Design Aspects of Coils for EDS Levitation Systems

Transcription

1 Design Aspects of Coils fo EDS Levittion Sstes M. Andiollo Diptiento di Ingegnei Elettic Univesità degli Studi di Pdov Pdov Itl T. Betoncelli. Cstelli De D. osti Diptiento di Elettotecnic Politecnico di Milno Milno Itl pesentl t M-Plnc-Institut fü Plspsi Gcing (Gen) tiin.etoncelli@ipp.pg.de ABSTACT: EDS sstes sed on ig fequenc supplied windings e convenient cndidtes in stndstill nd low otion pplictions wee stict ecnicl tolences e not pcticle. In tis ppe siple EDS sste sed on single levittion coil is nled n ipleenttion of nlticl foultions of te levittion foce nd of te veticl levittion stiffness. Suc etodolog cn e effective fo te petic nlsis to investigte te influence of te geoetic sies nd to optiie te sste pefonce ting into ccount te design constints. INTODUCTION In soe industil ppliction gnetic levittion e desile option povided tt it is cieved wit eltivel inepensive pptus using oust contol sste nd wen ecnicl tolences e not too sevee. To suc pupose EDS sstes sed on ig fequenc supplied windings cn e convenient cndidtes especill in stndstill nd low otion pplictions since levittion is independent fo te eltive otion etween te lod nd te ctive o pssive guidew. In its siplest configution n EDS levittion sste is epesented coil fced to n oiontl sl wit ig electicl conductivit σ nd gnetic peeilit μ μ (ig. ) Topson (). Suppling te coil wit n ltenting cuent of eltivel ig fequenc f nd povided tt te conducting plte ticness is lge tn te penettion dept δ/ fμσ te electodnic effect cn e epoduced eplcing te plte itself wit fictitious ige coil plced seticll to te el coil wit espect to te plte sufce (ig. ). Te in dwc of tis ngeent is epesented te siing of te coil suppl sste especill ting into ccount tt ost of te soed powe is epesented te ective coponent. In te vile fequenc suppl sste investigted te utos te ective powe is copensted pllel connected cpcito n llowing to opete ne te nti-esonnce condition. o te ppliction point of view te evesed ngeent levitting seet fied coil could e even oe ttctive povided tt te seet weigt is not ecessive neveteless it cn e nled ectl wit te se ppoc. Te esults nd te epeientl setup descied in tis ppe efes nw to te configution wit levitting coil. conducting sl ige coil el coil igue : Aonoetic view of te coil nd of its io ige (: levittion eigt) el coil conducting sl ige coil igue : Coil sies ( : coss section widt nd eigt : en coil dius).

2 ANALYTICAL OMULATIONS As peliin potesis te plte fced to te coil is ssued to e de of pefectl conducting teils so tt te ige pinciple is ectl pplicle. Mn nlticl nd pseudo-nlticl foultions elted to suc configution cn e etieved in litetue inl concened wit te evlution of coil self nd utul inductnces. Te electodnic effects cn e deived fo suc foultions ting te deivtive of te gnetic eneg wit espect to te displceent vile o te diect integtion of te epession of Loent foce ll ove te coils volue. Neveteless te ipleenttion of tese ppoces could esult fil oneous fo te coputtionl point of view if good ccuc is equied fo wide nge of coils configutions. An effective clcultion pocedue cn e pticull convenient wen te influence of te geoetic sies s to e investigted vi petic nlsis in ode to optiie te sste pefonce ting into ccount te design constints. A sotcut fo te clcultion of te levittion foce cn e otined ppling te vitul wo pinciple ting into ccount tt veticl coil displceent d esults in n opposite displceent d of te ige coil so te eltive displceent is d (ig.). Accoding to tis figue te vition of gnetic eneg due to te infinitesil veticl displceent d cn e otined s twice te diffeence etween te vlues of te sufce integl of te tngentil coponent A () of te gnetic potentil vecto geneted te ige coil on te uppe nd on te lowe fce of te coil i.e.: dw d dj A A d d d () wee J is te cuent densit nd A () is epessed ccoding to efeence fe wit te oigin plced in te cente of te ige coil te volue integl: μ J A ( ) () ( ) ( ζ ) cos cos d d dζ Te evlution of () cn involve te outines fo te clcultion of te well-nown coplete integls of te fist nd of te second ind K nd E. It is lso possile to use epessions sed on te nlticl foultions of te utul inductnce etween tin-wll solenoid nd dis coil Bic & Ael (). It is convenient to dopt pe unit nottion ssuing te levittion eigt s te sis quntit nd denoting te supescipt te pe unit vlues. Te levittion foce cn e teefoe epessed s: 4 J d () wee te function wit diensionless guents: ( ) μ cos d d dζ ( ) ( ζ ) cos (4) doesn t depend on te sste scle ut onl on te sie popotions. Teefoe (4) evidences tt te foce gows wit te powe of fou wit espect to te sste line sie te se cuent densit eing intined ccoding to well-nown lw scle. Te integtion of (4) fist wit espect to ζ nd ten wit espect to ields te foultion: g μ ( ) ( g( 4( )8 ) wit: ( 4( )8 )) d (5) ige coil igue : Appliction of te vitul wo pinciple elted to veticl displceent d to evlute te levittion foce.

3 Π ) ( K E g (6) wee K E nd Π e te coplete elliptic integls of te fist second nd tid ind espectivel. Te vege levittion foce/coil volue tio φ cn e dopted s pefonce inde nd cn e epessed s: s d J φ (7) Teefoe te pefonce ipoves popotionll to te sste scle since φ vies linel wit te se geoetic popotions eing intined. As egds te dnic eviou te veticl stiffness S / is fundentl pete to define te ngul fequenc of te undped oscilltions; ccoding to () (4) nd (5) S cn e otined s: d J S μ (8) wee: μ d (9) wit: K E () It s wot to e tt ccoding to te foultions () (5) (8) nd (9) onl doule nueicl integtion wit espect to te diensionless dil coodintes nd is needed to evlute nd S insted of te doule volue integtion equied te cude ppliction of te pinciple of te eneg vition. PAAMETICAL ANALYSIS Te ipleenttion of te ove pesented foultions llow quic nlsis of te sste pefonces s functions of te geoeticl sies. In pticul te dependence of te pefonce inde φ defined in (7) on te coss section spect tio / ws investigted fo diffeent vlues of te pe unit coil vege dius / te se coss section e eing intined. It cn e ecognied tt fo te function φ ppoces to te finite vlue φ epesented te foce/volue tio of n infinite lengt stigt wit te se coss section nd levittion eigt. It s teefoe convenient to nolie φ wit espect to φ. Te igue 4 llows to identif te optil spect tio of te coil coss fo diffeent vlues of te coil dius / ) / 5.5 ).

4 / igue 4: Nolied vlue of φ s function of / fo diffeent vlues of ). ; ). ; c) It cn e ecognied tt te vition of te coss section e el ffects te optil spect tio nd tt te dius on te cont s sligt influence on tis quntit. 4 APPLICATION TO A TESTING SETUP c) Tle : Coil Petes Sol Desciption Vlue n Nue of tuns 5 Coil ss.8 g C en esistnce.5 Ω Men coil dius 7 Coil coss-section widt 4 Coil coss-section eigt 6 Wit levittion eigt 7 te vege vlue of te levittion foce otined () is out.85 N. Accoding to te dt of Tle te pe unit volue is 8.7. Te epession () s function of nd te se volue nd cuent densit eing intined ws optiised in te Mtetic envionent: 75 configution wee consideed in out 75 s (ig.7). In te optiied configution (ig ) te levittion foce is out.5 N ( 6% incese). An lost pefect geeent wit te esults of edd cuent EM siultions (eltive diffeence less tn -4 ) ws veified fo ot te ctul nd te optiied configutions. An epeientl set-up ws cied out fo peliin fesiilit test nd llowed to cec te odel petes (Andiollo et l. 6). Te test configution includes (igues 5 6 nd Tle ): sque voltge single pse invete wit n open loop voltge nd fequenc contol; n output filte inductnce; cpcito n tuned to otin neesonnce condition wit te coil inductnce. As concens te coil its petes e epoted in Tle. vile fequenc\ voltge convete L s C d ig. 5: Cicuit dig of te suppl sste. levitting coil igue 6: Epeientl coil: ) oce guge ) wie detils ctul configution optiised configution igue 7: Pogess of te optiition pocedue. Tle : Epeientl Set-up Petes Desciption Vlue Invete fequenc nge Invete voltge nge 5 H 4 V Invete ted cuent A Coil s cuent densit 5. A/ ilte Inductnce L s.5 H Bn cpcitnce C d 77 μ (coil is) optiised configution ctul configution igue 8: Configutions of te ctul nd of te optiied coils. 4

5 5 CONCLUSIONS Te foultions epoted in tis ppe llow fst evlution of te pefonce (levittion foce nd veticl stiffness) of n EDS levittion sste sed on induced cuents in conducting plte igfequenc supplied coil. Te elp to identif te optil coil configutions ting into ccount vious design constints nd llowing ele spe of clcultion tie. Tei ectness is confied te copison wit te esults of te EM nlses. EEENCES Topson M.T.. Electodnic gnetic suspension Models scling lws nd epeientl esults IEEE Tns. on Eduction vol. 4 n. August : pp Bic S. & Ael C.. Ipoveent in clcultion of te self- nd utul inductnce of tin-wll solenoids nd dis coils IEEE Tns. on Mgn. vol. 6 n. 4 Jul : pp Andiollo M. Celi S. Cstelli De. Mui M. 6. Contol design spects fo n EDS levittion sste Speed Sposiu Toin (Itl) -6 M 6 N. 44 5