EFFECTS OF THE MOTOR ON THE STABILITY OF A SINGLE AXIS CONTROLLED MAGNETIC BEARING

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1 Pag 1249 EFFECTS OF THE MOTOR ON THE STABILITY OF A SINGLE AXIS CONTROLLED MAGNETIC BEARING Fad Ati Camag, camagf@usp.b Oswald Hikawa, hikaw@usp.b Escla Plitécica f Sã Paul Uivsity, EPUSP-PMR, Av. Pf. Mll Mas, 2231, , SP Bazil Isaias da Silva, isaias.silva@uifsp.b Fdal Uivsity f Sã Paul, Dp. f Exact Scics ad Eath, R. Pf. Atu Ridl, 720, , Diadma, SP, Bazil Olad Hm d Mll, ladh@usp.b Jsé Rbt Cads, cads@pa.usp.b Escla Plitécica f Sã Paul Uivsity, EPUSP-PMR, Av. Pf. Mll Mas, 2231, , SP Bazil Abstact. This wk is pat f th dvlpmt f a implatabl Vticula Assist Dvic (VAD) i which th pump t is suspdd by a sigl dg f fdm (1-DOF) magtic suspsi. I d t div d DAV s t, tw bushlss BLDC mt typs, axial ad adial achitctus, hav b dvlpd ad tstd i a magtic baig pttyp with activ ctl ly i 1-DOF f th t, i.., its axial dicti. I such baig achitctu, adial ad agula stability a assud by a cstat ad psitiv magtic stiffss btw tw pais f pmat magts wkig i attacti md ad placd i ach d f th baig s t. Thf, th BLDC mt applid t th baig ca caus t istability maily alg its passiv dictis, i.. axial ad adial, ad als alg its axial dicti,.g. if th axial lctmagtic actuats a vladd by th magtic fcs pducd by th mt. S, this pap psts sm f th bushlss mts dvlpmt stags ad sval xpimtal sults, cductd with th axial ad adial mts achitctus applid t th magtic baig, a als shw which dmstat th viability f th ppsal. Kywds: magtic baig, baiglss mt, bushlss DC mt, magtic suspsi, magtic baig. 1. INTRODUCTION Th Escla Plitécica f Sã Paul Uivsity (EPUSP) ad th Istitut Dat Pazzas f Cadilgy (IDPC) a cductig a jit pjct aimig th dvlpmt f a implatabl Vticula Assist Dvic (VAD). Basd a VAD f xtal us, dvlpd pviusly by th IDPC (Adad t al, 1996), th w VAD will us a magtic baig t suspd th t withut ay mchaical ctact f th t ad th VAD cmpts. With spct t th w VAD, auths alady ptd sults f plimiay studis (Hikawa t al, 2008). Th magtic baig achitctu that will b usd i th VAD ud dvlpmt is f a typ pstd at Silva ad Hikawa (2000) i which, th activ ctl is xcutd ly alg th axial dicti f a t (Fig.1). At ach xtmity f th t, a pmat magt is fixd. Facig ach f ths magts, ath magt is fixd t bas s as t hav a attacti fc btw ach pais f magts which assus adial ad tiltig stability f th baig t. As ach pai f magts wks i attacti md, th t axial dicti is ustabl. S, alg th axial dicti, th t stability is assud by a ctl systm cmpsd by a -ctact ss, a ctll, a amplifi ad tw actuats. I this wk this baig is fd as AMB-EPUSP. This baig is lctd maily bcaus f its simplicity i tms f mchaical cfiguati ad i tms f ctl systm: imptat facts t icas th liability f th baig itdd t b usd i a implatabl VAD. Figu 2 shws pssibl cfiguati f th VAD that adapts th AMB-EPUSP, shw i Fig.1, t th VAD- IDPC. Tw lctmagtic actuats with fmagtic c a placd at th upp ad lw xtmitis f th t. At th tp sufac f th lw actuat a cil is st s as t wk as a pb f a -ctactig iductiv gap ss. At bth xtmitis f th t cylidical a ath (NdFB) pmat magts a fixd. Th attacti fcs btw ths magts ad th fmagtic c cfi th t i a ctal psiti. Th axial psiti f th t is activly ctlld i th sam fashi as dscibd bf. Thus, by applyig th AMB-EPUSP th pblm f th lvitati f th VAD t is big slvd. Nw th pjct facs th pblm f divig th t s as t pump th bld. Csidig aspcts such as liability, fficicy ad small dimsis t aliz a implatabl VAD, th BLDC lctic mt typ atually aiss as th bst sluti f divig th t, istad f th lctic mt typs. Stictly spakig, a bushlss DC (BLDC) mt is lctd du t th sam as a magtic baig is chs, i.., th mt shuld t ctact th t, miimizig pblms f damag t th bld cmpts. Hwv, th magtic fcs that div f th t may itf i th magtic suspsi causig t istability. As dscibd at Silva ad Hikawa (2000), th t is stabl with spct t all dgs f fdm xcptig f its axial psiti. I th AMB-EPUSP, th distac btw magts at th xtmitis f th t must b lag tha th diamt f ths

2 Pag 1250 magts. Othwis th t iclis ad lss its tiltig stability. Thf it is asabl t xpct that th BLDC mt will itf i th magtic suspsi. As a fist stp i th study t ivstigat ths itfc, i this wk, tw typ f BLDC mt is dvlpd ad usd t div a t suspdd by th AMB-EPUSP: axial mt (Fig.3(a)) ad adial mt (Fig.3(b)). Psiti ss NS NS Elctmagts Magts Axial dicti SN SN Bas X Ctll Amplifi Figu 1. Th magtic suspsi AMB-EPUSP Elctmagtic actuats with fmagtic c Bld utlt Bld ilt Cylidical magts Gap ss Figu 2. DAV-IDPC with EPUSP magtic baig Elctmagtic actuats Elctmagtic actuats Stat cils Stat cils (a) Axial mt (b) Radial mt Figu 3. Evaluatd BLDC mts f th DAV-IDPC t Nxt sctis will dscib all stps xcutd, up t w, t allw th fial tsts: (i) dsig, cstucti ad tstig f th axial ad th adial BLDC mts; (ii) dsig, cstucti ad tstig f AMB-EPUSP ad th t t b div

3 Pag 1251 b bth BLDC mts ad (iii) stimat th BLDC mts bhavi usig FEM aalysis. Th fial xpimtal tsts xcuti aimd t idtify hw ach mt assmbl pti itacts with th AMB-EPUSP has t b ccludd yt. 2. BLDC MOTOR DESIGN O dsigig th BLDC mt usd th tsts, a clss cfiguati is adptd. This limiats ay udsid magtic fcs amg th t, th pmat magts ad th stat i c. Th clss BLDC had b usd by Asama t al (2004) t impv his mt balac ad t sav gy, i.., th magtic fcs pducd by th mt d t affct th magtic baigs. This appach has b cbatd by th Oshima (2007) aalysis, pitig that th t tqu was t affctd by th psc, absc, f ay fmagtic matial th t. Th absc f ay fmagtic matial th stat c limiats th cggig tqu whil impvs th mt pw dsity ducig th mt wight (Abulaga Emadi, 2004). A suitabl VAD BLDC mt must b abl t pump 5 lits f bld p miut at 100 mmhg, with th t at 2000 RPM (Asama t al, 2004; Lgd t al, 2008; d B ad Lvy, 2001). T achiv ths valus th mt must pvid a miimum tqu f Nm ad a miimum mchaical pw f 2.8W. Figu 4 shws th spcial shap a ath (NdFB) pmat magt usd i th BLDC mt t, axial ad adial typs. Th t uss 3 pais f this magt whil th clss stat widigs has b dsigd with th phass, ach phas with six cils ad ach cil with 22 tus f AWG 27 cpp wi. Th BLDC mt has b pwd by a cmmcial ctll (PICDEM MC LV, Micchip) usig a sslss algithm. Figu 4. Pmat magt usd th BLDC mt t I d t valuat th BLDC mt mai chaactistics its t was assmbld i a mchaical axis ad cctd t a dyammt. Th axial mt was abl t pvid Nm f maximum tqu at 3072 RPM ad 4.8 W f maximum mchaical pw at 3924 RPM. O th th had th adial mt was capabl t pvid Nm f maximum tqu at 2294 RPM ad 5.3 W f maximum mchaical pw at 4063 RPM. Thf, bth mts achitctus pst th quid VAD mt chaactistics. 3. MAGNETIC SUSPENSION DESIGN As th AMB-EPUSP mai chaactistics a dpdt f th magtic actuat ad f th pmat magts th t, th dsigd magtic suspsi must b aalyzd t bsv what chags ach BLDC mts achitctu causs i th magtic suspsi stability. Figu 5 shws th st-up usd f iitial tstig f th magtic suspsi. H, th t is div by cmpssd ai blw t th t piphy. A xtal cil ad a scillscp a usd t masu th t spd. Oscillscp Spd dtcti cil Elctmagtic actuats Figu 5. St-up f tstig th magtic suspsi.

4 Pag 1252 Th a th lmts that may dictly affct th fficicy f this magtic suspsi (Silva, 2005): (i) th actuat lctmagtic cstat k t (th ati f th cut fuishd t th actuat ad t th fc gatd by th actuat,) ad th actuat magtic cstat k h (th ati f th gap btw th magtic pai ad t th gatd magtic fc,). T impv ths valus th t wight was miimizd t a fial valu f 0.98 N (t impv th axial stiffss) ad th t hight was ducd t 84.6 mm (t impv th agula stiffss). Mv, a gap ss was dsigd i d t maximiz ss accuacy. O th fial assmbl th t has b magtically suspdd with 6.8 mm f ttal gap (upp gap plus lw gap). Th magtic suspsi xpimtal tsts gav th fllwig valus: lctmagtic cstat f 2.2 N/A ad a magtic cstat f 2.5 N/mm. Als, duig th magtic suspsi xpimtal tsts tw maj pblms w idtifid ad hav impactd th tsts with th tw BLDC mts ptis. Fist, a pblm f ubalacd tati was vifid. This ubalacd was t causd by t mass uqual distibuti but by th -uifmity i th magtizati f th magts. I bth magts fixd t th t thi magtizati ct did t cicid with thi gmtic ct. Du t this pblm, th t pstd adial scillatis v at vy lw spds (amplitud scillatis lag tha 2 mm i adial dicti). This pblm was slvd by slctig magts with uifm magtizati. Th scd pblm was dtctd duig tati tsts wh cmpssd ai was blw t th t piphy ad high spd was achd. Wh th tati spd achd spds btw 860 ad 1000 RPM, th t vibatd latally with amplituds f a fw millimts. Dspit ths t latal scillatis, th adial stiffss f th magtic suspsi was sufficit t kp th t stabl ad avidig its cllisi with th baig walls. Hwv, at high spds, a 2000 RPM, th t latal vibatis chagd suddly t agula vibatis ad caus th t t cllid t th baig wall. Ths t dyamic sac pblms bsvd h w simila t th Silva (2005) tst pblm dscipti. T avid ths pblms all tsts with th tw BLDC mt ptis w d with spds t high tha 600 RPM. Whv, this lw spd will t ivalidat th mt tsts. 4. THE BLDC MOTOR FEM ANALYSIS With th bhavi f th magtic suspsi idtifid ad th BLDC mt big patial, bth uits hav b itgatd t valuat th magtic itacti btw thm. Bf stat th xpimtal tsts ad aimig t stimat sm mt chaactistics, ach BLDC mt pti had b aalyzd usig a fiit lmt mthd (FEM) tl. Ths umical aalyss hav b usd t idtify hw fcs th t a affctd wh sm xtal fc chags th t psiti. O a gula VAD, th xtal fc shuld b gatd by th hat batig sm patit mvmt. 4.1 Th Axial BLDC Mt Figu 6 illustats th FEM mdl usd t aalyz th axial BLDC mt achitctu. Usig this simplifid mdl, th fcs actig th t culd b stimatd csidig difft t agl (aud z axis) ad difft widig cuts. Th aalysis is d csidig t spcific displacmt ad valuatig if th widigs iduc ay w fc th t, xcptig tqu. Th gatd fc amplitud ad its dicti a aalyzd t dtmi if it shuld b a pblm t. Fig.7 shws th th typs f magtic itfc that th axial mt may caus th suspdd t: (a) axial displacmt, (b) agula displacmt, ad (c) adial displacmt. Figu 6. FEM aalysis f th axial BLDC mt achitctu.

5 Pag 1253 Figu 7(a) illustats th mvig ffct f axial displacmt th t. Th fc gatd by th axial displacmt had b aalyzd t chck if it cats a psitiv t fdig t. Fig. 8 shws th axial fc iducd th t, whil th t is tatig, f difft valus f gap. Th axial fc cuvs shw that th fc is ivsly pptial t th gap, i.., as small is th t gap as high is th axial fc iducd th t by th axial stat. All fc cuvs smbl a saw tth shap ad has a bas fqucy that is 18 tims (sic th mt is 6 pls tims 3 phass) high tha th t spd. It is imptat t bsv that th magtic baig activ ctl must dictly cmpsat this axial fc. (a) Axial displacmt (b) Tiltig displacmt (c) Radial displacmt Figu 7. Daft f th axial BLDC mt achitctu assmbld t a 1-DOF magtic baig. Rsultat fc i axial dicti [N] is x a Z c f t t lta u s R -0,5 N -1,5 N -2,5 N -3,5 N -4,0 N 0 dg 20 dg 40 dg 60 dg 80 dg 100 dg 120 dg 0,0 N 0-1,0 N -2,0 N -3,0 N 0 agl aud th Z axis Agl f tati [dg] Gap 3.0mm 2.0mm Z axis fc (3mm gap) 2.5mm Z axis fc (2,5mm gap) Z axis fc (2mm gap) 1.0mm Z axis fc (1,5mm gap) Z axis fc (1mm gap) Z axis fc (0,5mm gap) 1.5mm Z axis fc (0,1mm gap) 0.5mm 0.1mm Figu 8. Rsults f th FEM aalyss f th axial fc vsus t agula displacmt ad f sval gaps pducd by th axial BLDC mt achitctu th t. Nw, th FEM aalyss a fcusd hw th axial fc is affctd by difft amut f t tiltig displacmts (Fig.7(b)). Csidig a dfault gap f 2 mm, th maximum tiltig f ±2 dg f th t is csidd. Fig. 9 shws hw th maximum ad miimum valus f th fc iducd th t i axial dicti (saw tth shap as shw i Fig. 8) chag with th t tiltig.. It is bsvd that 0 dg f tiltig, th fc vais fm 1.51 t 0.86 N). Th sam fc vais fm 1.29 t 0.71 N f a t tiltig f 2 dg. As a gal ul, th axial fc vais with th ivs f th tiltig amut, i.., as high is th t tiltig as lw is th axial fc iducd th t by th axial stat. Fially, th FEM aalyss a usd t vify hw th displacmt f th t i th adial dicti affcts th axial fc th t. Th aalyss idicatd that this ffct is t sigificat, at last f adial displacmts f ±2 mm.

6 Pag 1254 Aft aalyzig th ffcts f a vaity f t displacmts th axial fc, th tqu gatd by th axial mt is als aalyzd by FEM. Fig. 10 shws a family f tqu cuvs csidig difft widig cut valus fm 0.5 A t 2 A. As high is th cut as high is th tqu. Fig. 10 als shws xampl f th axial fcs th t t illustat thi latiship with th mt tqu,.g., th tqu achs a maximum valu wh th axial fc achs 50% f its pak valu. Rsultat fc i Z dicti [N] ,0 dg -1,5 dg -1,0 dg -0,5 dg 0,0 dg is x a Z c f t t lta u s l ia x A Maximum fc Z Avag fc Z Miimum fc Z Miimum Avag iclliati icliati [dg] Maximum Figu 9. FEM aalysis f th agula displacmt th axial BLDC mt 0,00 N -0,20 N -0,40 N -0,60 N -0,80 N -1,00 N -1,20 N -1,40 N -1,60 N gaus 0,000 Nm 60 gaus 120 gaus 180 gaus 240 gaus 300 gaus 360 gaus 0,0 N A 1.0A Axial fc (2A) Tqu [N.m] -0,005 Nm -0,010 Nm 0.01 t u q T -0,015 Nm -0,5 N -1,0 N ,5 N t c f is x a Z Axial fc [N] Tqu (0,5 A) Tqu (1 A) Tqu (1,5 A) Tqu (2 A) Z axis fc (2 A) -0,020 Nm A 2.0A -2,0 N ,025 Nm 0 agl aud th Z axis 180 Agl f tati [dg] -2,5 N 360 Figu 10. FEM aalyss f th tqu th axial BLDC mt 4.2 Th Radial BLDC Mt Figu 11 illustats th FEM mdl usd i th aalyss f th adial BLDC mt. Usig this simplifid mdl, th fcs actig th t ca b stimatd csidig difft tati agl ad difft widig cuts. Simila t th aalyss ccig axial mt, shw bf, th aalyss ccig adial mt is cductd csidig t spcific displacmt ad valuatig if th widigs iduc ay w fc t, xcptig tqu. Th gatd fc amplitud ad dicti was aalyzd t dtmi if it shuld b a pblm t. Sam displacmts shw i Fig.7 a csidd h. Th fist FEM aalyss csidd ffcts f th axial displacmts f th t (Fig.7(a)) th axial fc xtd by th stat th t. Axial displacmts i a ag f ±2 mm a csidd i th aalyss. Th scd aalysis csidd ffcts f tiltig displacmts f th t (Fig.7(b)) i a ag f ±2 dg, th axial fc. Fially, th thid aalysis csidd th ffct f adial displacmts f th t (Fig.7(c)) i a ag f ±2 mm th axial fc.

7 Pag 1255 Figu 11. FEM aalysis f th adial BLDC mt pti I ay f th abv aalysis, sigificat ffct f th displacmt th axial fc was bsvd. Ths sults diff fm ths aalytical sults btaid i th axial mt. All ffts gatd i th axial dicti must b cmpsatd by th AMB-EPUSP ctl systm. Thf, th absc f ifluc f th t displacmts th axial fc maks th adial mt m favabl t b usd with th AMB-EPUSP. Bsids th ifluc f t displacmts th axial fc, th tqu gatd by th adial mt was als aalyzd. Fig.12 shws a family f tqu cuvs csidig difft cut valus i th cils, fm 0.5 A t 2 A. As high is th cut, th high is th tqu. As i th axial mt, th tqu cuv scillats with a fqucy 18 tims (sic th mt has 6 pls ad div by 3 phass) high tha th t spd. Hwv ths scillatis d t imps limitatis t th us f th AMB-EPUSP. 0,000 Nm dg 60 dg 120 dg 180 dg 240 dg 300 dg 360 dg -0,005 Nm 0.5A Tqu [N.m] -0,010 Nm 0.01 t u q T -0,015 Nm -0,020 Nm A 1.5A Tqu (0,5A) Tqu (1A) Tqu (1,5A) Tqu (2A) -0,025 Nm 2.0A -0,030 Nm 0 agl aud th Z axis Agl f tati [dg] Figu 12. FEM aalyss f th tqu th adial BLDC mt 4.3 FEM Aalysis Cclusi Th FEM aalyss idicatd that th adial BLDC mt as th pfabl chic t div th VAD with AMB- EPUSP, bcaus th magtic suspsi ds t d t cmpsat axial fcs iducd t th t by th mt stat. All th fcs iducd th t scillat ud a bas fqucy 18 tims (sic th mt is 6 pls tims 3 phass) high tha th t spd. Ths fc scillati shuld b valuat th xpimtal tsts phas t dtmi ay ifluc th magtic suspsi stability.

8 Pag EXPERIMENTAL TEST Du t th t dyamic pblms dtctd th magtic suspsi, all plad xpimts with th BLDC mt ptis had t b chagd. Th igial dsig was basd sslss ad quid at last 2000 RPM t b bcm maagabl, as fft had b spt t impv th ctll sftwa. T pat at a lw spd, th BLDC mt ctll fimwa has b chagd t acclat fm 0 t 600 RPM i 20 scds bf shutdw. Oly th plimiay tst sults hav b disclsu i this wk. Figu 13(a) shws th xpimtal st-up f tsts with th axial BLDC mt. Th tsts hav cfimd th FEM aalyss, as th ctll has t cmpsat th axial fcs iducd by th mt. Fig.13(b) shws hw th cut th lctmagtic actuats icass fm 0.02 t 0.8A whil th mt spd chags fm 0 t 600 RPM. AMB- EPUSP Axial mt (a) St-up Cut 0.8A Axial psiti 0 RPM 600 RPM (b) Cut i th actuat Figu 13. Tstig th BLDC axial mt pti: (a) tst stad ad (b) basic tst sult Figu 14(a) shws th xpimtal st-up f tsts with adial BLDC mt. Th tsts hav cfimd th FEM aalyss, as th ctll ds t d t cmpsat ay axial fcs iducd by th mt. As shw i Fig.14(b), usig th adial mt, th cut i th lctmagtic actuat f th AMB-EPUSP v dcass, fm 0.2 t 0.06A whil th mt spd chags fm 0 t 600 RPM.

9 Pag 1257 AMB- EPUSP Radial mt (a) St-up Cut 0.2A -0.06A Axial psiti 0 RPM 600 RPM (b) Cut i th actuat Figu14. Tstig th BLDC adial mt pti 6. CONCLUSIONS Tabl 1 shws a summay f th BLDC mt ptis chaactistics, basd th plimiay tsts, wh th bst chaactistics a highlightd. Th FEM aalyss cbat th cmmdati f th adial BLDC mt pti as th bst chic t div th VAD with AMB-EPUSP magtic suspsi, bcaus it magtic suspsi ds t d t cmpsat ay axial fcs gatd by th mt. Hwv, as shw i Fig. 3, th adial BLDC mt assmblig shuld caus sm mchaical itfc with th VAD utlt, which may qui a m cmplx VAD dsig. Tabl 1. Chaactistics f th AMB-EPUSP magtic suspsi vsus BLDC mt pti Chaactistics Axial pti Radial pti Widigs Lss cpp M cpp Widigs m Small Nt citical Tqu Gd Btt Axial fcs Citical Nt lvat Radial fcs Nt lvat Nt lvat Gap Th axial fc chags th gap N pblm Chag mt gap Easy Rquis mt dsig Ilt itfc N mchaical itfc N mchaical itfc Outlt itfc N mchaical itfc Ys Suspsi affctd Ys N Suspsi ifluc Th gap chags icass with th t spd Miimal ifluc PID Ctll May qui dsig Satisfacty Bst chic N Ys

10 Pag 1258 Th iitial tsts cfim that th axial fc, gatd by th axial BLDC mt pti, iducs a stg istability th AMB-EPUSP magtic suspsi, dmadig high cut t ctl th t psiti. Th plimiay data idicat th cut ctll dsig will t b abl t guaat th magtic baig stability with axial mt high vlcitis, but futu tsts will cfim it t. O ay cas, additial study is cmmd t valuat th t dyamic istability f th AMB-EPUSP magtic suspsi with th t suudd by bld, sic th liquid vimt shuld absb th scillati gy (Vac t al, 2010) ad miimiz th sticti du t th magtic suspsi istability fqucis blw 5000 RPM. 7. ACKNOWLEDGEMENTS This wk civd fiacial suppts fm Fudaçã d Ampa à Psquisa d Estad d Sã Paul, FAPESP (Bazil), pcss umb 2006/ REFERENCES Abulaga, A.A. ad Emadi, A.. Dsig f high pfmac lia bushlss DC mt with ilss c. Th 4th Itatial Pw Elctics ad Mti Ctl Cfc, IEEE, Vlum 2, , Adad, A., Biscgli, J., Dikhuys, J., Susa, J.E., Ohashi, Y., Hmmigs, S., Gluck, J., Kawahit, K. ad Ns, Y. (1996), Chaactistics f a Bld Pump Cmbiig th Ctifugal ad Axial Pumpig Picipls: Th Spial Pump. Atificial Ogas, Vl.20(6), Asama, J., Fuka, T., Chiba, A., Rahma, A. ad Oiwa, T.. A w dsig f a Cmpact Ctifugal Bld Pump with a Magtically Lvitatd. ASAIO Jual, vl. 50, 6, p, B, R.M. ad Lvy, M.N.. Th Cadiac Pump. Cadivascula Physilgy, Cap.3, Msby Ic., 8a diçã, 68-79p, Challa, S.K.. Cmpaativ Study f Axial Flux Pmat Magt Bushlss DC Mt Opatig with th Widig Cctd i Sigl-Phas ad Tw-Phas Systm. 162p. Ts (Mstad) Agicultual ad Mchaical Cllg, Luisiaa Stat Uivsity, Luisiaa, Hikawa, O., Adad, A.J.P; Silva, I. ad Bck, E.G.P.. Magtic Suspsi f th f a Vticula Assist Dvic f Mixd Flw Typ. Atificial Ogas, Vl.32(4), p, Lgd, D., Atus, P., Bck, E., Adad, A., Biscgli, J. ad Otiz, J.. Cmputatial Fluid Dyamics Ivstigati f a Ctifugal Bld Pump. Atificial Ogas, Vl.32(4), p, Oshima, M.. Aalyss f Rtatial Tqu ad Suspsi Fc i a Pmat Magt Sychus Baiglss Mt with Sht-pitch Widig. Pw Egiig Scity Gal Mtig, IEEE, 7p, Silva, I. ad Hikawa, O.. A 1-DOF Ctlld Attacti Typ Magtic Baig, IEEE Tasacti Idusty Applicatis, Vl.36 (4), 1138, Silva, I.. Macais Magétics Híbids d tip ataçã cm Ctl Uiaxial p. Ts (Dutad) Escla Plitécica, Uivsidad d Sã Paul, Sã Paul, Vac, J., Zida, F. ad Muphy, B.. Machiy Vibati ad dyamics. 1.d. Jh Wily & Ss, Ic p 9. RESPONSIBILITY NOTICE Th auths a th ly spsibl f th pitd matial icludd i this pap.