A Matlab/Simulink Model of a Langevin s Ultrasonic Power Transducers

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1 Mtl/Simulink Model of Lngevin s Ultrsoni Power Trnsduers Igor Jovnović, Ugleš Jovnović nd Drgn Mnčić strt Ultrsoni sndwih trnsduer, lso known s Lngevin s trnsduer, is hlf-wve resonnt struture tht osilltes in thikness diretion. In this pper, new Mtl/Simulink model of prestressed unsymmetril ultrsoni sndwih trnsduer is presented. The sndwih trnsduer is modeled y pplying three-dimensionl (D) Mtl/Simulink models of piezoermi rings nd metl endings, whih re derived sed on the piezoermi ring model reently proposed y the uthors. By sde onneting the piezoermi rings model with metl endings model, omplete model of ultrsoni Lngevin s trnsduer is otined. Using this model one my determine ny trnsduer trnsfer funtion, wheret is tken into the ount the externl medium influene, s well s the influene of the thikness nd rdil modes of eh trnsduer omponent. The omprisons etween experimentl nd theoretil results re quite good nd vlidte the new design pproh. Index Terms Lngevin s trnsduer, Mtl/Simulink model, D model, Resonne frequeny hrteristis. I. INTRODUCTION Implementtion of ultrsoni trnsduers egn in 97, when Pul Lngevin designed the first piezoeletri sndwih trnsduer []. t the very eginning of its development, the si pplition ws in sonrs. In nowdys, tehnologil pplition of power ultrsound is exploited in mny rnhes of industry suh s mining, ultrsoni mhining, mteril proessing, utting, welding [2 4], sonohemistry [5,6] nd other ultrsoni liquid proessing pplitions [7]. Sndwih trnsduer, whih is most often lso lled Lngevin s trnsduer, is hlf-wve resonnt struture tht osilltes in thikness (longitudinl, extension, or xil) diretion. In the simplest form, sndwih trnsduer is onsisted of n tive lyer or soure of osilltions, mde of one or more pirs of piezoermi rings (Bloks nd 2, shown in Figure ), mehnilly ompressed etween metl endings y olt (Bloks 8, 9, nd, shown in Figure ). For industry pplitions, the piezoermi should possess gret eletromehnil oupling ftor, high Curie s temperture, low dieletri losses, nd stle time nd temperture properties. Metl endings re onsisted of: refletor (Bloks 5, 6 nd 7, shown in Figure ), whih represents rer prt of the trnsduer, nd n emitter (Bloks nd 4, shown in Figure ), whih trnsfers osilltions from Igor Jovnović, Ugleš Jovnović nd Drgn Mnčić re with the University of Niš, Fulty of letroni ngineering, 4 leksndr Medvedev, 8 Niš, Seri (e-mil: igor.ovnovi@elfk.ni..rs, ugles.ovnovi@elfk.ni..rs nd drgn.mni@elfk.ni..rs). soure to n operting medium. Metl endings re most ommonly mde out of mterils of different densities, in order to inrese osilltion mplitudes on the operting surfe of the emitter nd derese osilltion mplitudes on the refletor surfe, s well s to improve the dustment with the lod. Improvement of ultrsoni trnsduer performnes requires detiled investigtion of the mehnil nd eletril properties for different operting onditions. Modeling of more omplete trnsduer onstrutions is not possile using one-dimensionl model, whih is sed on solving the wve eqution long the trnsduer. Onedimensionl virtion theory is used where the longitudinl trnsduer dimension is greter thn the lterl dimension, therefore only the thikness modes re onsidered nd virtions in other diretions re negleted [8]. The reserh presented in this pper nlyses the Mtl/Simulink D mtrix model of the prestressed unsymmetril ultrsoni sndwih trnsduer. Ultrsoni sndwih trnsduer is modelled using the pproximte D mtrix model previously proposed in pper [9], whih tkes into the ount thikness nd rdil modes of osilltion s well s their mutul oupling. Piezoermi rings re represented s networks with four mehnil nd the single eletril ontts []. Similr pproh is employed to model pssive metl extensions sed on the D mtrix model of metl rings []. Metl prts re represented s networks with four or three ontts. II. MTLB/SIMULINK D MTRIX MODL OF TH ULTRSONIC TRNSDUCR This pper presents model of n ultrsoni sndwih trnsduer with single pir of piezoermi rings mehnilly onneted in series nd eletrilly in prllel. By mutully onneting ll trnsduer omponents in series nd in prllel, D eletromehnil model of omplete ultrsoni sndwih trnsduer is otined (Figure ). If n C exiting voltge is pplied on the eletril ontts while proper mient ousti impednes re pplied on the mehnil ontts it is possile to determine eh trnsfer funtion of suh system. ll model loks re onsisted of two si prts. First one lultes ll elements of the mtrix model sed on the inserted mteril properties. Seond one solves system of equtions using the lulted mtrix model elements. Models of piezoermi rings onsist of two loks used to ssign initil vlues of fores F nd F 4 ting from diretion Proeedings of 4th Interntionl Conferene on letril, letronis nd Computing ngineering, ITRN 27, Kldovo, Ser June 5-8, ISBN pp. LI.5.-5

2 of the seond piezoermi nd refletor, whih re otined from Blok 2 nd Blok 5 respetively. Bsed on the inserted ermi properties, ll elements re lulted =z (=,2,,4,5) [9], long with ll the neessry elements of system of equtions (): = 4 5 wherein: = nd: = =, +, +, + 4 5,,, = = =,,, F 4 2, +, +, F F ν 2 ν ν 4 I ( =,2,,4 ) ( =,2, ) ( =,2 ) F4 U () (2) () Differene etween two models of piezoermi rings, i.e. Blok nd Blok 2, is tht the mtrix of system of equtions Blok 2 (eqution (4)) is different from the mtrix of system of equtions (), hene the solution of the system of equtions is different. This differene origintes from the existene of ontt ring-shped surfes etween ermis, i.e. knowing mehnil veloities on these surfes, whih re lulted in Blok. Mehnil fores ting on the oint surfes re the sme while mehnil veloities hve the sme intensity ut opposite diretions. = ν 2 ν ν 4 I Inluding the eletril impedne Z, whih is from stndpoint of the power supply onneted in prllel to the eletril impedne of Blok (piezoeletri element), outputs of Blok 2 re mehnil fore nd veloity ting on the ring-shped surfes towrds the Blok (F 4 = ν + 2 ν ν + 44 ν I) nd towrds the trnsduer emitter (-ν ). Models of the emitter nd refletor re onsisted of two prts desried in Blok nd Blok 4 (emitter), nd in Blok 5 nd Blok 6 (refletor). Bsed on the geometril properties of these omponents nd their onnetion with the remining trnsduer omponents, it n e onluded tht models Blok 4 nd Blok 6 re nlogue. The sme nlogy pplies to Blok nd Blok 5, with the only differenes etween them eing their mteril properties nd their geometril dimensions. System of equtions, whih in the frequeny domin hrterizes Blok, is given in expression (5), tht is in expression (6) for Blok 4: (4) F F H = = 4 4 ν 2 ν ν 2 ν (5) (6) Fig.. Blok digrm of the ultrsoni trnsduer model. wherein H = F +( )F. Mehnil veloities (ν, ν 2 nd ν ) with the known veloity on the ring-shped surfe towrds the piezoermi (ν 4 ), otined from Blok 2, re used to lulte the mehnil fore F 4 ting towrds the piezoermi. The otined mehnil veloity on the ring-shped surfe towrds the seond prt of the emitter ν is forwrded

3 to Blok 4, wherein sed on it nd the ousti input impednes F 4 fore ting on tht surfe is lulted. The entrl olt is represented y Bloks 8, 9, nd. Due to the physil onnetions tht pproprite entrl olt prts hve with the remining trnsduer omponents, n nlogy etween Blok 9 nd Blok n e oserved. Therefore, in the following text only Blok 9 will e presented, whose outputs re mehnil veloities ting on the ylindril surfes towrds the middle prt of the entrl olt, i.e. towrds Blok, nd mehnil fores ting on the ylindril surfes of the entrl olt towrds the pproprite prts of the refletor tht is the emitter. System of equtions, whih in the frequeny domin hrterizes Blok 9 is given in expression (7). F2 = v v v Model of the middle prt of the entrl olt hs the simplest struture. Using it in eh simultion step the following instrutions re performed: initiliztion of mehnil fores ting on the oint surfes of ll trnsduer omponents; lultion of mehnil veloities on the sme surfes using known vlues of mient ousti impednes ting on the pproprite trnsduer omponents; otining finl nd urte initil mehnil fores. ll forementioned is performed using the iruit for solving equtions (8) ν 2 + ν ν = F2 = 2ν + ν 2 + 2ν F = ν + ν + ν (7) (8) F 2 = 2 ν + ν ν + 24 ν 4 nd F 4 = 4 ν + 42 ν ν + 44 ν 4. Ring-shped prt of the olt hed loted ove the refletor is in the model, opposed to the rest of the olt, represented y the four-port network (Blok 8) euse of its physil dimensions (ring struture). In this lok system of equtions (5) is lulted, ut in this se it pplies H = 2 2 F - F. III. RSULTS ND DISCUSSION The lulted nd experimentl results re otined using PZT8 piezoermi equivlent mteril [] with dimensions Ø8/Ø5/5mm. The refletor nd entrl olt mde out of stinless steel, its stndrd mteril prmeters re density 78kg/m, Poisson's rtio.29 nd Young s modulus of elstiity 2.9 N/m 2. The emitter is mde out of durlumin, its stndrd mteril prmeters re density 279kg/m, Poisson's rtio.4 nd Young s modulus of elstiity.68 N/m 2. The eletril impedne mesurements re done using HP494 Impedne/Gin- Phse nlyzer. In the following, the model is used to determine n input eletril impedne of the ultrsoni trnsduer, s well s mehnil impednes on the prtiulr trnsduer outer surfes. ll loks re msked (msk-lok) nd their properties re inserted in the window tht ppers y doule liking the orresponding lok. Prt of this window, in se of piezoermi rings, is shown in Figure 2, while the entire window in se of metl extensions is shown in Figure 2. Figure 2 lredy shows inserted ermi properties used in the lortory. To insert properties of non-predefined ermi it neessry to selet the "User-defined" option in the popup menu, this enles insertion of ll ermi properties individully. Mehnil onnetion of the ring-shped refletor prts (Blok 5 nd Blok 7), with the piezoeletri element (Blok ) is seril s n e seen in Figure. Their mutul onnetion in the trnsduer model is represented y the dder iruit of the refletor mehnil fores in the diretion of the piezoeletri element, while vlue of mehnil veloity on the ring-shped surfe of the piezoeletri element is diretly forwrded to the mentioned prts of the refletor. Blok 7 of the trnsduer model is used to solve system of equtions (9) in whih re known mehnil veloities ν 2 nd ν 4 long with mehnil fore F. = F ν 2 ν fter otining vlues of ν 2 nd ν 4, the remining mehnil fores re lulted s (9) () () Fig. 2. Interfe for insertion of piezoermi properties () nd metl ending properties (). If the designtion of trnsduer omponents dopts the nottion shown in Figures, nd orresponding to the prtiulr lok, simulted trnsduers hve the dimensions shown in Tle. In order to demonstrte ury of the proposed model,

4 Figure shows the mesured frequeny hrteristi of the ultrsoni trnsduer under low power level from whih it n e seen tht the input eletril impedne is in orrespondene with the simulted urves. TBL. DIMNSIONS OF TRNSDUCR USD IN XPRIMNTL NLYSIS Dimension Outer Inner Thiness (mm) dimeter dimeter Blok Blok Blok Blok Blok Blok Blok / Blok / Blok 8 8 / mesurements, re for piezoermis eletrilly onneted in prllel. IV. CONCLUSION The idel model, whih tkes into the ount ll prmeters, oundry onditions, ll existing resonnt modes nd onditions sed on whih the sndwih trnsduer properties depend, nnot e even relized. Therefore, the presented nlysis sought to otin s omprehensive s possile, ut yet simple model, whih, lthough it is pproximte, tkes into the onsidertion s muh eginning prmeters s possile. It is shown tht, lthough the trnsduer properties depend on mny prmeters, the gretest impt hs the length (thikness) of ll trnsduer omponents. Bsed on the presented model, it is possile to synthesize the trnsduer with predefined properties nd given resonnt frequeny, whih ws in ft the im of the presented nlysis. Bsed on the results otined y pplying the proposed trnsduer models, severl trnsduers tht were not presented in this pper were relized. ll of them hve een tested in mny pplitions. The mesurement results of the eletril properties of the otined eletromehnil systems vlidte this design pproh. CKNOWLDGMNT This work ws supported y the Ministry of dution, Siene nd Tehnologil Development of the Repuli of Seri under the proet TR5. Fig.. Simulted nd experimentl input eletril impedne versus frequeny for the ultrsoni trnsduer. With smll modifitions of trnsduer model, the frequeny dependeny of mehnil impedne on free ring-shped emitter surfe n e otined, whih is very importnt in pplition where suh eletromehnil system (trnsduer) is represented s sensor or s n energy hrvesting devie. In the first se, mehnil impedne is lulted when the eletril ontts re short iruit. Therefore, it is essentil to first short iruit the eletril ontts (U=V). The otined resonnt nd ntiresonnt frequenies in the trnsduer model, when the eletril onnetions re short iruit, re f s =9.8kHz nd f rs =4kHz. In the seond se, mehnil impedne is lulted when the eletril ontts re left open tht is when the input urrent is zero (I=). The otined resonnt nd ntiresonnt frequenies in the trnsduer model, when the eletril ontts re left open, re f o =2.kHz nd f ro =45.kHz. The results of this nlysis re esily otined due to the nture of the model implemented in Mtl/Simulink. The frequeny error ours due to the stndrd mteril properties of the piezoeletri elements nd the metl endings re used in the theoretil lultion nd the mehnil nd the dieletri losses in the omposite trnsduer re ignored. ll ove presented results, otined from model nd RFRNCS [] P.Lngevin, Frenh Ptent Nos: 529 ( ); 557 (5.8.92); (.7.924). [2] Z. Wng, J. Zeng, H. Song, F. L Reserh on ultrsoni exittion for the removl of drilling fluid plug, prffin deposition plug, polymer plug nd inorgni sle plug for ner-well ultrsoni proessing tehnology, Ultrsonis Sonohemistry, vol. 6, pp , My 27. [] J. L T. Monghn, T. T. Nguyen, R. W. Ky, R. J. Friel, R.. Hrris, Multifuntionl metl mtrix omposites with emedded printed eletril mterils frited y ultrsoni dditive mnufturing, Composites Prt B: ngineering, vol., pp , Mr. 27. [4] S. Kumr, C. S. Wu, G. K. Pdhy, W. Ding, pplition of ultrsoni virtions in welding nd metl proessing: sttus review, Journl of Mnufturing Proesses, vol. 26, pp. 295, pr. 27. [5] N. Pokhrel, P. K. Vin, N. Pl, Sonohemistry: Siene nd ngineering, Ultrsonis Sonohemistry, vol. 29, pp. 4-8, Mr. 26. [6] K. Gotoh, K. Hrym, pplition of ultrsound to textiles wshing in queous solutions, Ultrsonis Sonohemistry, vol. 2, no. 2, pp , Mr. 2. [7] N. N. Mhmun Y. G. dewuy dvned oxidtion proesses (OPs) involving ultrsound for wste wter tretment: review with emphsis on ost estimtion, Ultrsonis Sonohemistry, vol. 7, no.6, pp. 99-, ug. 2. [8] S. Lin, H. Tin, Study on the Sndwih Piezoeletri Cermi Ultrsoni Trnsduer in Thikness Virtion, Smrt Mterils nd Strutures, vol. 7, no., pp. -9, Jn. 28. [9] D. Mnčić, G. Stnčić, New Three-dimensionl Mtrix Models of the Ultrsoni Sndwih Trnsduers, Journl of Sndwih Strutures nd Mterils, vol., pp. 6-8, Jn. 2. [] I. Jovnović, D. Mnčić, V. Punović, M. Rdmnović, Z. Petrušić, Mtl/Simulink Model of Piezoermi Ring for Trnsduer Design, ICST 2,, (2).

5 [] I. Jovnović, D. Mnčić, V. Punović, M. Rdmnović, V.V. Mitić, Metl Rings nd Diss Mtl/Simulink D Model for Ultrsoni Sndwih Trnsduer Design, Siene of Sintering 44, (2). [] Five piezoeletri ermis, (Bulletin 66/F, Vernitron Ltd., 976).