VIBRATION MONITORING FOR FAULT DIAGNOSIS OF HELICOPTER PLANETRY GEARS. Biqing Wu, Abhinav Saxena, Romano Patrick, and George Vachtsevanos

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1 VIBRAIO OIORIG FOR FAUL DIAGOSIS OF HELICOPER PLAERY GEARS Biqing Wu, Abhinav Saxna, Romano Patrick, and Gorg Vachtsvanos School of Elctrical & Computr Enginring Gorgia Institut of chnology Atlanta, Gorgia Abstract: In this papr, vibration data analysis tchniqus ar invstigatd for fault diagnosis of hlicoptr plantary gars. A data pr-procssing tchniqu is introducd that achivs th sam rsult as th commonly usd im Synchronous Avraging with much lowr computational complxity sinc intrpolation is not rquird. A notion of using raw vibration data instad of th im Synchronous Avragd data is also prsntd that is mor suitabl for th analysis of vibration data producd by plantary garboxs and for th purposs of dtcting carrir plat crack fault. Basd on this notion, faturs such as th Harmonic Indx in th frquncy domain and th Intra-Rvolution Enrgy Varianc in th wavlt domain ar drivd. h faturs ar usd as inputs to fault classifirs and ar shown to dtct th fault succssfully basd on th tst data that is availabl. Copyright 5 IFAC Kywords: Fault Diagnosis, Vibration asurmnt and Data Analysis, im Synchronous Avraging, Plantary Gar Carrir Plat Crack, Fatur Extraction.. IRODUCIO asurmnt and analysis of vibration data producd by a garbox is important, ithr with a viw to rducing th nois lvl of a garbox or to assssing its mchanical condition. h majority of th availabl data analysis tchniqus for transmission systms ar basd on th im Synchronous Avraging (SA) of vibration signals (cclintic, t al., ; cfaddn, 987, 989, 99). It is assumd that a puls signal synchronizd to th rotation of a gar indicating th start of an individual rvolution is availabl. umrous rvolutions ar nsmbl avragd rsulting in an avragd data with a lngth corrsponding to a singl rvolution. h SA tchniqu is intndd to nhanc th vibration frquncis that ar multipls of th shaft frquncy, which in many cass ar mainly vibration rlatd to th mshing of th gar tth, whil avraging out othr componnts such as random vibrations and xtrnal disturbancs. h rsulting avragd data shows vibration charactristics of a gar in th tim domain ovr on complt rvolution, and diffrncs in th vibration producd by individual gar tth can b sn. Advancd local damag to gar tth can oftn b dtctd by dirct inspction of th tim avragd data (cfaddn, 99). Sinc th rotational spd of a transmission typically varis slightly during normal opration, th numbrs of th data sampls pr rvolution ar diffrnt for a givn sampling frquncy. Intrpolation is rquird to mak th sampl numbrs pr rvolution th sam bfor nsmbl avraging can b carrid out. Intrpolation transforms th vibration signal from th tim domain to th angl domain, and rdfins th sampling frquncy to b a function of angular position rathr than tim. In this papr, th SA tchniqu is compard with othr vibration data pr-procssing tchniqus in th frquncy domain. Sinc intrpolation, as rquird by th SA, is computationally dmanding and timconsuming, it is undsirabl spcially for on-lin ral-tim vibration monitoring. A simpl tchniqu is introducd that achivs th sam rsult as th SA with much lowr computational complxity sinc intrpolation is not rquird. h analysis and comparison btwn ths diffrnt prprocssing tchniqus ar prsntd in Sction. Whil tim domain avraging has provd its suprior prformanc for th analysis of fixd-axis gar vibration signals, problms aris whn it is applid to th vibration producd by picyclic garboxs. h problms ar mainly du to th motion of th plant gars and th multiplicity of contact rgions btwn th plant gars and th annulus gar, and btwn th plant gars and th sun gar (Kllr and Grabill, 3; cfaddn and Smith, 985). In (cfaddn, 99), a tchniqu for vibration sparation (or mapping) of ach individual plant within on rvolution was usd bfor tim avrags for th individual plant gars wr calculatd. Howvr, th tchniqu introducs additional complxity and rquirs dtaild gomtrical owldg of a plantary transmission systm (Forrstr, 998; Howard, 99; cfaddn, 994; Samul and Pins, ). Its usfulnss is limitd to plantary garboxs with crtain gomtric proprtis, and to th dtction of gar tooth faults. In this papr novl signal procssing and fatur xtraction tchniqus ar proposd for analysis of vibration producd by picyclic garboxs that ar basd on raw vibration data instad of tim synchronous avragd data. h tchniqus wr motivatd by a crack that was rcntly found in th

2 plantary carrir of th main transmission gar of a U.S. Army s UH-6A Blackhawk hlicoptr (Kllr and Grabill, 3). Work has bn carrid out to dvlop a simpl, cost-ffctiv tst capabl of diagnosing this fault basd on vibration data analysis tchniqus. Various Condition Indicators (faturs of th vibration data) of th carrir plat crack fault wr prsntd in (Kllr and Grabill, 3) with th SA tchniqu. Of ths faturs, only th Sidband Indx (SI) and Sidband Lvl Factors (SLF) wr consistntly succssful at dtcting th prsnc of a fault undr tst cll conditions. on of th faturs wr abl to dtct a crack undr on-aircraft conditions at th low torqu lvls tstd. h hlicoptr transmission plantary gar systm and vibration data rcordings ar brifly dscribd in Sction 3, whil Sction 4 prsnts th proposd signal procssing and fatur xtraction tchniqus. Faturs that ar abl to diffrntiat undr various tsting conditions th faultd and unfaultd plantary gars of th UH-6A Blackhawk hlicoptrs includ th Harmonic Indx in th frquncy domain and th Intra-Rvolution Enrgy Varianc in th wavlt domain. h Harmonic Indx fatur is dfind as th amplitud sum of all apparnt sidbands of a spcific gar mshing harmonic of th raw data, and th Intra-Rvolution Enrgy Varianc fatur is dfind as th varianc of th vibration nrgy around a spcific gar mshing harmonic within an individual rvolution. h raw vibration data instad of th SA data is usd to xtract th faturs sinc th formr provid bttr rsults. ot that th fault on th plantary gar is a crack in th carrir plat, and it is diffrnt from th usual tooth crack or brakag or from faults in a fixd-axis gar, in which cas various faturs basd on th SA signal ar sufficint to dtct and idntify th fault (cclintic, t al., ). It is possibl that th rsonanc frquncy of th plantary gar, which may indicat th plat crack fault, is avragd out, sinc th SA tnds to avrag out xtrnal disturbancs and nois that ar not in sync with th carrir rotation. Evn som mshing harmonics and thir sidbands may also b avragd out or rducd if thir initial phass at th start of ach carrir rotation ar diffrnt. Furthr vidnc of th validity of ths faturs basd on raw data is still rquird and a Finit Elmnt analysis mthod is activly pursud in an ffort to discovr th changs in th rsonanc frquncy. vrthlss, data analysis tchniqus basd on th SA ar not xcludd if nw data acquird from th tst cll or on-aircraft bcom availabl.. VIBRAIO DAA PREPROCESSIG h data sgmnt x m (n), for n,,...,, is dfind as th vibration data of rvolution # m of a total numbr of rvolutions aftr intrpolation, _ n and x ( ) for n,,..., as th tim avragd data. h Discrt Fourir ransform (DF) of th tim avragd data is givn by: X ( k) _ n x( n) n m x m, ( n) k,,...,. () A nw data prprocssing tchniqu involvs taking th DF of ach rvolution of th vibration data (no intrpolation rquird) and thn nsmbl avraging th complx numbrs (including th amplitud and phas information) of th corrsponding indics. h rational bhind this tchniqu is dscribd as follows. h frquncy rsolution of th DF is givn by f f shaft shaft, whr shaft is th tim lngth of ach individual rvolution and may vary slightly from on rvolution to anothr. If th priod of th gar shaft rotation,, is longr, th data shaft volum sampld in a rvolution is gratr. h frquncy rsolution is thn finr whil th sampling frquncy is th sam, rsulting in a highr numbr of frquncy indics. Howvr, th indx of th mshing frquncis and thir sidbands dos not chang. W can avrag th frquncis with common and corrsponding indics and discard th xtra frquncis of highr indics. h rsult obtaind using this prprocssing tchniqu is quivalnt to th DF of th tim synchronous avragd (SA) data (which will b xplaind in th following paragraphs), whil th intrpolation and rsampling as rquird in tim avraging is not ndd. In som sns w obtain th SA data in th frquncy domain. his procssing stp rducs th computational complxity sinc, in most cass, th DF (FF) is simplr and fastr than rsampling th vibration data, spcially whn th sampling frquncy is high. Sinc th DF opration is linar, th DF of th nsmbl avraging of th intrpolatd data is quivalnt to th nsmbl avraging of th DF of th intrpolatd data, as shown blow: X ( k) _ n x( n) n m m n x x m m, ( n) ( n) k,,..., () Fig. illustrats th DF of a SA data st, which can b calculatd by avraging th DF as shown in th right part of th figur. In th figur, th data points connctd by th dashd lins ar to b

3 avragd. Sinc th tim lngth of ach individual rvolution varis, th frquncy rsolution of th DF of ach individual rvolution varis as wll. SA (with intrpolatd data) Frquncy domain quivalnc f f f 3 Fig. DF of a SA data st 3 Fig. shows th avraging of th DF for multipl rvolutions without intrpolation. From th illustrations in th frquncy domain, it can b sn that th rsults ar quivalnt at th common indics to th DF of th SA data shown in Fig.. Sinc th variation in th rotational spd of a rotor shaft is vry small (usually th diffrnc in th sampl numbrs btwn two rvolutions of raw data is about.5%), th diffrnc btwn th DF of th SA data and th avraging of th DF of th raw data (without intrpolation) is at th nd of th spctrum axis and is ngligibl whn th sampling rat is vry high (for xampl khz). xtract and nhancd. Fig. 3 shows th data sampls in th angl domain and th corrsponding frquncy domain of th intrpolatd data, as in th SA. Fig. 4 shows th data sampls in th angl domain and th corrsponding frquncy domain of th data without intrpolation. Again, w can s that in th frquncy domain th two tchniqus ar quivalnt at th nontrivial frquncis. An attractiv data procssing tchniqu, diffrnt from th ons dscribd abov, is obtaind by avraging th amplituds of th DF of multipl rvolutions of th raw data (without intrpolation). h phas information in this cas is discardd, sinc th phass of diffrnt rvolutions may b diffrnt, in fact, thy may vary mor than th signal amplituds. his tchniqu will b usd in Sction 4 to driv usful faturs such as th Harmonic Indx. SA (with intrpolatd data) in th angl domain 36 Frquncy domain quivalnc Fig. 3 SA data sampls in th angl domain and th corrsponding frquncy domain Angl domain data (without intrpolation) 36 Frquncy domain f 3 Frquncy domain Fig. 4 ultipl rvolution data without intrpolation in th angl and frquncy domains f 3. PLAEARY GEAR PLAE CRACK f 3 Fig. ultipl rvolution data without intrpolation in th tim and frquncy domains Anothr prspctiv is providd by viwing th sampling of individual rvolutions in th angl domain. h frquncy in this cas is dfind in th angl domain, instad of th tim domain. It has a unit of rotor shaft frquncy instad of Hz, that is, th frquncis ar multipls of th shaft frquncy. It is a vry usful rprsntation sinc th tooth frquncy is always a spcific multipl of th shaft frquncy no mattr how th rotational spd of th shaft changs. ru frquncy valus may chang with th shaft rotational spd, howvr th frquncy valus as multipls of th shaft frquncy may not chang. his allows invariant charactristics of th vibration data across multipl rvolutions to b Epicyclic gars ar important componnts for many rotorcraft transmission systms. An picyclic gar systm is dfind by a sun/plant configuration, in which an innr sun gar is surroundd by two or mor rotating plants. Plantary systms ar a subst of picyclic gars dfind by a stationary outr ring gar. orqu is transmittd through th sun gar to th plants, which rid on a plantary carrir. h plantary carrir, in turn, transmits torqu to th main rotor shaft and blads. If th transducr is placd in clos proximity to th annulus, thn th dominant vibration snsd at th transducr will originat from th mshing of th plant and th annulus, not th vibration gnratd by th mshing of th sun and th plant gars. Assuming that th ring gar has Z a tth, and th rotational spd of th plantary carrir is f c, thn

4 th tooth mshing frquncy of th vibration snsd by th transducr is f x Z a f c (cfaddn and Smith, 985). Fig. 5 shows th carrir plat with a 3.5-inch crack of th main transmission gar. Sinc th plantary carrir is a flight critical part, a failur could caus an accidnt rsulting in loss of lif and/or aircraft. h discovry of th crackd plat rsultd in flight rstrictions on a significant numbr of th Army s UH-6A s. anual inspction of all transmissions is not only costly in trms of labor, but also tim prohibitiv. hr has bn xtnsiv work, thrfor, to dvlop a simpl, costffctiv tst capabl of diagnosing this fault basd on vibration data analysis tchniqus. 3¼ f Fig. 5 Plantary Carrir Plat with a Crack Vibration masurmnts of th main transmission gar wr ta at th Hlicoptr ransmission st Facility (HF) at Patuxant Rivr AS, D. h data was acquird using an acclromtr snsor suit intgratd into th Army s Vibration anagmnt Enhancmnt Program (VEP) systm. Du to safty considrations, th transmission was not run for an xtndd priod of tim, and only small sgmnts of data wr ta at six torqu sttings ranging from % to % in th tst cll, and two torqu sttings at % and 3% onaircraft (Kllr and Grabill, 3). Each sgmnt of th tst cll data is 8 sconds long and was acquird at a rat of khz, and for th on-aircraft data ach sgmnt is 5 sconds long and was acquird at a rat of 48 khz. A raw tachomtr signal synchronizd to th rvolution of th plantary gar carrir plat and th main rotor is also includd. h signal indicats th start of ach individual rvolution. h rotational frquncy of th main rotor is slightly mor than 4 Hz (it also varis a littl ovr tim), and, thrfor, th sgmnts of th tst cll and on-aircraft data hav 7 and complt rvolutions, rspctivly. Primarily, two signals from PortRing and Input snsors (th acclromtrs mountd on th lft hand sid of th ring gar of th main modul and of th input modul, rspctivly) provid important vibration signaturs of th carrir plat crack fault. 4. FEAURE EXRACIO W xtract a fatur for ach carrir rvolution and avrag it ovr rvolutions. Sinc a sufficint numbr of xprimnts or data ar not availabl to form a fatur distribution for statistical valuation purposs, w assum that a sgmnt consisting of rvolutions constituts an xprimnt providing a point in th distribution. h data lngth for vry vibration signal is about 7 rvolutions (8 sconds), and, thrfor, thr ar 7 fatur points in th distribution for ach torqu valu. fatur data points, for ach data sgmnt, ar availabl for on-aircraft data. Intrsting faturs in th frquncy and wavlt domains ar dscribd in th squl. 4. h Frquncy Domain: Harmonic Indx h fundamntal and harmonic mshing frquncis (including thir sidbands) of th plantary gar vibration signals ar important componnts and ar causd mainly by th mshing of th tth of th ring gar and th plantary gars (cfaddn and Smith, 985). hir frquncis ar rlatd to th carrir plat rotational frquncy and th tooth numbr of th ring gar. h plantary gar rfrrd in this papr has 8 tth, and thrfor th 5th mshing frquncy is 8 5 f c with f c bing th rotational frquncy of th plant carrir. h spctrum around th 5th mshing harmonic of th PortRing SA data from th faultd as wll as th unfaultd gars in th tst cll xprimnts shows that th faultd data has highr vibration lvls around th 5th harmonic for all torqu lvls xcpt th 9% torqu lvl. Howvr, obsrving th amplituds of th FF of on rvolution of th raw vibration data, whos spctral contnts ar obviously diffrnt from thos of th SA data, w can dtct a consistnt bhavior btwn th faultd and unfaultd data. h spctrum around th 5th mshing harmonic of th PortRing raw data from th tst cll xprimnts shows that th faultd data has a highr vibration lvl around th 5th harmonic for all torqu valus. ot that In ordr to obtain th spctra in this cas, th FF of on rvolution of raw data is ta and th amplituds of th corrsponding indx ar avragd ovr 83 rvolutions. h amplitud of a spcific indx corrsponds to th amplitud of th frquncy that is a multipl of th carrir shaft frquncy, sinc th tim lngth of th FF is of on rvolution long and th frquncy rsolution of th FF is th carrir shaft frquncy. For xampl, th componnt of indx 4 ( 8 5 ) is th 5th mshing harmonic for th FF of vry data sgmnt with a lngth of on rvolution, vn though th carrir shaft frquncy, f c, may b slightly diffrnt for ths individual rvolutions and th ral frquncy of th 5th mshing harmonic may b, thrfor, diffrnt. By aligning and avraging amplituds of th sam indx, th mshing frquncis and thir sidbands can b avragd and nhancd. h problm with this tchniqu rlats to th frquncy lakag, that is, th frquncis that ar not multipls of th carrir rotational frquncy, f c, show up in th surrounding frquncis that ar multipls of f c. So, it can only b usd to dscrib a frquncy band, such as in th Harmonic Indx fatur.

5 If, instad of th amplituds, w avrag th complx numbrs obtaind from th FF (including th amplitud and phas information), w arriv at rsults quivalnt to thos obtaind from th FF of th SA data at multipls of th carrir rotational frquncy, as was discussd in Sction. h advantag of this tchniqu is that it avoids th nd for intrpolation bcaus of th variation in th carrir rotational frquncy as in th SA. h diffrnc btwn amplitud avraging and FF avraging or th FF of th SA data is that som componnts may b avragd out or rducd in th lattr, and, thrby, th formr is mor fficint in distinguishing btwn faultd and unfaultd data. Basd on ths obsrvations and th analysis carrid out abov, raw vibration data ar prfrrd in th fatur xtraction procss in an ffort to diagnos th carrir crack fault in th plantary gars of th UH- 6A Blackhawk hlicoptr. o form th Harmonic Indx fatur, th Fourir ransform of th raw data of a tim lngth quivalnt to a carrir rvolution is ta and th amplituds of th 3 frquncis (with a rsolution of th carrir frquncy) to th lft and to th right of a spcific mshing harmonic ar summd up. Fig. 6 shows th Harmonic Indx around th 5th harmonic of th vibration data from th snsor at th Input location undr tst cll (uppr part) and on-aircraft (lowr part) conditions. In th figur, th fatur valus of th faultd carrir plat undr various load conditions ar in th contourd boundary. h faultd and unfaultd data points for ach load condition should li along lins vrtical to th x-axis. Howvr, for visualization purposs, th data points for ach torqu valu ar sprad out along th x-axis basd on th tim squnc of th points. All subsqunt fatur distributions ar plottd following this schm. h distributions of th Harmonic Indx show a clar sparation of th fatur valus xtractd for th faultd and unfaultd carrir plats. Fig. 6 Harmonic Indx around th 5th harmonic of Input in tst cll and on-aircraft In a similar way, Fig. 7 shows th Harmonic Indx around th th harmonic of PortRing. h points in th dashd lin boundary rprsnts th fatur valus from th additional data acquird from aircraft #5, which is an aircraft with a halthy main transmission plantary gar. h fatur shows clar sparation of th availabl data acquird from th faultd and unfaultd carrir plats as wll. On concrn about this fatur is that th fatur valus from aircraft # and #5 ar also quit apart, although both of thm hav halthy gars. h diffrncs in th vibration lvls may b du to th diffrnc btwn th aircrafts. Fig. 7 Harmonic Indx around th th harmonic of PortRing in tst cll and on-aircraft 4. h Wavlt Domain: Intra-Rvolution Enrgy Varianc h transducrs that sns th vibration signals ar bracd on th housing of th gar box and ar stationary rlativ to th rotating plantary gars and th carrir plat (cfaddn and Smith, 985). W xpct to obsrv an incrasd non-uniformity during on rvolution of th vibration data acquird from th gar systm with a crackd carrir plat than from a halthy gar systm. h Intra-Rvolution Enrgy Varianc fatur attmpts to dscrib this nonuniformity in th wavlt domain. o xtract wavlt faturs, th Complx orlt wavlt cmor7- was usd to comput th wavlt map for th raw vibration data with a lngth of on rvolution. Again, w focus on spcific frquncy bands and divid th wavlt map around th mth harmonic into blocks in th tmporal axis and th nrgy of ach block is calculatd. h Intra-Rvolution Enrgy Varianc fatur is th nrgy varianc of ths blocks and acts as an approximat indicator of th asymmtry or non-uniformity of th vibration in on carrir rvolution. Fig. 8 shows th distributions of th valus of th Intra-Rvolution Enrgy Varianc around th 5th mshing harmonic of th Input snsor data for th faultd and unfaultd carrir plats, rspctivly. h faturs can b usd as th inputs to a classifir to diagnos th plantary gar plat crack fault. h faturs of th Harmonic Indx of th 5th harmonic of Input and that of th th harmonic of PortRing ar providd as inputs to a Wavlt ural twork (Vachtsvanos and Wang, 998), which is accompanid with an appropriat dcision logic that dcidd upon th particular fault class that th faturs (symptoms) blong to. It is found out that th faturs provid sufficint information for corrct dtction of th fault.

6 Kllr, J. and P. Grabill (3). Vibration onitoring of a UH-6A ain ransmission Plantary Carrir Fault, th Amrican Hlicoptr Socity 59thAnnual Forum, Phonix, Arizona. cclintic, K.,. Lbold, K. aynard, C. Byington, and R. Campbll (). Rsidual and Diffrnc Fatur Analysis with ransitional Garbox Data, Procdings of th 54th ting of th Socity for achinry Failur Prvntion chnology, Virginia Bach, VA, Fig. 8 Intra-Rvolution Enrgy Varianc of Input in tst cll and on-aircraft conditions 5. COCLUSIOS Vibration data acquird from th main transmission plantary gars of th U.S. Army s UH-6A Blackhawk hlicoptrs in tst cll and on-aircraft conditions wr analyzd in an ffort to dtct th crack fault in plantary carrir plats. h plat crack is a nw typ of fault found in gar systms, and nw fatur xtraction tchniqus, othr than traditional ons that ar usd to dtct tooth cracks or brakag or faults in fixd-axis gars, wr invstigatd. It was found that th faturs labld as Harmonic Indx in th frquncy domain and Intra-Rvolution Enrgy Varianc in th wavlt domain ar abl to diffrntiat th data acquird from th faultd and unfaultd plantary gars and, thrfor, ar potntial candidats to dtct th plat crack fault in th plantary gars undr study. 6. ACKOWLEDGEE his work has bn supportd by th Dfns Advancd Rsarch Projct Agncy (DARPA), subcontract with orthrop Grumman Corporation undr program titld Structural Intgrity Prognosis Systm." h authors would lik to thank Dr. Jonathan A. Kllr of th U.S. Army ACO, Aviation Enginring Dirctorat at Rdston Arsnal, AL for providing th vibration data. 7. REFERECES Forrstr, D. (998). A mthod for th sparation of picyclic plant gar vibration signaturs, Procdings of Acoustical and Vibratory Survillanc thods and Diagnostic chniqus, pp , Snlis, Franc. cfaddn, P.D. and J.D. Smith (985). An Explanation for th Asymmtry of th odulation Sidbands about th ooth shing Frquncy in Epicyclic Gar Vibration, Procdings of th Institution of chanical Enginrs, Part C: chanical Enginring Scinc, 99(), cfaddn, P. D. (987). Examination of a tchniqu for th arly dtction of failur in gars by signal procssing of th tim domain avrag of th mshing vibration chanical Systms and Signal Procssing, (): cfaddn, P. D. (989). Intrpolation tchniqus for tim domain avraging of gar vibration, chanical Systms and Signal Procssing, 3(): cfaddn, P. D. (99). A tchniqu for calculating th tim domain avrags of th vibration of th individual plant gars and sun gar in an picyclic garbox, Journal of Sound and Vibration, 44(): cfaddn, P. D. (994). Window functions for th calculation of th tim domain avrags of th vibration of th individual plant gars and sun gar in an picyclic garbox, Journal of Vibration and Acoustics, 6: Samul, P. D. and D. J. Pins (), Vibration sparation and diagnostics of plantary gartrains, Procdings of th Amrican Hlicoptr Socity 56th Annual Forum, Virginia Bach, Va. Vachtsvanos, G. and P.Wang (998). "A Wavlt twork Framwork for Diagnostics of Complx Enginrd Systms," aintnanc And Rliability Confrnc, ARCO, Knoxvill. Howard, I.. (99). An invstigation of vibration signal avraging of individual componnts in an picyclic garbox, chnical Rport ARL- PROP-R-85, Australian Dpartmnt of Dfns: Aronautical Rsarch Laboratory.