unal f Engineeing Science and Technlg Vl. 6, N. 6 (011) 769-776 Schl f Engineeing, Tal s Univesit PERFORMANCE OPTIMIZATION OF LINEAR INDUCTION MOTOR BY EDDY CURRENT AND FLUX DENSITY DISTRIBUTION ANALYSIS M. S. MANNA 1, S. MARWAA 1, *, A. MARWAA 1 Electical & Instumentatin Engineeing Depatment, Facult f Engineeing, Electnics and Cmmunicatin Engineeing Depatment, Facult f Engineeing, Sant Lngwal Institute f Engineeing & Technlg, Lngwal Punjab, India *Cespnding Auth: mawaha_sanja@ah.c.in Abstact The develpment f electmagnetic devices as machines, tansfmes, heating devices cnfnts the enginees with seveal pblems. F the design f an ptimied gemet and the pedictin f the peatinal behaviu an accuate knwledge f the dependencies f the field quantities inside the magnetic cicuits is necessa. This pape pvides the edd cuent and ce flu densit distibutin analsis in linea inductin mt. Magnetic flu in the ai gap f the linea inductin mt (LIM) is educed t vaius lsses such as end effects, finges, effect, skin effects etc. The finite element based sftwae package COMSOL Multiphsics Inc. USA is used t get the eliable and accuate cmputatinal esults f ptimiatin the pefmance f LIM. The gemetical chaacteistics f LIM ae vaied t find the ptimal pint f thust and minimum flu leakage duing static and dnamic cnditins. Kewds: Linea inductin mt, Finite element methd, Edd cuent, Flu densit distibutin.. 1. Intductin Electmagnetic field analsis f electmechanical devices is usuall pefmed t achieve infmatin abut thei statina and dnamic pefmances. In man applicatins, a tw-dimensinal finite element analsis ables t pedict with sufficient appimatin device pefmances. Unftunatel, sme ce stuc-tues sme behaviu cnditins cannt be simulated b an equivalent D dmain and 769
770 M. S. Manna et al. Nmenclatues A Magnetic vect ptential, Vs/m B Magnetic flu vect, T B, B Magnetic flu densit in, diectin, T E Electic field in -diectin, V/m F Fce, N F n Fce in the nmal diectin, N F Fce in the -ais diectin, N G Gdness fact g Ai gap between pima and secnda stacks, mm Magnetic Intensit, AT/m Magnetic Intensit in -diectin, AT/m I 1 Cuent in pima sheet, A Suface cuent densit, A/m Pima suface cuent densit, A/m Pima vect suface cuent densit, A/m K c Cectin fact k ω Winding fact l Length f mve, mm P Numbe f ples Pima/mve ntatin S Secnda ntatin t Time, s v Velcit vect, m/s w Pima stack width, mm Geek Smbls β Chding fact µ Pemeabilit, N/A µ Abslute pemeabilit, N/A σ Cnductivit, S/m τ Ple pitch, mm ω Numbe f tuns Numbe f pima tuns ω 1 Abbeviatins DOF Degee f Feedm FEM Finite Element Methd LIM Linea Inductin Mt nl a 3D FE analsis pvides and accuate mdel f the electmagnetic pblem. In paticula ne f the main pblems usuall encunteed in the analsis f linea inductin mt is epesented b end effects. The edd cuents induced in unal f Engineeing Science and Technlg Decembe 011, Vl. 6(6)
Pefmance Optimiatin f Linea Inductin Mt b Edd Cuent 771 the cnducting plate ceate a cunte mmf which ppses the passage f the slt leakage flu. Thus the leakage eactance f the linea mt is deceased and me flu is cncentated in ai gap, esulting in an incease f the develped thust. This pape pesents the edd cuent and secnda ce flu densit distibutin f smalle sie LIM.. Linea Inductin Mt Mdel The tw dimensinal finite element analsis mdel f LIM has been designed with fllwing specificatins [1]. The gemetical view is shwn in Fig. 1. Numbe f phases: 3, numbe f ples: 3 Length f pima stack: 40 mm Width f magnet: 14 mm Length f mve: 170 mm eight f mve: 45 mm, eight f pemanent magnet teeth: 4 mm Thickness f back-in: 10 mm Ai gap length: vaied fm 0.5 mm t 3.5 mm Fig. 1. Gemet Oveview f LIM. The analsis f an LIM is caied ut in tems f electmagnetic field equatins. As we ae well awae that the sltted pima stuctue with its winding is b n means an ideal bunda cnditins, even a sufficientl simple ne. Whee, the slutin t the gvening field equatins can be btained. T educe the bunda value pblem the actual sltted stuctue is eplaced with smth suface and the cuent caing windings ae eplaced b fictitius, infinitel thin cuent elements called cuent sheets, having linea cuent densities (A/m). The cuent densit distibutin f the cuent sheet is the same as that f the slt-embedded cnduct cnfiguatins, such that the field in the ai gap emains unchanged. unal f Engineeing Science and Technlg Decembe 011, Vl. 6(6)
77 M. S. Manna et al. unal f Engineeing Science and Technlg Decembe 011, Vl. 6(6) The elatinship between the pima cuent sheet and the esulting ai gap field is given b the ai gap field equatins as given and E E E Ampee s law S ds dl we get Y S g t E µ Y σe g S σ µ In tems f B g t B g B S µ σ µ The gvening equatin which descibes the magnetic vect ptential in a single sided linea inductin mt is given b B v t A ta t σ µ 1 (1) whee σ is an equivalent cnductivit f mve s mateial taking accunt f tansvese edge effect [] and v is the velcit f mve. The cuent densit f the sheet at the pima sufaces is dented b. The cuent sheet distibutin is given b ( ) k t j e ω () is elated t pima cuent which is given b τ ω ω P I k 1 1 3 (3) whee ω 1 is the numbe f tuns, k w is the pima winding fact, τ is the ple pitch and P is the numbe f ples.
Pefmance Optimiatin f Linea Inductin Mt b Edd Cuent 773 And fm abve elatins the Gdness fact culd achieve as ωσµ G (4) gβ Fm Eq. (4) futhe cmputatin f fce acting n machine culd be deived [3] 0 l {( B B ) n n B B } ω F µ dl (5) 0 l {( B B ) n n B B } ω Fn µ dl (6) whee n and n ae the unit nmal diectin vects, ω is the pima stack width. In de t impve accuac, the LIM has been cmputed at diffeent ai gaps and it was bseved that ent-end-effect culd be educed t high etent with change in the ai-gap b keeping the speed f LIM at cnstant value f 36 m/s. 3. Finite Element Analsis Magnetic flu densit and edd cuent densit distibutin f the LIM mdel unde cnsideatin has been cmputed b using FEM based package. Tpe f elements ae used is Lagange linea. The efined mesh shwn in Fig. cnsists f 4644 elements with 356 degee f feedm (DOF). The numbe f bunda elements ae 67 and numbe f vete elements ae 140. Fig.. Meshing f LIM with Adaptive Refinement. 4. Simulatin Results The Dichlet bunda cnditin n LIM mdel has been empled. The suface plt btained f magnetic flu distibutin is shwn in Fig. 3. The magnetic flu densit f secnda ce has been analed alng the mt length duing the velcit f 36 m/s f mt. The ent end the magnetic field is weakened b the ent end effect. The field is builds up gaduall and ises shapl nea the eist end. Figue 4 shws the finge effect cleal with magnetiatin cntu. The finges ae me built up at the cente f mve ce as cmpaed t the bth end sides f LIM. unal f Engineeing Science and Technlg Decembe 011, Vl. 6(6)
774 M. S. Manna et al. Fig. 3. Magnetic Flu Densit Distibutin in LIM. Fig. 4. Magnetisatin Cntus f LIM. The suface cuent densit plt is shwn in Fig. 5, fm which it can be seen that edd cuent ae me when flu cncentatin is stng. On the the hand the leakage eactance f the LIM is deceased and me flu is cncentated int the ai gap esulting in an incease f the develped thust. The Simulatin esults with diffeent ai-gap fm 0.5 mm t 3.5 mm have been cmputed and cmpaed. It is fund that the ptimiatin in pefmance achieved f LIM whee the ai gap is 1 mm between the mve and stat, while the elative pemeabilit is fied in between 1.0345 t 1.5. The mateial ppeties have been kept cnstant pupsel t bseve the pefmance f LIM with gemetical chaacteistics. unal f Engineeing Science and Technlg Decembe 011, Vl. 6(6)
Pefmance Optimiatin f Linea Inductin Mt b Edd Cuent 775 Fig. 5. Suface Cuent Densit at LIM Pats with Diffeent Ai Gaps. 5. Effect f Ai Gap The effect f LIM gemet was analsed b man eseaches [4-11]. F each gemetical change f the LIM, the tth edd lss was calculated b finite element methd and cmpaed b analtical methd [1, 13]. The atis f these tw analtic and cmputed lsses wee temed as cectin fact K c f the given mdel. It has been nticed hee that the cectin fact is a functin f slt pitch, back plate thickness and mst significantl the ai gap between pima and secnda f the LIM as shwn in Fig. 6. Fig. 6. Cectin Fact f Diffeent Gemat Cnditins f LIM. 6. Cnclusins The pefmance f LIM can be impved b vaiatin in paametes like gemet chaacteistics, winding stuctue, mateial ppeties. In this pape the attempt has unal f Engineeing Science and Technlg Decembe 011, Vl. 6(6)
776 M. S. Manna et al. been made t ptimie the pefmance f LIM b vaing the ai gap f LIM, wheeas the paametes can als be va t bing ptimied mdel f LIM. Refeences 1. R, D.; Sauhashi, D.; Yamada, S.; and Iwahaa, M. (000). Fabicatin and develpment f a nvel flu-cncentatin tpe linea inductin mt. IEEE Tansactins f Magnetics, 36(5), 3555-3557.. Manna, M.S.; Mawaha, S.; and Mawaha A (008). Edd cuents analsis f inductin mt b 3D FEM. IEEE Tans. n POWERCON-08, 1-4. 3. Bldea, I.; and Nasa, S.A. (1985). Linea mtin electmagnetic sstems. hn Wile & Sns Inc., New Yk. 4. Manna, M.S.; Mawaha, S.; and Vasudeva, C. (008). Finite element methd as an aid t machine design: the state f at. Pceedings f Natinal Cnfeence n RAEE, C-. 5. Fetche,.; Williams, B.; and Mahmud, M. (005). Ai gap flu finging eductin in inducts using pen-cicuit cppe sceens. IEE pceedings 005. 6. Manna, M.S.; Mawaha, S.; and Mawaha, A. (006). 3D FEM cmputatin and analsis f EM fce f electical tating machines using FEM. IEEE Pceedings f PEDES-06 Intenatinal Cnfeence n Pwe and Electnics, Dives and Eneg Sstems f Industial Gwth. 7. Manna, M.S.; Mawaha, S.; Mawaha, A.; and Vasudeva, C. (009). Twdimensinal quasi-static magnetic field analsis f SLIM using adaptive finite element methd. Intenatinal unal in Recent Tends in Engineeing, (6), 50-5. 8. Manna, M.S.; Mawaha, S.; Mawaha A.; and Vasudeva, C. (009). Analsis f pemanent magnet linea inductin mt (PMLIM) using finite element methd. In Intenatinal Cnfeence n Advances in Recent Technlgies in Cmmunicatin and Cmputing, ARTCOM, 540-54. 9. Rdge, D.; Cles, P.C.; Allen, N.; Lai,.C.; Lenad, P..; and Rbets P. (1997). 3D finite element mdel f a disc inductin machine. Pceedings f IEE- EMD 97, 148-149. 10. Yahiaui, A.; and Buillant, F. (1994). D and 3D numeical cmputatin f electical paametes f an inductin mt. IEEE Tansactins n Magnetics, 30(5), 3690-369. 11. Vasudeva, C.; Mawaha, S.; Mawaha, A.; and Manna, M.S. (010). Ai gap effects n magnetic flu densit f linea inductin mt. Intenatinal unal f Engineeing and Infmatin Technlg, IEIT, (1), 37-40. 1. aiik, A..; and assan,.m. (009). Dnamic mdel f linea inductin mt cnsideing the end effects. Iaq unal f Electical & Electnic Engineeing, 5(1), 38-50. 13. Kuma, A.; Mawaha, S.; Mawaha, A. (010). Mechanical dnamics analsis f PM geneat using h-adaptive efinement. unal f Engineeing Science & Technlg, ESTEC, 5(1), 41-50. unal f Engineeing Science and Technlg Decembe 011, Vl. 6(6)