外圈多点故障诊断特征的变化规律,考虑滚动轴承外圈故障数量、故障间隔和载荷分布对故障特征的影响,采用五自由度动力学模型进行仿真分析。通过龙格库塔法对动力学方程进行数值求解,分析了滚动轴承外圈单点故障和多点故障的诊断特征。结果表明:当外圈具有多点故障时,随着故障数量和故障间隔的变化,故障特征频率各谐波的幅值会发生变化;当多点故障满足载荷相等和一定的间隔关系时,故障特征频率值与故障数量之间呈现对应的倍数关系。通过滚动轴承多点故障模拟试验验证了结论的正确性。     

The enhancement of fault detection and diagnosis in rolling element bearings using minimum entropy deconvolution combined with spectral kurtosis

Spectral kurtosis (SK) represents a valuable tool for extracting transients buried in noise, which makes it very powerful for the diagnostics of rolling element bearings. However, a high value of SK requires that the individual transients are separated, which in turn means that if their repetition rate is high their damping must be sufficiently high that each dies away before the appearance of the next. This paper presents an algorithm for enhancing the surveillance capability of SK by using the minimum entropy deconvolution (MED) technique. The MED technique effectively deconvolves the effect of the transmission path and clarifies the impulses, even where they are not separated in the original signal. The paper illustrates these issues by analysing signals taken from a high-speed test rig, which contained a bearing with a spalled inner race. The results show that the use of the MED technique dramatically sharpens the pulses originating from the impacts of the balls with the spall and increases the kurtosis values to a level that reflects the severity of the fault. Moreover, when the algorithm was tested on signals taken from a gearbox for a bearing with a spalled outer race, it shows that each of the impulses originating from the impacts is made up of two parts (corresponding to entry into and exit from the spall). This agrees well with the literature but is often difficult to observe without the use of the MED technique. The use of the MED along with SK analysis also greatly improves the results of envelope analysis for making a complete diagnosis of the fault and trending its progression.     

Bi-spectrum based-EMD applied to the non-stationary vibration signals for bearing faults diagnosis

Empirical mode decomposition (EMD) has been widely applied to analyze vibration signals behavior for bearing failures detection. Vibration signals are almost always non-stationary since bearings are inherently dynamic (e.g., speed and load condition change over time). By using EMD, the complicated non-stationary vibration signal is decomposed into a number of stationary intrinsic mode functions (IMFs) based on the local characteristic time scale of the signal. Bi-spectrum, a third-order statistic, helps to identify phase coupling effects, the bi-spectrum is theoretically zero for Gaussian noise and it is flat for non-Gaussian white noise, consequently the bi-spectrum analysis is insensitive to random noise, which are useful for detecting faults in induction machines. Utilizing the advantages of EMD and bi-spectrum, this article proposes a joint method for detecting such faults, called bi-spectrum based EMD (BSEMD). First, original vibration signals collected from accelerometers are decomposed by EMD and a set of IMFs is produced. Then, the IMF signals are analyzed via bi-spectrum to detect outer race bearing defects. The procedure is illustrated with the experimental bearing vibration data. The experimental results show that BSEMD techniques can effectively diagnosis bearing failures.     

Latent component-based gear tooth fault detection filter using advanced parametric modeling

In this paper, a new parametric model-based filter is proposed for gear tooth fault detection. The designing of the filter consists of identifying the most proper latent component (LC) of the undamaged gearbox signal by analyzing the instant modules (IMs) and instant frequencies (IFs) and then using the component with lowest IM as the proposed filter output for detecting fault of the gearbox. The filter parameters are estimated by using the LC theory in which an advanced parametric modeling method has been implemented. The proposed method is applied on the signals, extracted from simulated gearbox for detection of the simulated gear faults. In addition, the method is used for quality inspection of the produced Nissan–Junior vehicle gearbox by gear profile error detection in an industrial test bed. For evaluation purpose, the proposed method is compared with the previous parametric TAR/AR-based filters in which the parametric model residual is considered as the filter output and also Yule–Walker and Kalman filter are implemented for estimating the parameters. The results confirm the high performance of the new proposed fault detection method.     

多共振分量融合CNN的行星齿轮箱故障诊断

针对行星齿轮箱中各部件所激起的振动成分混叠、早期故障特征经常被较强的各级齿轮谐波成分以及环境噪声所湮没的问题,提出一种多共振分量融合卷积神经网络（multi-resonance component fusion based convolutional neural network,简称MRCF-CNN）的行星齿轮箱故障诊断方法。首先,对振动信号进行共振稀疏分解,得到包含齿轮谐波成分的高共振分量和可能包含轴承故障冲击成分的低共振分量;其次,构建多共振分量融合卷积神经网络,将得到的高、低共振分量和原始振动信号进行自适应的特征级融合,通过有监督的方式训练模型并进行行星齿轮箱故障诊断。对行星齿轮箱实验数据的分析结果表明,该方法能够有效分类行星齿轮箱中滚动轴承和齿轮的故障,成功对行星齿轮箱故障进行诊断,同时能够进一步增强卷积神经网络对振动信号所蕴含的故障信息的辨识能力。     

Intelligent condition monitoring of a gearbox using artificial neural network

This paper concentrates on a new procedure which experimentally recognises gears and bearings faults of a typical gearbox system using a multi-layer perceptron neural network. Feature vector which is one of the most significant parameters to design an appropriate neural network was innovated by standard deviation of wavelet packet coefficients. The gear conditions were considered to be normal gearbox and slight- and medium-worn and broken-teeth gears faults and a general bearing fault which were five neurons of output layer with the aim of fault detection and identification. A downscaled 2-layer multi-layer perceptron neural-network-based system with great accuracy was designed to carry out the task. In this research, vibration signals were recognised as the most reliable source to extract the feature vector which were synchronised by piecewise cubic hermite interpolation (PCHI) and pre-processed using the standard deviation of wavelet packet coefficients.