A wavelet approach to fault diagnosis of a gearbox under varying load conditions

Varying load can cause changes in a measured gearbox vibration signal. However, conventional techniques for fault diagnosis are based on the assumption that changes in vibration signal are only caused by deterioration of the gearbox. There is a need to develop a technique to provide accurate state indicator of gearbox under fluctuating load conditions. This paper presents an approach to gear fault diagnosis based on complex Morlet continuous wavelet transform under this condition. Gear motion residual signal, which represents the departure of time synchronously averaged signal from the average tooth-meshing vibration, is analyzed as source data due to its lower sensitiveness to the alternating load condition. A fault growth parameter based on the amplitude of wavelet transform is proposed to evaluate gear fault advancement quantitatively. We found that this parameter is insensitive to varying load and can correctly indicate early gear fault. For a comparison, the advantages and disadvantages of other measures such as kurtosis, mean, variance, form factor and crest factor, both of residual signal and mean amplitude of continuous wavelet transform waveform, are also discussed. The effectiveness of the proposed fault indicator is demonstrated using a full lifetime vibration data history obtained under sinusoidal varying load.     

A time domain approach to diagnose gearbox fault based on measured vibration signals

Spectral analysis techniques to process vibration measurements have been widely studied to characterize the state of gearboxes. However, in practice, the modulated sidebands resulting from the local gear fault are often difficult to extract accurately from an ambiguous/blurred measured vibration spectrum due to the limited frequency resolution and small fluctuations in the operating speed of the machine that often occurs in an industrial environment. To address this issue, a new time-domain diagnostic algorithm is developed and presented herein for monitoring of gear faults, which shows an improved fault extraction capability from such measured vibration signals. This new time-domain fault detection method combines the fast dynamic time warping (Fast DTW) as well as the correlated kurtosis (CK) techniques to characterize the local gear fault, and identify the corresponding faulty gear and its position. Fast DTW is employed to extract the periodic impulse excitations caused from the faulty gear tooth using an estimated reference signal that has the same frequency as the nominal gear mesh harmonic and is built using vibration characteristics of the gearbox operation under presumed healthy conditions. This technique is beneficial in practical analysis to highlight sideband patterns in situations where data is often contaminated by process/measurement noises and small fluctuations in operating speeds that occur even at otherwise presumed steady-state conditions. The extracted signal is then resampled for subsequent diagnostic analysis using CK technique. CK takes advantages of the periodicity of the geared faults; it is used to identify the position of the local gear fault in the gearbox. Based on simulated gear vibration signals, the Fast DTW and CK based approach is shown to be useful for condition monitoring in both fixed axis as well as epicyclic gearboxes. Finally the effectiveness of the proposed method in fault detection of gears is validated using experimental signals from a planetary gearbox test rig. For fault detection in planetary gear-sets, a window function is introduced to account for the planet motion with respect to the fixed sensor, which is experimentally determined and is later employed for the estimation of reference signal used in Fast DTW algorithm.     

Complex signal analysis for wind turbine planetary gearbox fault diagnosis via iterative atomic decomposition thresholding

The vibration signals from complex structures such as wind turbine (WT) planetary gearboxes are intricate. Reliable analysis of such signals is the key to success in fault detection and diagnosis for complex structures. The recently proposed iterative atomic decomposition thresholding (IADT) method has shown to be effective in extracting true constituent components of complicated signals and in suppressing background noise interferences. In this study, such properties of the IADT are exploited to analyze and extract the target signal components from complex signals with a focus on WT planetary gearboxes under constant running conditions. Fault diagnosis for WT planetary gearboxes has been a very important yet challenging issue due to their harsh working conditions and complex structures. Planetary gearbox fault diagnosis relies on detecting the presence of gear characteristic frequencies or monitoring their magnitude changes. However, a planetary gearbox vibration signal is a mixture of multiple complex components due to the unique structure, complex kinetics and background noise. As such, the IADT is applied to enhance the gear characteristic frequencies of interest, and thereby diagnose gear faults. Considering the spectral properties of planetary gearbox vibration signals, we propose to use Fourier dictionary in the IADT so as to match the harmonic waves in frequency domain and pinpoint the gear fault characteristic frequency. To reduce computing time and better target at more relevant signal components, we also suggest a criterion to estimate the number of sparse components to be used by the IADT. The performance of the proposed approach in planetary gearbox fault diagnosis has been evaluated through analyzing the numerically simulated, lab experimental and on-site collected signals. The results show that both localized and distributed gear faults, both the sun and planet gear faults, can be diagnosed successfully.     

Constrained adaptive lifting and the CAL4 metric for helicopter transmission diagnostics

This paper presents a methodology for detecting and diagnosing gear faults in the planetary stage of a helicopter transmission. This diagnostic technique is based on the constrained adaptive lifting (CAL) algorithm, an adaptive manifestation of the lifting scheme. Lifting is a time domain, prediction-error realization of the wavelet transform that allows for greater flexibility in the construction of wavelet bases. Adaptivity is desirable for gear diagnostics as it allows the technique to tailor itself to a specific transmission by selecting a set of wavelets that best represent vibration signals obtained while the gearbox is operating under healthy-state conditions. However, constraints on certain basis characteristics are necessary to enhance the detection of local wave-form changes caused by certain types of gear damage. The proposed methodology analyzes individual tooth-mesh waveforms from a healthy-state gearbox vibration signal that was generated using the vibration separation synchronous signal-averaging algorithm. Each waveform is separated into analysis domains using zeros of its slope and curvature. The bases selected in each analysis domain are chosen to minimize the prediction error, and constrained to have approximately the same-sign local slope and curvature as the original signal. The resulting set of bases is used to analyze future-state vibration signals and the lifting prediction error is inspected. The constraints allow the transform to effectively adapt to global amplitude changes, yielding small prediction errors. However, local waveform changes associated with certain types of gear damage are poorly adapted, causing a significant change in the prediction error. A diagnostic metric based on the lifting prediction error vector termed CAL4 is developed. The CAL diagnostic algorithm is validated using data collected from the University of Maryland Transmission Test Rig and the CAL4 metric is compared with the classic metric FM4.     

Application of Generalized Composite Multiscale Lempel–Ziv Complexity in Identifying Wind Turbine Gearbox Faults

Wind turbine gearboxes operate in harsh environments; therefore, the resulting gear vibration signal has characteristics of strong nonlinearity, is non-stationary, and has a low signal-to-noise ratio, which indicates that it is difficult to identify wind turbine gearbox faults effectively by the traditional methods. To solve this problem, this paper proposes a new fault diagnosis method for wind turbine gearboxes based on generalized composite multiscale Lempel–Ziv complexity (GCMLZC). Within the proposed method, an effective technique named multiscale morphological-hat convolution operator (MHCO) is firstly presented to remove the noise interference information of the original gear vibration signal. Then, the GCMLZC of the filtered signal was calculated to extract gear fault features. Finally, the extracted fault features were input into softmax classifier for automatically identifying different health conditions of wind turbine gearboxes. The effectiveness of the proposed method was validated by the experimental and engineering data analysis. The results of the analysis indicate that the proposed method can identify accurately different gear health conditions. Moreover, the identification accuracy of the proposed method is higher than that of traditional multiscale Lempel–Ziv complexity (MLZC) and several representative multiscale entropies (e.g., multiscale dispersion entropy (MDE), multiscale permutation entropy (MPE) and multiscale sample entropy (MSE)).     

Vibration signal models for fault diagnosis of planetary gearboxes

A thorough understanding of the spectral structure of planetary gear system vibration signals is helpful to fault diagnosis of planetary gearboxes. Considering both the amplitude modulation and the frequency modulation effects due to gear damage and periodically time variant working condition, as well as the effect of vibration transfer path, signal models of gear damage for fault diagnosis of planetary gearboxes are given and the spectral characteristics are summarized in closed form. Meanwhile, explicit equations for calculating the characteristic frequency of local and distributed gear fault are deduced. The theoretical derivations are validated using both experimental and industrial signals. According to the theoretical basis derived, manually created local gear damage of different levels and naturally developed gear damage in a planetary gearbox can be detected and located.     

Research on dynamics and fault mechanism of spur gear pair with spalling defect

This study focuses on the nonlinear dynamic and vibration characteristics of spur gear pair with local spalling defect to explore the spalling mechanism. The dynamic model of the gear pair with spalling defect and time-variant mesh stiffness is established to investigate the effect of spalling defect on mesh stiffness and dynamic response. The analytical solutions of the system which is deduced into four different stages of the gear with the time-variant stiffness in a mesh period are obtained. The dynamic responses with the evolvement of sapll are analyzed by using time history, phase contrail, Poincaré section and spectrum analysis. The spalling characteristics are also evaluated by employing statistical techniques, which shows that the spalling failure is suitable to be detected under low velocity and small excitation. The gearbox with spalling defect is designed and the experiments are carried out to get the dynamic characteristics of the spalling vibration signals. The results obtained herein show the good agreement qualitatively with the theoretical analysis, which provides a theoretical basis to spalling fault diagnosis of gearbox.     

Application of multi-scale chirplet path pursuit and fractional Fourier transform for gear fault detection in speed up and speed-down processes

Demodulation is very important for gear fault detection. However, the demodulation is substantially complicated by the non-stationary nature of the signal during the speed-up and speed-down processes. As such, we propose a new technique to detect gear faults under such conditions based on the multi-scale chirplet path pursuit (MSCPP) algorithm and the fractional Fourier transform (FrFT) method. With the MSCPP algorithm, the instantaneous frequency of the signal component with the largest energy in the multi-components gear vibration signal can be estimated. Then according to the estimated instantaneous frequency, the vibration signal segment whose instantaneous frequency curve approximated as either an ascending or descending linear segment can be obtained from the original gear vibration signal. In other words, the vibration signal segment that can be regarded as a multi-component linear frequency modulated (LFM) signal is extracted. As the FrFT is suitable for multi-component LFM signal analysis, it is then applied to demodulating this vibration signal segment and hence detecting local gear faults based on the revealed modulation phenomenon. The effectiveness of the proposed method has been demonstrated by both simulation and experimental data.     

Feasibility of a phased acoustic array for monitoring acoustic signatures from meshing gear teeth

This paper investigates the feasibility of sensing damage emanating from rotating drivetrain elements such as bearings, gear teeth, and drive shafts via airborne paths. A planar phased acoustic array is evaluated as a potential fault detection scheme for detecting spatially filtered acoustic signatures radiating from gearbox components. Specifically, the use of beam focusing and steering to monitor individual tooth mesh dynamics is analyzed taking into consideration the constraints of the array/gearbox geometry and the spectral content of typical gear noise. Experimental results for a linear array are presented to illustrate the concepts of adaptive beam steering and spatial acoustic filtering. This feasibility study indicates that the planar array can be used to track the acoustic signatures at higher harmonics of the gear mesh frequency.     

Fusion Domain-Adaptation CNN Driven by Images and Vibration Signals for Fault Diagnosis of Gearbox Cross-Working Conditions

The vibration signal of gearboxes contains abundant fault information, which can be used for condition monitoring. However, vibration signal is ineffective for some non-structural failures. In order to resolve this dilemma, infrared thermal images are introduced to combine with vibration signals via fusion domain-adaptation convolutional neural network (FDACNN), which can diagnose both structural and non-structural failures under various working conditions. First, the measured raw signals are converted into frequency and squared envelope spectrum to characterize the health states of the gearbox. Second, the sequences of the frequency and squared envelope spectrum are arranged into two-dimensional format, which are combined with infrared thermal images to form fusion data. Finally, the adversarial network is introduced to realize the state recognition of structural and non-structural faults in the unlabeled target domain. An experiment of gearbox test rigs was used for effectiveness validation by measuring both vibration and infrared thermal images. The results suggest that the proposed FDACNN method performs best in cross-domain fault diagnosis of gearboxes via multi-source heterogeneous data compared with the other four methods.     

Feature separation using ICA for a one-dimensional time series and its application in fault detection

Principal component analysis (PCA) is a method that transforms multiple data series into uncorrelated data series. Independent component analysis (ICA) is a method that separates multiple data series into independent data series. Both methods have been used in fault detection. However, both require signals from at least two separate sensors. To overcome this requirement and utilize the fault detection capability of ICA and PCA, we propose to use wavelet transform to pre-process the data collected from a single sensor and then use the coefficients of the wavelet transforms at different scales as input to ICA and PCA. The effectiveness of this method is demonstrated by applying it to both a simulated signal series and a vibration signal series collected from a gearbox. The results show that the method of combining wavelet transform and ICA works better than the method of combining wavelet transform and PCA for impulse detection based on a one-dimensional vibration data series.     

基于BP神经网络的变速箱故障诊断方法研究

针对变速箱的工作时间不能真实反映实际健康状况的问题,通过提取变速箱的振动信号作为状态参数,建立了基于BP神经网络的变速箱故障诊断模型。该模型首先提取振动信号中对故障反映灵敏的成分作为特征值,获得BP神经网络的训练数据,并通过对比确定最优的隐含层节点数,确定BP神经网络的结构参数。模型训练结束后,以验证数据为例进行故障诊断研究,并对诊断结果进行评估。评估结果表明,该模型准确度高,具有较好的应用和推广价值。     

Comparisons of MFDFA,EMD and WT by Neural Network,Mahalanobis Distance and SVM in Fault Diagnosis of Gearboxes

A method for gearbox fault diagnosis consists of feature extraction and fault identification. Many methods for feature extraction have been devised for exposing nature of vibration data of a defective gearbox. In addition, features extracted from gearbox vibration data are identified by various classifiers. However, existing literatures leave much to be desired in assessing performance of different combinatorial methods for gearbox fault diagnosis. To this end, this paper evaluated performance of several typical combinatorial methods for gearbox fault diagnosis by associating each of multifractal detrended fluctuation analysis (MFDFA), empirical mode decomposition (EMD) and wavelet transform (WT) with each of neural network (NN), Mahalanobis distance decision rules (MDDR) and support vector machine (SVM). Following this, performance of different combinatorial methods was compared using a group of gearbox vibration data containing slightly different fault patterns. The results indicate that MFDFA performs better in feature extraction of gearbox vibration data and SVM does the same in fault identification. Naturally, the method associating MFDFA with SVM shows huge potential for fault diagnosis of gearboxes. As a result, this paper can provide some useful information on construction of a method for gearbox fault diagnosis.     

Investigation of the influence of oil film thickness on helical gear defect detection using Acoustic Emission

This paper reports an investigation into the use of Acoustic Emission (AE) for monitoring gear teeth defects under varying lubrication regimes in helical gears. The investigation used a back-to-back gearbox test-rig with oil-bath lubrication. Variation in oil film thickness was achieved by decreasing the gear metal temperature with nitrogen gas whilst the gears were in operation. Results demonstrate a clear relationship between AE activity, operating temperature and specific film thickness. In addition, results show that there are lubricating conditions that may prevent AE from identifying the presence of gear defects.     

Vibro-acoustic propagation of gear dynamics in a gear-bearing-housing system

This work developed a computational process to predict noise radiation from gearboxes. It developed a system-level vibro-acoustic model of an actual gearbox, including gears, bearings, shafts, and housing structure, and compared the results to experiments. The meshing action of gear teeth causes vibrations to propagate through shafts and bearings to the housing radiating noise. The vibration excitation from the gear mesh and the system response were predicted using finite element and lumped-parameter models. From these results, the radiated noise was calculated using a boundary element model of the housing. Experimental vibration and noise measurements from the gearbox confirmed the computational predictions. The developed tool was used to investigate the influence of standard rolling element and modified journal bearings on gearbox radiated noise.     

基于激光自混合传感器的齿轮局部故障振动信号分析

建立了齿圈局部故障调频现象模型,分析了故障轮齿啮合频率及其倍频两侧边频带的产生机理,给出了齿圈局部故障特征频率的计算公式,建立了倒频谱分析模型。采用激光自混合传感器,分别从径向和轴向两个方向采集齿轮箱振动信号波形。在齿轮箱1Hz和2Hz两种不同输出转频下,分别研究了无故障齿轮箱和故障齿轮箱的振动信号特征。通过实验研究验证了理论推导结果。     

Dynamic modelling of spur gear pair and application of empirical mode decomposition-based statistical analysis for early detection of localized tooth defect

Gears are one of the most common and important machine components in many advanced machines. An improved understanding of vibration signal is required for the early detection of incipient gear failure to achieve high reliability. This paper mainly consists of two parts: in the first part, a 6-degree-of-freedom gear dynamic model including localized tooth defect has been developed. The model consists of a spur gear pair, two shafts, two inertias representing load and prime mover and bearings. The model incorporates the effects of time-varying mesh stiffness and damping, backlash, excitation due to gear errors and profile modifications. The second part consists of signal processing of simulated and experimental signals. Empirical mode decomposition (EMD) is a method of breaking down a signal without leaving a time domain. The process is useful for analysing non-stationary and nonlinear signals. EMD decomposes a signal into some individual, nearly monocomponent signals, named as intrinsic mode function (IMF). Crest factor and kurtosis have been calculated of these IMFs. EMD pre-processed kurtosis and crest factor give early detection of pitting as compared to raw signal.     

Gearbox vibration monitoring using extended Kalman filters and hypothesis tests

The efficiency of many maintenance programs is heavily dependent on the detection accuracy of the condition monitoring system. Condition indicators that are sensitive to environmental or operational variables of no interest will inevitably reflect irrelevant fluctuations and thus mislead the subsequent analysis. In consideration of this phenomenon, a fully automatic and robust vibration monitoring system for gearboxes is proposed in this study. The primary objective here is on how to exclude the effects of variable load conditions. The proposed technique features a number of appealing advantages, which include extended Kalman filter-based time-varying autoregressive modeling, automatic autoregressive model order selection with the aid of a non-paired two-sample Satterthwaite's t′-test, a highly effective and robust condition indicator (the means of one-sample Kolmogorov-Smirnov goodness-of-fit test), and an automatic alert generating mechanism for incipient gear faults with the aid of a Wilcoxon rank-sum test. Two sets of entire lifetime gearbox vibration monitoring data with distinct variable load conditions were used for experimental validation. The proposed condition indicator was compared with other well-known and/or recently proposed condition indicators. The results demonstrate excellent performance of the proposed technique in four aspects: the effectiveness of identifying the optimum model order, a minimum number of false alerts, constant behavior under variable load conditions, and to some extent an early alert for incipient gear faults. Furthermore, the proposed condition indicator can be directly employed by condition-based maintenance programs as a condition covariate for operational maintenance decision analysis. It provides a quantitative and more efficient means for exchanging condition information with maintenance programs in comparison with the widely used non-parametric time-frequency techniques such as wavelets, which rely on visual inspection.     

Subway Gearbox Fault Diagnosis Algorithm Based on Adaptive Spline Impact Suppression

In the signal processing of real subway vehicles, impacts between wheelsets and rail joint gaps have significant negative effects on the spectrum. This introduces great difficulties for the fault diagnosis of gearboxes. To solve this problem, this paper proposes an adaptive time-domain signal segmentation method that envelopes the original signal using a cubic spline interpolation. The peak values of the rail joint gap impacts are extracted to realize the adaptive segmentation of gearbox fault signals when the vehicle was moving at a uniform speed. A long-time and unsteady signal affected by wheel–rail impacts is segmented into multiple short-term, steady-state signals, which can suppress the high amplitude of the shock response signal. Finally, on this basis, multiple short-term sample signals are analyzed by time- and frequency-domain analyses and compared with the nonfaulty results. The results showed that the method can efficiently suppress the high-amplitude components of subway gearbox vibration signals and effectively extract the characteristics of weak faults due to uniform wear of the gearbox in the time and frequency domains. This provides reference value for the gearbox fault diagnosis in engineering practice.     

A Simplified Formulation to Estimate Influence of Gearbox Parameters on the Rattle Noise

Occurrence of gear rattle in transmission systems can result in severe vibration and noise, which in applications such as automobiles is an important source of user discomfort. As a result , the reduction of the rattling noise has attracted lot of concerns. The rattling noise level is affected by several gearbox parameters, an understanding of which is essential to prevent the expensive design modifications at later stages of product development. To develop such understanding at the gearbox design stage, this paper analytically evaluates the gear parameters’ effect on the root mean square of the wheel gear acceleration under idling condition, which is known to be linearly correlated to the rattling noise level. Therefore, this evaluation allows for an investigation of the gear parameters’ influence on the rattling noise as well. This method is then verified by comparing the analytical results with the simulation results from a dynamic model built in SIMPACK as well as previously published experimental results. Thus, the proposed analytical evaluation method can optimize the gearbox specifications at the design stage to reduce the gear rattle noise level.