Theoretical and experimental investigations on the match between pulse tube cold fingers and linear compressors

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1 IOP Confn Sis: Mils Sin n Engining PAPER OPEN ACCESS Thoil n xinl invsigions on h h bwn uls ub ol fings n lin ossos To i his il: Jun Tn l 015 IOP Conf. S.: M. Si. Eng Rl onn - Cosso iion ool Ajun Rvi, Luksz Sznj n In Bnn - A Cyogn Ryl wih Puls Tub Cyoool fo Ronnsing Hliu n Niogn C Wng n B Lihnwl - Soll Cosso Oil Pu Anlysis S Bnh Viw h il onlin fo us n nhnns. This onn ws ownlo fo IP ss on 4/07/018 :0

2 CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) oi: / x/101/1/01048 Thoil n xinl invsigions on h h bwn uls ub ol fings n lin ossos Jun Tn 1,, Hizhng Dng 1, Li Zhng 1, 1 Nionl Lbooy fo Inf Physis, Shnghi Insiu of Thnil Physis, Chins Ay of Sins, No. 500 Yuin Ro, Shnghi, Chin Univsiy of Chins Ay of Sins, No.19A Yuqun Ro, Bijing, Chin E-il: n_zhun@163.o Abs. Th h bwn h ol fing n h lin osso of h Siling-y uls ub yoool lys vil ol in oiizing h osso ffiiny n in ioving h ol fing ooling fon. To vl h h hnis bwn h lin osso n uls ub ol fing (PTCF), il nlyss hv bn o unsn h inions bwn h. Bs on h hoil invsigions, boh of h sign ho of h PTCF o h h givn lin osso n vs ho of h lin osso o h h givn PTCF hv bn oos. In o o vify h vliiy of hs hois n hos, ul PTCF n lin osso vlo o h h xising lin osso n PTCF, sivly. Th xinl suls show goo gns wih h siul ons. 1. Inouion Th Siling-y uls ub yoool (SPTC) hs wi viy of ion liions in ivil, os n iliy fns fils [1 ]. Gnlly, SPTC n b ivi ino wo s: on is h lin osso n h oh n h s h uls ub ol fing (PTCF) inluing ll of h ining oonns. Th oil h bwn h PTCF n h lin osso of h SPTC lys vil ol in oiizing h osso ffiiny n in ioving h ol fing ooling fon. Svl shs h so lvn suis on h h. Fo xl, Hun l. [3] i ou h invsigion of gs ffs on h sonn hisis of h Siling yl yoool. Dyni inions bwn h hnil sys n h woking flui w sui n hi xins xlo h ff of woking flui hisis on h hnil sons n h ff of yogni u on h oo un n ison liu. Wkln [4] invsig so issus involv in hing lin ossos o hoousis yoools. Th suls ini h hing h ousi lo o h oiu hnil lo fo h iul osso oul b us o xiiz h osso ffiiny o h inu ow. Bs on h suy of Wkln [4], Swif [5] invsig h s whih woul ff h osso ffiiny n qui h lion bwn h ool ousi in n h ffiiny. Howv, boh suis by Wkln [4] n Swif [5] h whol ol fing s n ousi in, whs invsigions on h ins of h sifi oonns of h ol fing w no. Ko n Jong [6] sui h yni bhvio of h lin osso in SPTC n foun h, h yni bhvio of h ison in h lin osso ws ily influn by h lo oniion n h flow in of h inn ub Conn fo his wok y b us un h s of h Civ Coons Aibuion 3.0 lin. Any fuh isibuion of his wok us inin ibuion o h uho(s) n h il of h wok, jounl iion n DOI. Publish un lin by L 1

CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) 01048 oi:10.1088/1757-899x/101/1/01048 woul ff h yni sons of h ison s wll s h ooling fon.

As shown in h bov liu suvy, lhough vious suis gv so xlnions o suggsions on h h bwn h lin osso n h PTCF, ny qusions sill s o b solv.

On h oh hn, fo n xising PTCF, sifi invsigions hv lso slo bn o sign h oil lin l osso o h i. In o o vlo high fon SPTCs fo il liions, i is nssy o suy hs obls hooughly n giv l xlnion of h h hnis.

3 CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) oi: / x/101/1/01048 woul ff h yni sons of h ison s wll s h ooling fon. Alhough h nlysss onsiing h ynis of h lin osso n h ho-hyulis of h SPTC w n nw sign oh fo b ooling fon ws oos, fuh suis s on h ho hv no bn o. As shown in h bov liu suvy, lhough vious suis gv so xlnions o suggsions on h h bwn h lin osso n h PTCF, ny qusions sill s o b solv. Fo xl, on h oil ousi in o h h xisingg lin osso is known, how os on g o sign h PTCFF wih h n ousi in? Fw invsigions hv bn i ou o vll h influns of h s of h lin osso on h ooling fon whn h o PTCF. On h oh hn, fo n xising PTCF, sifi invsigions hv lso slo bn o sign h oil lin l osso o h i. In o o vlo high fon SPTCs fo il liions, i is nssy o suy hs obls hooughly n giv l xlnion of h h hnis. In his, sysi hoil invsigions inluing h h of h PTCF fo givn lin osso n h vsl h of h lin osso fo givn PTCF hv bn o vl h inions bwn h. Fuho, sign ho of h PTCF o hiv h oil hing fo h givn lin osso will b oos,, whih is bs on h lil iui nlogy (ECA) ol onsiing h influn of vy oonn of h PTCF. A sign ho of h lin osso o hiv h oil hing fo h givn PTCF will b u fow s wll. Sifi xinl invsigions will b i ou o vify h vliiy of h h hoy n sign hos.. Thoil nlyss FIGURE 1 shows shi of SPTC wih ul-oos lin osso s iv uni. Th PTCF onsiss of n fool, gno, ol h xhng, uls ub, ho h xhng, n inn ub n svoi. Though h onning ub, h PTCF is onn o h lin osso. Figu 1. Shi of SPTC wih ul-oos lin osso. Th os ion govning quions of h lin osso h fo bln n h volg onil bln of h oo. To silify h nlysis, osillions in h lin osso n h PTCF ll ssu o b on-insionl n sinusoil, n h influns of h bk ssu in h lin osso ngl. Fo h oo, h govning quions n b win s Eqs. (1) n () [7]: x() x() LBi( ) = + b + kxx () + ξ () A (1) i() () V () = L + R i( ) + BLx Mnwhil, h isln of h ison n b xss in Eq. (3) s fn oin. x() = X sin( ω ) (3) wh L is h oil lngh in h gni fil, B is h innsiy of h gni fil, i() is h oo un, is h ss of oving, x() is h isln of h ison, b is h hnil offiin, k x is h xil siffnss of h flxu sings, ξ is h ssu oion offiin fo h

CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) 01048 oi:10.

4 CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) oi: / x/101/1/01048 ul-oos onfigguion, A is h isonn suf, V() is h oo voolg, L iss h oil inunn, R is h oil sisn n, X is h liu of h ison n n ω is hh ngul fquny. Thoughh Eqs. (1), () n (3), h lioons bwn n h lin osso n h PTCF P sblishh. Sifi nlyss wih hs quions will b i ou in h nx ssion..1. Thoil nlyss n sign ho of h PTCF F o h h h givn lin ossso Aoing o hh ECA ol of h SPT TC oos by Tn n Dng [8], h of h PTCF n b nlogous o h ob binion of h bsi fllui lns lik sissn, inn n olinn, n h whol PTCF F n b nllogous o n AC lil iui. A ong h o onns of h PTCF, h uuls ub n h svooi n b g s o olin, n hus h yni ssus in h onsn. Th T foool, ol h xhng n ho h xhng us o ovi h xhng ong h wokingg gs, h solli wll n h nvion n, n hy shoul b k sy uss, sivly. In h ECA ol, hi ins ll h obinions of h sisn, inn nn olin. Fo h gno, u gin will inou onnoll sou, whhih will fff h volu u flow ogh wih h olinn. Fo h inn ub b, oingg o h ECA A hoy [8], h viionn of volu flow us bby h olin is l o h lol ssu, n h ssu hhng us by h inn in n sisn on is l o h h lol vollu flow. Hn, h ol inn of h inn ub is h obbinion of h h h kin s of ins. Th quivln lil iui of hh whol PTCF n b suuiz s shown in FIGURE F. Figu. Equiivln lil iui of h SPTC. Bss on h nlyss b bov, h PT TCF n b sign n oiizz by jusing h insioons of h oonn s by s. Th siifi sign flow fl h n b su iz s shown inn FIGURE 3. 3 On h insions oof h PTCF oonns known, h sifi ssu, volu fflow n h in h innl of h PT TCF n b lul... Thoil nlyss n sign ho of h lin osso o h hh givn PTC CF Bss on h siil s o ohs oos by Wkln [4] n h boov quion ns, fuh lionss bwn h ss of h lin osso o n h PT TCF n b -u s follows. Fo h ul-oos lin o osso, hh oo u un n b b xss s Eq. (4)), n h ffiiny h h li inu ow onvs o h PV V ow h h inl of h PTCF n b b win s Eq. (55). i ( ) = X sin (ω ) ( k x ω ξ Z ω A sinθ ) BL + os (ω ) ( bω + ξ Z ω A os θ ) π Dg g3 Z B L A Z os θ 6μ Lg η= Z os θ A B L + bb B L + R A 4 ( ξ Z os θ + b / A ) + ( ξ Z si s n θ + ( ω k x / ω ) / A ) (4) (5) Th fis in h nuo of o Eq. (5) is h PV ow h ison suf, n h son n is 3

CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) 01048 oi:10.1088/1757-899x/101/1/01048 h PV ow loss uu o h sl ln [[9].

Th gs fo n b ivii ino wo o s. On is ou of hs wih ison isl n whih os wok on h ggs, lik gs, nsoing hh PV ow o h PTC CF.

Th sonn fqunyy of h lin oo boos: ξ Z sin θ 1 kx A ωξ (6) fn = π In o o hiv high h fon of h llin oo,, h woking g fquny sshoul o oxi o h sonnn fquny.

(4), (5) n (6), h sifi of h sign flow w h of h lin o sso o h hh givn PTC CF n b su iz inn FIGURE 4. Figu 3. Flow h of hh sign ho of h h h givnn lin ossso.

Flow h of h sign ho of h lin n osso o h h givn PTCFF An svvl inills n b su uiz ffo signing g h lin osso o h h PTCF s follows: Fiss, onsiinng h il liions, h gni

5 CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) oi: / x/101/1/01048 h PV ow loss uu o h sl ln [[9]. Th so on in h noinno is h hnil ingg loss of h oo, n h h ls iis h Joul h h u o h h oil sisn. In iiion, h yni ssu h ison suf ovis iioi gs fo on h iison. Th gs fo n b ivii ino wo o s. On is ou of hs wih ison isl n whih os wok on h ggs, lik gs, nsoing hh PV ow o h PTC CF. Th oh is in hs wih h isl n whih will no on nsu wok, lik gs s ing, foin ng nw ss-sing sys. Th sonn fqunyy of h lin oo boos: ξ Z sin θ 1 kx A ωξ (6) fn = π In o o hiv high h fon of h llin oo,, h woking g fquny sshoul o oxi o h sonnn fquny. Ao ing o h nnlysis of h h PTCF, h liu n hs n ngl of h inn lso funions off woking fquny. Th h oil fquny bos h so oluion of his nssnnl qquion. Aoing o Eqqs. (4), (5) n (6), h sifi of h sign flow w h of h lin o sso o h hh givn PTC CF n b su iz inn FIGURE 4. Figu 3. Flow h of hh sign ho of h h h givnn lin ossso. PTCF o Figu 4. Flow h of h sign ho of h lin n osso o h h givn PTCFF An svvl inills n b su uiz ffo signing g h lin osso o h h PTCF s follows: Fiss, onsiinng h il liions, h gni fill innsiy shoul b s high s ossibl,, whih nns h h il wih h lgs vilbl ngy ou sshoul b h hosn. Son, bs on h on iion of h sonn s of h lin n osso givn by b Eq. (6), h oi l oving ss n h xil siffnss of h flxu sings n b hiv. Thii, whn xing no infflun on hh sign of oh o s, h volu oof h oo oil in h gni fil shoul b sign o b s biig s ossibl o hiv high h oo ffiiny. Fouuh, kingg oh vib bls onsn, iffniing Eq. (5) wih w s o of ison A n ssing h sul qul o o zo will gg h oi u vlu of o A o hiv h high hs oo ffiiny s followss: 4

CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) 01048 oi:10.1088/1757-899x/101/1/01048 Aoil = 4 ( bb B L + R b + ( k x / ω ω ) 4 Rξ Z ) (7) An fifh, bs on Eqs.

L( oil ) = (k B L ( k x ω ξ Z ω A sin θ ) ω ξ Z ω A sin θ ) + ( bω + ξ Z ω A os θ ) x (8) On h lngh, h wi i n h ooil inun known, h wi wing syl n b inn oing o h i-o inuo fouls bs on h Whl W oxiion

Siu ulions n xinl suls Aoinng o h bbov nlyss, nw inn-lin PTCF F will b v vlo o h giv vn lin ossso vlo in h uhos lbooy, n nw ul-o os lin osso o will b vlo o h givn oxil PTCF, o vify h h vliiy of o h

Dvvlon off h PTCF o o h h ggivn lin osso Fo h givn lin osso, h gnius of h gni fil innsiy B, h oil lngh in gni fil L, h sings xil siffnss k x, h ovin ng ss, h h ison suf A, h oil sisn R, h oiil inun

FIG GURE 5 n FIGURE 6 show h siiul fon off h xisingg oo wih h iffn lius n hss ngls of h PTCF i n, sivly.

6 CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) oi: / x/101/1/01048 Aoil = 4 ( bb B L + R b + ( k x / ω ω ) 4 Rξ Z ) (7) An fifh, bs on Eqs. ()) n (4), h hs ngl bwn h oo volg n un n b obin. In o o k high fffiiny, h vlu of h oo ow w fo shooul oxi o 1. Thfo, h vlu of h oil inun n b h hiv o gin h oi l ow fo. f Is xssioon is shown in Eq. (8). L( oil ) = (k B L ( k x ω ξ Z ω A sin θ ) ω ξ Z ω A sin θ ) + ( bω + ξ Z ω A os θ ) x (8) On h lngh, h wi i n h ooil inun known, h wi wing syl n b inn oing o h i-o inuo fouls bs on h Whl W oxiion [10]. 3. Siu ulions n xinl suls Aoinng o h bbov nlyss, nw inn-lin PTCF F will b v vlo o h giv vn lin ossso vlo in h uhos lbooy, n nw ul-o os lin osso o will b vlo o h givn oxil PTCF, o vify h h vliiy of o h bov hois n n sign hoss Dvvlon off h PTCF o o h h ggivn lin osso Fo h givn lin osso, h gnius of h gni fil innsiy B, h oil lngh in gni fil L, h sings xil siffnss k x, h ovin ng ss, h h ison suf A, h oil sisn R, h oiil inun L, h xxiu ison liu Xx n hnil b n ll b g s known s. Aoing o hoil nlyss, h h bwn is fon n h in of o PTCF is ssiul. FIG GURE 5 n FIGURE 6 show h siiul fon off h xisingg oo wih h iffn lius n hss ngls of h PTCF i n, sivly. In FIGURE E 5, h oo o li inu ow inss wih h in ns of hh liu of PTCF i n un iffn vlus of h in hs ngl. Wih h h s liu, h xiss n oil hs ngl fo h lin ossso o hivv h highss li inu ow. In n iion, whn w h in hss ngl is sll hn zo, h oo li inu ow willl s wih w h sing hs ngl. E 6 shows h viions of h oo ffiiny wih w h ins of h liu of h PTCF FIGURE inn. As h hnil loss l ouns fo vy y sll oion of h innu ow, h oo ffiiny n b us o sn h viiion of h fffiiny of onving hh li in u ow ino PV ow. Fo h hs ngl, h xiss n o il in o quui h high hs oo ffiiny, sivly. Wih h s oof h hs ngl, h o il oo ffiiny inss. Fo his lin osso, h siul suls show h, wih ngiv hss ngls, h h highs wih in in h ng of 108 P s/3 o P s/3. oo fffiiny nn b hiv Figu 5. Siulions off h oo li inu ow wih iffn lius n hs ngls off h PTCF in. 5 Figu 6. Siuliions of h ooo ffiiny wiih iffn lius n hs ngls of hh PTCF i n.

CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) 01048 oi:10.1088/1757-899x/101/1/01048 Aoing o hh ECA o l n siggn ho of PTCF sib bov, nw in-lin PTCF hs bnn sign oo h h xising lin osso o.

7 CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) oi: / x/101/1/01048 Aoing o hh ECA o l n siggn ho of PTCF sib bov, nw in-lin PTCF hs bnn sign oo h h xising lin osso o. As i hs bn b isuss in h io o sion, h o onn of h PTCF xs n fff on h PTCF P i n n hhus ffs h PTCF ooling fon. In o o show hhis in il n l wy, hh influn of h oonn will b onu on o h vllo PTCF F. Fo x l, FIGURE E 7 shows siul suls oof h influnn of uls ub lnghh on h PTC CF in n n ffiiny of h h ool. W Wih h uuls ub ln ngh inssing fo 40 o 14 40, h liu of PTCF inn gullyy ss, whs n oil ool ffiiny y bov 18.44% xiss in h uls ub lnggh ng off 80 o 100. In F FIGURE 8, h h s viiions wih h in ns of h inn ub lnngh. In iiion, h hng of h ool ffiiny is g,, fo 18.4% % wih h inn ub lnghh of 1 o zo wih h lngh of 3. I lso sho ows h h inn ub b lys vil ol in influning h ooling fon of h PTCF. P Moo ov, h oooling u lso shows g ff on h PTC CF in n h o ool ffiin ny. As show wn in FIGU URE 9, h liu of PTCF in inss liil, whs h ool ffiiny oof Cno h hivs h xiu 110 K, wih h oo oling u insiing fo 60 K o 10 K. Th sifi inn-lin PTCF ws nufu n ssbl. Th ooy y ws hn n h wih h givn osso n s. FIGU URE 10 show ws h oisons of h xin nl suls n h siul suls of h h oool ooling fon. Boh of hh viion nnis of h siiul oooling iy n h si ul ffiiiny of Cno g w wih h x inl suls w wll. Th h ool n ovi 4 o ws oo oling u of 80 K wih h li inu ow nging fo o 75 W oo 190 W. Th h vg ffiiny off Cno of h ool hs bov 17%. Figu 7. Influn of uuls ub lngh on PTCF in n oooling fon. Fig gu 8. Influn of inn ub lngh on PTCF i n n o ooling fo n. Figu 9. Influn of oooling u u on PTCF in n oooling fon. Figu u 10. Coisons bwn h siul suls n h xinl ons of h ooling fo n. 6

8 CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) oi: / x/101/1/ Dvvlon off h lin osso oo h h givn g PTCF Fo 60 K oxill PTCF vlo in h uhos lbooy, nw lin osso hs bn vlo o h i. Fis, oing o hh oos ECA E ol,, h oolingg fons of h PTCF siul, n 57 Hz hs bn hiv s h h oil woking w fqquny. By fixing f h fquny 57 Hz n jusin ng h volu flow h inl of h PTCF CF, h liiu n hs nngl of h i n of h PTCF un iffn ooling iy hvv bn qu ui. As shown inn FIGURE 11, wih h ooling iy insing fo W o 5.5 W, h liu of inn hs sll s n h hss ngl hs sll ins. I n bb oughly o onsi h h liu n hs ngl of h in k onsn n hi vlus P s/3 n -8 gs, sivly. FIGU URE 1 n 13 show h influns oof oil inun on oo oow fo, n influn ns of isoon i on o h ool fonn, siv vly. Th oil oving ss, h xil siffnss oof h flxu sings, h ison i n h oil inunn n b hiv oingly. A nnw lin oosso ws w sign by h h ho nion bov, nn hn nu ufu n ssbl. Th 60 K PTC CF h w wih h v vlo lin ossso ws s un iffn woking oniions. Wih h w woking fquny of 57 Hz, h siul ooling fon n xinl on n o in FIGU URE 14. Th h oool hivs W o 5.5 W 60 K wihh h li inu ow insing g fo 97 W o 49 W, n 9.6% of o Cno ffiiny hs bn liz. Tn nnis of hh siul suls gnlly g onnsisn wih h hos of h xinl ons. Anlysss show h h 60 K o oxil PTCF ws siul by h vlo ECA ool, whih is i inly bs on h inn-lin PTCF. On of h in iffns bwn h inlin n h oxil goil ngnns lis in h ol h xhngs. Th flow vss in 180 gs in h ol h xhng of hh oxil PT TCF n qu uis o vvoi volu,, whs h in-linn oun os nih. Ths iffns will l o o viionn fo h siul s sul. H Hn, n iil offfiin of 0.8 hs bn in h siulion o u his viion. Aiionnlly, in FIG GURE 14, fo o h oolinng iy lg hn 4 W, h ifffn bwn h xinl n si ul li inu oows bo s lg. So o os h iiffn bwn h xinl n siul oo oling ffiinny. Th n nlyss giv h followinng sons. A lg ooling iy ns o li ows, n hus h h un bos lg oinglly. As h Joul h u o h oil sisn n is ooionl o h squ of h h un, hh u u of h oo uun lg li in nu ow inss sh hly. This subsqunly will su ul in h insss of h oo oil sissn n hnil s wll, boh of whhih onibu u o h oo looss. Thfoo, h n li inu ow bos lg n hh ooling ffiiny boss low oingly. Figu 11. Siulions of o liu n hs ngl of h 60 K PTCF. Figu 1. Cooling fo n of h h ool wih iffn isonn i. 7

9 CEC 015 IOP Conf. Sis: Mils Sin n Engining 101 (015) oi: / x/101/1/01048 Figu 13. Influns of oil inun on oo ow fo Figu 14. Coisons C off ooling fon bwn h siul n h xin nl ons. 4. Conlusions n isussionss Th oiil h bwn b h ol fing n h lin osso of h SPT TC lys viil ol in oiizing h osso ffiiny n in ioving h h ol fing ooling fon. Howv, h xising suis on o h h h only fous oon hiving g h oill in of PTCF o h h lin oosso, o on king so siffi nlyss of o fw o onns of h ol fing g fo h hingg. In his, h inion bwn h PTCF F n h lin n ossso hs bn n nlyz in il wy, n h sysi invsigions on h wo-wy y hing, nly hing h PTCF foo givn linn osso n hing h liin osso fo gi givn PTCF hv h bn hoilly. Fuho, F, sign ho of h PTCF o h hiv h oil hing fo h givn linn osso is oo os, whih is bs on n h ECA ol onsiing h infflun of vy ooonn off h ol fing. An sign ho of h lin osso o hiv h oil hing foo h givn PTCF is u u fow ss wll. In o o vifyy h vliiy y of hs hois n hos, n ull PTCF n lin o sso w vlo o h h givn lin oosso nn PTCF, ssivly. Thh xinl suls ll show gooo gns wih h siul ons. Rfn ns [1] Rbugh R. A viw of u uls ub figion. Av A Cyog En ng 1990; 35: [] Ross J RG. Aoos ools: 50-y qus fo lo ong-lif yog gni oolingg in s. In n: Ti hus KD, R RP, ios. Cyo gni ngining: fify ys y of oggss. Nw Yok: Y Sinng Publishs; [3] Hunn MK, Collinns SA, Johnson DL l. Invsigion of gs ffs on yoool sonn hisis. Cyoool C ; 9: [4] Wkln RS. Us of lo yni ivvs in h oousi figos. JJ.Aous.So.A 0000; 107(): [5] Swif f GW. Th oousis: A unifying siv fo f so ng gins n f figos. Swikly (PA)): Aousill Soiy of Ai A Pubbliions, [6] Ko J n Jong S. S Anlysis on h silingg-y uls ub figo in onsiiion of ynis of linn ossso. Cyognis 008; 448: [7] Mqqu E, Rbugh R, Kil K P. Dssign quion ns n sling g lws fo linn osssos wih flxu sinngs. Cyooo ols 1993; 77: [8] Tn J n Dng HZ. H An lil iui nlogy o l fo nlyss n oi izions off h Siliing-y ulss ub yoool. Cyoggnis 015;; 71:18 9. [9] R JS, Dvy G, G D MW W l. Cossion lossss in yoo ools. Cyoools 004; 13: [10] Whhl H. Inun fo uls fo iul n squ u oils. In n: Poinggs of IEEE 70: ;

Acoustic characterization of an ultrasound surgical transmitter in the linear and nonlinear regime of working

Acoustic characterization of an ultrasound surgical transmitter in the linear and nonlinear regime of working Aousis 8 Pis Aousi hiion of n ulsoun sugil nsmi in h lin n nonlin gim of woing A. Posi B. Ivnčvić n D. Svil b Fuly of Elil Engining n Comuing ns 3 1 gb Coi b Bosi Insiu Avni Vćslv Holv bb 1 gb Coi nonio.osi@f.h