INDUCTANCE OF A PLUNGER-TYPE ELECTROMAGNET

Transcription

1 NDUCTANCE OF A PUNGER-TYPE EECTROMAGNET Grgor A. CVDJAN, Aln DOAN, Vor CMOV, Al hsn CANAKOGU * Unvrsy of Crov, Ron, * Dlpnr Unvrsy, Khy, Try ps 5, RO- Crov, Tl: +45/4574, E-l : gvdjn@lh.v.ro Asr n h ppr, n prnl nd FEM vrfon of rly ond, nrnl ndn forl for plngr yp gn s prford. A nw, fsr, hod for h llon sng Mhd s ssn nd rondd.. - NTRODUCTON n [] forl for nrnl ndn of plngr-yp gn s ddd, sng h hod of powr pproon of ondry ondons n D onnd rgons. Th proposd forl, whh s no onsdron h or sron, h prs r gps nd h vron n lrg ls of h worng gp, s dffl o pply s of h fnon os z F, z d ;, onnng n propr ngrl. n h ppr, hod for h vlon of hs fnon, sng Mhd, s proposd nd wo vrfons of h forl r prford: sng fn ln hod nd prnl drnons of h ol ndn for lrg rng of h gp vron. Th prnl vls r oprd wh h s of nrnl ndn, lld wh forl gvn n [] nd rnl ndn lld wh fn ln hod Qfld nd f. Fg. Plngr - Typ Mgn.-CACUATON OF F, z Th vls of ws n sng h rondons gvn n []. Th rondons fro [] n lso sd. Th fnon onn n propr ngrl, dffl o ll, n prssd n rs of Bohr ngrls or gnrlzd Frsnl ngrls []: os d ;,, sn d,,

2 For w hv vdnly C,, os sn W wll onsdr lso h oplnry ngrls ; os sn C d ; S d 4 Thy ssfy h qons: C S,, sn os For lrg h followng qons n sfl []: whr P Q M M P P sn os Q Q r s sd h Pohhr syol O O os sn M M 5 7 n n... n 8 Th ov srs r lrnng nd h rnon rror s lss hn h frs ngld r. For, h rror, for + n rs, s lss hn T! For rror lss hn - hr r nogh 7 rs. To vod h llon of propr ngrls w propos o ll h oplnry ngrls 4, sng Mhd, s follows: C S whr C S C, S, C S os d sn d!! Th ngrls n qons r no propr nd n sy lld wh good prson y Mhd. Th vls of h fnon F lld wh 9, nd r gvn n fg.. Usng h sson z z d d o hng h ngron vrl wh n, h fnon F n prssd n rs of h oplnry ngrls 4 F z, z z os z C z os z z, d sn z S z, 9 Th oplnry ngrls hv h followng srs rprsnon []: C S!! Fg.. Th fnon F, z Th fnon F n sy lld lso sng h qons. Rplng n 5 nd 9 w on: F, z os z Q z, 4 z Th ls r, n ordng wh 7 n wrn s

3 M Q z, 5 z For z > n lld wh n sol rror lss hn -, f M = 5. Th vls of Qz, r gvn n fg.. W n s h for lrg z hs r n ngld. n h progr gvn n ppnd of [] hs r s ngld, for z lrgr hn 9. Ths orrsponds o n sol rror sllr hn -4. ; ; 9 Th nrpolon offns n sld followng h rondons []: ; /.8 /.9 /.7 /.8 / for /. / for /. / for /.5 / for / or, for lrgr gps, h rondons []: ; Fg.. Th fnon 5. NTERNA NDUCTANCE Th ndn orrspondng o h gn fl n h wo wndows of h gn fg. ordng o [], n wrn n h for n w G n hs forl h ol ross-son s onsdrd o hv h wndow dnsons:,. Th qvln r gp, sng h noon fro fg. 7 Th gn fld n vrs porons of h gn n pprod nglng h lg fl: w ;... Th offns nd hv h prssons []: Th propr vls rsl fro h qons Th Forr offns r h d 4 4 sn h F sn F,, Th onsn G fro h qon s gvn n fg. fro [] nd n lld, ng rs n h qon:

4 G sn sh d h 4. FEM AND EXPERMENTA VERFCATON 4 For FEM nd prnl vrfon h lrogn shown n fg. nd 4, wh h dnsons n gvn n h n l, ws sd g w R whr g s h or hnss,, r h ol dnsons, w h nr of rns nd R h don rds for rnl ndn llon. Th rlv prly ws onsdrd for ll h porons of h or. n h n l, r gvn h D gn fld nrgy pr lngh W n wo lrl sds of h ol p o dsn R = nd h gn nrgy W n n h wo gn wndows, oh lld y Qfld progr for pprn rrn dnsy of A/,.. ol rrn.8 [A] 5 w n n wo olns h orrspondng rnl nd nrnl ndns n / r gvn, lld wh h forls W W ; n n nd n h ls oln h horl vls lld wh h forl. Usng h rnl ndns drnd wh FEM nd h drnd y FEM nd lld wh qon nrnl ndn, h ol ol ndn ws lld, onsdrng for nrnl ndn h or hnss g nd for rnl ndn h rs of n rn hlf lngh: o o l g g n n l l g g g 7 n h ls l, hs vls r oprd wh prnl d ond for fdng volg U = 5 V, 5 z nd h rrns gvn n h l, onsdrng h ol rssn R =. : U o R 8 Th lrgr dffrn wn h prnl d nd lld ndns for sll r gp n plnd y h lrd shp of h plngr whh s no fl fd, l n fg. nd hs lso T shp nsd of. Th sllr plngr r gvs sllr ndn. Ths plnon s sppord y h good grn of h forl rsls wh h FEM d. o o o o / o [] [A] [] [] [] For gps lrgr hn 5 h dffrns r sllr hn 8 %, whh n onsdrd pl. FEM QFD, FEMM W W n n n [] [J/] [J/] [/] [/] [/] W n osrv n fg. 7 good grn wh h FEM d dffrns lss hn 4.5%. Fg. 4 Th prnl odl

5 Fg. 7. nrnl ndn lld wh ln nd drnd y FEM s Fg. 5. Ernl gn fld for h gp W =. J/, w = 898 A 5 nods, 547 lns 5. DEP PROGRAM A sr-frndly Dlph progr lld PTM. ws l y h ls o-hor, whh drn vry fs h onsn G nd nrnl ndn n sng h forls nd 4 nd gvn n [] lgorh for F fnon llon. Th progr lls lso h vor gn ponl for gvn pons n h wo dons: ol ross-son nd h r gp. Th rsls n sord n fls nd h grphs n p. Fls. For olor n pgs offrd y hs progr r shown n h n svrl fgrs. Fg. nrnl gn fld for h gp w = 898 A, W n =.54 J/ 444 nods, 7 lns Fg. 8. Dlph progr n n

6 n fg. 8 h dnsons of h prnl odl r nrodd. Fg.. Th gn vor ponl vls Fg. 9. Th prr G s fnon of for for ro of wndow dnsons n h fgr ov h onsn G s lld for for shps of h rnglr wndow. Th nd o ll h grphs for G s rond 4 sonds, for opr wh 8 Mz prossor. Th n ns r los nsnnos. - CONCUSONS. Th forl, onsdrng h ol ross-son ql o wndow dnsons, gvs h vls of h nrnl prl ndn of plngr-yp lrogn whh r n good grn wh h vls ond sng FEM hod dffrns lss hn 4.5 %.. For ol gn ndn vlon, wo vls of lnr ndns n onsdrd: nrnl ndn n, whh s lpld y h or hnss g nd h rnl ndn, whh s lpld y h rs of h n rn of h ol lngh 7. ACKNOWEDGEMENT Th hors grflly nowldg profssor vn Yhv fro Thnl Unvrsy of Sof for h hlp n progr F plnon nd sslon. REFERENCES Fg.. Th nrnl ndn n s fnon of h gp Th n n lls h vor gn ponl n h wo dons or wndow nd r gp,.. h gn fl pr dph, wn h zro fl ln A = n fg. nd h sld pon, n [W/].. G. A. Cvdjn l., ndn of plngryp gn, EEE Trns. on Mgns, vol. 4, no. 5, Sp. 998, pp G. A. Cvdjn l., Powr Approon of Bondry Condons, Sond Conf. Eropnn sr ls Mhods Nrqs n Elrogns, yon, 9- Mrs 997, NUMEEC 97, Bn, A. Erdly, ghr Trnsndnl Fnon, vol., M. Grw-ll, N. Y., 95

7 Ths don ws rd wh WnPDF vll hp:// Th nrgsrd vrson of WnPDF s for vlon or non-orl s only.