NON-CONTACT GAS TURBINE BLADE VIBRATION MEASUREMENT FROM CASING PRESSURE AND VIBRATION SIGNALS A REVIEW

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1 Poceedng of the 8 th IFToMM Intenatonal Confeence on Rotodynamc Septembe 2-5, 200, KIST, Seoul, Koea NON-CONTACT GAS TURBINE BLADE VIBRATION MEASUREMENT FROM CASING PRESSURE AND VIBRATION SIGNALS A REVIEW Gaeth L. Fobe School of Mechancal and Manufactung Engneeng, The Unvety of New South Wale Sydney, NSW, Autala Robet B. Randall School of Mechancal and Manufactung Engneeng, The Unvety of New South Wale Sydney, NSW, Autala ABSTRACT Th pape peent a ummay of a ecent eeach pogam, focung on a new method of non-contact ga tubne blade vbaton meauement ung cang peue and vbaton gnal. Cuently the domnant method of non-contact meauement of tubne blade vbaton employ the ue of a numbe of poxmty pobe located aound the engne pephey meaung the blade tp (aval) tme (BTT). Depte the nceang ablty of th method thee tll ext ome lmtaton, vz: the equement of a lage numbe of eno fo each engne tage, dffculte n dealng wth multple exctaton fequence, eno beng located n the ga path, and the nablty to dectly meaue the natual fequency of a gven blade. Smulaton etablhed wth a phyc baed model along wth expemental meauement ae peented n th pape, ung ntenal peue and cang vbaton meauement, whch have the potental to ectfy ome of thee poblem. INTRODUCTION The geatet caue of falue n ga tubne come fom blade fault, epoted to be up to 42% of total ga tubne falue []. Blade vbaton unavodable and nheent n the opeaton of any ga tubne and wthout pope degn fo the exctaton foce peent, blade vbaton can be a caue of blade degadaton and lead to falue. It paamount that blade vbaton can be meaued and blade fatgue be etmated n the degn tage. Hgh cycle fatgue (HCF) fom thee nheent blade vbaton the laget ngle caue of component falue n moden mltay acaft ga tubne engne, exceedng the numbe attbuted to low cycle fatgue, cooon, ovete, manufactung pocee, mechancal damage, and mateal [2]. Anothe pomnent need that ha aen, whch eque the pecfc meauement of blade vbaton n cuent tubne, the tuaton when they ae un beyond the degn lfe o ae ubject to dffeent condton fom thoe fo whch they wee ognally degned. Fo ntance, ome electcty plant n the Aa Pacfc egon ae facng the dlemma of havng to un the tubne beyond the ognal manufactue ecommended unnng hou n ode to contnue to povde an unnteupted electcty upply [3]. It clea that ga tubne blade vbaton meauement eental. Ga tubne blade vbaton meauement thu motvated by the dee to acque two pncpal pece of nfomaton, ethe the blade foced vbaton magntude and fequency, o to etmate the modal paamete of the blade. The mpetu fo th nfomaton geneally dven, epectvely, by the need fo nowledge of HCF etmate fo blade lfe, o the ue of blade modal paamete value fo condton montong of the blade. Meauement of blade vbaton can be acheved wth the dect attachment of tan gauge to the blade uface, howeve the attachment of eno to all blade wthn the engne neve deable, and cetanly not pactcal outde of the degn tage. Th due not only to the cot of ntumentng each blade, but addtonally becaue of the complexte of bngng the meaued gnal to an extenal montong devce. Th need to be done ethe wth the ue of lp ng o a wele telemety ytem. Stan gauge ae alo located on the engne wong uface aea, uch that they affect the aeofol uface, and ae expoed to the hah ntenal engne envonment, th not beng conducve to eno longevty. Such ae the dffculte of dect meauement of blade vbaton, non-contact blade vbaton meauement ha been ought, wth BTT method howng the mot pome and ecevng eeach attenton nce the 970. Depte the pome of BTT method they ae tll not wthout lmtaton o hotcomng fou decade afte the ntal ue. It wa ecently popoed that blade vbaton would have an affect on the cang wall peue and cang vbaton, and thu meauement of thee paamete could be ued fo montong of blade vbaton paamete [4]. The enung eeach pogam whch wa undetaen to follow up th popoal evewed n th pape. The peented wo may be dvded nto thee ecton, thee beng: () Dect meauement of blade vbaton ampltude, whch could be ued fo etmatng blade HCF a ft popoed n Ref. [5], by phae demodulatng the meaued ntenal cang peue. Reult ae hown heen fo mulated tubne peue gnal. () The popoton of ndectly meaung oto blade natual fequence by vayng the otaton peed uch that the blade exctaton taveed the blade natual fequency, allowng an obevable nceae n the cang vbaton pectum at th engne peed, wa gven n Ref. [4]. The eult fom mulated cang vbaton gnal ung th ndect blade natual fequency meauement ae gven. `

2 () Latly, t wa uggeted that oto blade natual fequence could be meaued dectly fom the tochatc cang vbaton epone [6], and th wa late vefed expementally [7]. Both analytcal and expemental eult obtaned fom the above eeach ae peented. PHASE DEMODULATION OF INTERNAL PRESSURE SIGNAL If a blade excted by one ngle domnant dcete fequency, then the moton of the blade tp fo the th blade can be tated, wthout lo of genealty, a: ROTOR BLADE PRESSURE PROFILE AND MOTION Ftly, the geneaton of the ntenal peue nde a ga tubne and the aocated oto blade moton wll be deved, nce all the followng analy technque ae baed on th devaton. A tated eale, blade vbaton n a ga tubne nheent and unavodable. Th nevtable blade vbaton develop fom the unteady peue feld though whch the oto blade pa dung otaton. It ntated by the tanfe of the ntenal ga pang fom otatng to tatonay fame of efeence a t pae though dffeent engne tage. Th can be vualed wth the ad of a.5 tage tubne chematc a n Fg.. It evdent a the flud pae fom the nlet to the outlet though the nlet gude vane (IGV ), though the oto tage, and fnally though the tato tage the change n flud otaton wll caue fluctuatng foce on all the blade nde the engne, and thu wll caue them to vbate. Geneally oto blade wll be excted by domnant fequence at tato pang fequence (SPF). The exctaton on the th blade could then be mathematcally decbed a: f ( t) = F0 Cq co q ( Ω t + γ q + γ ) () q= 0 The above foce can be of any hape dependng on the elected Foue ee co-effcent of C, γ. q q x( t) = X n( Ω ( t) + γ ) (2) Fo the cae of ynchonou vbaton n a ga tubne, a potve ntege and often efeed to a the engne ode of exctaton. If the blade have well epaated mode and the exctaton le elatvely cloe to one of the natual fequence then X and γ can found fom the oluton of the foced vbaton of the ngle degee of feedom ytem fo the mode of nteet of the oto blade. Wth the aumpton that the tme aveaged peue pofle aound any blade contant, the peue pofle aound any blade can be decbed by a hamonc ee, gven by: j[ ( t ) ] P Re A Pe θ +Ω + α + γ = (3) = 0 whee j = and A and γ ae the ampltude and phae of the coepondng Foue ee. It een that equaton (3) a otatng wave fom of any hape dependng on the elected Foue ee co-effcent of A, γ and ntal phae offet of α. Fo ntance n Fg. 2 a peue pofle hape plotted, contng of a aed cone whch pan one half blade pacng befoe and afte each blade, fo 6 oto blade. α Ω Fg. (a) longtudnal ecton of.5 tage tubne, (b) co ecton of.5 tage tubne howng wae nteacton between blade ow Along wth the fluctuatng peue foce on the blade caung them to vbate, the oto blade and ndeed the tato blade wll have a tatc peue pofle whch wll develop a the flud pae ove the blade aeofol uface. Wth th nowledge of the peue nteacton nde a ga tubne, analy of the cang peue and vbaton gnal wll now be hown n ode to acheve the econtucton of ome of the blade vbaton paamete. Fg. 2 Schematc of mple ft hamonc peue dtbuton fo a 6 bladed aangement wthout blade moton If we now mae the aumpton that the peue pofle aound one blade follow the moton of that blade when t vbate aound t equlbum poton, then the peue 2 `

3 pofle fo the th blade wll be modulated by the blade moton x( t ) uch that the peue pofle can now be wtten a: j[ ( t) x( t) ] P Re A Pe θ +Ω + + α + γ = (4) = 0 If we mplement the Lauent powe ee expanon of an exponental functon n tem of Beel functon: e = J x t (5) x 2( t t) n n ( ) n= then t can be een that P n the fom of equaton (5), uch that P can now be wtten a: P = Re A Pe Jn X e = 0 n= j[ θ +Ω ( t ) + α + γ ] jn[ Ω ( t) + γ ] ( ) (6) Now tang the eal pat fo all hamonc ( θ + Ω ( t) + α + γ ) P = A PJn ( X )co = 0 n= + n( Ω ( t) + γ ) (7) A the meaued peue at the cang wall, mathematcally epeented n equaton (7), a phae modulated gnal, then phae demodulaton would eult n obtanng nfomaton about the modulatng fequency.e. x( t ) and the tp deflecton X. It on th mple peme of the phae demodulaton of the ntenal peue that t popoed that nfomaton about oto blade vbaton can be obtaned. Howeve the phae demodulaton of the gnal, a gven n equaton (7), not a taghtfowad poce a th type of gnal volate ome aumpton fo ue wth conventonal demodulaton technque. Fo conventonal phae demodulaton, the maxmum modulaton fequency mut cetanly be le than half the cae fequency to avod alang. It can be een that fo the ntenal peue gnal th aumpton wll neve be atfed, a multple cae fequence ext at hamonc of haft peed, wth the modulatng fequency telf alo a multple of haft peed. How to ovecome the alang and demodulaton poblem of a gnal of th type wll now be ntoduced. A mplfed example If we loo at the pecal cae of =, whee the numbe of tato blade, and γ = 0, then: Ω = Ω = ω Fo llutaton, f we alo lmt < then we can ee the pectum of the peue gnal wll be a um of dcete hamonc of wth et of deband at ± ω. Fo ntance the fequency at Ω wll be made up of a component fom Ω and ( ) Ω + ω, ee Fg. 3 Ω Ω ω Ω+ω Ω 2ω Ω+2ω Ω 3ω Ω+3ω fequency Fg. 3 Dcete pectum fo cae fequence and modulatng deband ± ω. Value of the meaued peue gnal pectum can be taen at fequency locaton of Ω, ω Ω, ω + Ω, thee beng epectvely y, y, y +. ( ) ( ) ( ) y = A PJ0 X + A PJ X ( ) ( ) ( ) y = A PJ X + A PJ 0 X ( ) ( ) ( ) y+ = A PJ X + A PJ 2 X 2 (8)-(9) A P, A( ) P, X ae all unnown. Now wtng equaton (8)-(9) n matx fom: y = [ y y y ] + T y = Dx (0)() ( ) ( ) ( ) ( ) ( ) ( ) A P x = A( ) P (2)-(3) J0 X J X D = J X J0 X (4) J X J 2 X Although () not lnea, t lnea fo any value of X and can be olved by the lnea leat quae optmzaton of the ove-detemned ytem of equaton (2) -(4). The etmate fo the unnown co-effcent at any value of X gven, n the leat quae ene, by: [8] T - ˆ = ( ) To fnd the optmal value of T x D D D y (5) X to ft the ytem of equaton, the non-lnea leat quae gd each undetaen to maxme g ( x ) [8], whee 3 `

4 ( ) ( ) - T T T g x = y D D D D y (6) A gnal, of the type expeed n equaton (7), that doe not confom to the geneal equement of conventonal phae demodulaton can theefoe be demodulated wth a nonlnea leat quae gd each ft of the pectum. The ytem futhe complcated when noe peent n the gnal; howeve utlng two meauement locaton at a nown angula offet fom each othe, th lmtaton can be ovecome. Futhe eult and complete devaton of the nonlnea leat quae gd each phae demodulaton algothm can be found n Ref. [5, 9]. Implementaton wth moe ealtc peue gnal Now ceatng a moe ealtc ntenal tubne peue gnal wth value a gven n Table, ubttuted nto equaton (4), wth a ngle nown domnant oto blade dvng fequency at SPF, the eult fo the etmaton of the oto blade vbaton ampltude ae hown n Fg. 4 It can be een that fo the mulated gnal wth ealtc amount of noe the ampltude geneally etmated to wthn a 0% eo fo SNR ato le than 3. The nomaled gd pacng efe to a deceang pacng between etmated value of X fo whch the leat quaed eo mnmal ove the vaable pace. Table. Paamete value fo the example wth moe ealtc nput value. No. of No. of max X tato oto α cae γ Ω (ad) blade blade hamonc (ad) (ad) (Hz) Etmate of X π 9 π 7 SNR = Inf SNR = SNR = SNR = actual Nomaled gd pacng Fg. 4 Convegence of X etmate fo nceang nomaled gd pacng wth paamete fom Table wth nceang SNR a hown. Actual value of X alo a hown. It hould be noted that phae demodulaton of the ntenal peue gnal to etmate actual oto blade vbaton 0 ampltude eque the aumpton to be met that the peue at the blade tp eaonably un-alteed compaed wth that at the cang uface. INDIRECT MEASUREMENT OF BLADE NATURAL FREQUENCIES FROM CASING VIBRATIONS A non-ntuve meauement of blade condton wthn a ga tubne the goal of mot condton montong of thee ytem, a method of meaung blade vbaton paamete wthout the need to place any eno n the ga flow path would be optmal. It wll now be hown that the blade natual fequence of the oto blade may be etmated ndectly by weepng the engne peed ove a ange of peed, uch that engne ode exctaton fequence excte the blade natual fequency. Th method mla to the ndect BTT method [0, ] whch ue the ame engne weepng technque, to monto a blade natual fequency o that t could ubequently be ued to monto blade tuctual degadaton. Only one othe autho nown to have pevouly attempted to fnd a coelaton between cang vbaton and blade condton [2]. Mathouda et al [2] ued an nvee flteng technque to econtuct the ntenal peue gnal wthn a ga tubne fom the meaued cang vbaton by contuctng tanfe functon between the two gnal. Th demontated that the ntenal peue gnal and cang vbaton ae ndeed coelated to one anothe. The popoed method of meaung cang vbaton to detemne blade vbaton chaactetc ha a dcenble advantage ove cuent tp tmng technque, a t doe not eque pefoaton of the cang, lendng telf to much eae applcaton to extng, and n the degn of new, tubne. The cang of a ga tubne, unde tet condton, can be excted by two goup of foce [2], vz: (a) foce fom the engne and unnng gea though cang/beang attachment, (b) foce fom the aeodynamc/tuctual nteacton wthn the engne. The econd goup of foce, (b), undetood to be domnant, can then be futhe boen down nto t peumed conttuent; () nteacton wth the otatng peue pofle aound each oto/tato blade, () popagaton of acoutc wave nde the cang, () peue fluctuaton due to tubulent and mpulve flow. If the ft conttuent of the econd goup of foce, vz (b)(), hghlghted then t can be een that th exctaton foce ae fom the otatng ntenal peue whch wa deved n the pevou ecton and gven n t mot geneal fom n equaton (4). Thee foce ae the domnant contbuto to the detemntc cang wall peue and vbaton. Eentally the cang vbaton wll act n a mla manne to the ntenal cang peue whch dve t moton, afte t ha paed though the lnea tme nvaant (LTIV) flte of the cang tuctual tanfe functon. The mathematcal devaton of the cang vbaton wll not be gven hee fo bevty but can be found n Ref. [6, 9]. The popete peent n the cang vbaton pectum can howeve be dcued wth epect to the cang peue, a the tanfe though the cang wll only povde an ampltude and phae modfcaton of the peue gnal. 4 `

5 Detemntc cang vbaton fo a mulated tubne Cang vbaton eult ae hown fo a mulated tubne wth the paamete gven n Table 2. The blade ae modelled a uncoupled ngle degee of feedom png/ma/dampe ytem, wth a domnant exctaton fequency at SPF aumed to be only exctng a ngle blade mode wth a nomnal natual fequency of 500Hz. Shown n Fg. 6 the detemntc cang vbaton epone fo a mulated tubne when the cang modelled a a ccula ng unde the nfluence of an ntenal peue gnal, of the ame fom a that gven n equaton (4), fo an engne peed of Hz. Inpecton of equaton (4) and Fg. 6 how that dcete hamonc of engne peed wll be peent. A the engne peed wept ove a ange uch that the exctaton fequency, 5 Ω, tavee the blade natual fequency, 500Hz, the dplacement of the oto blade vbaton wll be nceae a wll the hamonc of the engne peed, epecally the exctaton fequency deband, thee beng BPF±SPF. Thu, f a watefall plot made of the detemntc cang epone pectum ove a ange of unnng peed, an nceae n the engne peed hamonc wll be een when the blade natual fequency excted, n th cae when Ω = 00Hz, a can be een n Fg. 5. Th nceae mot evdent when obevng the ft potve SPF deband, whch ndcated, and wth the ft SPF deband plotted n Fg. 7 ove the ange of engne peed. The nceae n deband ampltude vey evdent n Fg. 7 by the nceae n ampltude when the natual fequency taveed. epone ampltude db (el. 2E 8 mm) epone fequency (Hz) Fg. 6 Analytc cang adal epone at Hz haft peed n efeence to Fg. 5. Indcated by double aow BPF, othe aow ndcate BPF SPF epone amp (mm) 4 x ± haft peed (Hz) Fg. 7 Ft potve SPF deband ampltude plotted agant the haft nput peed. Clealy ndcated the pea n the epone ampltude when the blade natual fequency taveed by the foce fequency beng 5Ω. DIRECT MEASUREMENT OF BLADE NATURAL FREQUENCIES FROM CASING VIBRATIONS Fg. 5 Watefall plot of analytcal cang epone pectum fo engne haft peed of Hz. The analytcal model cont of 6 oto blade 5 tato blade wth a oto blade natual fequency of 500Hz. Indcated by the aow the nceae n the ft potve SPF deband when the blade natual fequency taveed. Table 2. Paamete fo mulated tubne No. of Swept engne peed tato (Hz) blade Roto blade natual fequency (Hz) No. of oto blade It wa hown that the ndect meauement of oto blade natual fequence could be acheved by obevng the detemntc poton of the tubne cang vbaton gnal a the engne peed wept ove a ange of peed. It would howeve be much le etctve f the blade natual fequency etmate could be acheved fom cang vbaton meauement at any gven engne unnng peed. Th ha been hown to be achevable f the tochatc poton of the tubne cang epone obeved ntead. A nheent a blade vbaton n the unnng of a ga tubne engne, o the peence of tubulence n the flud flow wthn the engne. Th tubulence wll alo dve blade moton along wth the detemntc peue foce. The foce on any oto blade can then be decbed, ncludng tochatc foce and dven pedomnantly by tato pa hamonc a: 5 `

6 f ( t) = F0 b ( t) Cq co q ( ω t + γ q + γ ) (7) q= 0 the Foue co-effcent can be gven value to decbe b t modelled a a whte andom any haped mpule. ( ) vaable wth zeo mean, howeve n pactce the tubulence wll be omewhat bandlmted and coloued. A befoe f the oto blade ae modelled a a ngle degee of feedom ytem, the pectum of the blade moton wll eult fom the multplcaton of the foce pectum, whch wll dplay the ame ft ode tattc a that of the b t, and the blade tanfe functon. The andom vaable ( ) pectum of the blade moton wll thu be tochatc n natue and n the enemble aveage epone the blade moton pectum wll coepond wth that of the ampltude of the blade tanfe functon. Th poce hown chematcally n Fg. 8 wth the ntantaneou pectum of the blade foce, equaton (7), multpled by the blade tanfe functon eultng n the ntantaneou pectum of the blade epone. = Fg. 8 Schematc of the devaton the tochatc blade foced moton Now that the blade moton nown, the ntenal peue unde the nfluence of the tochatc blade moton can be deved, obevng equaton (4) t can be een that th equaton can be eaanged a: P A Pe e j θ t α γ j x( t ) +Ω + + (8) = 0 = Re The left-hand component of the exponental functon n equaton (8) detemntc and t pectum wll be a dcete et of hamonc of haft peed, Ω. The pectum of the eal pat of the ght-hand component of the exponental functon n equaton (8), wll have the ame fom a the pectum of the blade moton x( t ). The pectum of the otatng peue foce wth the ncluon of the tochatcally foced blade moton wll theefoe be made fom the convoluton of the pectum of the detemntc poton of the otatng peue. Th poce hown chematcally n Fg. 9. It can be een that the ntantaneou otatng peue pectum wll now be made up of a ee of naowband pea located at haft peed, Ω, plu and mnu the blade natual fequency, due to th convoluton. Th a gnfcant eult a t how the tochatc poton of the cang peue pectum wll contan dectly meaueable nfomaton about blade natual fequence. = Fg. 9 Schematc of the devaton of ntenal peue pectum Once agan the cang vbaton wll contan the ame gnal popete a that of the ntenal peue gnal jut deved, afte t ha paed though a LTIV flte. Reult wll be hown fo analytcally deved ntenal peue and cang vbaton gnal along wth expemental meauement taen on a mplfed tet g whch wll now be befly decbed. Moe nfomaton on the tet g and the data captue and pot poceng pocedue can be found n Ref. [7, 9]. UNSW tet g The UNSW tet g cont of a oto aangement wth 9 flat blade, dven by an electc moto whch cuently capable of unnng at peed up to 2500pm. A toodal ng n font of the bladed aangement, uppled wth hgh peue a, poduce x a jet whch act le talng edge flow fom upteam tato blade ow, exctng the oto blade at multple of haft peed. A mcophone fluh mounted n the cang n the vetcal plane above the oto blade to meaue the peue nde the cang, along wth an acceleomete located at the ame locaton to meaue cang vbaton, hown n Fg. 0. One blade wa alo ntumented wth an acceleomete placed nea the oot of the blade, wth the gnal unnng though a et of lp ng mounted on the nput haft. The ft bendng, toonal and econd bendng mode natual fequence wee obeved fom the ntumented blade epone pectum and ae lted n Table 3 fo tatonay and 200pm haft peed. Fg. 0 Expemental tet g. () A jet located on a toodal ng whch uppled wth hgh peue a. (2) locaton of mcophone and acceleomete mountng 2 6 `

7 Table 3 UNSW tet g 9 th blade natual fequence Mode Statonay 200 pm t bendng 6.3 Hz 8.8 Hz t toon 55 Hz Hz 2 nd bendng 720 Hz Hz Dect natual fequency etmaton eult The powe pectum, ove a lmted fequency ange of the meaued peue gnal, hown n Fg.. The edual gnal ovelad on the ynchonouly aveaged detemntc gnal. The dcete gnal can be een to be made up of multple dcete pea at hamonc of haft peed. The edual gnal n Fg. can be een to be elatvely flat, fo the ntenal peue gnal, wth et of pea paced at multple of haft peed. The zoomed pectum n Fg. 2 how th moe clealy. The cang vbaton gnal n Fg. (c) can be een to alo have othe non-hamoncally elated pea coepondng to the tuctual eonance of the cang whch ae excted by the ntenal peue. db el. E 5 Pa db el. E 5 Pa db el. E 5 m (a) (b) (c) old vetcal lne; the othe dahed vetcal lne how the coepondng multple of haft peed ± the econd bendng mode natual fequency. Analytcal eult ae alo hown, Fg. 2(b), fo the mulated peue gnal wth the ame opeatng paamete a the expemental tet g;.e. 9 oto blade, 6 tato blade, and 200pm haft peed, and econd bendng mode blade natual fequency of Hz. The ame hamonc ee hown n Fg. 2(c) fo the meaued peue gnal and n Fg. 2(d) fo the cang vbaton gnal wth a econd bendng mode natual fequency etmated to be 736 Hz when the nput haft peed unnng at 2000pm. Th coepond well wth the expected nceae n natual fequency whch would eult fom centfugal tffenng, a een n the nceae n natual fequence fom tatonay meauement and thoe at 200pm, cf. Table 3. db el. E 5 Pa db el. E 5 Pa db el. E 5 m db el. E 5 m (a) (b) (c) (d) Fg. Powe pectum of meaued peue and cang vbaton gnal, epaated dcete and edual gnal ovelad on each othe. (a) 200pm peue gnal. (b) 2000pm peue gnal. (c) 2000pm cang vbaton gnal. Zoomed ecton ndcated. The zoomed pectum hown n Fg. 2(a) hghlght the naow band pea cented aound multple of haft peed. A hamonc cuo at multple of haft peed hown by the Fg. 2 Zoomed pectum of the meaued edual gnal a ndcated n Fg. Vetcal lne at haft peed pacng, vetcal lne at haft peed econd bendng mode natual fequency, vetcal lne at haft peed + econd bendng mode natual fequency. (a) 200pm peue gnal. (b) 200pm analytcal peue gnal. (c) 2000pm peue gnal. (d) 2000pm cang vbaton gnal 7 `

8 Wthn the fequency ange hown fo the mulated peue gnal, Fg. 2(b), only the hamonc at multple of haft peed mnu econd bendng mode natual fequency ae vble, whch pedomnantly the cae alo fo the meaued gnal at 200 pm. Geneally t mght be peumed that the ft bendng mode would be domnant n the epone; howeve, a een, the econd bendng mode the mot domnantly excted blade mode vble n the meaued gnal, th beng confmed by meauement of the actual blade epone eult whch can be found n Ref. [7, 9]. Th thought to be due to the fact that the peue fluctuaton ae elated to the acceleaton of the blade athe than the dplacement and a thu gve nceang weghtng to hghe mode and eult n the econd bendng mode beng at leat a tong a the ft mode. CONCLUSIONS The ue of non-contact blade vbaton meauement though the analy of a ga tubne ntenal peue and cang vbaton gnal wa outlned n th pape. Etmaton of oto blade vbaton ampltude fom the non-conventonal phae demodulaton of a mulated ntenal peue gnal howed pome fo conductng HCF etmate wth a lmted numbe of pobe and povdng obut ampltude etmate n the peence of meauement noe. Futhe eeach envaged to be undetaen wth expemental vefcaton of the effectvene of th blade vbaton meauement technque. Meauement of oto blade natual fequence whch could be ubequently ued fo the montong of blade health wa hown to be achevable fom cang vbaton meauement. A gnfcant advantage ove othe non-contact blade vbaton meauement technque offeed wth the ue of acceleomete tanduce a the eno doe not need to be located wthn the ga flow path and ae elatvely ealy eto mounted on extng equpment. Montong of the tochatc poton of the cang vbaton gnal alo epeent a notewothy mpovement ove cuent noncontact blade vbaton technque a the analytcal and expemental eult howed pome n the meauement of blade natual fequence at any engne unnng peed. The next tep to be caed out n elaton to the ue of cang vbaton meauement to detemne oto blade natual fequence an nvetgaton nto the ablty of the method to olate a ngle faulty blade n an expemental envonment. opeatng envonment Houton, TX, USA: ASME, New Yo, NY, USA. [2] Cowle, B.A., Hgh cycle fatgue n acaft ga tubne - an nduty pepectve. Intenatonal Jounal of Factue, 996. : p [3] Lm, M.H. and M.S. Leong, Dagno fo looe blade n ga tubne ung wavelet analy. Jounal of Engneeng fo Ga Tubne and Powe, (2): p [4] Fobe, G.L. and R.B. Randall. Smulated Ga Tubne Cang Repone to Roto Blade Peue Exctaton. n 5th Autalaan Conge on Appled Mechanc Bbane, Autala. [5] Fobe, G.L. and R.B. Randall, Smulaton of Ga Tubne blade vbaton meauement fom unteady cang wall peue, n Acoutc 2009: Reeach to Conultng. 2009, Autalan Acoutcal Socety: Adelade. [6] Fobe, G.L. and R.B. Randall. Detecton of a Blade Fault fom Smulated Ga Tubne Cang Repone Meauement. n 4th Euopean Wohop on Stuctual Health Montong Kaow, Poland. [7] Fobe, G.L. and R.B. Randall. Ga Tubne Cang Vbaton unde Blade Peue Exctaton. n MFPT Dayton, Oho. [8] Handel, P., Popete of the IEEE-STD-057 foupaamete ne wave ft algothm. IEEE Tanacton on Intumentaton and Meauement, (6): p [9] Fobe, G.L., Non-contact ga tubne blade vbaton montong ung ntenal peue and cang epone meauement. 200, The Unvety of New South Wale: PhD Detaton. p. 2. [0] Heath, S., A New Technque fo Identfyng Synchonou Reonance Ung Tp-Tmng. Jounal of Engneeng fo Ga Tubne and Powe, (2): p [] Zeln, M. and G. Zlle, Noncontact Blade Vbaton Meauement Sytem fo Aeo Engne Applcaton. Amecan Inttute of Aeonautc and Atonautc, 2005(ISABE). [2] Mathouda, K., E. Lou, and K.D. Papalou. Cang vbaton and ga tubne opeatng condton Toonto, Ont, Can: Publ by Amecan Soc of Mechancal Engnee (ASME), New Yo, NY, USA. ACKNOWLEDGEMENTS Gateful acnowledgment made fo the fnancal atance gven by the Autalan Defence Scence and Technology Oganaton, though the Cente of Expete n Helcopte Stuctue and Dagnotc at UNSW. REFERENCES [] Mehe-Homj, C.B. Bladng vbaton and falue n ga tubne pat A: bladng dynamc & the 8 `