2507 ingxenye yamakhemikhali yeshubhu yensimbi engagqwali, I-Equivalent Thermal Network Simulation Study ye-Rare Earth Giant Magnetostrictive Transducer

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Okubalulekile ekwakhiweni kwe-giant magnetostrictive transducer (GMT) ukuhlaziya okusheshayo nokunembile kokusatshalaliswa kwezinga lokushisa.Ukumodela kwenethiwekhi eshisayo kunezinzuzo zezindleko eziphansi zokubala nokunemba okuphezulu futhi kungasetshenziselwa ukuhlaziywa kokushisa kwe-GMT.Kodwa-ke, amamodeli akhona ashisayo anemikhawulo ekuchazeni lezi zindlela zokushisa eziyinkimbinkimbi ku-GMT: izifundo eziningi zigxila ezimeni ezimile ezingakwazi ukuthatha izinguquko zokushisa;Ngokuvamile kucatshangwa ukuthi ukusatshalaliswa kwezinga lokushisa kwezinduku ezinkulu ze-magnetostrictive (GMM) kufana, kodwa i-gradient yokushisa kuyo yonke induku ye-GMM ibaluleke kakhulu ngenxa yokungaphatheki kahle kwe-thermal, ukusabalalisa okungafani nokulahlekelwa kwe-GMM akuvamile ukungeniswa ku-thermal. imodeli.Ngakho-ke, ngokucubungula kabanzi lezi zici ezintathu ezingenhla, lo mbhalo usungula imodeli ye-GMT Transitional Equivalent Heat Network (TETN).Okokuqala, ngokusekelwe kumklamo kanye nesimiso sokusebenza kwe-HMT ye-longitudinal vibratory, ukuhlaziya okushisayo kuyenziwa.Ngalesi sisekelo, imodeli yento yokushisisa isungulelwa inqubo yokudlulisa ukushisa kwe-HMT futhi amapharamitha emodeli ahambisanayo ayabalwa.Ekugcineni, ukunemba kwemodeli ye-TETN yokuhlaziya izinga lokushisa kwe-transducer kwe-spatiotemporal kuqinisekiswa ngokulingisa nokuhlola.
I-giant magnetostrictive material (GMM), okuyi-terfenol-D, inezinzuzo ze-magnetostriction enkulu kanye nokuminyana kwamandla aphezulu.Lezi zakhiwo eziyingqayizivele zingasetshenziswa ukuthuthukisa ama-giant magnetostrictive transducers (GMTs) angasetshenziswa kuzinhlelo zokusebenza eziningi ezinjengama-acoustic transducer angaphansi kwamanzi, ama-micromotor, ama-linear actuators, njll. 1,2.
Okukhathaza kakhulu amandla okushisa ngokweqile kwama-GMTs angaphansi kolwandle, okuthi, lapho esebenza ngamandla aphelele kanye nesikhathi eside sokuvusa amadlingozi, angakwazi ukukhiqiza amanani abalulekile okushisa ngenxa yokuminyana kwamandla aphezulu3,4.Ukwengeza, ngenxa ye-coefficient enkulu yokwanda okushisayo kwe-GMT kanye nokuzwela kwayo okuphezulu ekushiseni kwangaphandle, ukusebenza kwayo okuphumayo kuhlobene eduze nezinga lokushisa5,6,7,8.Ezincwadini zobuchwepheshe, izindlela zokuhlaziya ukushisa kwe-GMT zingahlukaniswa zibe izigaba ezimbili ezibanzi9: izindlela zezinombolo nezindlela zepharamitha ehlanganisiwe.I-finite element method (FEM) ingenye yezindlela ezivame ukusetshenziswa kakhulu zokuhlaziya izinombolo.Xie et al.[10] isebenzise indlela yesici esilinganiselwe ukuze ilingise ukusatshalaliswa kwemithombo yokushisa yedrayivu enkulukazikazibuthe futhi yaqaphela idizayini yokulawula izinga lokushisa nesistimu yokupholisa yedrayivu.UZhao et al.[11] usungule ukulingisa okuhlanganyelwe kwesici esilinganiselwe senkambu yokugeleza eneziyaluyalu kanye nenkambu yezinga lokushisa, futhi wakha idivayisi yokulawula izinga lokushisa yengxenye ehlakaniphile ye-GMM ngokusekelwe emiphumeleni yokulingisa into enomkhawulo.Kodwa-ke, i-FEM idinga kakhulu mayelana nokusetha imodeli nesikhathi sokubala.Ngalesi sizathu, i-FEM ithathwa njengosekelo olubalulekile lwezibalo ezingaxhunyiwe ku-inthanethi, ngokuvamile phakathi nesigaba sokuklama isiguquli.
Indlela yepharamitha ene-lumped, evame ukubizwa ngokuthi imodeli yenethiwekhi yokushisa, isetshenziswa kakhulu ekuhlaziyeni kwe-thermodynamic ngenxa yesimo sayo esilula sezibalo kanye nesivinini sokubala esiphezulu12,13,14.Le ndlela idlala indima ebalulekile ekuqedeni ukulinganiselwa kokushisa kwezinjini 15, 16, 17. I-Mellor18 yaba ngowokuqala ukusebenzisa isekethe ethuthukisiwe efana ne-thermal T ukuze imodeli yenqubo yokudlulisa ukushisa kwenjini.Verez et al.I-19 idale imodeli enezinhlangothi ezintathu zenethiwekhi eshisayo yomshini wokuvumelanisa ozibuthe unomphela onokugeleza kwe-axial.U-Boglietti et al.20 wenze isiphakamiso samamodeli enethiwekhi eshisayo amane eyinkimbinkimbi ehlukahlukene ukuze abikezele ukuguquguquka kokushisa kwesikhashana kuma-stator windings.Ekugcineni, u-Wang et al.21 basungule isifunda esilinganayo sokushisa esinemininingwane yengxenye ngayinye ye-PMSM futhi bafingqa isibalo sokumelana nokushisa.Ngaphansi kwezimo ezivamile, iphutha lingalawulwa ngaphakathi kwe-5%.
Ngawo-1990, imodeli yenethiwekhi yokushisa yaqala ukusetshenziswa kuma-converter anamandla aphansi aphansi.U-Dubus et al.22 uthuthukise imodeli yenethiwekhi yokushisa ukuze achaze ukudluliswa kokushisa okumile kusidlidlizi esinezinhlangothi ezikabili zelongitudinal kanye nenzwa yokugoba yekilasi IV.U-Anjanappa et al.23 wenze ukuhlaziya okushisayo kwe-2D okumile kwe-magnetostrictive microdrive esebenzisa imodeli yenethiwekhi eshisayo.Ukutadisha ubudlelwano phakathi kohlobo olushisayo lwamapharamitha we-Terfenol-D kanye ne-GMT, u-Zhu et al.I-24 isungule imodeli elinganayo yesimo sokumelana nokushisa nokubala kokususwa kwe-GMT.
Ukulinganisa kwezinga lokushisa kwe-GMT kuyinkimbinkimbi kakhulu kunezinhlelo zokusebenza zenjini.Ngenxa ye-thermal and magnetic conductivity enhle kakhulu yezinto ezisetshenziswayo, izingxenye eziningi zenjini ezicatshangelwa ekushiseni okufanayo zivame ukuncishiswa zibe i-node eyodwa13,19.Kodwa-ke, ngenxa yokungashintshi kahle kwezinga lokushisa kwama-HMM, ukucatshangwa kokusatshalaliswa kwezinga lokushisa okufanayo akusalungile.Ngaphezu kwalokho, i-HMM inokungeneka kukazibuthe okuphansi kakhulu, ngakho-ke ukushisa okukhiqizwa ukulahlekelwa kazibuthe ngokuvamile akufani nenduku ye-HMM.Ukwengeza, ucwaningo oluningi lugxile ekufanisweni kwesimo esizinzile esingabaleli ukushintsha kwezinga lokushisa ngesikhathi sokusebenza kwe-GMT.
Ukuze kuxazululwe izinkinga ezintathu zobuchwepheshe ezingenhla, lesi sihloko sisebenzisa ukudlidliza kwe-GMT longitudinal njengento efundwayo futhi imodela ngokunembile izingxenye ezihlukahlukene ze-transducer, ikakhulukazi i-GMM rod.Imodeli yenethiwekhi yokushisa elinganayo elinganayo (TETN) GMT idaliwe.Imodeli yesici esilinganiselwe kanye nenkundla yokuhlola yakhelwe ukuhlola ukunemba nokusebenza kwemodeli ye-TETN yokuhlaziya izinga lokushisa le-transducer le-spatiotemporal.
Idizayini kanye nobukhulu bejiyomethri be-HMF ezungezayo ngobude buboniswa ku-Fig. 1a no-b, ngokulandelanayo.
Izingxenye ezibalulekile zifaka izinduku ze-GMM, amakhoyili asezindaweni, omagnethi baphakade (PM), amajoka, amaphedi, ama-bushings, neziphethu ze-belleville.Ikhoyili evusa amadlingozi ne-PMT ihlinzeka ngenduku ye-HMM ngendawo kazibuthe eshintshanayo kanye nenkundla kazibuthe echema ye-DC, ngokulandelanayo.Ijoka nomzimba, okuhlanganisa ikepisi nomkhono, kwenziwa ngensimbi ethambile ye-DT4, ene-permeability ephakeme kazibuthe.Yakha imjikelezo kazibuthe evaliwe nge-GIM ne-PM rod.Isiqu esiphumayo kanye nepuleti lokucindezela zenziwe ngensimbi engenazibuthe engu-304.Ngemithombo ye-belleville, i-prestress ezinzile ingasetshenziswa esiqwini.Lapho i-current eshintshanayo idlula ikhoyili yedrayivu, i-HMM rod izodlidliza ngokufanele.
Emkhiwaneni.2 ibonisa inqubo yokushintshanisa ukushisa ngaphakathi kwe-GMT.Amarodi e-GMM namakhoyili asendle yimithombo emibili eyinhloko yokushisa kwama-GMT.Inyoka idlulisela ukushisa kwayo emzimbeni ngokuhambisa komoya ngaphakathi kanye nesivalo ngokuhambisa.Induku ye-HMM izodala ukulahlekelwa kazibuthe ngaphansi kwesenzo sensimu kazibuthe eshintshanayo, futhi ukushisa kuzodluliselwa egobolondweni ngenxa yokuguquguquka emoyeni wangaphakathi, nakuzibuthe ongunaphakade kanye nejoka ngenxa yokuhambisa.Ukushisa okudluliselwe kukesi bese kuchithwa ngaphandle nge-convection kanye nemisebe.Uma ukushisa okukhiqizwayo kulingana nokushisa okudlulisiwe, izinga lokushisa lengxenye ngayinye ye-GMT lifinyelela esimweni esizinzile.
Inqubo yokudlulisa ukushisa ku-GMO ene-longitudinally oscillating: a - umdwebo wokugeleza kokushisa, b - izindlela zokudlulisa ukushisa eziyinhloko.
Ngokungeziwe ekushiseni okukhiqizwa ikhoyili ye-exciter ne-HMM rod, zonke izingxenye zesekethe kazibuthe evaliwe zithola ukulahlekelwa kazibuthe.Ngakho, uzibuthe unomphela, ijoka, ikepisi kanye nomkhono kuhlanganiswe ndawonye ukuze kuncishiswe ukulahlekelwa kazibuthe kwe-GMT.
Izinyathelo eziyinhloko zokwakha imodeli ye-TETN yokuhlaziywa kwe-thermal ye-GMT zimi kanje: izingxenye zeqembu zokuqala ezinamazinga okushisa afanayo zihlangene futhi zimelela ingxenye ngayinye njengenodi ehlukile kunethiwekhi, bese ihlobanisa lawa ma-node nenkulumo efanele yokudlulisa ukushisa.conduction ukushisa kanye convection phakathi node.Kulesi simo, umthombo wokushisa kanye nokukhishwa kokushisa okuhambisana nengxenye ngayinye kuxhunywe ngokuhambisana phakathi kwenodi ne-voltage enguziro evamile yomhlaba ukuze kwakhiwe imodeli elinganayo yenethiwekhi yokushisa.Isinyathelo esilandelayo ukubala imingcele yenethiwekhi eshisayo yengxenye ngayinye yemodeli, okuhlanganisa ukumelana nokushisa, umthamo wokushisa nokulahlekelwa kwamandla.Ekugcineni, imodeli ye-TETN isetshenziswa ku-SPICE ukuze ilingise.Futhi ungathola ukusatshalaliswa kwezinga lokushisa kwengxenye ngayinye ye-GMT noshintsho lwayo esizindeni sesikhathi.
Ukuze kube lula ukwenza imodeli nokubala, kuyadingeka ukwenza lula imodeli yokushisa futhi ungayinaki izimo zemingcele ezingenamphumela omncane emiphumeleni18,26.Imodeli ye-TETN ehlongozwayo kulesi sihloko isuselwe ekuqageleni okulandelayo:
Ku-GMT enamawindi amanxeba ngokungahleliwe, akunakwenzeka noma kudingekile ukulingisa indawo yomqhubi ngamunye.Amasu okumodela ahlukahlukene aye athuthukiswa esikhathini esidlule ukuze enze imodeli yokudluliswa kokushisa nokusabalalisa izinga lokushisa ngaphakathi kwama-winding: (1) ukuhanjiswa kwe-thermal okuhlanganisiwe, (2) izibalo eziqondile ezisekelwe ku-conductor geometry, (3) i-T-equivalent thermal circuit29.
Inhlanganisela ye-thermal conductivity kanye nezibalo eziqondile zingabhekwa njengezixazululo ezinembe kakhulu kunesekhethi ye-T elinganayo, kodwa zincike ezintweni eziningana, njengezinto ezibonakalayo, i-geometry yomqhubi kanye nomthamo womoya osele ekujikeni, okunzima ukunquma29.Ngokuphambene nalokho, i-T-equivalent thermal scheme, nakuba imodeli elinganiselwe, ilula kakhulu30.Ingasetshenziswa kukhoyili evusa amadlingozi ngokudlidliza kwe-longitudinal kwe-GMT.
Umhlangano ojwayelekile oyisilinda ongenalutho osetshenziselwa ukumela ikhoyili ye-exciter kanye nomdwebo wayo wokushisa olingana no-T, otholwe esixazululweni se-equation yokushisa, uboniswa kufig.3. Kucatshangwa ukuthi ukugeleza kokushisa kukhoyili ye-excitation kuzimele ku-radial ne-axial directions.Ukushisa kwe-circumferential akunakwa.Kusekethe ngayinye elinganayo T, amatheminali amabili amelela izinga lokushisa elihambisanayo le-elementi, kanti itheminali yesithathu i-T6 imele izinga lokushisa elimaphakathi le-elementi.Ukulahlekelwa kwengxenye ye-P6 kufakwa njengomthombo wephoyinti endaweni yezinga lokushisa elimaphakathi elibalwe “esibalweni sokulahlekelwa ukushisa kwekhoyili yenkundla”.Esimeni sokulingiswa okungama-station, umthamo wokushisa u-C6 unikezwa i-equation.(1) iphinde yengezwe endaweni yokushisa emaphakathi.
Lapho i-cec, ρec ne-Vec imelela ukushisa okuthile, ukuminyana kanye nevolumu yekhoyili evusa amadlingozi, ngokulandelana.
Etafuleni.I-1 ibonisa ukumelana nokushisa kwesekethe ye-thermal elingana ne-T yekhoyili ye-excitation enobude be-lec, i-thermal conductivity λec, irediyasi yangaphandle rec1 kanye nerediyasi yangaphakathi rec2.
Amakhoyili e-exciter kanye namasekhethi awo ashisayo alingana no-T: (a) ngokuvamile ama-elementi ayisilinda angenalutho, (b) amasekhethi ashisayo afana ne-axial kanye ne-radial T-equivalent thermal.
Isekethe elinganayo T iphinde yabonisa ukuthi inembile kweminye imithombo yokushisa eyisilinda13.Njengoba iwumthombo oyinhloko wokushisa we-GMO, induku ye-HMM inokusabalalisa kwezinga lokushisa okungalingani ngenxa yokushisa kwayo okuphansi, ikakhulukazi eduze kwe-eksisi yenduku.Ngokuphambene nalokho, i-radial inhomogeneity ingase inganakwa, njengoba ukushisa kwe-radial kwenduku ye-HMM kuncane kakhulu kunokushisa kwe-radial flux31.
Ukuze umele ngokunembile izinga le-axial discretization yenduku futhi uthole izinga lokushisa eliphakeme kakhulu, induku ye-GMM imelelwa amanodi angu-n ahlukaniswe ngendlela efanayo ku-axial direction, futhi inani lama-node n elimodeliswa induku ye-GMM kufanele libe yinqaba.Inombolo ye-axial thermal contours elinganayo ingu-n T umdwebo 4.
Ukuze unqume inani lamanodi n asetshenziselwa ukumodela ibha ye-GMM, imiphumela ye-FEM iboniswa kufig.5 njengereferensi.Njengoba kuboniswe emkhiwaneni.4, inani lamanodi n lilawulwa kuhlelo olushisayo lwenduku ye-HMM.I-node ngayinye ingalingiswa njengesekhethi elingana no-T.Ukuqhathanisa imiphumela ye-FEM, kusukela ku-Fig. 5 ibonisa ukuthi i-node eyodwa noma ezintathu azikwazi ukukhombisa ngokunembile ukusatshalaliswa kwezinga lokushisa kwenduku ye-HIM (cishe ngo-50 mm ubude) ku-GMO.Uma i-n inyuselwa ku-5, imiphumela yokulingisa ithuthuka kakhulu futhi isondele ku-FEM.Ukwengeza n ngokuqhubekayo kunikeza imiphumela engcono ngezindleko zesikhathi eside sokubala.Ngakho-ke, kulesi sihloko, ama-node angu-5 akhethiwe ukuze afanekisele ibha ye-GMM.
Ngokusekelwe ekuhlaziyeni okuqhathanisayo okwenziwayo, isikimu esishisayo sokushisa se-HMM rod siboniswa kumfanekiso 6. I-T1 ~ T5 izinga lokushisa elijwayelekile lezigaba ezinhlanu (isigaba 1 ~ 5) senduku.I-P1-P5 ngokulandelana imelela amandla okushisa aphelele ezindawo ezihlukahlukene zenduku, okuzoxoxwa ngayo ngokuningiliziwe esahlukweni esilandelayo.I-C1~C5 amandla okushisa ezifunda ezahlukahlukene, angabalwa ngefomula elandelayo
lapho i-crod, i-ρrod ne-Vrod ichaza umthamo wokushisa othize, ukuminyana kanye nevolumu ye-HMM rod.
Kusetshenziswa indlela efanayo neyekhoyili ye-exciter, ukumelana nokudlulisa ukushisa kwenduku ye-HMM ku-Fig. 6 kungabalwa ngokuthi
lapho i-lrod, i-rrod kanye ne-λrod imelela ubude, irediyasi kanye nokusebenza okushisayo kwe-GMM rod, ngokulandelanayo.
Ngokudlidliza kwe-longitudinal GMT efundwe kulesi sihloko, izingxenye ezisele nomoya wangaphakathi kungenziwa imodeli ngokucushwa kwenodi eyodwa.
Lezi zindawo zingathathwa njengeziqukethe isilinda esisodwa noma ngaphezulu.Uxhumano lokushintshanisa ukushisa olwenziwayo engxenyeni eyisilinda kuchazwa umthetho we-Fourier wokuqhuba ukushisa ngokuthi
Lapho u-λnhs kuwukuqhutshwa kwe-thermal kwento, i-lnhs ubude be-axial, i-rnhs1 kanye ne-rnhs2 iyirediya yangaphandle nengaphakathi yesici sokudlulisa ukushisa, ngokulandelanayo.
I-equation (5) isetshenziselwa ukubala ukumelana nokushisa kwe-radial kulezi zindawo, okumelelwa yi-RR4-RR12 kuMfanekiso 7. Ngesikhathi esifanayo, i-Equation (6) isetshenziselwa ukubala ukumelana nokushisa kwe-axial, okumelelwe kusuka ku-RA15 kuya ku-RA33 emfanekisweni. 7.
Umthamo wokushisa wesifunda esisodwa esishisayo se-node yendawo engenhla (okuhlanganisa i-C7-C15 ku-Fig. 7) inganqunywa ngokuthi
lapho u-ρnhs, cnhs, kanye nama-Vnh kuwubude, ukushisa okuthile, kanye nevolumu, ngokulandelana.
Ukudluliswa kokushisa okuguquguqukayo phakathi komoya ongaphakathi kwe-GMT kanye nengaphezulu lekesi nendawo ezungezile kumodelwa ngesiphikisayo esisodwa se-thermal conduction kanje:
lapho u-A eyindawo yokuxhumana futhi u-h kuyi-coefficient yokudlulisa ukushisa.Ithebula 232 ibala amanye ama-h ajwayelekile asetshenziswa ezinhlelweni ezishisayo.NgokweThebula.Ama-coefficients okudlulisa ukushisa angu-2 okumelana nokushisa kwe-RH8-RH10 kanye ne-RH14-RH18, emele ukuguquguquka phakathi kwe-HMF nendawo ezungezile emkhiwaneni.7 zithathwa njengenani elingaguquki elingu-25 W/(m2 K).Ama-coefficient asele okudlulisa ukushisa asethwe alingane no-10 W/(m2 K).
Ngokwenqubo yokudlulisa ukushisa kwangaphakathi eboniswe kuMfanekiso 2, imodeli ephelele yesiguquli se-TETN iboniswa kuMfanekiso 7.
Njengoba kuboniswe emkhiwaneni.7, ukudlidliza kwe-GMT longitudinal kuhlukaniswe amafindo angu-16, amelwe amachashazi abomvu.Amanodi okushisa avezwe kumodeli ahambisana nezinga lokushisa elimaphakathi lezingxenye ezifanele.Ukushisa kwe-ambient T0, izinga lokushisa lenduku ye-GMM T1~T5, izinga lokushisa lekhoyili ye-exciter T6, izinga lokushisa elihlala unomphela likakazibuthe i-T7 ne-T8, izinga lokushisa lejoka T9~T10, izinga lokushisa lekesi T11~T12 ne-T14, izinga lokushisa lomoya wasendlini T13 kanye nezinga lokushisa lenduku ephumayo T15.Ngaphezu kwalokho, i-node ngayinye ixhunywe kumandla okushisa omhlaba ngokusebenzisa i-C1 ~ C15, emele umthamo oshisayo wendawo ngayinye, ngokulandelanayo.I-P1~P6 isamba esiphelele sokushisa kwenduku ye-GMM kanye nekhoyili ye-exciter ngokulandelanayo.Ukwengeza, ukumelana nokushisa okungu-54 kusetshenziselwa ukumela ukumelana ne-convective ne-convective ekudluliseni ukushisa phakathi kwama-node aseduze, abalwe ezigabeni ezedlule.Ithebula 3 libonisa izici ezihlukahlukene ezishisayo zezinto zokuguqula.
Ukulinganisa okunembile kwamavolumu okulahlekelwa nokusabalalisa kwawo kubalulekile ekwenzeni ukulingisa okuthembekile okushisayo.Ukulahlekelwa ukushisa okukhiqizwa i-GMT kungahlukaniswa kube ukulahlekelwa kazibuthe kwe-GMM rod, ukulahlekelwa kwe-Joule kwekhoyili ye-exciter, ukulahlekelwa komshini, nokulahlekelwa okwengeziwe.Ukulahlekelwa okwengeziwe kanye nokulahlekelwa kwemishini okucatshangelwayo kuncane uma kuqhathaniswa futhi kunganganakwa.
Ukumelana nekhoyili ye-ac excitation kuhlanganisa: i-dc resistance Rdc kanye nokumelana nesikhumba ama-Rs.
lapho u-f no-N kungubuningi kanye nenani lokujika kwamandla ashukumisayo.I-lCu kanye ne-rCu yirediyi yangaphakathi nangaphandle yekhoyili, ubude bekhoyili, kanye nerediyasi yentambo kazibuthe yethusi njengoba kuchazwe inombolo yayo ye-AWG (American Wire Gauge).I-ρCu iwukumelana komgogodla wayo.I-µCu amandla kazibuthe womongo wawo.
Inkambu kazibuthe yangempela ngaphakathi kwekhoyili yensimu (solenoid) ayifani nobude benduku.Lo mehluko ubonakala ikakhulukazi ngenxa yokungena okuphansi kazibuthe kwezinduku ze-HMM ne-PM.Kodwa i-longitudinally symmetrical.Ukusatshalaliswa kwendawo kazibuthe kunquma ngokuqondile ukusatshalaliswa kokulahlekelwa kazibuthe kwenduku ye-HMM.Ngakho-ke, ukukhombisa ukusabalalisa kwangempela kokulahlekelwa, induku yezigaba ezintathu, eboniswe kuMfanekiso 8, ithathwa ukuze ilinganiswe.
Ukulahlekelwa kazibuthe kungatholwa ngokulinganisa iluphu ye-hysteresis eguquguqukayo.Ngokusekelwe kungxenyekazi yokuhlola eboniswe kuMfanekiso 11, amalophu amathathu e-hysteresis ashukumisayo akalwa.Ngaphansi kwesimo sokuthi izinga lokushisa le-GMM rod lizinzile lingaphansi kuka-50°C, ugesi we-AC ohlelekayo (Chroma 61512) ushayela ikhoyili yasendle ebangeni elithile, njengoba kubonisiwe kuMfanekiso 8, imvamisa yendima kazibuthe ekhiqizwa ukuhlolwa kwamanje kanye nokuminyana okuguquguqukayo kazibuthe okuwumphumela kubalwa ngokuhlanganisa i-voltage eyenziwe kukhoyili yokungeniswa exhunywe kwintonga ye-GIM.Idatha eluhlaza yalandwa kusukela kusiloga sememori (MR8875-30 ngosuku) futhi yacutshungulwa kusofthiwe ye-MATLAB ukuze kutholwe amaluphu ashukumisayo e-hysteresis aboniswe ku-Fig. 9.
I-hysteresis loop elinganisiwe: (a) isigaba 1/5: Bm = 0.044735 T, (b) isigaba 1/5: fm = 1000 Hz, (c) isigaba 2/4: Bm = 0.05955 T, (d ) isigaba 2/ 4: fm = 1000 Hz, (e) isigaba 3: Bm = 0.07228 T, (f) isigaba 3: fm = 1000 Hz.
Ngokusho kwezincwadi 37, isamba sokulahlekelwa kazibuthe kwe-Pv ngeyunithi ngayinye yevolumu ye-HMM singabalwa kusetshenziswa ifomula elandelayo:
lapho i-ABH iyindawo yokulinganisa ku-BH ijika ku-magnetic field frequency fm elingana ne-excitation current frequency f.
Ngokusekelwe endleleni yokuhlukanisa ukulahlekelwa kwe-Bertotti38, ukulahlekelwa kazibuthe ngeyunithi ngayinye yesisindo Pm ye-GMM rod kungavezwa njengesamba sokulahlekelwa kwe-hysteresis Ph, ukulahlekelwa kwamanje kwe-eddy kanye nokulahlekelwa okumangalisayo Pa (13):
Ngokombono wobunjiniyela38, ukulahlekelwa okumangalisayo kanye nokulahlekelwa kwamanje kwe-eddy kungahlanganiswa kube yitemu eyodwa ebizwa ngokuthi ukulahlekelwa okuphelele kwamanje kwe-eddy.Ngakho, ifomula yokubala ukulahlekelwa ingenziwa lula ngale ndlela elandelayo:
ku-equation.(13)~(14) lapho i-Bm iwubude obukhulu bokuminyana kazibuthe bamandla kazibuthe ajabulisayo.I-kh ne-kc iyisici sokulahlekelwa kwe-hysteresis kanye nenani eliphelele lesici sokulahlekelwa samanje se-eddy.