Vibration-based rolling element bearing diagnostics is a very well-developed field, yet researchers continue to develop new diagnostic algorithms quite frequently. Over the last decade, data from the ...Case Western Reserve University (CWRU) Bearing Data Center has become a standard reference used to test these algorithms, yet without any recognised benchmark it is difficult to properly assess the performance of any proposed diagnostic methods. There is, then, a clear need to examine the data thoroughly and to categorise it appropriately, and this paper intends to fulfil that objective. To do so, three established diagnostic techniques are applied to the entire CWRU data set, and the diagnostic outcomes are provided and discussed in detail. Recommendations are given as to how the data might best be used, and also on how any future benchmark data should be generated. Though intended primarily as a benchmark to aid in testing new diagnostic algorithms, it is also hoped that much of the discussion will have broader applicability to other bearing diagnostics cases.
•We provide a thorough benchmark analysis of the CWRU Bearing Data.•Three established diagnostic techniques are applied.•We provide the diagnostic outcomes for all data sets as a benchmark reference.•We discuss the records at length and identify data problems and anomalies.•We give recommendations as to how best to use the data for algorithm development.
•The cepstrum pre-dates the FFT, despite having one common author (John Tukey).•The cepstrum is a “spectrum of a log spectrum” and separates input and transfer path.•Families of harmonics and/or ...sidebands can be identified, assessed, and/or removed.•Analytical form of the complex cepstrum can be curve-fitted for modal analysis.•Time signals can now be edited using the real cepstrum.
It is not widely realised that the first paper on cepstrum analysis was published two years before the FFT algorithm, despite having Tukey as a common author, and its definition was such that it was not reversible even to the log spectrum. After publication of the FFT in 1965, the cepstrum was redefined so as to be reversible to the log spectrum, and shortly afterwards Oppenheim and Schafer defined the “complex cepstrum”, which was reversible to the time domain. They also derived the analytical form of the complex cepstrum of a transfer function in terms of its poles and zeros. The cepstrum had been used in speech analysis for determining voice pitch (by accurately measuring the harmonic spacing), but also for separating the formants (transfer function of the vocal tract) from voiced and unvoiced sources, and this led quite early to similar applications in mechanics. The first was to gear diagnostics (Randall), where the cepstrum greatly simplified the interpretation of the sideband families associated with local faults in gears, and the second was to extraction of diesel engine cylinder pressure signals from acoustic response measurements (Lyon and Ordubadi). Later Polydoros defined the differential cepstrum, which had an analytical form similar to the impulse response function, and Gao and Randall used this and the complex cepstrum in the application of cepstrum analysis to modal analysis of mechanical structures. Antoni proposed the mean differential cepstrum, which gave a smoothed result. The cepstrum can be applied to MIMO systems if at least one SIMO response can be separated, and a number of blind source separation techniques have been proposed for this. Most recently it has been shown that even though it is not possible to apply the complex cepstrum to stationary signals, it is possible to use the real cepstrum to edit their (log) amplitude spectrum, and combine this with the original phase to obtain edited time signals. This has already been used for a wide range of mechanical applications. A very powerful processing tool is an exponential “lifter” (window) applied to the cepstrum, which is shown to extract the modal part of the response (with a small extra damping of each mode corresponding to the window). This can then be used to repress or enhance the modal information in the response according to the application.
This tutorial is intended to guide the reader in the diagnostic analysis of acceleration signals from rolling element bearings, in particular in the presence of strong masking signals from other ...machine components such as gears. Rather than being a review of all the current literature on bearing diagnostics, its purpose is to explain the background for a very powerful procedure which is successful in the majority of cases. The latter contention is illustrated by the application to a number of very different case histories, from very low speed to very high speed machines. The specific characteristics of rolling element bearing signals are explained in great detail, in particular the fact that they are not periodic, but stochastic, a fact which allows them to be separated from deterministic signals such as from gears. They can be modelled as cyclostationary for some purposes, but are in fact not strictly cyclostationary (at least for localised defects) so the term pseudo-cyclostationary has been coined. An appendix on cyclostationarity is included. A number of techniques are described for the separation, of which the discrete/random separation (DRS) method is usually most efficient. This sometimes requires the effects of small speed fluctuations to be removed in advance, which can be achieved by order tracking, and so this topic is also amplified in an appendix. Signals from localised faults in bearings are impulsive, at least at the source, so techniques are described to identify the frequency bands in which this impulsivity is most marked, using spectral kurtosis. For very high speed bearings, the impulse responses elicited by the sharp impacts in the bearings may have a comparable length to their separation, and the minimum entropy deconvolution technique may be found useful to remove the smearing effects of the (unknown) transmission path. The final diagnosis is based on “envelope analysis” of the optimally filtered signal, but despite the fact that this technique has been used for 40 years in analogue form, the advantages of more recent digital implementations are explained.
•A novel tool is presented based on the integration of Cyclic Spectral Coherence.•Focuses at the selection of the optimum integration band which can lead to an IES.•The tool is presented as an ...1/3-binary color map.•The method has been evaluated on two cases under steady and time varying conditions.•The method is compared with state of the art methodologies.
Demodulation methods are widely used for bearing diagnostics, based often on the (Squared) Envelope Spectrum after band pass filtering. One of the main challenges of these methods is the detection of a suitable band for signal demodulation under varying speed conditions. Angular resampling methods may synchronize the impulsive nature of bearing damages with a certain periodicity, in the case of large speed fluctuations. On the other hand, the time-invariant carrier frequencies may spread over the broadband of the spectrum, making impossible the application of many band selection tools. Lately, focus has been targeted to cyclostationary-based tools, such as the Cyclic Spectral Correlation and the Cyclic Spectral Coherence, which achieve a high performance in detecting hidden cyclic periodicities. Initially, these methods have been represented in the Frequency-Frequency domain, however they have been extended, to the Order-Order and the Order-Frequency domains, to be able to describe signals under varying speed conditions. The integration of these bi-variable maps over a specific frequency band results to an equivalent to a demodulated spectrum. Therefore, the challenge is the selection of the proper integration band to obtain these demodulated spectra for bearing diagnostics. In this paper, a novel tool called the Improved Envelope Spectrum via Feature Optimization-gram (IESFOgram) is proposed as a band selection tool for the demodulation of the bi-variable map (CSC or CSCoh) for bearing diagnostics. The method is represented in a 1/3-binary tree and is applicable under constant and variable speed conditions. The methodology is tested and validated on real data captured on a laboratory planetary gearbox and on an aircraft engine gearbox, under both constant and varying speed conditions. Furthermore, the methodology is compared in terms of performance with the Fast Kurtogram and the Autogram-based methods.
This paper presents the application of the spectral kurtosis technique for detection of a tooth crack in the planetary gear of a wind turbine. The work originated from a real case of catastrophic ...gear failure on a wind turbine, which was not detected by currently applied methods. Nevertheless, several sets of complete vibration data were recorded and analyzed. The authors explored a number of methods commonly applied in online vibration monitoring and diagnostic systems. Those methods did not react to the failure until a few minutes before the failure. Then the method of time domain averaging of the meshing vibration is investigated. In this case, however, averaging does not detect any trace of the tooth crack, primarily because of the extreme frequency range (>four decades) of the fault symptoms. The application of the method is shown, and then the limitations of the averaging in such a case are presented and discussed. Finally, the authors propose a method based on spectral kurtosis, which yields good results. This method was able to detect the existence of the tooth crack several weeks before the gear failure.
•We propose a novel vibration-based approach for monitoring and predicting gear wear.•Approach suitable for two main wear phenomena, gear profile change and surface pitting.•An effective and ...efficient surface pitting model is developed in the proposed methodology.•Effectiveness of approach validated using vibration data from lubricated and dry tests.
Gear wear often results in both tooth profile changes caused by abrasive wear, and fatigue pitting. Being able to accurately monitor and predict the profile change (i.e., the wear depth in the direction normal to the gear surface) and surface pitting propagation can bring enormous benefits to industrial practice. However, there is a lack of efficient, reliable, and effective tools to do so. To address this, this paper proposes a gear wear monitoring and prediction approach through the integration of: (i) a dynamic model, to simulate the dynamic responses of the gear system; (ii) two tribological models, to estimate wear depth (in the direction normal to the gear surface) and pitting density (on the gear surface); and (iii), model updating, by comparing simulated and measured vibration signals.
More specifically, a 21-degree-of-freedom dynamic model is used to simulate a spur gearbox setup and produce simulated vibrations and contact forces between the meshing gear teeth. Using the contact pressure (calculated from the force) as an input, the wear depth and pitting density are then predicted by the tribological models and used to modify the gear geometry profile and contact area in the dynamic model. The developed approach allows the dynamic model and the wear models to communicate so that both the gear tooth profile change and pitting density can be simulated continuously. To guarantee accurate prediction results from the models, novel approaches are developed to update the wear coefficients in the tribological models by comparing simulated and measured vibrations. The paper demonstrates the ability and effectiveness of the proposed vibration-based methodology in monitoring and predicting gear wear, specifically the tooth profile change and surface pitting propagation, using measurements from both a lubricated test, dominated by surface pitting propagation with mild tooth profile change, and a dry test dominated by tooth profile change.
•A vibration-based wear mechanism identification procedure is proposed.•Wear evolution is tracked using an indicator of vibration cyclostationarity (CS).•The correlation between surface features and ...vibration characteristics is investigated.•Methods validated using lubricated and dry gear wear tests.
Fatigue pitting and abrasive wear are the most common wear mechanisms in lubricated gears, and they have different effects on the gear transmission system. To develop effective methods for online gear wear monitoring, in this paper, a vibration-based wear mechanism identification procedure is proposed, and then the wear evolution is tracked using an indicator of vibration cyclostationarity (CS). More specifically, with consideration of the underlying physics of the gear meshing process, and the unique surface features induced by fatigue pitting and abrasive wear, the correlation between tribological features of the two wear phenomena and gearmesh-modulated second-order cyclostationary (CS2) properties of the vibration signal is investigated. Differently from previous works, the carrier frequencies (spectral content) of the gearmesh-cyclic CS2 components are analysed and used to distinguish and track the two wear phenomena. The effectiveness of the developed methods in wear mechanism identification and degradation tracking is validated using vibration data collected in two tests: a lubricated test dominated by fatigue pitting and a dry test dominated by abrasive wear. This development enables vibration-based techniques to be used for identifying and tracking fatigue pitting and abrasive wear.
Gear tooth wear is an inevitable phenomenon and has a significant influence on gear dynamic features. Although vibration analysis has been widely used to diagnose localised gear tooth faults, its ...techniques for gear wear monitoring have not been well-established. This paper aims at developing a vibration indicator to evaluate the effects of wear on gear performance. For this purpose, a gear state vector is extracted from time synchronous averaged gear signals to describe the gear state. This gear state vector consists of the sideband ratios obtained from a number of tooth meshing harmonics and their sidebands. Then, two averaged logarithmic ratios, ALR and mALR, are defined with fixed and moving references, respectively, to provide complementary information for gear wear monitoring. Since a fixed reference is utilised in the definition of ALR, it reflects the cumulated wear effects on the gear state. An increase in the ALR value indicates that the gear state deviates further from its reference condition. With the use of a moving reference, the indicator mALR shows changes in the gear state within short time intervals, making it suitable for wear process monitoring. The efficiency of these vibration indicators is demonstrated using experimental results from two sets of tests, in which the gears experienced different wear processes. In addition to gear wear monitoring, the proposed indicators can be used as general parameters to detect the occurrence of other faults, such as a tooth crack or shaft misalignment, because these faults would also change the gear vibrations.
•The effects of tooth wear on gear transmission error and gear vibrations are clearly explained.•An averaged logarithmic ratio (ALR) is introduced to represent the changes in the gear conditions.•The efficiency of ALR has been demonstrated using the results of wear particle analysis.•ALR can also be used as a general parameter for gear condition monitoring.
Gear wear introduces geometric deviations in gear teeth and alters the load distribution across the tooth surface. Wear also increases the gear transmission error, generally resulting in increased ...vibration, noise and dynamic loads. This altered loading in turn promotes wear, forming a feedback loop between gear surface wear and vibration. Having the capability to monitor and predict the gear wear process would bring enormous benefits in cost and safety to a wide range of industries, but there are currently no reliable, effective and efficient tools to do so. This paper develops such tools using vibration-based methods.
For this purpose, a vibration-based scheme for updating a wear prediction model is proposed. In the proposed scheme, a dynamic model of a spur gear system is firstly developed to generate realistic vibrations, which allows a quantitative study of the effects of gear tooth surface wear on gearbox vibration responses. The sliding velocity and contact forces from the model are used in combination with the well-known Archard wear model to calculate the wear depth at each contact point in mesh. The worn gear tooth profile is then fed back into the dynamic model as a new geometric transmission error, which represents the deviation of the profile from an ideal involute curve and is thus zero for perfect gears. New vibration responses and tooth contact forces are then obtained from the model, and the process repeated to generate realistic gear wear profiles of varying severities. Since the wear coefficient in the model is not constant during the wear process (and in any case is difficult to estimate initially), measured vibrations are compared with those generated by the model, so as to update the coefficient when a deviation from predictions is detected. With the continually updated dynamic wear model, the wear process can be well monitored, and at any particular time the best possible prediction of remaining useful life can be achieved. The paper illustrates the ability and effectiveness of the proposed scheme using measurements from a laboratory gear rig.
•We propose a vibration-based scheme for updating gear wear prediction.•Prediction based on models of gearbox dynamics and abrasive wear.•Updating of wear constant based on comparing simulated and measured vibration.•Scheme allows reliable wear prediction using simple modelling tools.•Scheme experimentally validated on run-to-failure dry test with spur gears.
•The evolving spall sizes were measured during run-to-failure experiments for REBs.•Four measurements (acceleration, AE, IAS, and displacement) were compared.•Displacement was the best for spall size ...estimation, and acceleration comes next.•IAS correlates well with spall size, albeit not a direct quantitative size.•AE was found poor in both quantification and tracking of natural spall size.
Bearing prognostics is an important aspect in condition-based maintenance (CBM), and a key step to successful prognostic methods is the ability to quantify the fault severity of the bearing. Previous studies have resulted in some severity assessment methods based on certain types of signals, such as vibration, acoustic emission (AE) and instantaneous angular speed (IAS), however, their performances were not compared, especially in terms of their ability to track the severity of naturally growing spalls. In this paper, four measurement approaches were tested on the same rig for bearing run-to-failure experiments, and their signals were analysed individually and compared. It was found that IAS and radial load (a proxy for displacement) required less processing to provide a reliable assessment of bearing fault severity, acceleration required sophisticated techniques to extract spall-size estimates, whereas AE could not track fault evolution accurately.
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