The Transducer Influence on the Detection of a Transient Ultrasonic Field Scattered by a Rigid Point Target

Transcription

1 Rev. Eneg. Ren. : Physique Enegéique 1998) The Tansdue Influene on he Deeion of a Tansien Ulasoni Field aeed by a Rigid Poin Tage H. Khelladi * and H. Djelouah ** * Insiu d Eleonique, ** Insiu de Physique UTHB, B.P. 3, El Alia, 16111, Alge Absa The use of ulasound in he deeion of defes impoves he mehods of Non Desuive Tesing NDT). Among he pinipal poesses of deeion, he eho-mode is he mos used. Beause of he impoane of his lae in NDT, we have analysed he effes, on he shape of he ansien ulasoni field, of he defe posiion and of some paamees onsiuing he deeion line. As he ansdue plays leading ole in he deeion of defes, he influene of is haaeisis damping sie and nominal fequeny) has been invesigaed in he pesen sudy. Résumé L uilisaion des ulasons dans le domaine de la déeion des défaus a pou bu d amélioe les méhodes de onôle. Pami les pinipaux poédés de déeion, l ého-mode es le plus uilisé. En aison de l impoane de e denie en onôle non desuif des maéiaux, nous avons analysé l influene de la posiion e de la vaiaion de eains paamèes de la haîne de la haîne de sondage su la fome du hamp ulasonoe impulsionnel déeé pa le apeu éepeu. Dans e pésen avail, nous nous sommes spéialemen inéessés à l influene des aaéisiques du ansdueu amoissemen, aille, e féquene nominale) sahan qu il joue un ôle déeminan dans la déeion des défaus. Mos lés: Tansdueu plan Ulaons Eho-mode Diffaion imulaion numéique. 1. INTRODUTION In Non Desuive Tesing of maeials, all he infomaion is inluded in he signal deeed by he ansdue. This lae ansmis and eeives he ulasoni waves whih popagae in he medium o analye. This, i is impoan o ake ino aouns is influene on he shape of he deeed signal. The qualiy of he NDT analyses deeion sensiiviy, peision in he defe loaliaion, esoluion... ) is ondiioned by eah elemen of he deeed line. A good inepeaion of he diffeen deeed signals neessiaes a onol on how eah elemen of he deeed line opeaes. Theefoe, he expeimene needs o know he influene of eah elemen ha onsiues he deeion line. Moeove, a physial phenomenon suh as he saeing is geneally pesen and an lead o an eoneous diagnosis. In he pesen wok, he effes of he adial and axial defe posiion on he aveage pessue deeed by he eeiving ansdue ae invesigaed. Theeafe he influene of he ansdue haaeisis sie, nominal fequeny, fao of damping ) is examined in ou analysis.. DERIPTION OF THE DETETION LINE As shown in figue 1, he ulasoni equipmen in he NDT is simple enough [1}. Fig. 1: ynopsis diagam of he deeion line The volage geneaed by he eleial pulse simulaes a pieoelei ansdue ha podues pulses whih popagae in he medium o be analyed popagaion medium); hese ulasoni waves undego a 49

2 5 H. Khelladi e al. efleion in he pesene of any disoninuiy in he popagaion medium. A eeiving ansdue allows he deeion of hese efleed waves. An analysis of hese waves pemis he loaliaion of he defe and he evaluaion of is dimensions. 3. TRANIENT ULTRAONI FIELD ATTERED BY AN INONIFIED POINT TARGET The ulasoni waves emied by he ansmiing ansdue undego a efleion in he pesene of any disoninuiy in he popagaion medium. This disoninuiy an be epesened by a poin age, having an aousi impedane muh lage han ha of he popagaion medium. o he efleion oeffiien a he inefae fluid/age an be onsideed as equal o uniy oal efleion). A simple onfiguaion is onsideed, whee he sufae of he age is paallel o he sufae T of he ansdue. In he ase of an isoopi, homogeneous and lossless fluid, and in he hypohesis of linea aousi, i is easy o pove ha nea he axis, he aveage pessue deeed by he eeiving ansdue is given by [] - [5] : p ) v ) P ier, ) v ) ρ φ ier, ) 1) whee denoes a ime onvoluion, ρ is he densiy of he popagaion medium a es, is he veo posiion of he poin age; P ier is he ansmi-eeive impulse esponse fo he pessue; φ ier is he ansmieeive impulse esponse fo he aousial poenial. P ier, ) ρ φie, ) φie, ) ) T, ) φ ier φie, ) φie, )) 3) T is he popagaion veloiy of he aousi waves in he fluid, φ ie, ) is he spaial impulse esponse. The aousi pessue, a any poin in he fluid, an be deemined afe deiving he expession of φ, ). ie Fig. : Geomey fo he deeminaion of he field saeed by a igid poin age As shown in figue, wo egions ae defined aoding o whehe he pojeion of he poin M is on he sufae T of he pison o on he sufae B of he baffle. The fis aea oesponds o he die adiaion one. I is fomed by a saigh ylinde pependiula o he ansdue plane, and whose basis is he sufae. The seond aea epesens he shadow one, and is onsiued by he emainde of he half spae. In he ase of a iula pison wih a adius a, he expession of φ, ) is summaied in Table. 1. ie

3 IPE : The Tansdue Influene on he Deeion 51 The ansdue nomal veloiy v ) has been simulaed by he funion defined by Funh/Mulie [6], and i epesens a damped sinusoid of fequeny ω, onaining N yles N), and having a duaion of τ π N / ω. Table 1: Analyi expession of φ ie, ) fo any posiion ξ off-axis min min < < 1 Region I : ξ < a φ ξ + + ie, ) a R Aos 1 max π ξ R max Region I : ξ > a The nomal veloiy is given by : < min 1 ξ + + φ a R ie, ) Aos 1 min π max ξ R > max N N + 1 ν. sin ω ). < < sin ω LLL LLL LLL N + 1 N v ) 4) LLL LLL LLL LLL LLL LLL LLL LLelsewhee Using equaion 4), he vaiaion of he nomalied nomal veloiy vesus he ime is ploed in figue 3. Then, he onvoluion inegal has been evaluaed using he Fas Fouie Tansfom. Fig. 3: imulaion of he veloiy wavefom fo : N, f.5 MH, v o 1-4 mm/µs 3.1 Influene of he age posiion on he deeed pessue field On axis ase As shown in figue 4a, fo a poin age on he axis, he ansmi-eeive impulse esponse fo he poenial φ ier,, ) is made up of wo eangula funions. I begins a wih a onsan value ha lass + + a + a unil 1 his ineval epesens he plane wave egime) and finishes a. A a fahe posiion of he age, he duaion of he plane wave egime deeases Fig. 4d). The ansmi-eeive impulse esponse fo he pessue PiER,, ) is onsising of 3 suessive Dia peaks Fig. 4b). The fis and he hid peaks possess he same polaiy, have a weigh of ρ, while he T seond one has an inveed polaiy and a weigh of ρ. T The pessue p ) is onsising of hee omponens having he same wavefom han he ansmiing ansdue nomal veloiy Fig. 4 ). This esul an be inepeed by hese equaions. P,, ) ρ v ) [ δ ) δ 1 ) + δ )] 5) T P,, ) ρ [ v ) v 1 ) + v )] 6) T

4 5 H. Khelladi e al. Fig. 4: Vaiaion effe of he age posiion on φ ier, P ier and p ) fo : a 1,7 mm, f.5 MH, N, ξ mm, b.4 mm. The delays of hese hee pulses oespond espeively o he popagaion imes, 1 and a epesens he ime popagaion fom he ansdue ene o he age, hen afe efleion bak o he ansdue ene. oesponds o wo diffeen aousi pahs oveed duing he same duaion. The fis pah is fom he ansdue ene o he age, afe efleion o he edge of he ansdue; he seond pah is fon he edge of he ansdue o he age, hen afe efleion o he ansdue ene. As pessues add, he ampliude of he seond pulse is wie ha of he fis one. + a oesponds o he popagaion ime fom he edge of he ansdue o he age hen afe efleion fom he age, bak o he edge of he ansdue. Thus, a any insan < he pessue is null on he eeive, sine i has no been eahed by any peubaion. The finie dimension of he ansmiing-eeiving ansdue has no influene beween he insan ime ineval is alled he plane wave egime. In his ase, he pessue is equal o he podu of he oeffiien by he paile veloiy delayed by. Howeve, fom he insan 1, he pessue field inludes in addiion he waves semming fom he peiphey of he pison. These waves, alled edge waves, expess he diffaion by he bounday of he pison and he poin age. Refeing o figue 5, fo a poin age on he axis, he pessue deeed by he eeiving ansdue is made up of hee pulses whose delays depend on he age posiion. Fo a age lose o he ansdue Fig. 5a, 5b, 5, 5d and 5e), he hee pulses ae sepaaed in he ime. On he ohe hand, a a fahe posiion, he delay beween he hee pulses beomes smalle, ausing hei ovelap as an be seen in Fig. 5f) Off-axis ase Fo a poin age off-axis, he siuaion is slighly moe ompliaed Fig. 6). In his ase, diffeen insans oesponding o he aival of he waves ae defined. oesponds o he aousi pah fom poin H of he soue o he age hen bak o he same poin H of he soue. The poin H epesens he ohogonal pojeion of he poin M on he ansdue Fig. ).

5 IPE : The Tansdue Influene on he Deeion 53 Fig. 5: Influene of he age posiion on he deeed pessue fo : a 1.7 mm, f.5 MH, N, ξ mm, b.4 mm a ξ) oesponds o wo diffeen aousi pahs oveed duing he same peiod of ime. The fis pah is fom poin H of he soue o he age, hen o he loses edge of he soue; he seond pah is fom he loses edge of he soue o he age, hen o he poin H of he soue. + a ξ) oesponds o he aousi pah fom he loses edge of he soue o he age hen o he loses edge of he soue ξ + a ) oesponds o wo diffeen aousi pahs oveed duing he same peiod of ime. The fis pah is fom poin H of he soue o he age hen o he fahes edge of he soue; he seond pah is fom he fahes edge of he soue o he age hen o he poin H of he soue. 4 + ξ + a ) + + a ξ ) oesponds o he aousi pah fom he fahes edge of he soue o he age hen o he loses edge of he soue. 5 + ξ + a ) oesponds o he aousi pah fom he fahes edge of he soue o he age hen o he fahes edge of he soue. In his ase he ansmi-eeive impulse esponse fo he poenial φ ier, ) begins a wih a onsan value ha lass unil 1, Fig. 6a); his ineval epesens he plane wave egime. Fo a given posiion of he age, he duaion of he plane wave deeases when ξ ineases Fig. 6d).

6 54 H. Khelladi e al. Fig. 6: Vaiaion effe of he age posiion on φ ier, PiER 11 and p ) fo : a 1.7 mm, f.5 MH, N, Z 15 mm, b.4 mm I is impoan o noie ha off-axis, he ansmi-eeive impulse esponse fo he pessue PiER, ) pesens an impoan numbe of disoninuiies Fig. 6b). PiER, ) is null eveywhee, exep a he insans epesened by a Dia peak wih a weigh of ρ ), l,,, and whee he disoninuiy ous Fig. 6b). Fig. 7: Influene of he age posiion on he deeed pessue fo : a 1.7 mm, f.5 MH, N, Z mm, b.4 mm The pessue field is onsiued by he plane wave whih has he same wavefom han he ansmiing ansdue nomal veloiy, followed by he edge waves saggeed in he ime.

7 IPE : The Tansdue Influene on he Deeion 55 Le us poin ou ha he pulse ampliude elaive o he insans 1 and 3 is moe impoan han ha of insans, 4 and 5. Fo he fis seies of pulses, eah insan oesponds o wo diffeen aousi pahs; heefoe he onibuion is wie as muh. On he ohe hand, fo he seond seies of pulses, eah insan oesponds o one aousi pah Fig. 6f). A small vaiaion of he paamee ξ leads o a noieable hange ompaaively o he on axis pessue. On he axis, he pessue is onsiued by hee pulses and wih ampliude aios given by 1: : 1 Fig. 5). While, fo a vaiaion equal o.5 of he paamee ξ/a, he pessue is omposed of six pulses Fig. 7). Fo a highe value of he paamee ξ, he ampliude of he fis pulse deeases, his is due o he effe of he seond pulse whih possess an inveed polaiy Fig. 7f). 3. Tansdue haaeisis influene on he deeed pessue field 3..1 Nominal fequeny As file ansdue nominal fequeny ineases, he hee pulses deeed by he eeiving ansdue ae sepaaed in he ime Fig. 8a, 8b, 8 and 8d). Fo a bee deeion of he diffaion phenomena, a ansdue wih a high nominal fequeny mus be used. 3.. Damping The duaion of he hee pulses deeed by he eeiving ansdue depends on he numbe of yles in he ansdue nomal veloiy v ). In paie, he numbe of yles depends on Fig. 8: Influene of he ansdue nominal fequeny on he deeed pessue fo : a 1.7 mm, N, Z mm, ξ mm, b.4 mm whole he eleoaousi line, espeially he damping of he ansdue. Fo his eason, i is advisable o use a wide-band ansdue. Refeing o Fig. 9a, 9b and 9), i appeas ha ineasing he numbe of yles ineases he duaion of he hee pulses, ausing an ovelap of he diffeen pulses, and leading o a diffiuly in he inepeaion of he deeed pessue Fig. 9d). o fo a good inepeaion of he deeed pessue, we mus use no only sho pulses o exie a wide-band ansdue having a high nominal fequeny bu also a eeive having a suiable band-pass ie The ansdue adius affes he ampliude of he deeed signal. Moe he adius of he ansdue deeases, moe he ampliude of he signal ineases Fig. 1a). This an be explained by he a ha he ampliude of he signal is popoional o he aio. Fuhemoe, we obseve ha fo a ansdue possessing an impoan sie, he deeed pulses ae esolved in ime. ine in his ase he aousi pah elaive o 1 and is ineased, he seond and hid pulses ae delayed Fig. 1d). In geneal, he diffaion phenomena ae pepondean fo a small apeue.

8 56 H. Khelladi e al. Fig. 9: Influene of he numbe of he yles on he deeed pessue fo: a 1.7 mm, f,5 MH, Z mm, ξ mm, b.4 mm 4. ONLUION The influene of he ansdue haaeisis on he ulasoni field saeed by a igid poin age has been invesigaed. I has been noied ha he deeed pessue is losely elaed o he haaeisis pesened by he ansdue. Fo a bee signal analyses, i is advisable o use a songly damped ansdue, possessing a high nominal fequeny and having an impoan sie, in ode o avoid he ovelapping of he pulses even fo ages fa fom he ansdue. The genealiaion of his model, by aking ino aoun he effe of he age sie on he deeed pessue field, will be he subje of a nex sudy. Fig. 1: Influene of he ansdue sie on he deeed pessue fo : f.5 MH, N, Z mm, b.4 mm, ξ mm REFERENE [1] J.L. Pe1leie, La Paique du onôle Indusiel pa Ulasons, ommuniaions aives, ENAM, Pais. [] H. Khelladi e H. Djelouah, Modélisaion en Eho-mode du hamp Ulasonoe Impulsionnel Diffaé pa une ible Ponuelle, onféene Maghébine su le onôle Non-Desuif, Alge, 8-3 Juin [3] A.J. Hayman and J.P. Weigh, Obsevaions of Popagaion of Vey ho Ulasoni Pulses and hei Refleion by mall Tages, J. Aous. o. Am., 63 ), pp , [4] M. Ueda and H. Ihikawa, Analysis of an Eho ignal Refleed fom a Weakly aeing Volume by a disee Model of he Medium, J. Aous. o. Am., 7 6), pp , [5]. M. Laen and J.P. Weigh, Tansmi-eeive Mode Responses fom Finie ied Tages in Fluid Media, J. Aous, o. Am., 8, 6), pp. 1-11, [6] A. Ilan and J.P. Weigh, The Popagaion of he ho Pulses of Ulasound fom a iula oue oupled o an Isoopi olid, J. Aous. o. Am., 88, ), 199.