Special Tool for Investigation and Controlling of Induction Skull Melting Processes

Transcription

1 Intenatonal Sentf Colloquum Modellng fo Savng Resoues Rga, May 7-8, 00 Speal Tool fo Investgaton and Contollng of Induton Skull Meltng oesses I oznak, A ethenkov Abstat Speal tool fo nvestgaton and ontollng of oxdes nduton skull meltng s pesented n the pape It s allows to ontol the poess and eeve some physal melt popetes, ondutvty fo nstane Defnton of the ondutvty s based on nvese poblem soluton Condutvty of the alumnum oxde melt was detemned fo dffeent tempeatue Intoduton Thee ae lots of moden tehnologal poesses of synthess of new oxdes ompounds ae based on the nduton skull meltng (ISM) Combnaton of nduton heatng method and skull meltng tehnque allows to get hghe pue substane [] Synthess of oxdes ompounds s haatezed by hgh melt tempeatue and, usually, oxdaton envonment Absene of elable popetes data of oxde melts at hgh tempeatue and oxdaton envonment do not allow adequately desgn tehnologal equpment fo lqudphase synthess of new substanes One of those popetes s ondutvty whh nfluenes on powe soues dstbuton and ndetly on tempeatue and hydodynam felds n the melt pool Fom the othe sde, montong and ontol system s essental attbute of any moden equpment Hgh tehnologal poess lke ISM eques adaptve ontol system Synthess of the montong and ontol system eques havng mathematal model of ontol objet Contol System and Expemental Data oessng Method Wokng of the adaptve montong and ontol system s based on olleton and poessng of pmay nfomaton about meltng poess Data poessng s ealzed by means of mathematal model n eal tme Values of ontol paametes ae esults of alulaton Advantage of the poposed ontol system s multfunton one The system allows addtonally nvestgatng melt popetes, ondutvty fo nstane Blok dagam of the montong and ontol system of nduton skull meltng s pesented on Fg In geneally, ISM ealzaton eques hgh fequeny and hgh voltage of powe supply Fom the othe hand, numbes of tehnologal poesses ae haatezed of hangng of load paametes that esults to hangng nput mpedane of load ut Theefoe, powe supply should povde hgh output voltage and opeatng stablty fo hangng load paametes n wde ate Vauum tube geneato mostly povdes the equements Thus, paallel sheme of the load ut s onsdeed whh t s typal fo vauum tube geneato 58

2 HF GENERATOR CAACITORS INDUCTION SYSTEM U f U + T me 3 b U U=F( ) COMUTER T me σ me DATA BASE Fg Stutue of the ontol system oeedng fom the theoy of nduton heatng, the onsdeed eletomagnet nduton system s desbed as an equvalent elet sheme [] Assumpton that the eletomagnet system nvolves soues that vay n omplane wth the sne law allows a tanston nto the omplex plane thus smplfyng appeably mathematal despton of the system wthout a onsdeable msalulaton, U, I, I - Fg shows the equvalent elet sheme of the load ut, whee: U apato and nduto voltages; apato and nduto uent espetvely; b, x b esstane and eatane of buses;, x nduto esstane and eatane; с, x с - apato esstane and eatane;, x - edued esstanes and eatane of the melt; 3, x 3 - edued esstanes and eatane of the old uble The poblem s geneally to defne all paametes of the sheme n ode to fnd the values of ontol paametes Expeene shows t s possble pesely to measue values suh as voltages and powe losses n hgh fequeny nduton systems Theefoe moe avalable nput data fo the ontol system an be suh as powe losses n the nduto, uble, voltage at apato o nduto Let see moe ommon and fequently used ase when buses and nduto onneted sequentally n one oolng wate ut In ths ase onsequene of alulaton steps s the next U x I b I U x b x If elet losses n the apato ae negleted, the apato voltage veto wll have the eatve omponent only Then, the apato eatane s defned as: x = / ωc x x 3 3 Fg Equvalent elet sheme of the load ut The powe fato of the nduton system togethe wth buses s alulated as follows: ( b )/ ( U ωc) osϕ =, whee: b - total elet losses n the buses and nduto, - powe n the melt, 3 - elet losses n the uble 59

3 Imagnay omponent of the apato uent: U I x I = / x m U ( ) Induto uent modulus: Fg 3 Equvalent elet sheme of the nduto wth the load I = I / ( m ) os ϕ Induto uent eal omponent: I = I osϕ ( e ) Total esstane of the buses and nduto: b = b / Iи Veto modulus of the nduto voltage s measued The nduto uent veto s deved fom alulaton of equvalent elet sheme paametes Ths enables one to poeed to the equvalent elet sheme of the nduto (Fg 3) and detemne ts nput mpedane In ths ase the nduto esstane and eatane s detemned as: = = U I( e) / I, x U I( m) / I Buses eatane: x b = x x Unfotunately, sum powe of elet losses n the uble and powe n the melt + 3 s measued It takes to know the values of powe n the melt and elet losses n the uble sepaately fo the next step alulaton Sepaatng and 3 s ealzed by means of the mathematal model Thus, edued uble esstane: = I 3 3 / Redued esstane of the melt: / I = Total edued esstane of the melt and uble s defned as: 60

4 U ( m ) b U ( e )b U ( e ) U b = + 3 Resstane of the nduto: = Buses esstane: U ( m ) U U (m ) b = b owe losses n the nduto: ϕ = I I (m ) I ( e ) ϕ I ( m ) Fg 4 Veto dagam of uents and voltages n the nduton system I owe losses n the buses: = b b owe fato of the nduto wthout buses: = / x os ϕ + As a esult of the mathematal alulatons all elements values of the equvalent sheme wee found The values sngle-valued detemne ntegal enegetal haatests of ISM Anyone fom these paametes o thes ombnaton an be used as nput paametes of the ontol system The veto dagam (Fg 4) shows demonstably the phase and ampltudnal elatons between uents and voltages n the nvestgated sheme Mathematal Model In the pape suggest eletomagnet model based on ombned appoah [3, 4] The model s moe avalable fo nvestgaton of nduton systems wth sltted uble Inteo poblem of omputaton of eletomagnet feld n the load s solved by fnte element method (FEM) and exteo poblem s solved by ntegal equaton method (IEM) FEM s used fo alulaton eletomagnet poblem n melt Influene of soues (nduto uent) s takng nto aount by means of ntegal equatons Ths appoah allows to get dstbuted paametes n the nvestgatng system wth a lot of fnte elements and shot tme of alulaton Condutve sltted uble s sees dffult fo mathematal analyss ISM IEM allows easy to alulate the omplated nduton systems wth sltted uble The sltted uble s desbng by pas of one-loop solenods wth antphase uents n the model It allows to smplfy the 3D poblem up to D Usng FEM fo soluton nteo poblem s defned by omplated shape of pool melt 6

5 Aodng to the seonday soues method [5] eletomagnet feld n ondutve egon s alulated usng onduton uents Fedholm's equaton seond knd desbes a dstbuton of eletal feld stength E n ondutng non-magnet egon: + jω σ j E j MjdS + jω S S k k ( M M ) π R E σ E ds = U () Intenal poblem s desbed D dffeental equaton elatve veto magnet potental k l A µ + R A A + R R z R A = jωσ A () Aea ntegal S aounts the nfluene of ondutng pats of the nduton system exept sltted uble, aea ntegal S does the nfluene of the sltted uble Soluton of the equaton system ( - ) s ealzed by blok-teaton method n onfomng to follow algothm Intal dstbuton of ondutve uents s stated Equaton () s solved, wheeupon uent soue ae detemned 3 Bounday ondtons at the sufae of ondutve egon ae detemned 4 Solve nteo poblem, wheeupon seonday uents soues n ondutve egon ae detemned 5 Retun to pont Stop of teatve poess s qualfed by ahevement of dffeene between all dstbuted paametes n the uent and pevous teatons gven value As a esult of the mathematal alulatons all dstbuted and ntegal paametes ae detemned In ase when ondutvty σ of melt s known nput data fo mathematal model an be any one: b, + 3, U o U If ondutvty σ of melt s unknown the nput data should be all of them In ths ase wll solve nvese poblem elatve σ and the esult of alulaton wll and 3 sepaately and value of ondutvty 3 Results and Dsusson Fg 5 Desgn and bas dmensons of the nduton system wth sltted ble Numeal alulatons wee aed out fo detemnaton of eletal ondutvty of melt of alumnum oxde (qualfaton pue ) Expemental data eeved dung ISM wee used n alulatons Sketh of the nduton system wth sltted old uble s shown at Fg 5 Bas dmensons, expemental data and numeal esults ae pesented n Tab Calulaton of nvese poblem was stated n suh a way as to mnmze eo between esults of alulatons and expemental data dependng on the melt ondutvty 6

6 Tab Expemental and alulatons data Bas * T me, f, U + 3,,, 3, σ, dmensons, MHz C kv kw kw kw kw kw (Ohm m) - m Expemental data Calulaton h me =70 me =65 h nd = nd =470 h me =0 me =760 h nd =860 nd = * Bghtness tempeatue (λ=065 µm) The values of the eletal ondutvty of the melt obtaned by ths tehnque ae aveaged values wthn the melt pool volume They ae elated to the sufae tempeatue of the melt T me Auay of the eletal ondutvty value s estmated sepaately fo evey ase Deeasng tempeatue gadent of the melt esults to neasng of the defnton auay of the eletal ondutvty values Note, suggested appoah allows to get of oxdes melt ondutvty n vauum, net and a envonments Refeenes [] V I Alexandov, V V Osko, A M okhoov et al Obtanng of hghe tempeatue mateals by a tehnque of det hgh fequeny meltng n old ontane Mosow J ogess of hemsty Vol XLVII, 978 (In Russan) [] A E Slukhotsky, V S Nemkov, N A avlov et al Induton heatng nstallatons L: Enegozdat, 98 (In Russan) [3] oznak I Mathematal models fo analyss of D and 3D eletomagnet felds n nduton systems fo metals meltng 3 th Assembly of sentsts - St etesbug, SbGETU, 998 (In Russan) [4] Demdovth V, oznak I Combned method of eletomagnet feld alulaton n nduton uble funaes oeedngs of 40 Intenatonal wssenshaftlhes kolloquum, ILMENAU (Gemany), , p37-4 [5] VSNemkov, VBDemdovh Theoy and omputaton of nduton heatng nstallatons L: Enegy, 988 (In Russan) Authos: ethenkov, Ande Eletotehnal Unvesty, of opov Steet St etesbug - Russa Tel (8) , E-mal m@malaxonu hd oznak, Igo Eletotehnal Unvesty, of opov Steet St etesbug - Russa Tel: (8) , E-mal: go@p394spbedu, vpoznak@eltehu 63