Ultrasonic Measurement of Air Gap Between Metal Walls Using Bending Waves

Transcription

1 Ultrsonic Mesurement of Air Gp Beteen Metl Wlls Using Bending Wves Alex Krpelson Kinectrics Inc. E-mil: 1. Introduction Design, contining to metl lls (e.g. tubes, pltes, or other prts) ith ir/gs gp beteen them, is typicl in mny industries. Becuse of vrious resons (ging, size chnge, temperture nd rdition influence, vibrtions, creep, mechnicl displcements nd others) this ir gp chnges during product lifetime. Such chnge cn led to system mlfunction nd even dmge. In order to prevent this, the gp idth, e.g. beteen to concentric metl tubes (this is the most typicl cse), should be continuously monitored. Very often ccess to the tubes is possible only from ithin the inner tube (IT), hich cn be filled ith ter. Typiclly the gp idth is mesured by using eddy-current technique. The trnsmit coil, locted inside the IT, induces lo frequency current flo round the circumference of both tubes. This flo cretes rection field hich ffects the pick-up voltges in the receive coil. The chnge in the overll rection field due to the locl proximity beteen tubes cretes the typicl response signl. Hoever, the ccurcy of such mesurements is rther lo. Theoreticlly, to improve the ccurcy, the high-frequency eddy current probe cn be used. Hoever, due to electromgnetic field ttenution in the metl ll of the IT, such probe provides only lo mplitude response. Moreover, the results of eddy-current mesurements re ffected by chnges in mteril electric conductivity, tube ll thickness, nd others. The only lterntive technique, hich cn be used for ccurte gp mesurement, is the ultrsonic (UT) method, hich currently is extensively used for tube inspection. Ultrsound is not ffected by vritions in electricl conductivity or permebility, nd it cn provide the desired ccurte mesurements nd 100% mpping. Besides, the UT equipment is portble nd inexpensive; orks from ithin the IT filled ith ter; nd cn stnd rdition nd temperture. The objective of this pper is to describe results of the fesibility study concerning bilities of lo-frequency UT bending (flexurl) ves in the IT ll to mesure the ir gp beteen to concentric metl tubes ith ccess only from ithin the IT.. Stndrd Pulse-Echo Technique Unfortuntely, the simplest pulse-echo (PE) UT technique ith norml bem trnsducer locted inside the IT cnnot be used for ir gp mesurement. If gp beteen tubes is filled ith ter, then the UT trnsducer, locted inside the IT nd orking in PE mode, cn esily generte high mplitude reflections from the outside surfce (OS) of the IT nd the inside surfce (IS) of the outer tube (OT), thus providing the ccurte bsolute gp mesurement. The experiments ere performed using computerized scnning rig, Winspect softre for dt cquisition nd processing, SONIX STR-81G digitizer crd, nd UTEX UT-340 pulser-receiver. Set-up contined to concentric metl tubes: the IT ith ll thickness 4mm nd inside dimeter

2 103mm, nd the OT ith ll thickness 1mm nd inside dimeter 130mm. The IT s filled ith ter. At first, 1mm gp beteen the IT nd OT s filled ith ter, nd 10MHz trnsducer (focl length FL=33mm nd perture dimeter D=9.5mm) locted inside the IT in ter ith terpth WP=9mm s pplied in PE mode. Experiments shoed tht gp could be relibly nd ccurtely mesured, see Fig. 1. The time-of-flight beteen 1 st IT OS reflection nd 1 st OT IS reflection is 1.µs. For ultrsound velocity in ter 1.5mm/µs it gives 1mm gp idth, hich mtches ith mechniclly mesured gp idth. IT IS reflection nd IT OS reflection IT/OT 1mm gp 1 st IT OS reflection 1 st OT IS reflection nd OT IS reflection Figure 1. A-scn of IT/OT 1mm ide gp filled ith ter. Probe: norml bem 10MHz trnsducer ith FL=33mm, D=9.5mm nd WP=9mm locted inside IT in ter nd orking in PE mode. Hoever, hen gp is filled ith ir, it turned out tht mplitude of the UT signl reflected from OT s extremely ek nd could not be detected t the existing noise level. It occurred becuse ultrsound prcticlly did not pss through interfce metl/ir. The response mplitude is determined, mong other fctors, by trnsmission pressure coefficient [1-] Z T p =, Z1 + Z (1) here Z 1 is the coustic impednce of the medi here coustic bem comes from (Z 1 =31Mryl for metl tube in our cse), nd Z is the coustic impednce of the medi here coustic bem goes in (Z = Mryl for ir in our cse).

3 3 As result, for interfce IT/ir the trnsmission coefficient T p =0.003%; it corresponds to 90dB ttenution. Tht is hy the UT response, reflected from the OT IS hen gp filled ith ir, cnnot be detected. For ter Z =1.5Mryl nd respectively T p =10% for interfce IT/ter. Tht is hy the UT signl, reflected from the OT IS, hen gp is filled ith ter, cn be esily detected. So, the signl reflected from the OT, hen gp is filled ith ir, is extremely ek, besides tht there re mny strong multiple reflections ithin the IT ll. These signls bsolutely msk ek reflection from the OT: see Fig shoing vrious reflections for 8mm gp including PE response from OT IS rriving t ~50µs fter 1 st IT OS reflection. Multiple reflections ithin the IT ll Reflection from interfce ir/ot is very ek nd should be there for 8mm gp Figure. A-scn of 8mm gp filled ith ir. Probe: norml bem 10MHz trnsducer ith FL=33mm, D=9.5mm nd WP=9mm locted inside IT in ter nd orking in PE mode. Note tht t lo gin the hole picture is, of course, much clener, but there is no chnce tht reflection from the interfce ir/ot cn be detected. At high gin theoreticlly it could be detected, if it ould not be msked by very strong multiple reflections. Thus, the obtined results sho tht stndrd PE method cnnot be used for ir gp mesurement. Becuse of this some other UT technique should be used to ccurtely mesure ir gp beteen to concentric metl tubes. A fe ttempts ere mde to use UT technique, hich genertes stnding resonnt coustic ves ithin the gp in order to mesure its idth. Since the resonnt stnding ve in comprison ith running one hs much lrger mplitude, the response cn probbly be detected nd used for gp mesurement. Such resonnt method is nlogous to contct UT resonnt thickness guging technique. The proposed resonnt method hs been experimentlly tested; it turned out tht it relly lloed incresing sensitivity times in comprison ith stndrd PE technique, hoever even the best obtined results ere not sufficiently sensitive nd effective for prcticl ppliction.

4 4 3. Lo-Frequency Bending Oscilltions of Tube Wll In order to effectively trnsmit coustic signl through ter nd metl tube ll into ir nd receive the reflected signl, one should use the IT ll s thin membrne performing bending (flexurl) oscilltions. Lo-frequency bending oscilltions of the IT ll in the trnsmission mode cn be excited e.g. by smll vibrtion shker locted inside the IT in ter. The oscillting tube ll ill ork then s rther efficient rditor of lo-frequency coustic ves in ir. After reflecting from the OT the ir ve ill come bck to the IT nd excite secondry flexurl oscilltions (symmetric Lmb ves) in the IT ll. Such ves ill excite the longitudinl leky ves trnsmitted in ter inside the IT, hich cn be received by lofrequency trnsducer-receiver positioned there. The proposed method, using bending oscilltions of the IT ll to trnsmit nd receive coustic ves propgting in three medi (ter, metl, nd ir), is probbly the only technique mong lrge vriety of UT methods, hich possesses sufficient effectiveness. It turned out (see belo) tht by forcing the IT ll to vibrte s hole, i.e. to ork s thin membrne, performing lo-frequency flexurl oscilltions, it s possible to trnsmit in ir (trnsmission mode) nd in ter (reception mode) the coustic ves ith required mplitude. Recll, tht lo-frequency bending oscilltions of thin pltes ere used for long time to trnsmit sonic ves beteen vrious medi (gs, solid, nd liquid) ithout huge loss; nd no other UT method cn do it. For instnce, so clled crbon microphones, idely used some time go, ere very efficient: they converted ek sound ves into flexurl vibrtions of thin metl membrne; these vibrtions in turn cused vrying pressure in grphite poder, hich entiled the grphite resistnce chnge. Another exmple is the bility of hydrophone (sonr) to detect even ek sound, generted inside submrine in ir nd trnsmitted through bot metl hull into outside ter; only flexurl vibrtions of the hull re ble to trnsmit very ek sonic ve from ir into ter through metl lyer ith sufficient intensity. 3.1 Theoreticl bckground Consider metl plte of thickness h in z-direction nd infinite in to other directions x nd y, djcent ter hlf-spce semi-infinite in z-direction t the front surfce z=0, nd djcent ir hlf-spce semi-infinite in z-direction t the bck surfce z=h. In generl cse, flexurl ve propgting in thin plte (symmetric Lmb ve) should be ccompnied by leky longitudinl ves propgting in the ter nd ir djcent to the plte. To describe this phenomenon system of the folloing equtions is needed [3-4]. First eqution is the eqution for mechnicl displcement in bending ve propgting in thin plte (Euler-Bernoulli plte eqution). (Expression bending ve in thin plte mens tht plte thickness is smll compred ith bending velength; oscilltions re only in z-direction perpendiculr to the plne of the plte; displcement, prticle velocity nd strin re uniform in norml direction, i.e. they do not depend on coordinte z; ve is propgting in to directions x nd y, i.e. ve vector hs only to components in the plte plne) ξ ξ ξ ξ ρ p h = D P ( x, y, z, t) z= 0 + P ( x, y, z, t) z= h, () 4 4 t x x y y

5 here ( x, y, t) 5 ξ is the mechnicl displcement of the plte in z-direction; ρ p is the density of 3 plte mteril; h is the thickness of the plte; = E h 1 ( 1 σ ) D is the flexurl rigidity (bending modulus) of the plte; E is the Young s modulus of plte mteril; σ is the Poisson s rtio of P x y, z, t is the pressure exerted by ter on the plte, hich cn be plte mteril; (, ) z= 0 ϕ expressed in terms of the ter velocity potentil P = ρ ; P ( x, y, z, t) z= h is the t pressure exerted by ir on the plte, hich cn be expressed in terms of the ir velocity potentil ϕ P = ρ ; ρ is the density of the ter; ρ is the density of the ir; ϕ ( x, y, z, t) is the t ϕ x, y, z t is the ir velocity potentil. ter velocity potentil; ( ), Using expressions for P nd P eqution () cn be ritten s follos ξ t ξ x ξ ξ ϕ ϕ, (3) x y y t t ρ h p = D + + ρ z= 0 ρ 4 4 z = h Second eqution is the ve eqution for velocity potentil ϕ describing the leky longitudinl ve ccompnying flexurl ve in plte nd propgting in ter hlf-spce djcent to the plte t z = 0 nd locted t z < 0 : ϕ x ϕ + y ϕ + z 1 = c ϕ t (4) here c is the speed of propgtion of sound in ter. Third eqution is the ve eqution for velocity potentil ϕ describing the leky longitudinl ve ccompnying flexurl ve in plte nd propgting in ir hlf-spce djcent to the plte t z = h nd locted t z > h : ϕ ϕ ϕ = x y z c ϕ t (5) here c is the speed of propgtion of sound in ter. Forth eqution is the boundry condition t the interfce plte/ter t z = 0. The norml component of the ter prticle velocity t the surfce must be equl to the prticle velocity of the plte: ξ ( x, y, t) ϕ ( x, y, z, t) = t z (6) Fifth eqution is boundry condition t the interfce plte/ir t z = h. Norml component of the ir prticle velocity t the surfce must be equl to the prticle velocity of the plte: z = 0,,

6 6 ( x, y, t) ϕ ( x, y, z t) ξ =, t z (7) Equtions (3)-(7) describe propgtion of bending ve in thin plte (symmetric Lmb ve) nd to relted leky ves in the djcent medi, ter nd ir. To solve system (3)-(7), nlyze the idelized cse nd ssume tht solution cn be presented in complex form s three ssocited continuous plne trveling ves: ξ ( x, y, t) = Aexp[ i( kx + ky ωt) ], (8) ϕ ( x, y, z, t) = B exp[ i( kx + ky + kz ωt) ], (9) ϕ ( x, y, z, t) = C exp[ i( kx + ky + kz ωt) ], (10) here A, B nd C re the mplitudes of the respected ves; k is the ve number of bending ve in the plte; ω is the ngulr frequency; k is the ve number of plne leky longitudinl ve in ter in z-direction; nd k is the ve number of plne leky longitudinl ve in ir in z-direction. The ssumed solutions (8)-(10) describe model, here flexurl continuous trveling ve (symmetric Lmb ve) propgtes in thin plte infinite in to directions (formul (8)). Amplitude A nd frequency ω of this ve depend on the externl driving force, hich excites this ve. The ve number k of the bending ve in plte nd frequency ω re connected by the dispersion formul obtined belo. The flexurl trveling ve in plte genertes to continuous plne trveling leky longitudinl ves propgting in ter (formul (9)) nd ir (formul (10)) ith the sme frequency ω but different mplitudes B nd C. Both leky ves re ssocited ith bending ve in the plte nd propgte long the plne of the plte (i.e. in x nd y directions) ith the sme ve number k. But in z-direction norml to the plne of the plte they propgte ith specific ve numbers k nd k. Substitute (9) nd (10) into (4) nd (5) respectively nd obtin formule for the ve numbers k nd k s moduli of the complex functions: (11) (1) k k z = h = ω k, c = ω k, c No substitute (8), (9) nd (11) into (6) nd derive formul for mplitude B of the leky ve in ter s modulus of the complex function:

7 7 (13) B = ω Ac ω c k Substitute (8), (10) nd (1) into (7) nd derive formul for mplitude C of the leky ve in ir s modulus of the complex function: ω Ac i h ω c k C = exp ω c c k (14) And t lst, substitute (8), (9) nd (13) into (3) nd, neglecting very ek pressure ϕ P = ρ exerted by ir on the plte, obtin the dispersion formul t (15) ρ ω ω c 4 c k = ( 4 D k 4 ρ hω ) The obtined solution (8)-(15) describes trveling continuous flexurl ve (symmetric Lmb ve) propgting in thin metl plte nd ccompnied by to trveling continuous plne leky ves propgting in the djcent medi, ter nd ir. Recll tht mplitude A of the bending ve nd frequency ω depend on the externl driving force, hich excites the oscilltions. In our cse in the trnsmission mode this force is exerted by vibrtion shker locted inside the IT in ter nd impcting the IT IS. In the reception mode this force is exerted by n ir ve impinging on the IT OS. Of course, this solution is the pproximte one bsed on the folloing ssumptions: 1. The plte s ssumed infinite in x nd y directions. Tht is hy there is only one trveling bending ve in these to directions: no reflections from plte boundries.. The ter nd ir ere ssumed infinite in x nd y directions nd semi-infinite in z direction. Tht is hy there re only one trveling leky ve in ter nd one in ir in ll three directions: no reflections from boundries. 3. It s ssumed tht excittion force s continuous ith frequency ω. 4. The problem (3)-(7) s solved for plte but tube ll is curved in circumferentil direction. 5. It s ssumed tht there re only plne leky ves in the ter nd ir (see formule (9) nd (10)), hile in relity these leky ves re more complex. Note tht lthough the obtined solution (8)-(15) bsed on such ssumptions is vlid only for the idelized cse, but the model predictions hve pproximte vlidity for rel cse. Formule (8)- (15) llo clculting (more precisely, estimting) the min prmeters of vrious coustic ves used to effectively trnsmit signls from ter into ir nd bck through metl plte.

8 8 To prove efficiency of this method in comprison ith stndrd UT PE technique, evlute the energy trnsmission coefficient T E for the cse, hen the incident ve from ir impinges on the front surfce of thin metl plte djcent to ter t the bck surfce. It cn be done using formule (8)-(15) or much simpler pproximte expression from [4] W Z T p T 1 10log 1 E = = +, WI Z (16) here W T is the poer in the ve trnsmitted from ir into ter through metl plte; W I is V p the poer in the ir incident ve; Z p = i ω ρ p h 1 is the specific coustic c impednce of the plte ith ir t the front surfce nd ter t the bck surfce; V p is the phse velocity of flexurl ve in the plte; Z = ρ c is the chrcteristic coustic impednce of the ir. Substitute ll necessry prmeters of the metl plte, ir nd ter into (16) nd obtin tht T E = 58dB. It mens tht poer of the trnsmitted coustic ve in ter is ~800 times less thn poer of the incident coustic ve in ir, nd respectively [1-] coustic pressure in ter is ~8 times less thn pressure of the incident coustic ve in ir. Very similr results for T E vlue ere obtined using formule (8)-(15) nd expressing mplitude B of the ve in ter through mplitude C of the ve in ir. For comprison note, tht for norml longitudinl ve trnsmitted from ir into ter through the sme metl plte, the energy trnsmission coefficient T E = 10dB. It mens tht poer of the trnsmitted ve in ter is ~10 6 times less thn poer of the incident ve in ir. This vlue s clculted using trditionl formul for T E nd stndrd numbers of chrcteristic coustic impednces of ter, ir nd metl [1-]. Respectively, the coustic pressure in ter is ~10 3 times less thn pressure of the incident coustic ve in ir. The obtined number of trnsmission coefficient T E = 58dB for technique using the bending ve in thin metl plte locted beteen ir nd ter, nd mgnitude T E = 10dB for trditionl UT PE method for this three-lyer medium, clerly demonstrte efficiency of the bending-ve technique (difference in T E is bout 10 3 ). Moreover, these numbers explin high sensitivity of bending ve method in both exmples described erlier. The obtined results llo ssuming tht method using bending ve in thin plte locted beteen ter nd ir cn be prospective for mesuring the ir gp beteen to concentric metl tubes. 3. Some problems relted to bending-ve technique Despite very prospective high potentil sensitivity, the bending-ve method hs t lest to mjor chllenges, hich should be ddressed in order to mke this technique orkble for gp mesurement.

9 9 First problem is very high level of the bckground coustic noise - strong signls relted to different ves nd multiple reflections ithin the IT ll. As mtter of fct, flexurl vibrtions of the IT ll, excited by vibrtion shker, generte very strong direct response in trnsducer-receiver. The mplitude of this response is bout times greter, thn the expected mplitude of the ve crrying informtion bout the IT/OT gp. Moreover, the shpes nd spectr of these to types of ves re similr. Therefore, some specil technique should be used to distinguish comprtively ek response, generted by coustic ves in the ir gp, t the bckground of nlogous but much stronger signl, excited directly by the IT ll bending oscilltions. To overcome this difficulty one cn e.g. employ number of sensitive receivers nd then cross-correlte their signls - method idely used in seismocoustics. To solve our problem, it s suggested to use some high resolution nlog-to-digitl converter (t lest 1bit, becuse 1 =4096) nd to identicl trnsducers locted in one xil plne but oriented t prt in rdil direction nd one shker (impct hmmer) positioned in the middle beteen them in the sme xil plne (see Fig. 3). Trnsducer 1 IT OT Impct hmmer Wter Air gp Trnsducer Figure 3. Schemtic of gp mesurement system, consisting of to identicl trnsducers, locted in one xil plne but oriented t prt in rdil direction, nd one impct hmmer positioned in the middle beteen them in the sme xil plne. Such system should give identicl responses, hen to gps fcing the opposite trnsducers re equl. If these gps re not equl, the responses of trnsducers should differ, becuse ves propgting in ir gps ill rech probes t different times. As result, digitizing signls of these to trnsducers ith high ccurcy nd subtrcting one from other, it my be possible to detect the gp-ves, hich rrive to the respective trnsducers t different moments of time. It ill llo correlting the received signl ith gp idth. Second problem is vritions in the IT nd inspection system prmeters, hich ffect the received signls. Such IT prmeters, s shpe (e.g. ovlity), ll thickness, inside dimeter, nd physicl chrcteristics of tube mteril, my differ from one tube to nother nd my even vry in one tube. Probes nd impct hmmer cnnot be bsolutely symmetriclly positioned nd

10 10 oriented in the module-holder; module itself cn never be perfectly centered; nd probes cnnot be exctly identicl. All these prmeters re the influentil essentil ones, becuse they strongly ffect the outcome of mesurements. Therefore, some specil technique should be used to distinguish response, generted by coustic ve in ir gp, from signls vritions, initited by numerous chnges in prmeters of the IT nd inspection system. It s suggested tht such signl processing methods s verging, filtering, nd cross-correltion, should seprte the responses (gp-ves), crrying informtion bout gp idth, from signl vritions, generted by chnges in the IT nd inspection system prmeters. It s expected tht using ll methods mentioned bove, it ould be possible to minimize the bckground coustic noise, obtin good gp-ve responses for different gps, nd correlte the received signl ith gp idth. Hoever, due to very simplified experimentl setup (see Section 4 belo), it did not hppen. Therefore, it s decided to use only reltive mesurements to chrcterize the gp nd to try lso the other technique employing only one trnsducer nd impct hmmer locted close to it: just bove or belo the trnsducer (Fig. 4). IT OT Impct hmmer Wter Air gp Trnsducer Figure 4. Schemtic of gp mesurement system, consisting of one trnsducer nd impct hmmer positioned just bove the probe. One trnsducer method gives only bsolute mesurement results unlike reltive difference in to trnsducers technique. Therefore, the hole mesurement system should be ccurtely clibrted, nd this is not esy becuse mny fctors led to signl vritions. The other possibility is to use gin reltive mesurements compring signls obtined t different ngle positions of the system. Note, tht one trnsducer method hs significnt dvntge in comprison ith to trnsducers technique: there is no need to cre bout probes similrity, nd the hole mechnicl setup is simpler. Therefore, the number of fctors leding to mesurement errors is less, nd so the totl error is smller. 3.3 Experimentl setup

11 11 Since this project s just fesibility study, only preliminry experiments ere performed. Tests ere done using very simple nd therefore inccurte mechnicl setup contining the IT nd OT instlled on specil holder ith micrometer to chnge nd mesure the ir gp. The mesurement system included dt cquisition softre bsed on MATLAB, digitizer crd (4- Bit nd 04.8kS/s), high-sensitive lo-frequency coustic emission (AE) sensors, high-sensitive lo-frequency vibrtion ccelerometers, nd mechnicl spring-loded mnul impct hmmer. To perform the experiments, to different setups employing to or one trnsducer ere used s shon in Figs 3 nd 4, respectively. Pieces of the IT nd OT ~00mm long ith impct hmmer nd trnsducer-receivers positioned inside the IT ere instlled on stndrd three xis trnsltionl scnning system ith rotry motion cpbility. 3.4 Test procedure At first simple tests ere performed in order to estimte the sensitivity of bending-ve method nd compre it to theoreticl predictions. These experiments ere done exciting very ek sonic ves in ir outside the OT nd trying to detect them using trnsducer locted inside the IT in ter. Then the min series of experiments s performed using to different methods ith to or one trnsducers s presented in Figs. 3 nd 4. In to trnsducers method their signls ere digitized, verged, filtered, cross-correlted, nd then subtrcted. In one trnsducer technique the received signl s digitized, verged, filtered nd cross-correlted t vrious ngle positions of trnsducer nd impct hmmer. At first, the nominl gp (8mm everyhere beteen IT nd OT) s set using micrometer. Then the IT s hit by impct hmmer ten times, nd signls received by trnsducers ere verged nd processed. This procedure s performed for different gps. Experiments ere done using different trnsducers: high-sensitive 15kHz AE sensors R1.5-UC- 1, high-sensitive 30kHz AE sensors R3UC-1, nd high-sensitive vibrtion ccelerometers ith center frequency 10kHz. To increse mplitude of the received signls nd mke them less distorted nd more uniform, tests ere lso performed employing specil mde trnsducer cps, hich contour the IT IS. Experiments ere done t different ter-pths from 0 to 3mm. Using specil softre ritten in MATLAB, vrious signl processing methods ere employed. The received signls ere verged over ten hits to decrese the rndom errors. Then FFT s performed nd signls spectr ere nlyzed. In ddition, the verged signls ere filtered using different lo-pss, high-pss nd bnd-pss filters. Finlly, the envelopes of the received signls f ( t) hve been nlyzed by performing the Hilbert trnsform ( t) ( t ) 1 f 1 F Hi = π t 1 this signl. The best results ere obtined in time domin using 15kHz nd 30kHz AE sensors ith cps nd 0-50kHz lo-pss filter. 4. Results nd discussion 4.1 Sensitivity estimtes At first, signls generted by ek sound in ir (finger snp) nd received by the AE sensor ere compred for to cses: hen sensor s locted on the open spce in ir nd hen it s in ter inside the IT. In both cses the signls ere esily detectble, but signl mplitude in the d t t 1 of

12 1 second cse s ~31 times less. Tking into ccount tht piezoelectric trnsducer in the reception mode mesures coustic pressure of the incoming UT ve nd tht pressure is proportionl to squre root of the coustic poer [1-], one obtins tht poer in the second cse s ~900 times less. This result is in greement ith vlue of energy trnsmission coefficient (16) for three-lyer medi nd bending ve excited in thin metl plte locted beteen ir nd ter. Then experiments ith to tubes, IT nd OT instlled on specil holder ith AE sensor inside the IT in ter, ere performed. A ek sound in ir generted by finger snp outside the OT s esily detected by the sensor, lthough its mplitude s ~4 times less thn signl mplitude in previous experiment ith one tube. It mens tht ek sonic ve, hich psses through ir, OT metl ll, IT/OT ir gp, the IT metl ll, ter lyer, nd impinges on the AE sensor, relly gives esily detectble signl. In generl, these experiments confirmed clcultions, performed in Section 3.1 nd proved tht AE sensor, positioned inside the IT in ter, is extremely sensitive even to very ek sonic ves excited outside the OT. Such result llos ssuming tht ek coustic ves in the ir gp, generted by bending oscilltions of the IT ll (hich ere excited by n impct hmmer from ithin the IT), nd reflected from the OT IS, cn be detected by this AE sensor. 4. Accurcy of mesurements First of ll, to decrese mesurement error the verging procedure s used. During tests the IT s hit by impct hmmer ten times, nd signls received by trnsducer ere verged over ten hits to decrese the rndom errors. Ten redings (before verging) for one trnsducer nd obtined errors of mesurement (red verticl lines re the error brs) for 10 hits of impct hmmer re presented in Fig. 5. Figure 5. Ten redings for one 15kHz AE sensor ith cp nd mesurement error brs. One cn see tht trnsducer redings relted to different hits re more or less similr to ech other, but error is rther lrge - bout 5-10% mesured vlue. Note, tht it could be esily decresed to ~1%, if electro-mgnetic vibrtion shker s used insted of mnul mechnicl spring-loded impct hmmer.

13 13 The second source of errors s lo mechnicl ccurcy of the system. Initilly, it s expected, tht in to trnsducers method hen gp is nominl everyhere (i.e. gps re equl 8mm on to opposite sides of the IT), the hole system (tubes, trnsducers, impct hmmer, holder, etc) ould be symmetric nd signls received by both trnsducers should be similr ithin mesurement ccurcy. The symmetric signls ere expected to pper only hen gps ere different t to opposite sides of the IT (see Fig. 3). Hoever, even t equl gps the redings of to trnsducers ere different. Most probbly such fctors s lo mechnicl ccurcy of the system, difference beteen trnsducers prmeters, poor centering, positioning nd orienttion of impct hmmer nd AE sensors in reltion to ech other nd IT IS, led to such lrge differences beteen responses. It s lso expected, tht in one trnsducer method hen gp is nominl 8mm everyhere round the IT, the signls received by trnsducer t vrious ngle positions should be similr ithin mesurement ccurcy. Different signls ere expected to pper only hen gps differed t different ngles. Hoever, it turned out tht even t equl nominl gps everyhere round IT the trnsducer redings ere different. Dt fter verging for one trnsducer t vrious ngle positions of this trnsducer nd impct hmmer nd t 8mm nominl gp everyhere round the IT re presented in Fig.6. 0deg 45deg 90deg 180deg 70deg Figure 6. Averged dt for one 30kHz AE sensor ithout cp t vrious ngle positions nd t nominl 8mm gp everyhere round the IT. It is cler tht trnsducer responses re very different t vrious ngles, prticulrly fter 300µs. Most probbly, the lo mechnicl ccurcy of the system entiled such lrge differences beteen responses. For future prcticl ppliction of bending-ve technique it is bsolutely necessry to decrese the mesurement errors. To do it, first of ll, n electro-mgnetic shker ith consistent force output should be employed. Then, the hole mechnicl setup should be redesigned to provide required high ccurcy. Such prmeters of trnsducer s center frequency, dimeter, bndidth, mteril of protector, nd shpe of front surfce, should be optimized to obtin high sensitivity nd decrese signl distortion. And finlly, the most pproprite signl processing methods

14 14 (verging, filtering, cross-correltion, nd so on) providing the best detection nd ccurte mesurement should be determined nd employed. 4.3 Differences beteen responses mesured in to trnsducers method The described experimentl setup hs been used in n ttempt to obtin correltion: gp size - difference beteen to trnsducers responses. Mesurements ere performed for vrious gps; for ech gp signl differences from trnsducers ere digitized, verged, nd filtered. At first, the nominl 8mm IT/OT gp s set using micrometer. Then the IT s hit by impct hmmer 10 times, nd signls received by 15kHz AE sensors ith steel cps ere filtered using lo-pss filter 0-50kHz. This procedure s used for mesurements t different gps from 8 to 0mm. AE sensors ere oriented in the direction, long hich gp chnges, s in Fig. 3. The obtined signl differences beteen AE sensors t vrious gps re shon in Figs. 7 nd 7b. Figure 7. Differences beteen responses from to 15khZ AE sensors ith steel cps t vrious gps. One cn see difference beteen mplitudes of responses t vrious gps. Amplitudes of peks ithin rnge µs consistently increse hen gps decrese from 8 to 0mm. Also there is consistent time shift beteen peks relted to different gps: peks t 110, 380, nd 40µs. Similr plots ere obtined using 30kHz AE sensors ith steel nd delrin cps nd 0-60kHz lo-pss filter. Therefore, one cn conclude tht employing to trnsducers method, despite ll inccurcies nd limittions of the experimentl setup, it gives results, hich llo correlting gp size rther consistently ith mplitude nd time position of the response. At the sme time, note tht very smll differences beteen vrious responses should not be tken into ccount, becuse they cn be smller thn mesurement error. As n exmple, Fig. 7b shos grphs ith error brs for responses presented in Fig. 7.

15 15 Figure 7b. Differences beteen responses from to 15kHz AE sensors ith steel cps for signls shon in Fig. 7 ith error brs. 4.4 Responses mesured in one trnsducer method Employing one trnsducer method mesurements ere performed for vrious gps too. For ech gp signls from trnsducer ere digitized, verged, nd filtered. At first, the nominl 8mm gp s set. Then the IT s hit by impct hmmer 10 times, nd signls received by 15kHz AE sensor ith steel cp ere filtered using lo-pss filter 0-50kHz. AE sensor nd hmmer ere oriented in gp chnge direction, s in Fig. 4. The obtined signls from AE sensor t vrious gps re shon in Fig. 8. 0mm 1mm mm 4mm 6mm Figure 8. Responses from 15kHz AE sensor ith steel cp t vrious gps. There re definite differences beteen mplitudes of responses t vrious gps. Although these differences re not lrge, one cn clerly see tht mplitudes of peks ithin rnge -0-00µs consistently decrese hen gps decrese from 6 to 0mm. Similr plots ere obtined using 30kHz AE sensors ith delrin cp nd 0-60kHz lo-pss filter. So, it is possible to conclude tht employing one trnsducer method, despite ll

16 16 inccurcies nd limittions of the testing setup, it gives results, hich llo correlting gp size more or less consistently ith mplitude of the response. 4.5 Responses mesured t vrious offsets of testing setup Another series of experiments s performed to determine ho the received signl vries depending on chnges in the test system prmeters nd tube chrcteristics, becuse it is necessry to distinguish response, generted by coustic ve in ir gp, from signl vritions, initited by these chnges. Experiments ere done t different trnsducer offsets, then t vrious ngle positions of probes nd shker, nd finlly on different IT smples. At first, series of experiments s performed using to trnsducers method t different offsets: smll (~1.5mm) nd lrge (~3mm) by moving trnsducers nd impct hmmer in to perpendiculr rdil directions. Mesurements t ech offset ere performed for vrious gps; for ech gp signls from to 15kHz AE sensors ith cps ere digitized, verged, filtered, nd then subtrcted. The objective of these experiments s to check bility of testing system to distinguish different gps t vrious offsets. Typicl results re presented in Figs mm 4mm 8mm Figure 9. Differences beteen responses from to 15kHz AE sensors ith cps t smll 1.5mm offset t vrious gps.

17 17 0.5mm 4mm 8mm Figure 10. Differences beteen responses from to 15kHz AE sensors ith cps t lrge 3mm offset t vrious gps. As one cn see in Figs. 9-10, the differences beteen mplitudes of responses t vrious gps re consistent nd cn be observed t different offsets. Amplitudes of ll peks ithin rnge µs consistently chnge, hen gp vries from 8 to 0.5mm. Similr results ere obtined for rdil offsets in to perpendiculr directions pplying one trnsducer method. Then the sme series of experiments hs been performed for 30kHz AE sensors using to trnsducers nd one trnsducer methods. All obtined responses ere similr to ones presented in Figs Therefore, the setup used for mesurements gives results, hich llo correlting gp size rther consistently ith mplitude of the response even t pretty lrge 3mm offset. It mens tht mesuring technique nd setup ere pretty robust to centering. 4.6 Responses obtined t vrious ngle positions The next series of experiments s performed using one trnsducer method nd to trnsducers method t different ngle positions of testing system by rotting rod ith trnsducers nd impct hmmer. Mesurements t ech ngle position ere performed for vrious gps. At ech gp signls from 30kHz AE sensors ere digitized, verged, nd filtered. It s expected tht dt obtined t vrious ngles ould be for sure different, becuse chnge of the trnsducer ngle position ith respect to the smll gp leds to chnge of the response shpe due to vritions of time-of-flight of different ves crrying informtion bout this gp. The gol of these experiments s to check the bility of testing system to distinguish vrious gps t different ngle positions of the system. Responses for to trnsducers method obtined t 45 0 nd 90 0 ngles ith respect to smll gp ngle position re presented in Figs

18 18 Figure 11. Differences beteen to 30kHz AE sensors t 45 0 ngle position t different gps. Figure 1. Differences beteen to 30kHz AE sensors t 90 0 ngle position t different gps. There is obviously consistent difference beteen mplitudes of peks ithin rnge µs. Similr responses ere obtined for other ngle positions, for 15kHz sensors nd in one trnsducer method. All these results demonstrte tht t different ngle positions of mesuring system the responses relted to vrious gps cn be esily distinguished.

19 19 Second group of tests relted to different ngle positions of the system s performed ith objective to use mesurements, obtined t vrious ngle positions, for gp chrcteriztion by compring responses relted to different ngles. Responses for one trnsducer method for to gps re presented in Figs Figure 13. Responses from one 30kHz AE sensor t vrious ngle positions of this trnsducer nd impct hmmer nd t nominl 8mm gp everyhere round the IT. Figure 14. Responses from one 30kHz AE sensor t vrious ngle positions of this trnsducer nd impct hmmer hen 4mm gp is locted t 0 0. As one cn see in Fig. 13, the responses obtined t vrious ngles re more or less similr ithin mesurement error (it could be expected, becuse gp equls 8mm everyhere round the IT, nd therefore setup is symmetric). There is no consistent difference beteen vrious responses. Theoreticlly, t proper testing setup ith smll mesurement error, ll grphs in Fig. 13 ere supposed to coincide, becuse t 8mm gp everyhere round the IT nothing should

20 0 depend on the ngle position of testing system. On the other hnd, Fig. 14 clerly demonstrtes tht hen 4mm gp is locted t 0 0, responses relted to vrious ngle positions of the testing system re quite different. There is consistent difference beteen mplitudes of peks ithin rnge µs, hen trnsducer ngle position chnges from 0 to Response ith minimum peks mplitudes (dshed red line) corresponds to 0 0 ngle of testing system, hen trnsducer/hmmer orienttion coincides ith smll gp orienttion (see Fig. 4). Response ith mximum peks mplitudes (solid blck line) corresponds to ngle position of the testing system, hen trnsducer/hmmer orienttion is opposite to smll gp orienttion. At ll other ngle positions the responses hve peks ith intermedite mplitudes. Similr responses ere obtined for 15kHz sensor nd in to trnsducers method. All these results demonstrte tht testing setup provides dt, hich llo correlting gp size nd position of smll gp more or less consistently ith mplitude of the response t different ngle positions of the system. It mens tht results obtined t different ngle positions of the setup cn probbly be used for gp mesurement. 4.7 Mesured responses for vrious tubes The lst series of experiments s performed using one nd to trnsducers method nd different IT smples in order to check ho response depends on vritions of such prmeters s tube shpe (e.g. ovlity), dimensions (inside dimeter nd ll thickness), nd mteril properties (microstructure, grin size, inhomogeneities, imperfections, etc). Tests ere done using three ne different IT smples ##-4. (The initil IT smple #1 hs been used during ll previous experiments). Mesurements of ech ne smple ##-4 ere performed for vrious gps; for ech gp signls from 30kHz AE sensors ere digitized, verged, filtered, nd subtrcted. Results for to ne different IT smples # nd #4 re presented in Figs Figure 15. Differences beteen responses from 30kHz AE sensors for tube # t vrious gps.

21 1 Figure 16. Differences beteen responses from 30kHz AE sensors for tube #4 t vrious gps. The gol of these experiments s to check the bility of the system to distinguish vrious gps using different tube smples, becuse IT shpe, dimensions, nd mteril chrcteristics my differ from one tube to nother nd my even vry in one tube. As one cn see in Figs , for different ne IT smples the differences beteen mplitudes of responses t vrious gps chnge rther consistently, hen gp vries from 8 to 0mm. Anlogous results ere obtined for 15kHz sensor nd in to trnsducers method. Therefore, it is possible to conclude, tht experimentl setup gives results, hich llo correlting gp size ith mplitude of the response for different tube smples. It mens tht, despite vritions in the IT shpe, dimensions, nd mteril properties, responses relted to vrious gps cn be distinguished in different tubes. 5. CONCLUSIONS The fesibility study s performed to estimte the bility of coustic lo-frequency bending-ve technique to ccurtely mesure ir gp beteen to concentric metl tubes. Method is bsed on tpping the IT IS by impct hmmer, locted inside the IT in ter, nd detecting the response of lo-frequency sonic ve trnsmitted through the ir gp nd reflected from the OT. The tube ll vibrtes s hole performing the bending (flexurl) oscilltions nd trnsmitting the sonic ves in the ir gp. These ves, propgting ithin the gp nd reflected from the OT, cn be detected by lofrequency high-sensitive coustic trnsducer-receiver locted inside the IT in ter. Theoreticl nlysis predicts tht this technique should be very sensitive nd probbly it my be very useful for mesuring ir gp beteen to tubes. The mjor problem is high level of the bckground coustic noise - strong signls, relted to different ves nd multiple reflections ithin the IT ll. It s suggested to use high resolution nlog-to-digitl converter nd to identicl trnsducers oriented t

22 180 0 prt in rdil direction nd one impct hmmer positioned in the middle beteen them. Such system should give identicl responses, hen to gps fcing the opposite trnsducers re equl. If these gps re not equl, the responses of trnsducers ill differ. As result, digitizing signls from to trnsducers nd subtrcting one from the other, it probbly ill be possible to detect the gp-ve nd size the gp. The second problem is vritions in the IT nd test system prmeters, hich ffect the received signls. Such IT prmeters, s shpe (e.g. ovlity), ll thickness, dimeter, nd chrcteristics of mteril, my differ from one tube to nother nd my even vry in one tube. Probes nd impct hmmer re lys positioned ith some tolernce nd probes cnnot be bsolutely identicl. Averging, filtering, nd cross-correltion should help to seprte the responses, crrying informtion bout ir gp, from signl vritions, generted by chnges in the IT nd inspection system prmeters. The experimentl setup included specilly developed dt cquisition softre bsed on MATLAB, 4-Bit digitizer crd, 15kHz nd 30kHz AE sensors, mnul mechnicl spring-loded impct hmmer, nd tube holder ith micrometer. Received signls ere verged, filtered nd processed; nd their spectr nd envelopes ere nlyzed. Sensitivity mesurements confirmed clcultions nd proved tht bending-ve technique is extremely sensitive even to very ek sonic ves. Unfortuntely, the mesurement error of experimentl setup s pretty lrge becuse of lo mechnicl ccurcy, difference beteen trnsducers prmeters, poor centering nd orienttion of impct hmmer nd AE sensors. To decrese the mesurement errors, first of ll, n electro-mgnetic shker ith consistent force output should be employed nd the hole mechnicl setup should be more ccurte. Trnsducer prmeters should be optimized to obtin high sensitivity nd decrese signl distortion. And finlly, the most pproprite signl processing methods should be determined nd employed. Despite ll inccurcies nd limittions of the testing system, the setup hs been used to nlyze correltion beteen gp size nd received signls. Obtined dt sho tht despite lo ccurcy the bending-ve technique llos correlting gp rther consistently ith mplitude nd time position of trnsducer response. Series of experiments s performed to determine ho chnges in the IT nd system prmeters ffect the performnce. Tests ere done t different trnsducer offsets, vrious ngle positions of the system, nd on fe different IT smples. It s necessry to check bility of the testing system to distinguish different gps t vrious probe offsets, t different ngle positions of the system, nd on different tube smples. Obtined dt demonstrte tht bending-ve technique nd experimentl setup llo correlting gp size rther consistently ith mplitude of the response even t pretty lrge probe offsets, t different ngle positions of the system, nd on different tube smples. It mens tht mesuring technique nd setup re pretty robust to centering, responses obtined t vrious ngle positions cn be used for gp mesurement, nd gp idth cn be determined in different tubes. 6. REFERENCES 1. V. A. Shutilov, Fundmentl Physics of Ultrsound, Gordon nd Brech Science Publishers, Ne York, 1988.

23 3. Nondestructive Testing Hndbook. Second Edition. Vol. 7. Ultrsonic Testing. Americn Society for Nondestructive Testing Inc, L. D. Lndu nd E. M. Lifshits, Theory of Elsticity, Pergmon Press, Oxford, D. Pierce, Acoustics, McGr Hill, N-Y, 1981.