A NOVEL ULTRASONIC THERMOMETRY FOR MONITORING TEMPERATURE PROFILES IN MATERIALS

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1 XIX IMEKO World Cogress Fudametal ad Appled Metrology September 6, 009, Lsbo, Portugal A OVEL ULRASOIC HERMOMERY FOR MOIORIG EMPERAURE PROFILES I MAERIALS Ikuo Ihara, Maabu akahash Dept. of Mech. Eg., agaoka Uversty of echology, agaoka, Japa, Ihara@vos.agaokaut.ac.jp Graduate Studet of agaoka Uversty of echology, agaoka, Japa, takaham@st. agaokaut.ac.jp Abstract A ew ultrasoc method for motorg the temperature dstrbuto sde a materal beg heated or cooled s preseted. he prcple of the method s based o the temperature depedece of the velocty of ultrasoc wave propagatg through a materal. A effectve verse aalyss coupled wth a fte dfferece calculato s used to determe the oe-dmesoal temperature dstrbuto sde a thck plate. o verfy the practcal feasblty of the ultrasoc method, expermets have bee demostrated. A sgle sde of a steel plate of 30 mm thckess s heated by cotactg wth a heater of 00 ºC ad subsequetly cooled dow by water. Ultrasoc pulse-echo measuremets are the performed for the steel durg the heatg ad coolg. A chage the trast tme of logtudal ultrasoc waves across the steel s cotuously acqured ad used to determe the temperature dstrbuto sde the steel. he temperature dstrbuto ad ts traset varato determed by the ultrasoc method almost agree wth those obtaed usg thermocouples stalled the steel. hus, t s verfed that the preset method ca be a promsg meas for real-tme motorg of temperature profles materals beg heated or cooled. Keywords: ultrasoc thermometry, temperature dstrbuto, verse aalyss. IRODUCIO I varous felds of egeerg ad scece, t s ofte requred to measure teral temperature of a materal beg heated at hgh temperatures. hs s because the temperature s a mportat factor whch s closely related to materal propertes. I materal dustres, ot oly teral temperature but also ts dstrbuto sde the materal s ofte requred to be measured because such temperature dstrbuto plays a mportat role materal productos. For example, the cases of castg or mouldg processes for metals ad polymers, o-le formato o temperature gradet sde the de or mould s dspesable for makg a effectve process cotrol. It s kow that such temperature gradet durg materal processg drectly flueces the productvty ad qualty of fal products. herefore, t s desrable to realze a effectve techque for o-le measuremets of the teral temperature dstrbutos materals beg processed. Although a covetoal thermocouple techque s wdely used for temperature measuremets, t s ot always acceptable for obtag the spatal dstrbuto of temperature because of ts lmtato of stallato to a de or mould. I addto, the thermocouple may ot be approprate for motorg a traset varato of temperature because of ts relatvely slow tme respose measuremet. Ultrasoud s expected to be a effectve meas for motorg the teral temperature ad ts gradet of materals because of ts capablty to probe the teror of materals ad ts hgh sestvty to temperature []-[8]. he advatages of usg ultrasoud are cosdered that t may provde o vasve ad quattatve measuremets for the teral temperature of materals uder heatg or coolg. It s also attractve that ultrasoc measuremets provde a faster tme-respose tha covetoal thermocouple techques. I our prevous works [9], [0], effectve methods cosstg of a ultrasoc pulse-echo measuremet ad a verse aalyss were proposed ad appled to heated slcoe rubber ad steel plates to demostrate the feasblty of temperature motorg. Although the ultrasoc method had successfully motored the temperature dstrbuto ad ts varato durg heatg, further mprovemet of the verse aalyss has bee requred to overcome some problems such as dffculty usg the thermal boudary codto of a materal beg heated ad a tme-cosumg process the aalyss. I ths work, a mproved ultrasoc method that overcomes the problems metoed above has bee proposed. he method cossts of a ultrasoc pulse-echo measuremet ad a verse aalyss coupled wth a oedmesoal fte dfferece calculato. he method has bee appled to temperature dstrbuto motorg of a steel plate uder heatg ad coolg.. EMPERAURE DEERMIAIO BY ULRASOUD It s kow that the velocty of ultrasoc wave propagatg through a medum chages wth the temperature of the medum. he prcple of temperature measuremet by ultrasoud s based o the temperature depedece of the ultrasoc wave velocty. Assumg a oe-dmesoal temperature dstrbuto a medum, the trast tme t L of a ultrasoc pulse-echo propagatg the drecto of the temperature dstrbuto ca be gve by

2 t L L dx, () 0 v( ) where L s the thckess of the medum, ad v() s the ultrasoc velocty whch s a fucto of temperature. he temperature depedece of velocty depeds o the materal property ad may have a approxmate lear relato wth temperature for a certa temperature rage. I geeral, the temperature dstrbuto a medum beg heated ca be gve as a fucto of locato x ad tme t. Such a temperature dstrbuto (x, t) s subjected to the thermal boudary codto of the heated medum. herefore, o the bass of (), f a approprate verse aalyss wth a certa boudary codto s properly used, t could be possble to determe the temperature dstrbuto from the trast tme t L measured for the heated medum. I fact, such ultrasoc determato of temperature dstrbuto of a heated slcoe rubber plate was demostrated our prevous work [9]. 3. IVERSE AALYSIS FOR DEERMIIG EMPERAURE PROFILE I the preset work, we attempt to perform a ultrasoc determato of the temperature dstrbuto a thck plate whose sgle sde s beg heated by cotactg wth a hot medum, or cooled wth a cold medum. o vestgate the temperature dstrbuto of such plate, we cosder a oedmesoal usteady heat coducto problem wth a costat thermal dffusvty. Assumg that there s o heat source the plate, the equato of heat coducto s gve by [], () t x where s temperature, x s the dstace from the heated or cooled surface, t s the elapsed tme after the heatg or coolg starts, s the thermal dffusvty. It s kow that the temperature dstrbuto ca be estmated by solvg () uder a certa boudary codto. I actual heatg processes, however, the boudary codto s ot always beg held stable ad ofte beg chaged trasetly durg heatg. Such boudary codto s usually qute dffcult to kow ad eve to measure. Because of lttle kowledge about boudary codto, temperature dstrbuto s hardly determed from (). hs kd of problematc stuato ofte occurs whe the plate s heated by cotactg wth a very hot medum such as molte metals. o overcome the problem metoed above, a effectve method for evaluatg the teral temperature dstrbuto s proposed. he method cossts of a ultrasoc pulse-echo measuremet ad a verse aalyss coupled wth a oe-dmesoal fte dfferece calculato. he advatage of the method s that o boudary codto at the heatg surface s eeded. A oe-dmesoal fte dfferece model cosstg of a large umber of small elemets ad grds s used for aalyzg heat coducto a thck plate. Cosderg that the sgle sde of the plate havg a uform temperature at tme step s heated by cotactg wth a hot medum, temperatures at each pot sde the plate at tme step + that s a very short elapsed tme, ca be gve by [] (,, ) r (3) ατ r (4) h where, s the umber of the grd, ad are dces correspodg to spatal coordate ad cosecutve tme, respectvely. s the temperature of each grd pot at tme step. r s take to be less tha 0.5 accordg to the stablty requremet called the vo euma stablty crtero. s the tme step ad h s the grd terval. We defe = as the heated surface that s cotacted wth a hot or cold medum ad defe = as the other sde that has o heat source. It s ow requred to obta the temperatures at the both sdes of the plate, + ad +, so that the temperature dstrbuto of the plate could be totally determed. It s possble to assume the temperature + to be a kow value because such temperature at a low temperature sde ca easly be obtaed usg ay covetoal techque such as a thermocouple. However, the temperature at the heated surface, +, s usually dffcult to kow. Although the + s ukow uless the thermal boudary codtos at both eds of the plate are gve, t s possble to estmate the + f the fte dfferece calculato s coupled wth the trast tme of ultrasoud propagatg through the plate. Usg a cocept of trapezodal tegrato, the trast tme t L gve () ca be approxmately calculated from t L h h, (5) v v v From (5) ad the relato betwee temperature ad ultrasoc velocty, the temperature of the heated surface at tme step +, +, ca be gve by t t Ah L L r where, t L ad t L + are the trast tmes measured at the tme step ad +, respectvely. It should be oted that (6) s derved uder the assumpto that the temperature depedece of ultrasoc velocty has a lear relato show as follows, (6) A B, (7) v( ) where, A ad B are costats obtaed expermetally. hus, the temperature of the heated surface at tme step +, +, ca the be determed from (6) whe the trast tmes t ad t + are measured. Oce the temperatures of all grd pots the plate at the tme step +, +,, +, are determed, we ca determe the temperature dstrbuto at ext tme step + from the same procedure usg the trast tmes t + ad t + measured at the tme step +. Accordg

3 to such procedure, we ca cotuously obta the teral temperature dstrbuto as log as the ultrasoc trast tme measuremet s cotued. Fg. shows the flowchart of the verse aalyss for determg the temperature dstrbuto. ultrasoc sgal s 00 MHz. Sgal fluctuato due to electrcal ose measuremets s reduced by takg the average of te ultrasoc sgals. 5. RESULS ext tme step SAR IPU (,...,) MEASUREME COMPUE (=,,-) MEASUREME t L Fg. 3 shows ultrasoc echoes reflected from the bottom surface of the plate durg heatg. We ca see a hgh sgal-to-ose rato eve the secod echo. he trast tme through the steel plate ca be precsely determed from the tme delay betwee the frst ad secod echoes, by takg a cross-correlato betwee them. Fg. 4 shows the varato of the temperature at 5 mm from the bottom surface of the steel durg heatg ad coolg. As we expected, the temperature rapdly creases wth measuremet tme mmedately after the cotact of the heater, ad the markedly decreases just after the water coolg starts. he varato of the trast tme of ultrasoc YES COMPUE Fg. Flowchart of the verse aalyss for determg the temperature dstrbuto. 4. EXPERIME I order to verfy the feasblty of the proposed method for determg temperature dstrbuto, the method has bee appled to a thck steel plate beg heated ad cooled. Fg. shows a schematc dagram of the expermetal setup used. hs system provdes ot oly ultrasoc pulse-echo measuremets but also temperature dstrbuto measuremets usg thermocouples, so that we ca verfy the valdty of the ultrasocally determed temperature dstrbuto, by comparg wth that measured usg the thermocouples. A steel plate (JIS type: SKD6) of 30 mm thckess s used as a specme. At frst, the bottom surface of the plate s heated by cotactg wth a heater of 00 ºC for a perod of 50 s, ad the the surface s cooled by water. A ultrasoc trasducer of MHz s stalled o the top surface of the steel plate to make pulse-echo measuremets for the steel. o obta a referece value of the temperature dstrbuto sde the plate, fve thermocouples, C - C5, are serted to the plate. I addto, aother thermocouple C6 s used to measure the temperature at the top surface of the plate. Ultrasoc pulse-echo measuremets are performed durg the heatg ad coolg, ad echoes reflected from the bottom surface ad temperatures at each posto are cotuously acqured every 0. s wth a PC based real-tme acqusto system. he samplg rate of COIUE? O ED Ampltude (arb. ut) Dsplay Wave form emp. Ultrasoc rasducer Coupler 30 mm Water 0 o C Steel plate 3 o C Bottom surface PC A/D board Pulser/ Recever Amp. hermocouples C6 C5 C4 C3 C C Heater 00 o C Fg. Schematc of the expermetal setup for ultrasoc temperature motorg st echo t L d echo me delay (s) Fg. 3 Ultrasoc echoes reflected from the bottom surface of the steel plate.

4 emperature ( o C) emp. (C) Water coolg rast tme Measuremet tme (s) Fg. 4 Varatos of the trast tme of the ultrasoc wave ad temperature the steel plate durg heatg ad coolg. rast tme (s) wave the steel s also show Fg. 4. We ca see that the tedecy of the varato of the trast tme durg heatg ad coolg s smlar to that of the temperature. However, we ca also see the dfferece of ther varato rates betwee the heatg ad coolg. I partcular, the decrease rate of temperature the begg of coolg s qute dfferet from that of trast tme, whch s much sgfcat tha the dfferece betwee ther crease rates heatg. hs s because of the dfferece of the temperature gradet sde the steel betwee heatg ad coolg processes. he trast tmes measured durg the heatg ad coolg are used for the verse aalyss to determe the temperature dstrbuto ad ts varato. Sce the pror formato o the temperature depedece of ultrasoc velocty s eeded for the aalyss, we exame the relatoshp betwee the velocty ad temperature for the steel the temperature rage up to 50 o C. It has bee foud that the velocty chage s almost lear wth temperature the temperature rage ad therefore the temperature depedece s approxmately gve to be v ( ) , (m/s) (8) Usg the trast tme show Fg. 4 ad the temperature depedece of (8), the varato of temperature dstrbuto the plate s estmated from the proposed verse aalyss. I the estmato, the temperature of the steel before heatg, 3.3 o C, s used as the tal codto. Also, the temperature C6 s used as the kow value. he estmated temperature dstrbutos are show Fg. 5, where the ultrasocally estmated results are compared wth those measured usg thermocouples. he tme show Fg. 5 deotes the elapsed tme after the heatg starts. It ca be see that the temperature dstrbuto estmated ultrasocally ad ts varato almost agree wth those measured usg thermocouples, whle there are dscrepaces betwee them the rage of hgh temperatures. Although the reaso for the dscrepacy s ot clear at ths momet, t s terestg that the proposed ultrasoc method seems to be effectve to motor a traset varato teral temperature dstrbuto of C) t s 50 s 0 s 5 s hermocouple Heatg Ultrasoud Coolg 0 s 0 0 s Dstace from heated surface (mm) materals beg heated or cooled. It s oted that t takes about 8 ms to calculate a temperature dstrbuto at each tme step from the measured ultrasoc data, whch s fast eough to make a real-tme motorg. 6. COCLUSIOS A ew ultrasoc method for motorg teral temperature gradet of materals s preseted. he advatage of the method s that o boudary codto at the heatg surface s eeded for the motorg. he feasblty of the method has bee demostrated through a expermet wth a steel plate beg heated ad cooled. A ucertaty aalyss s ow beg doe to estmate the accuracy the preset method ad the result wll be reported the ear future. Although further techcal mprovemets the measuremet ad aalyss are eeded, t s hghly expected that the method could be effectve the o-le motorg of the traset varato of the temperature profle of materals beg processed at hgh temperatures. It should be oted that o-cotact thermometry wth the proposed ultrasoc method s also possble f ay o-cotact ultrasoc measuremet techque such as a laser-ultrasoud s employed. ACKOWLEDGMES Facal supports by the Grat--Ad for Scetfc Research (B ) from the Japa Socety for the Promoto of Scece, ad oyota Motor Co. are apprecated. REFERECES 0 s 0 s 50 s 00 s 350 s Fg. 5 Varato of temperature dstrbuto the steel plate wth elapsed tme, estmated by the ultrasoc method ad thermocouples. he umbers the fgure deote the elapsed tme after heatg starts. [].-F. Che, K.-. guye, S.-S. We ad C.-K. Je., emperature measuremet of polymer extruso by

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