Tracking Bearing Degradation using Gaussian Wavelets

Size: px

Start display at page:

Download "Tracking Bearing Degradation using Gaussian Wavelets"

Vivian Gilmore
5 years ago
Views:

1 Trackig Bearig Degradatio usig Gaussia Wavelets Toy Galati 1 1 Aerospace Divisio, Defece Sciece ad Techology Group, 56 Lorimer Street, Fishermas Bed, Victoria, 37, Australia Abstract This paper ivestigates the use of Gaussia wavelets for trackig the degradatio of rollig elemet bearigs. Spalls i bearig raceways or rollig elemets lead to impacts which excite structural resoaces. Gaussia wavelets are show to correlate well with these structural resoaces whe they appear i the measured vibratio sigal. Impacts are deemed to be detected i the vibratio sigal wheever the correlatio with the Gaussia wavelet exceeds a predetermied level. As the spalled area icreases i the bearig over time, the correspodig rate of impacts icreases. Bearig degradatio is tracked through moitorig the impact rate measured usig the Gaussia wavelet. The techique is validated o vibratio data obtaied from a aturally occurrig fault i the epicyclic plaet gear bearig i a helicopter mai rotor gearbox. Keywords: Bearig Fault, Gaussia Wavelet, Progosis. Itroductio May vibratio aalysis techiques for rollig elemet bearig health moitorig have bee developed to date. A recet overview [1] shows that the focus has bee primarily o detectio ad diagosis. A diagosis iforms you that a bearig is faulty, but does ot provide iformatio about how rapidly the bearig is deterioratig, or what its remaiig useful life is. These are importat cosideratios whe developig or implemetig maiteace policy. Whe a rollig elemet passes over a localised raceway spall, or a spall o a rollig elemet passes ito the cotact zoe, the correspodig impulse respose excites structural resoaces. These structural resoaces are localised ot oly i frequecy, but also i time, due to structural dampig. Wavelets are also localised i both frequecy ad time, ad it is this property which has bee used successfully for bearig fault diagosis [1, ]. The approach developed i this paper is iteded to be applied after diagosis of a fault, ad focuses o trackig bearig degradatio over time. I essece, the approach uses a optimal wavelet to mimic the bearig fault impulse respose i the measured vibratio sigal. A wavelet is deemed optimal if it is well correlated with the bearig fault impulse respose i the vibratio sigal. As the umber of spalls icrease over time (i.e. as the bearig degrades), the rate of impulse geeratio, ad cosequetly the wavelet correlatio rate, also icrease over time. Thus, moitorig the correlatio rate provides a meas of moitorig the degradatio of the bearig. The idea described above is depedet o a good correlatio betwee the wavelet ad the impulse respose to the bearig fault i the measured vibratio sigal. For this reaso, Gaussia wavelets are chose because of their geeral similarity to trasiet structural 17 th Australia Aerospace Cogress, 6-8 February 17, Melboure

2 vibratios [3]. However, the wavelets still eed to be optimised (or tued) to the specific structural respose of the mechaical system of iterest. Procedure for Trackig Bearig Degradatio The procedure for trackig bearig fault degradatio ca be divided ito two mai steps. The first step is to fid the optimal Gaussia wavelet that produces a good correlatio with the bearig fault impulse respose i the measured vibratio sigal. A coditioal optimisatio usig the Cotiuous Wavelet Trasform (CWT) is used to fid the optimal Gaussia wavelet parameters. To facilitate this, Gaussia wavelets are itroduced first before details of the optimisatio procedure are preseted. The secod step, Degradatio Moitorig, ivolves usig the optimal Gaussia wavelet parameters foud i the first step to moitor the degradatio of the bearig over time. A sigle-scale CWT, usig the optimal Gaussia wavelet parameters, is used to idetify the bearig fault impulse resposes i the measured vibratio sigal. A cumulative cout of the umber of correlatios is extracted from the sigle-scale CWT by first zeroig all poits of the CWT which fall below a pre-set threshold, ad the itegratig this modified CWT over time. The cumulative correlatio cout ca the be used as a idicator of the cumulative degradatio of the bearig over time, ad its derivative to estimate the rate of degradatio. Gaussia Wavelets The family of Gaussia wavelets are derived from the expoetial (Gaussia) fuctio, G t exp t t,. For 1,,, we defie the th Gaussia wavelet,, where G t, to be the ormalised th derivative of the Gaussia fuctio G () (t), that is: G t d G t, (1) dt where is a ormalisatio coefficiet. Some examples of Gaussia wavelets are show i Fig. 1. Fig. 1: Gaussia wavelet examples for orders =1,, 3, 3 ad 1 17 th Australia Aerospace Cogress, 6-8 February 17, Melboure

3 Fidig the Optimal Gaussia Wavelet The CWT is used to fid the Gaussia wavelet which best simulates the impulse respose of the bearig fault. Let y(t) deote the vibratio sigal, the the CWT of y(t) usig a Gaussia wavelet of order is give by: W t, d, () s s, t y G where s is referred to as the scale parameter. Note that whilst s ca be ay real umber, for this applicatio sufficiet fidelity is achieved through cosiderig oly positive iteger values for s, i.e. s 1,,. For digital applicatios, the vibratio sigal ad Gaussia wavelet are sampled at discrete time poits oly. Cosequetly, to avoid aliasig whe applyig Eq., the scale, s, must be sufficietly large for the wavelet order. Coversely, for each scale s there is a maximum wavelet order. To facilitate this, a empirical relatioship was derived which provides a upper boud for as a fuctio of s: 1 1 s. (3) Fidig the optimal wavelet parameters is formulated as a costraied optimisatio problem i terms of the CWT of the bearig vibratio sigal: E ˆ, arg max E, s, (4), s, 1, dt (5) s s W, s t where ˆ ad ŝ are the optimal wavelet order ad scale respectively. Whe performig the optimisatio i Eq. (4), the followig two costraits are employed: (C1) The wavelet parameters, ad s, are costraied to satisfy Eq. 3. (C) The maximum should be take from a proper turig poit of E(,s). The first costrait is ecessary to avoid aliasig. E(,s) is said to reach a proper turig poit at the specific poit (,s) if (i) E(,s) > E(-1,s) ad (ii) E(,s) > E(+1,s). I some cases, the iequality i (ii) caot be assessed because the specific pair (+1,s) does ot satisfy the costrait i Eq. 3. This is further illustrated i Fig. 3 i the sectio Fidig the Optimal Gaussia Wavelet Parameters below. I order for the solutio of Eq. 4 to be well correlated with the bearig fault impulse respose, the sigal to oise ratio of the impulse respose must be reasoably high; i.e. the impulse respose must ot be masked by other sigal compoets. For all but the simplest applicatios, this implies that y(t) be appropriately filtered to separate the bearig impulse respose from the other sigal compoets such as the gear meshig vibratio ad other urelated spectral cotet. 17 th Australia Aerospace Cogress, 6-8 February 17, Melboure

4 Bearig Degradatio Moitorig The optimal wavelet parameters, ˆ ad ŝ, determie a uique Gaussia wavelet which best correlates with the bearig fault impulse respose. At each poit i time that a bearig fault W ˆ,, t. impulse is geerated, a correspodig peak will occur i the sigle-scale CWT, The method proposed here is to obtai a estimate of the cumulative cout of the peaks i W ˆ,, t through the itegratio of a modified form of the sigle-scale CWT, W ˆ,, t. The modified form of the sigle-scale CWT, deoted w ˆ,, t, is obtaied by filterig out the backgroud oise usig a pre-determied threshold level, w. That is, let w ˆ,, t Wˆ,, t W ˆ,, t w ad w ˆ,, t otherwise. The, the followig measure is for all t such that proportioal to the cumulative correlatio peak cout: t 1 C( t) wˆ,, d, (6) ad its derivative with respect to time, C (t), will be approximately proportioal to the bearig fault impulse respose rate, ad thus to the rate of degradatio of the bearig at time t. Bearig Fault Test Bearig Fault Applicatio A Bell 6 helicopter mai rotor gearbox was tested i DST Group's Helicopter Trasmissio Test Facility (HTTF) as part of the research program ito developig coditio moitorig, diagostic, ad progostic capability for helicopter trasmissio systems. The Bell 6 mai rotor gearbox is show i Fig.. The test, which ra for approximately 16 hours, succeeded i iitiatig ad growig a aturally occurrig fault o the plaet gear spherical-roller bearig. Spallig damage occurred mostly o the ier races as show i Fig., with some of the rollig elemets also damaged (ot show). The photos i Fig. were take at the ed of the test. There was very little damage to the outer race, which is itegral with the plaet gear. Durig the test, vibratio data were recorded from accelerometers fitted to the gearbox housig i a umber of differet locatios. Shaft rotatios were tracked usig tachometers fitted to both the iput ad output shafts of the gearbox. Wear debris were moitored i real time usig a MetalSCAN 1 debris moitorig system fitted ito the oil scavege lie upstream of the oil filter. 1 A oil debris moitorig system produced by GasTOPS, 17 th Australia Aerospace Cogress, 6-8 February 17, Melboure

Fig. : Bell 6 mai gearbox (left), plaet gear ad plaet bearig (right) Bearig Sigal Isolatio Fidig the optimal Gaussia wavelet requires a good sigal to oise ratio for the bearig fault sigal.

5 Fig. : Bell 6 mai gearbox (left), plaet gear ad plaet bearig (right) Bearig Sigal Isolatio Fidig the optimal Gaussia wavelet requires a good sigal to oise ratio for the bearig fault sigal. The raw vibratio sigals recorded durig the test are domiated by the complex harmoic series from the iput pio/bevel gear meshig, ad the epicyclic gear meshig. Sigal compoets related to the bearig fault are much lower i amplitude. The bearig fault sigal must therefore be separated from these domiat spectral compoets before the wavelet method ca be employed. Separatio of the bearig fault sigal was previously achieved by Dr N. Sawalhi, as described i Ref. 4, i which he also correctly diagosed the plaet bearig fault. The techique he used for separatig the bearig fault sigal from the gear meshig ad other domiat spectral cotet was a combiatio of Discrete-Radom Separatio (DRS) ad bad-pass filterig. The same techique is applied for this aalysis. Fidig the Optimal Gaussia Wavelet Parameters The optimal Gaussia wavelet parameters are obtaied usig the DRS ad bad-pass filtered vibratio sigal, whe the fault is i its icipiet just-detectable stage, which occurs 8 hours ito the test. A plot of E(,s) for two values of scale s is show i Fig. 3 (left plot). Each E(,s) plot termiates at the maximum value of determied by the costrait i Eq. 3. The right side plot i Fig. 3 is a colour-map of E(,s) over a rage of (iteger) scales ad wavelet orders. The amplitude of E(,s) is displayed o the map usig a reverse grey-scale from to 5, with amplitude icreasig as the colour darkes. The aalysis was performed blidly, i.e. Dr Sawalhi did ot kow what type of fault was preset i the gearbox durig his aalysis. 17 th Australia Aerospace Cogress, 6-8 February 17, Melboure

6 Fig. 3: Left: E(,4) ad E(,5). Right: E(,s) order-scale colour-map The plot of E(,4) illustrates how the costrait i Eq. 3 ca lead to a local maximum that is ot a turig poit. A similar result occurs for s < 4, although these results are ot as obvious i the colour-map plot. For E(,5), a proper turig poit ad local maximum occurs at = 69. I the colour-map plot it is clear that proper turig poits (ad correspodig local maxima) are obtaied for s 5 ; however, the global maximum (at proper turig poits) occurs at s = 5. Hece the optimal Gaussia wavelet parameters are, ˆ 69 ad s ˆ 5. Trackig the Degradatio of the Plaet Gear Bearig The optimal Gaussia wavelet, with parameters ˆ 69 ad s ˆ 5, was applied to the DRS ad bad-pass filtered plaet bearig fault data. Due to the limited umber of data sets available with the bearig i a healthy state, the threshold level, w, was set usig a multiple w 1.5 max W ˆ,, t. of the maximum value of the CWT o the first available data file: The value of the multiplier, 1.5, was ot foud to be sigificat, with the techique workig well for values up to 1.4. A plot of C (t) coverig the duratio of the test is show i Fig. 4 (left). For compariso, the cumulative mass of wear debris obtaied from the MetalSCAN sesor is plotted i Fig. 4 (right). Fig. 4: Left: Gaussia wavelet correlatio method. Right: Cumulative mass of wear debris The wear debris data ca reasoably be expected to provide a good measure of the cumulative degradatio of the bearig over time. A compariso of the two plots i Fig. 4 idicates that C (t) has a very similar tred to the cumulative mass of wear debris; however, the first 17 th Australia Aerospace Cogress, 6-8 February 17, Melboure

7 sigificat icrease i C(t) occurs at a earlier time (~15 hours) tha that of the cumulative mass (~1 hours). Further testig will be required to determie the sigificace of this, e.g. whether it might be a artefact of optimisig the wavelet to the filtered vibratio sigal at a particular poit i the test, ad whether it is repeatable i other experimetal tests. Coclusios The method proposed i the paper uses Gaussia wavelets to track the degradatio of rollig elemet bearigs, ad is applied post diagosis. Vibratio ad wear debris data obtaied from a full-scale test of a helicopter mai trasmissio were used for evaluatio. The Gaussia wavelet method was show to perform well at trackig the degradatio of the plaet gear bearig for the duratio of the test. The results show i Fig. 4 may well be suitable for fusig vibratio ad wear debris data to predict the remaiig useful life of rollig elemet bearigs. Ackowledgemets The author ackowledges the School of Mechaical ad Maufacturig Egieerig, Uiversity of New South Wales, Australia for providig the computer code used to filter the test data usig the Discrete-Radom Separatio (DRS) techique. The author ackowledges Mr Riyazal Hussei from DST Group for providig the cumulative mass of wear debris data from the MetalSCAN sesor recordigs. Refereces 1. El-Thalji, I ad Jatue, E., A summary of fault modellig ad predictive health moitorig of rollig elemet bearigs, Mechaical Systems ad Sigal Processig, Vol. 6, Issue 1, 15, pp Sawalhi, N ad Radall, R.B., Localised fault detectio ad diagosis i rollig elemet bearigs: A collectio of state of the art processig algorithms, Proceedigs of the Eighth DSTO iteratioal Coferece o Health ad Usage Moitorig, AIAC15, Melboure Australia, Liu, B. ad Lig, S.F., O the selectio of iformative wavelets for machiery diagosis, Mechaical Systems ad Sigal Processig, Vol. 13, Issue 1-, April, pp Sawalhi, N., Diagostics, Progostics ad Fault Simulatio for Rollig Elemet Bearigs, PhD thesis, The Uiversity of New South Wales, Australia, th Australia Aerospace Cogress, 6-8 February 17, Melboure

Orthogonal Gaussian Filters for Signal Processing

Orthogonal Gaussian Filters for Signal Processing Orthogoal Gaussia Filters for Sigal Processig Mark Mackezie ad Kiet Tieu Mechaical Egieerig Uiversity of Wollogog.S.W. Australia Abstract A Gaussia filter usig the Hermite orthoormal series of fuctios