Scanning Laser Vibrometer Measurement of Guided Waves in Rails

Transcription

1 8th Wold Confnc on Nondstuctiv Tsting, 6- Ail, Duban, South Afica Scanning Las Vibomt asumnt of Guidd Wavs in Rails Phili W. LOVEDAY, Caig S. LONG CSIR atial Scinc and anufactuing; Ptoia, South Afica Abstact Guidd wav basd insction and monitoing systms fo ailway tacks oat at fquncis wh as many as 4 mods of oagation may xist. Duing th dvlomnt of such systms it is advantagous to b abl to masu th amlitud of th individual mods of oagation. Th availability of scanning las vibomt systms has mad it ossibl to masu th dislacmnt o vlocity at a lag numb of oints on th ail sufac. Th contibution of ach mod of oagation may b stimatd fom th masud fquncy sonss by using a sudo-invs tchniqu and mod sha infomation comutd fom a smi-analytical finit lmnt modl. Scanning las masumnts w fomd in th fild at distancs of m and 5m fom a tansduc usd to tansmit th guidd wavs. A scan of 43 masumnt oints was usd to masu 5 mods at 4kH. Kywods: Guidd wavs in ails, mod masumnt, scanning las vibomt. Intoduction Railway tacks snt an ootunity to xloit th advantags of guidd wav ultasound fo NDT alications, as th ails a ssntially on-dimnsional wavguids allowing tansmission ov considabl distancs fom fixd tansduc locations. To utili this hnomnon it is oftn dsiabl to b abl to masu th oagation in tms of individual mods of oagation o individual tavlling wavs. This situation occus whn on wishs to masu th attnuation of aticula mods of oagation with distanc o whn dvloing a tansduc to xcit a aticula mod of oagation. Th masumnt of flction and tansmission cofficints also quis masumnt of individual mods of oagation. This oblm has bn invstigatd by vaious authos and fo vaious stuctus [-5]. A simila oblm is ncountd whn dsigning tansduc aays fo tansmitting o civing scific guidd wavs [6]. If th mod shas a known this infomation can b utilid in th xtaction o saation ocss. In th cas of is, th cicumfntial sha dos not chang with fquncy, but in ails th mod shas vay with fquncy and nd to b dtmind numically. od shas and dission lations obtaind fom a smianalytical finit lmnt SAFE analysis hav bn usd in th mod xtaction ocss [7]. Th mod xtaction thoy is sntd bifly in sction. In [7] a fw mods of oagation w xtactd fom masumnts in th lab using ton-bust xcitation. A lativly low fquncy ang was usd wh only ight mods a abl to oagat and a st of 5 masumnt oints was abitaily slctd. At high fquncis, wh btwn and 4 mods oagat, th oblm bcoms mo comlicatd. Th us of a scanning las vibomt maks it ossibl to masu sonss at a lag numb of masumnt oints, limitd only by accssibility. Som of th actical issus involvd in foming scanning las masumnts in th fild will b discussd in sction 3. Fild masumnts and th alication of th mod xtaction ocss to ths masumnts a dscibd in sction 4.

2 . od xtaction thoy An intuitiv xlanation of how th mod shas can b usd to saat th oagating mods in cylinds is ovidd in [6] bfo th mo gnal cas is statd. Th dscition sntd h is simila to that in [7]. Th fquncy sons of th wavguid, fa fom th xcitation tansduc and oth igulaitis can b wittn as a suosition of th oagating mods: N i 3, =, wh i is th dislacmnt of dg of fdom i of mod sha and is th wavnumb of mod. A SAFE analysis of th ail ovids th tm i. Fild masumnts may b fomd at a sing fquncy using a continuous sin wav xcitation o simultanously at a numb of fquncis. W wish to xtact th magnitud and has of ach oagating mod fom ximntal tim sons masumnts. If w fom masumnts at diffnt oints ach at a distanc and location on th ail cicumfnc and in a aticula diction, th sons can b wittn as a suosition of th contibutions of th fowad oagating mods, which can b wittn in th fom D = as: = m m m m m L L. Th mod sha matix D is assmbld fom infomation fom th SAFE modl whil vcto is assmbld by foming a FFT on ach of th masud tim domain signals. atix D has dimnsion [ x m], whil is [m x ] and is [ x ]. If is qual to m numb of masumnt oints qual to numb of mods th matix D is squa and can b invtd. Howv, w xct a btt sult if w us additional masumnt oints > m and solv th ov-dfind systm of quations in a last-squas sns. This can b convnintly achivd by using th oo-pnos gnalisd invs also calld th sudo invs. W xct that th matix D will b ank m if th a at last m diffnt oagating mods at th fquncy of intst. Th gnalisd invs of D, in this cas, is * * ] [ D D D D =, wh D* is th Hmitian tansos of D and an stimat of is obtaind fom ~ = D. Th condition numb of th mod sha matix was studid as a mans fo slcting a st of masumnt locations [8]. If it is ncssay to includ both fowad and backwad oagating mods this can asily b don as th backwad oagating mods a also ovidd by SAFE analysis. Th systm is thn,

3 f [ D D ] b. 3 b Th accuacy of th xtaction ocss can b chckd by comuting th dislacmnts at ach scan oint fom th mod sha matix and th xtactd modal cofficints. D ~ = ~ 4 In this way w can masu how wll th xtactd valus fit th masud valus and w can dfin an avag man squad o: 3. Imlmntation in th fild f = [{ ~ } { }] * ~ ERROR = 5 Vaious issus nd to b considd whn foming masumnts in th fild. Th slction of masumnt oints is dtmind by accssibility of th masumnt oints and th tim availabl to fom scans. asumnts of th hoiontal dislacmnt on on sid of th ail can b fomd lativly asily as ths masumnts a not svly disutd by assing tains. asumnts of vtical dislacmnt on th cown and on th foot of th ail can b fomd by ositioning th scanning had abov th ail. Ths scans can only b fomd btwn tains. A study of th slction of masumnt oints [8] showd that th vtical masumnts a vy imotant fo dtcting most of th oagating mods and can b usd alon without th hoiontal masumnts. Th hoiontal masumnts a usful to sulmnt th vtical masumnts but cannot b usd without th vtical masumnts. Considing that th ail bounday conditions chang whn a tain asss, which may chang th oagating mods it is ncssay to fom th vtical and hoiontal masumnts btwn tains. Whil it is not ncssay to know th distanc fom th xcitation tansduc it is vy imotant to know th lativ osition of ach scan oint. Th scanning systm usd in this sach did not hav a gomty masumnt unit so th ositions of th masumnt oints had to b masud manually. This was achivd by masuing th hysical osition of th vtical masumnt oints on th ail and thn calculating th osition of th oth oints fom th mio angls of th scanning had whil also taking into account th hight diffnc btwn th had and th foot of th ail. Th location of hoiontal masumnt oints could b dtmind in a simila fashion with th quimnt that th axial osition lativ to th vtical scan should b masud as cafully as ossibl. Th masumnt oints usd do not coincid with nod ositions in th SAFE modl, thfo th mod shas w intolatd to ovid dislacmnts at th masumnt oints. Th scan angls usd w u to aoximatly 5º fo a scan lngth of lss than m. Th scan angl could b takn into account by including axial dislacmnt comonnts of th mod shas dictd by th SAFE modl. An ali invstigation showd that th influnc of this was ngligibl and this was not don in this study. Th xcitation of th ail may b fomd by vaious mthods. In this wok a small iolctic tansduc was glud to th ail. It is ssntial that th xcitation is atabl and stabl ov th tim of th scan. Th ositioning of th tansduc influncs th oagating mods that a xcitd. In addition, th scanning systm quis a fnc signal to synchoni th masumnts. Whn th scan is fomd clos to th xcitation

4 tansduc it is ossibl to us th xcitation signal as th fnc signal. Whn lag distancs a involvd it is ossibl to us a scond iolctic tansduc as a snso to ovid th fnc signal. Th xcitation signal could b a ton bust as was usd in th lab if th masumnt distanc is small o it can b a continuous signal such as andom nois if many fquncis a to b masud simultanously. If masumnts at lag distancs a to b fomd a btt signal to nois atio will b obtaind by using a singl fquncy sin wav xcitation and ating th scan to masu oth fquncis. 4. Fild masumnt sults asumnts w fomd on Tansnt s Coal Link lin using a Polytc scanning las vibomt PSV-4-- as shown in figu. Th ail ofil is S-6-SAR, which is simila to UIC6. Significant ail ofil ginding has bn fomd ov th yas on this ail and th hight of th ail was ducd by 4mm in th SAFE modl to account fo this. Th dission cuvs, of oagating mods, comutd fom a SAFE modl a shown in figu. Th high dnsity of oagating mods in th fquncy ang 3 to 5 kh is illustatd. Figu. Positioning of snso had abov ail 6 Wavnumb ad/m Gou Vlocity m/s Fquncy kh Figu. Comutd dission cuvs Fquncy kh

5 Only th vtical dislacmnts w masud ov a ang of oints. It is ossibl to masu hoiontal dislacmnts on on sid of th ail and to includ ths in th mod masumnt ocdu. This dos qui that th ositioning of th hoiontal oints lativ to th vtical oints is accuatly known. Figu 3 shows a scan fomd clos m to th xcitation tansduc and a scan fomd at a distanc of 5m fom a diffnt xcitation tansduc. In th fist scan th function gnato of th Polytc scanning systm oducd a Vk, 4 kh sin signal, which was amlifid to Vk to div th tansmit iolctic tansduc. Th Vk signal was usd as th fnc signal fo th scanning systm. In th scond scan a saat function gnato was usd at th tansmit station amlifid to 8Vk and no connction to th scanning systm was ossibl bcaus of th distanc involvd. Instad, a scond iolctic tansduc was bondd to th ail and th signal dtctd by this tansduc was usd as th fnc signal by th scanning systm. It is ssntial to hav a fnc signal so that th lativ has of th masumnts at ach oint can b masud. Figu 3. Tyical scan sults at m and 4kH to and 5m and 37 kh bottom Th mod xtaction ocdu dscibd in sction 3 was alid to th 4kH scan, which has 43 masumnt oints. Onc th mods a xtactd th dislacmnt at ach oint can b calculatd and th o btwn th actual masud valu and th fittd valu dtmind. As th lastic modulus of th ail at 4 kh was not known a ang of modulii was usd and th bst fit was found. Th o, comutd by 5, is shown as a function of lastic modulus in figu 4 wh it is sn that a modulus of 5 GPa oducd th bst fit. Th masud and fittd dislacmnt amlitud at ach masumnt oint is shown in figu 5. Th oints hav bn odd in th diction acoss th ail so th oints on on foot a lottd fist followd by th oints on th had and thn th oints on th oth foot.

6 It is vidnt that th lastic modulus of 5 GPa oducd th bst fit scially on th had of th ail... Av RS Eo nm x Elastic odulus GPa Figu 4. Dtmining th lastic modulus that oducs th lowst o E = 5 GPa asud Extactd Abs. Dislacmnt m.5 x -9.5 E = GPa asud Extactd Abs. Dislacmnt m Point Num.5 x -9 E = 3 GPa asud Extactd Point Num Abs. Dislacmnt m Point Num Figu 5. asud and fittd dislacmnt amlituds fo diffnt lastic modulii Th amlituds of th modal cofficints xtactd by th ocss, a listd in tabl. Th mod shas w scald to hav unity maximum valu. Th tabl shows th wavnumbs fo th 5 oagating mods at 4 kh. Slctd mod shas a shown in figu 6 fo uoss of discussion. Tabl shows that th xtaction ocss vals that mods 9, and a dominant and that th fowad tavlling wav is lag comad to th backwad tavlling wav. Ths mods all hav significant vtical motion of th had, which is xctd. Th xtaction ocss indicatd som sons of mods 5 and 3. In aticula th backwad oagating mod 3 was lag than th fowad tavlling mod, which would not b xctd. Th mod shas of ths two mods val that th is vy littl vtical motion in ths mods at ou masumnt oints. This would mak it difficult to masu ths mods using only f b

7 th vtical masumnt oints. In addition, th xtactd amlituds would hav small influnc on th fittd cuvs as ths mods contibut an insignificant amount. This is illustatd by moving ths two mods fom th xtaction ocss. This is quivalnt to stting th amlitud of ths mods to o. It was sn that this had ngligibl influnc on th amlitud of th oth xtactd mods. Th o in th cuv fit was also unaffctd. Th amlituds of th xtactd mods aas to b alistic as thy a small than th maximum masud dislacmnt amlituds. Pvious xinc with insufficint o ooly slctd masumnt oints oducd lag xtactd modal amlituds that fittd wll du to mod cancllation ov th masumnt gion but would dict vy lag amlituds outsid th masumnt gion. Extaolation to oth distancs with th modal cofficints in tabl would not sult in unalistically lag amlituds. od No. Wavnumb ad/m Tabl. Extactd mod amlituds Fowad Amlitud nm Backwad Amlitud nm Fowad Amlitud od 5 & 3 xcludd nm Backwad Amlitud od 5 & 3 xcludd nm

8 .8 od: Fquncy: 4 kh. Wavnumb: 6.33ad/m.8 od: 5 Fquncy: 4 kh. Wavnumb: ad/m od: 9 Fquncy: 4 kh. Wavnumb: 94.55ad/m.8 od: Fquncy: 4 kh. Wavnumb: 97.94ad/m od: Fquncy: 4 kh. Wavnumb: ad/m.8 od: 3 Fquncy: 4 kh. Wavnumb:.4345ad/m Figu 6. Slctd mod shas at 4 kh comutd by SAFE. Contou lots show hoiontal to, vtical middl and axial bottom dislacmnts sctivly. 5. Conclusions A tchniqu fo masuing th individual mods of oagation in ails fom scanning las vibomt masumnts was sntd. asumnts w fomd in th fild, which dmonstatd th caability of foming scans vn whn th oagating mods a small at a distanc of 5m fom th xcitation. Th xtaction ocss was alid to xtact 5 mods at 4 kh and aas to accuatly masu th individual mods of oagation.

9 Acknowldgmnts Accss to ailway tack fo fild masumnts was ovidd by Tansnt and is gatfully acknowldgd. Funding fo this oct was ovidd by th CSIR Statgic Rsach Panl. Rfncs. D. Allyn and P. Cawly, A two-dimnsional Foui tansfom mthod fo th masumnt of oagating multimod signals, J. Acoust. Soc. Am., Vol. 89, 59-68, 99.. D. J. Thomson, Eximntal analysis of wav oagation in ailway tacks, J. Sound Vib., Vol. 3, No. 5, , D. Gsll, D. Pofuns and J. Dual, asumnt of th dission lation of guidd non-axisymmtic wavs in filamnt-wound cylindical stuctus, Ultasonics, Vol. 38, 57-5,. 4. F. Lana di Scala and J. cnamaa, asuing high-fquncy wav oagation in aiload tacks by oint tim-fquncy analysis, J. Sound Vib., Vol. 73, , T. Hayashi and. uas, od xtaction tchniqu fo guidd wavs in a i, NDT and E., Vol., No., 63-75, P. D. Wilcox, Guidd-Wav Aay thods in Encyclodia of Stuctual Halth onitoing, P.W. Lovday, asumnt of odal Amlituds of Guidd Wavs in Rails, Poc. of SPIE, Vol. 6935, P.W. Lovday and C.S. Long, odal amlitud xtaction of guidd wavs in ails using scanning las vibomt masumnts, to aa in Rv. Pog. QNDE,.