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Magnetic Levitation

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Title:
Magnetic Levitation
Creator:
Matthew Sodano
Jared Bouldin
Publication Date:

Subjects

Subjects / Keywords:
Magnetic Levitation
Halbach Array
Magnets
Levitation
Eddy Current
Mag Lev

Notes

Abstract:
In the past ten years, magnets and the magnetic fields they create have been part of a ma- jor boost in modern technology. Maglev trains and Eddy braking are two examples of the many applications that use changing magnetic fields to create magnetic levitation or mag- netic braking. Companies like Hendo have produced hoverboards using strong neodymium magnets, utilizing their strong magnetic fields. These magnets are configured in a Halbach array which creates an amplified field on one side of the array and a diminished field on the opposite side. When this array is positioned in a circular pattern and spun, the changing magnetic field produces a lift force that can carry as much as 192 kg. Although the con- struction and application of this array has already been completed, there is currently no theory relating all of the variables part of this hovering machine. Using empirical data, a relationship between all of these variables can be found and then derived from Faraday’s law of induction.
Acquisition:
Collected for SUNY Oswego Institutional Repository by the online self-submittal tool. Submitted by Matthew Sodano.

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Source Institution:
SUNY Oswego Institutional Repository
Holding Location:
SUNY Oswego Institution
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All applicable rights reserved by the source institution and holding location.

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MagneticLevitation JaredBouldin,MatthewSodano December9,2019

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Abstract Inthepasttenyears,magnetsandthemagneticeldstheycreatehavebeenpartofamajorboostinmoderntechnology.MaglevtrainsandEddybrakingaretwoexamplesofthe manyapplicationsthatusechangingmagneticeldstocreatemagneticlevitationormagneticbraking.CompanieslikeHendohaveproducedhoverboardsusingstrongneodymium magnets,utilizingtheirstrongmagneticelds.ThesemagnetsareconguredinaHalbach arraywhichcreatesanampliedeldononesideofthearrayandadiminishedeldonthe oppositeside.Whenthisarrayispositionedinacircularpatternandspun,thechanging magneticeldproducesaliftforcethatcancarryasmuchas192kg.Althoughtheconstructionandapplicationofthisarrayhasalreadybeencompleted,thereiscurrentlyno theoryrelatingallofthevariablespartofthishoveringmachine.Usingempiricaldata,a relationshipbetweenallofthesevariablescanbefoundandthenderivedfromFaraday'slaw ofinduction.

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1 1Introduction Manipulationsofmagneticeldscontinuetobegrowingasapartoftechnologicaladvancementsandhavethepotentialtocreateimportantcivilianapplications.Maglevtrainsare themostrecentadvancementthatuseeddycurrents,causedbychangingmagneticelds,to acceleratetrainsupto375mph[1].Furtherresearchonthesechangingmagneticeldscanbe doneonasmallerscale.Oneapplicationisahoverboard.TheHendohoverboardusesthis ideatocreateamagneticlevitationdevice[2].Thedeviceconsistsoffourmagneticrotors connectedtoapadinwhichapersonorobjectcanstandon.Hoveringoveraconductive surface,whichisnormallycopperoraluminum,thedeviceisessentiallyfrictionlessandcan movewitheaseandlittleexternalforce. Insideoftherotors,themagnetsarearrangedinaHalbacharray[2].Thisisexplainedfurtherinadierentsection.Whentherotorsarespunathighspeeds,thechanging magneticeldcreatesaneddycurrentintheconductivesurface.Theeddycurrentinturn createsanopposingmagneticeld,withanetforcethatisperpendiculartotheconducting surface[3].Hendo'sworkwithmagneticlevitationinspiredthisindependentstudyandour workisbasedontheirpatent.However,wewishtoextendtheinformationknownabout magneticlevitationbyquantifyingtherelationsbetweenthelevitationforce,angularvelocity,distance,power,andthicknessofconductingsurface.Notethatallguresreferenced canbeviewedintheappendix. 2HalbachArray Halbacharraysareusedallthroughoutscienceandaidsgreatlyintheadvancementsof technology.Theyareusedinfreeelectronlasersandparticleaccelerators[4].AHalbach arrayisalsoakeycomponentwhencreatingmagneticlift.Asimple,linearHalbacharray canbeviewedinFigure1.Inthisarray,thenorthisindicatedbyanupwardarrow.When magnetsarealignedinthismanner,therearetwostrengthsofeldsproduced,astrongand

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2 Figure1:AlinerHalbacharraythatshowsthepositioningofmagnetsandthestrongand weakeldproducedbythisarray[3]. weakside[4].Thestrongsideisproducedbytheconstructiveinterferenceofthemagnetic eldswhiletheweaksideisaresultofdestructiveinterference.Theweaksidehasamagnetic eldthatismorethanhalfthatofthestrongsideandcanbegivenbythefollowingequation [2], F x;y = F 0 e ikx e )]TJ/F34 7.9701 Tf 6.587 0 Td [(ky where F 0 isthemagnitudeoftheeldatthesurfaceofthearrayand k isthespatial frequency 2 .Thepullforceisdeterminedbythestrengthoftheoverallmagneticeld. Havingalinearvisionisimportanttoreferencewhenthisarraybecomescircular.Thecircularcongurationofthisarrayallowforeasierrotation,lessairfrictionandanevenstronger eld.ThecirculararraycreatedcanbeseeninFigure2.Thisisjustablueprintthatwas usedasareferencetocreateourownrotorFigure3. Toshowthatthemagneticeldis,infact,strongerandthatourarrayiscorrect, magneticlmwasplacedontopoftheweakandstrongsideoftherotor.Thedarkerspots indicateastrongereldwhilethelighterareasindicateaweakereld.Theseimagescanbe seeninFigure4andFigure5respectively.

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3 Figure2:AcircularHalbacharrayusedasareferencewhencreatingourownmodel[2]. Figure3:TherotordesignedfortestingusingtheHendomodelasareference.

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4 Figure4:AnimageshowingthestrongmagneticeldproducedbythecircularHalbach array.Thedarkerareasindicateastrongmagneticeld. Figure5:AnimageshowingtheweakmagneticeldproducedbythecircularHalbacharray. Thelighterareasindicateaweakmagneticeld.

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5 3Theory NowthatHalbacharraysareunderstood,itisimportanttounderstandwhatishappeningto causethemagneticlift.Whenapermanentmagnetismovednearaconductiveobject,such asametalobject,eddycurrentsareestablishedintheconductiveobject,whichgenerate anopposingmagneticeld.Forexample,whenapermanentmagnetisdroppedthrougha copperpipe,anopposingmagneticeldisgeneratedwhichsignicantlyslowsthemagnetas comparedtoanon-magneticobjectdroppedthroughthepipe.Thiseectisdescribedby theFaradayLenz'slaw. " = )]TJ/F33 11.9552 Tf 10.494 8.087 Td [( t WhereepsilonistheelectromotiveforceV,phiisthemagneticuxT/ m 2 ,andtistime. Asthelawstates,whenthemagneticeldthroughanareaischangedovertimethere willbearesultantpotentialvoltage.Itisthispotentialthatcreatestheeddycurrentsin theconductingsurface.Ampere'slawsdeclareswheneveracurrentismovingitwillgenerate amagneticeld.Thismagneticeldmadebytheeddycurrentsisamirrorimageofthe originalmagneticeld,whichcausesopposition.However,whentheeldsarechangingfast enoughtherewillbeenoughverticalforcetocounteractgravity. 4Construction Inordertobetterunderstandandanalyzethemechanicsofmagneticlevitationwedevised anapparatustoperformexperimentswith.Makingfourequalrotors,similartoHendo, wouldbeexpensive,timewastingandineective.Therefore,onerotorwasmadesothat testingcouldbeanalyzedmoreclearly.Apictureoftheexperimentalsetupmaybeseenin theFigure6.Thesourceofourmagneticeldisaspecicallydesignedrotorwhichcontains 60.25inneodymiumcubemagnetsN52.UsingaGaussmeterwefoundthatthestrongside oftherotorhasamagneticeldof.18Tonitssurface.Throughoutthesemestertherotor

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6 Figure6:Experimentalsetup. wasredesignedandrebuiltmultipletimestomakeitlighter,safer,andeasiertomanipulate. ThenaldesignisshownbelowinanimagefromAutoCADshowingeachcomponentthat composestherotor.The3DprintedPLArotorconsistsoftwelverowsthathavevemagnets ineachrowcreatingacircularHalbach.Sothatthemagnetsdonotipandstayinplace, thereisacoverwhichisblue.Thesetwopartsarescreweddowntogethertoensurethatthe magnetsinsideoftherowsdonotmove.Thethirdpartarethegateswhichcloseothese rows.Thesegatesensurethatthemagnetsdonotshootoutoftheirslotsoncetherotoris spinning.Thegatesarefrictiontted,butalayerofagorillaglueandepoxymixisapplied tothegatestosolidifytheirplacement. Poweredby412V20Ahbatteriesconnectedinseriesa170kvbrushlessDCmotor spinsthe3Dprintedrotor.AnArduinoUnoanda60AelectronicspeedcontrollerESC areusedtovarythespeedatwhichthemotoroperates.Inadditiontospeedcontrolthe Arduinoalsointerpretshallsensordatatooutputrevolutionsperminute.Unfortunately,at thistimethecodeusedtointerpretthehallsensorisnotoperatingcorrectly. WhilemostofthesemesterwasspentdesigningtherotorandtroubleshootingESC problemstherestwasspentcreatingarigthatcouldholdthemotorandrotorstable.The structureoftherigisconstructedoutofunistrutsteelandplywood.Thestructurewas designedtoimmobilizetherotorsothatthecopperplatemaybeadjustedupanddown totesttherelationbetweenheightandmagneticlift.Thecopperplateisonascalewith

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7 5gdivisionstomeasurethemagneticliftforce,underthescaleisascissorjackallowingfor easymanipulationofheight.Wechosea3/8inthick1sq.ft.copperplateasourconducting materialduetoitslowresistanceandhighconductivity.Whileitismoreexpensivethan aluminiumitisalso63%moreconductiveleadingtoagreateropposingmagneticeld[5]. 5Testing Afterwedesignedtheexperimentalsetup,testingofmagneticlevitationanditsvariables began.Thegoalofourtestingistokeepsomevariablesconstantandchangeothers,to createawellformulatedempiricalfunction.Thesevariablesincludethethicknessofthe conductingdevice,angularvelocityofthespinningrotoranddistancebetweentherotor andconductingsurface.Thesechangingvariableswillbetestedinregardstotheforceit producesandgraphedindividuallytoseeitsroleintheoverallmagneticlevitation. Althoughtestinghasnotcommencedyet,wearecondentwehaveastrongplan fortesting;withasolidfoundationandpropermaterialstoworkwith,itwillmaketesting thesechangingvariablessmoothandeliminatesomeerrorsthatpreviouslyhadbeentaken intoaccount.Onceeveryvariableistestedandweknowforcertaintherelationshipsbetweenthesechangingfactorsandtheliftforceproduced,thiswillmakecreatingamagnetic levitationdeviceeasier,morecostecient,andgivesomedirectiontofuturestudentsand engineerswhomaywanttoworkwithmagneticlevitation. 6Conclusion Whilethissemester'sindependentstudyofmagneticlevitationdidnotproducethefunctions wehadhopedfor,wewereabletobuildasolidfoundationforfuturetesting.Alongthe waywewereabletolearninvaluableskillsandtechniquesthatmayhelpuswithanyother researchwemaypursue.Afterfuturetestinghasbeencompletedandanempiricalformula isfound,aformulamaybederivedtoexplaintherelationshipsbetweenmagneticlevitation

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8 andangularvelocity,distance,power,andthicknessofconductingsurface.Throughthis project,wehopetogaingreaterfundingforPhysicsClubandshowourndingsanddata tootherstudentsofSUNYOswegoandthescienticcommunity.

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9 7References 1.Hendo..HE3.0datasheet.doi:http://hover.arxpax.com/wp-content/uploads/2016/09/HE3.0Datasheet-Rev2.pdf 2.Henderson,G..Magneticlevitationofastationaryormovingobject.doi: https://patents.google.com/patent/US20140265690 3.Veritasium..Electromagneticlevitationquadcopter. doi:https://www.youtube.com/watch?v=pCON4zfMzjU 4.Masi,James..OverviewofHalbachmagnetsandtheirapplications.Electrical ManufacturingandCoilWindingExpo2010-2013.134-139. 5.WireandCable,Networking,SecurityandUtilityPowerSolutions.n.d..Retrieved fromhttp://www.anixter.com/.

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10 8Appendix Figure7:ElectronicsthatincludeanArduinoUno,motorcontrollerandcircuitboard Figure8:Representationofeddycurrentsinducedbytheappliedmagneticeld.