floating.windmill.x

The ��� axle and its Application to a FloatingWindmill

SanzaKazadi,Chan-HeeKoh, Kevin Kim, Kyle Jung,Brian Kim, Hubert WangJisanResearchInstitute515 S. Palm Ave., #3

Alhambra, CA 91803, [email protected]

Abstract—We describe and analyze a magnetic bearing builtusing a permanent magnet assembly. The magnetic bearingcomprisesa conical female magnet assemblyand a rotationallysymmetric identically polarized male piece.The opposition of thetwo parts producesa force between them which tends to holdthem apart and aligned along an axis of symmetry. We describethe bearing and its usein generatingan ��� axle,or an axle havinga friction of some ���� . Finally, we integrate this ��� axle into awindmill design in which a single point of contact exists on themain axle.

Keyword-floating windmill; magneticlevitation; -axle

I . INTRODUCTION

The most important reasonthat machinery breaksdown isthe continual rubbing or rolling contactof the various partsthat make up the machine. Most machinescontainparts thatare coupled togetherusing a variety of mechanisms whichallow partsto move over oneanother. Therearethousands ofvarietiesof mechanisms for allowing the coupled motion ofparts,eachof which is designedto limit movement,vibration,friction, or othermany motion-relatedproperties.Despitethemyriad of inventionsdesigned to assistin the motion of onepart over another, all fall short of providing one importantservice- removing all friction betweenmoving partsin a waythat does not require the expenditurepower.

Thevalueof sucha mechanismcannotbeoverstated.Thereare a number of pressureand liquid-based systemswhichsupport machinery, making sure that partsdo not comeintocontact[2], [8], [15], [17]. An example of this systemis therolling spherefountain, in which a marble ball rolls on aflow of waterwith a negligible amount of friction. The mainlimitation with this systemis that it requiresa constantflow ofwaterandenergy. As a result,suchsystemsdo not find theirway into mostcomplex machinery.

Magnetic bearing systemswhich are powered magneticsystemsthat hold axles in place with magneticfields, alsoallow machinery to run without contact[6], [9], [13], [14],[16]. However, such systemsare power intensive, and donot easily find their way into the majority of machinery,particularly those machines involved in the generation ofpower. This mechanism may be used in certain machineswhere the vast expenditure of power is permissiblebut theplacement of frictionlessaxlesis necessary.

This paperdiscussesa new unpowered technology whichmay be usedto reducefriction. The technology allows two

parts of a systemto be held apart and aligned by an arrayof permanentmagnets. This arrangementessentiallycreatesfrictionless joints which then can be usedothersystemsthathave coupled moving parts.When applied to a vertical axlewind turbine (VAWT), this magnetic technology enablestheaxle to have only one point of contact(the point where theaxle touchesanother part of the machine) on oneendandthemagnetic ball andsocket on the other.

The remainder of the paper discussesthe magneticballandsocket alongwith its various functions.Section2 reviewsthecurrent windmills with their advantagesanddisadvantagesto determinewhich is best suited to the magnetic ball andsocket.Section3 introducesthebasicmagnetic ball andsockettechnology. Section4 describesthe process of integrating theaforementioned magnetic ball and socket to the windmill.Section5 offers somediscussionandconcluding remarks.

I I . REVIEW OF STANDARD WINDMILL DESIGN

Thereare many differentwindmills that are in use today.Thesewindmills range from oneswith horizontal axis bladeson modern wind turbinesto oneswith vertical axes.Althoughthe horizontal axle wind turbine (HAWT) is more common,we will be focusing mainly on the vertical axeswindmills orvertical axis wind turbines (VAWT), which are divided intothreeclasses:SavoniusWind Turbine(SWT), Darrieus WindTurbine (DWT), and the giromill [3], [5], [7]. The SavoniusWindmill is usuallycharacterizedby theSshapedrotorviewedfrom the top. The Darrieus Windmill is designed in such away that the air foils are symmetrical and have zero riggingangles;that is, the anglethat the aerofoils are set relative tothe structureon which they are mounted. The giromill is aversion of the DWT.

A. Savonius Wind Turbine

Savoniuswindmills arecharacterized by the shapeof theirblades.The initial designof the Savonius windmill derivesfrom cutting a circular cylinder along the central plane andmoving the semicirclesalongthe cutting plane[10]. This de-sign,however, hasevolvedandbeenmanipulatedinto variousforms. Thewindmill is a drag-typedevice; theangleof attackis relatively high and the rotor usesthe drag to run itself,despitethe fact that the dragreducesits efficiency.

Figure 2.1: A sideview of the Savoniuswind turbine.

The Savoniuswind turbine:

� is relatively easyto maintainbecausethe moving partsare built closeto the ground and also becauseit is lessexpensive thanthe HAWT;� hasthe bladesthat arevertical and therefore areable tocatchthewind at any horizontalangle,stultifying theyawmechanism (the mechanism that allows the windmill toturn to the wind) ;� usually hasa lower tip-speedratio and is therefore lesslikely to breakat high wind speeds.

Savonius wind turbines generally are built on a vertical axisutilizing a bearing systemconsistingof at leasttwo bearingas-sembliesat thebottom andtop of theturbine. Theinactivationof eitheroneof thesebearings, eitherfrom mechanical failureor for some other reason,requires that the central axis bedisassembledand the bearing assemblyreplaced. The costofsucha replacement canbe in the tensof thousands of dollars.

B. Darrieus Wind Turbine

The Darrieus rotor is a lift device, characterizedby curvedbladeswith an air-foil crosssection[12]. The rotor on thisdevice is shapedin sucha way that the windmill runswith apressuredifference betweenthe two sidesof the blade.TheDarrieuswind turbine generally hasthe samestructureastheSavonius wind turbine (SWT) in terms of the ball bearingplacement andthe generator location.

This wind turbine canattainhigh speedsby reducing dragdueto its rotorshape(it essentiallychops theair asit spinsandhasvery little air resistance),which increasesthe possibilityof it wearingdown. The ball bearings have a high possibilityof weardueto metalfatigue,thegearboxcanfail dueto wear,andhigh tip-speed ratio (TSR) canrender the windmill itselfunstable.Theserotors have a relatively low starting torqueand have high power output every given rotor weight. Thesewindmills have a ratherhigh efficiency of about 35% [1], buttheir reliability is low as the TSR tendsto be very high: thehigher the TSR, the lower the reliability.

Figure 2.2: A Darrieuswind turbineviwed from the top down. The axlein the centeris orientedperpendicularto the ground.

Thesewindmills have various advantages:1) The bladeson the DWT are able to attain very high

speedsbecauseof their shape.2) Thewindmill canspin in onedirectionregardlessof the

direction of the wind.3) High TSRmakesit a suitablemechanism for generating

power.4) Thesewindmills have a high airfoil pitch angle(angle

of attack),improving theaerodynamicswhile decreasingdrag.

The Darrieus windmill alsohasits disadvantages:1) It hasa low reliability becauseof the high TSR andthe

high torque ripple (the amount of torque measuredbysubtracting the minimum torqueduring one revolutionfrom the maximum torquefrom thesamemotor revolu-tion) it produces.

2) The windmill is unstabledueto its speed.3) Some windmills usually need starters because some

Darrieus windmills arenot self starting.These windmills each usually have two ball bearings anda generator. Again, the ball bearings and the gears in thegenerator are the numerouspoints of failure that causemanyproblems.The high speedsthat the Darrieuswindmills attainonly quicken the wear and metal fatigue on the machinery[11].

Thegiromill is anothertypeof DWT that,insteadof curvedbladesfrom top to bottom, hasstraightbladesperpendicularto the ground. The windmill is orientedin sucha way that itlooks like the letter “H” when at a standstill.The operatingmechanism is about the sameas the DWT but the giromilltendsto bemore stableasthe“egg-beater”stylebladescreatemoretorqueripple thanthe straightblades.

C. Conventional Wind Turbines

The conventional windmills are forms of the HAWT andhave rotors that only run when the wind is blown on them[4]. Consequently the wholewindmill mustbe turnedto meetthe wind for it to function: modern yaw devicestypically usesensorsto turn the windmill to the wind. Thesewindmillshave lift basedrotors that, like the DWT, run as a result ofa differencein pressureon both sidesof the blades.Thesetypesof windmills aregenerally usedto generate power. Thesewindmills have their advantages:

1) The bladesare to the side of the windmill’s centerofgravity, making it stable.

2) The towerscanbe tall dueto its stability.3) Most of thesewindmills areself-starting4) They have an efficient power output.

Theseconventional wind turbines also have their disadvan-tages:

1) Thesewindmills have difficulty operating nearground.2) They have trouble functioning in turbulent winds be-

causethe yaw device andbladebearingrequiresmoothwind flows.

3) Their massiveness makes them both cumbersomeandcostly to maintain(transportation and installationmakeup morethan20% of the equipmentcost.

Figure 2.3: A conventionalwind turbine.

Thesewindmills have many points of failure such that themalfunction of any onepoint canrenderthe machine useless.Conventional wind turbineshave an axle that is connectedtothe bladeson one end and to the gearbox of the generatoron the other. The ball bearingholding the axle is one pointof failure and the gearboxes are another. The yaw device iscomprised of a gearbox run by a motor, making it anotherpoint of failure.

D. CommonProblems

The main weaknessof the wind turbines discussedis themaintenancenecessaryandthe wearcausedby certainpointsof failures (i.e. ball bearing assemblies,gearboxes, etc.). Incurrent wind turbines, replacingthesepoints of failures canbecome very expensive andrender the turbine inefficient. Forexample, the ball bearing assemblyreplacement in a windturbine can cost up to $10,000[18] because of the needofcranesandcrews. This paper will introduce a new technologyand discussa way to remedy thesepoints of failures andhopefully drasticallyreducethe costof repairs whenthey arenecessary.

I I I . THE BALL AND SOCKET

Thestaticmagneticball andsocket is comprisedof adistinctmale and a female part. When these parts are combined,they exert magnetic forces on each other which simulatethe mechanicsof a conventional ball and socket design. Thefemalesupport in this designis a conewith a cavity locatedwithin theinterior of thecircularbase.Lining thecavity of the

femalesupport aremagnetsslottedinto a number of groovesthatareevenly distributedin a circle on theinterior wall of theconical cavity. Thesearesetat a uniform angleto the axis ofsymmetry about thecone’s axisof symmetry, parallelwith theinterior wall. Rotationalsymmetryis achieved from the evenplacement of thesemagnets,which allows thedevice to rotatecontinuously without change to either the field of objectsorthe resultingvectorfields. In addition, the magnetic polesarealignedandconsequently producea stable,even force that isusedto createtherotationally invariant ”socket” magneticfieldwhich the femalesupport simulates.

A magnet or a setof magnets canbeusedto createthemalesupport, which is placedon thebaseof thestructureandwithinthe femalecavity. Thesemagnets are comprised of the samematerial as the magnets locatedwithin the female support.Regardlessof the number of magnetsused,the malesupportmust have a singular pole facing outwards, with repulsiveforces of equal size formed in a spherical radius aroundthe male support. These repulsive forces define the ”ball”magnetic field usedin this device.

The staticmagneticball andsocket is formed by centeringthefemalesupport directlyabove themalesupport andparallelto the baseof the device. The magnetic forces mentionedpreviously in both the male and female supports align andrepeleachother, thusproducingthe levitation required in thisparticular design.The designis illustratedin Figure3.1.

Figure 3.1: Theseare two examplemagneticball andsocket assemblies.Theconicalregion containsa magnetassemblywhich providesa rotation-ally invariant pseudoconical magneticcavity. The basemagnetcreatesatoroidal magnetic“ball” which fits “into” the magneticsocket.

Thereare numerous benefitsthat arisefrom the useof mag-netic forces in the creationof the static magneticball andsocket, themainbenefitinvolving thesuspensionof thefemalesupport above the malesupport. Becausethis designpreventscontact betweenthe two supports, the suspensioneliminatesfriction. The absenceof any discernible friction prevents theloss of energy releasedas heat while also mitigating therequirement for cooling elementsthat would otherwise berequired for the heatgeneratedthrough this friction. The two

repulsive forcesalsocreatea stableposition,which allows forthe horizontal stabilizationof the device with respectto theground without lossof rotationalsymmetry.

Figure3.2: Thisfigureillustratestwo instantiationsof the“ball andsocket”assembly. In each one, bar magnetsoriented at �� �� from vertical arearrangedin a conical array at ����� intervals. The juxtaposition of thisconewith the “ball” configurationproducesa restorative force that is bothvertical andhorizontal.

Figure 3.2 illustrates two slightly different conical regionsin which ten bar magnets orientedat ����� from vertical areevenly placedaroundthe conical region. DiagramA hasbarmagnetswith dimensions of ����������� �����������!�"� orientedarounda cylindrical basemagent of diameter ��� and width �#� ��� .DiagramB hasslightly smallerdimensions, with eachmagneton the female support $&%"'��(�)$&%"'��(�*$+� orientedaroundamale supporting magnetof diameter $�� and width $&%,'-� .Themagnetic field of eachbar magnet is oriented perpendicularlyto one pair of sides.The resulting conical arrangementhasa rotational symmetrywith respectto .�/�01� where 0 is aninteger.

For

ce b

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Space Between Magnets (cm)3.0 3.4 3.8 4.2 4.6 5.0 5.4 5.8 6.2 6.6

4

5

6

7

8

9

10

11

12

Figure 3.3: This illustratesthe force betweenthemagneticball andsocketpiecesasa function of distancebetweenthem.The force increasesasthedistanceincreasesuntil it reachesa maximumanddecreases.

Figure3.3illustratestheforcebetweenthetwo asa function ofthedistancebetweenthem.Notably, the force increasesasthetwo partsapproachoneanother. However, the repulsive forverapidly disappearsif the two piecescome too close to one

another due to an attractingnode in the centerof the cone.It is likely that this node would not exist in a true conicalmagnetic field. Useof this technology would thereby requirean application that did not produce transientforces greaterthanthe maximum, thereby causingthe two partsto collapseinto oneanother.

Magnitude of Misalignment from the center (cm)

For

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27.0 27.2 27.4 27.6 27.8 28.0 28.2

2.2

2.4

2.6

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3.2

3.4

3.6

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Figure 3.4: This figure illustratesthe transverseforce asa function of theangulardeflectionof the socket. All anglesare in radiansand all forcesare in Newtons.

Figure3.4illustratesthetransverseforcebetweenthetwo partsasa function of horizontaldisplacement. This tendsto increaseas the two parts approach one another. Applications wouldtherefore be quite stableas the forces involved increaseandpush the two sidesof the ball and socket apart as they aremoved closerto oneanother. This meansthat vibrations andtransientforceswould not be in danger of overpowering thedevice andcausinga catastrophic failure.

The ball and socket provides soft stabilizationboth alongtheaxesof the two magnetic fieldsandperpendicular to it. Asa result,it hasa wide varietyof potential in thestabilizationofboth stationaryandmoving pieces.Becauseof the scalabilityof magnetic assemblies,we expect that the designdescribedabove could be scaledup linearly with a concomittant linearincreasein eachof theforcesinvolved.In thenext section,weshall investigatehow to usethis to build an �2 axle which canreduce the frictional forcesof the axle to somesmall 43*� .

IV. +2 AXLE

As we’ve seenin theprevioussection,themagnetic ball andsocket assemblyutilizes permanent magnets to provide bothvertical andtransversestabilization.This is quiteadvantageousbecauseit meansthatthedevicehasmany of thecharacteristicsthatwe’d like it to have in order to usein anaxle.We have notas yet beenable to provide the type of stabilizationrequiredto placethis device at bothendsof theaxle,but usinga singlemagnetic ball and socket assembly, we are able to createanaxle with a single point of contact. Sucha device hasmanyadvantages,which we discussbelow.

Figure 4.1: This figure illustrates the basic 576 axle. At the bottom isa magneticball-and-socket assembly. An axle collinear with the axis ofsymmetryof the coneis connectedto the magneticsocket.

Theaxleis diagrammaticallyillustratedin Figure4.1. Theaxlecomprisesa rigid cylindrical rod with its centralaxis alignedwith the axis of the cone,attachedto the centerof the coneat oneend,and insertedinto a socket at the otherend.Suchan axle has a single point of contact at one end, at whichpoint it contactsthe wall, and a freely floating end. In thisconfiguration,theaxlecanbeusedasif theendwith theball-and-socket is fixedwith a ball bearing. Becausethe fixed endwith a ball bearing is the only point of contact, this point isthe only placewherefriction canoccur. As a result, the axleso described hasonly this onepracticalpoint of failure.

Figure 4.2: This figure illustratestwo orientationsof the 586 axle.On theleft, theverticalorientationsupportsall of theweight,leaving little frictionat the contactpoint. On the right, the horizontalorientationputspressureon the ball andsocket aswell as the singlecontactpoint.

In practice, the axle may be used at any angle. However,the angle at which the axle is utilized varies betweentwoextremes: completely vertical or completelyhorizontal. Thedifferentorientationsaredepictedin Figure4.2.In thehorizon-tal arrangement,the weight of the axle is distributedbetweenthebearing andtheball andsocket.In thisscenario,thefrictionon the bearing on oneend is not negligible. This becomes apointof failurefor thedevice.Moreover, themagneticball andsocketactslikeaspring,vibrating onoccasionwhenthedeviceis in use.In this configuration,vibrationsof the systemmightbe significantenough to allow the detachment of the bearingon the opposite end.This would be a critical failure. Finally,any loading of theaxledistributestheweightbetweenthetwoends,againcausingthe type of difficulties just described.

Theverticalconfigurationfindsall theweightof the �2 axlesquarely restingon the magnetic ball andsocket. As a result,the actual contact friction of the axle can be fractionallyvanishing. This meansthat the bearing will typically be usedto keeptheaxlefrom tipping andto keepit in placevertically.However, the actualwear on the device can be infinitesimal.Theweightis actuallyrestingon themagnetic ball andsocket.As a result,thesystemwill experienceverticalvibrations.Thesystemwill be protectedfrom vibrations by the vertical limitof the bearing at the opposite endof the axle.

Oneof the importantconsequencesof theverticaldesignofthe +2 axle is that the axle’s frictional wear at the bearingend decreases as the load increases.This is a result of acounterbalance againstgravity providedby theball andsocket.This meansthat several devices that are traditionally limitedbecauseof difficulties causedby friction canbe designed andbuilt so that suchlimitationsareerased.For usein windmills,this meansthat the large rotor holding the blades may bebalanced against gravity using the +2 axle, mitigating theneedfor expensive bearings that ultimately fail and requireexpensive maintenance.Other devices, such as the Crookesradiometer, might be designedon a larger scalebecause theparts of the devices that cause prohibitive friction wouldno longer causethe sameproblem. In the next section,weexamine the applicationof this device to windmill systems.

V. INTEGRATION OF WINDMILL

The +2 axle is a simple application of the magnetic balland socket that createsmany different opportunities for thegeneration of windmill systemsthat require relatively littlemaintenance.In this section,we examine the designof wind-mills basedon this design.

As mentioned previously, the use of a vertical axle ispreferredover a horizontalaxle.This meansthat thewindmilltype that will benefit in designmore from the �2 axle is theVAWT. This windmill requires very few changesto its basicdesign- the bottom bearing assemblycan be replacedwitha static magnetic assemblywhile the top bearing may bereplaced by a single bearing assemblyconsistingessentiallyof a cup andbearing.

Savoniuswind turbinesutilizing the +2 axle needonly havethe magnetic ball and socket assemblyand the top bearingassemblyratherthanthe multiple bearing assembliesthat aretypically used.This limits the repaircostof theSavoniustypewindmill. Moreover, removing a complete bearingassemblyand changing it to a single bearing in a cup reduces theoverall cost. The magneticball and socket may be expectedto compare in cost to the bearing assemblytypically used.The Darrieus type windmill is similarly improved in its cost.However, as the Darrius type windmill suffers from lowreliability dueto highTSR,the +2 axle canmitigatethisdesignflaw, as it is unlikely to suffer from high speeds.As a result,the �2 axle may be expectedto improve the reliability andtherefore value of the Darrius type windmill. We illustrate asimplegiromill in Figure 5.1.

Figure 5.1: This figure illustrates the use of the 576 axle in building asimple giromill. The axle supportsthe completeweight of the giromillallowing for very small frictional losses.

Oneimportant designrequirementof the +2 axle derives fromthe useof a “flexible” bearing assembly. The ball andsocketassembly, aswe have seenearlier, is not rigid; it is possibletopushit from thesideandmovetheaxle.This is aproblemfroma designsensebecause if transverseforcespushwith enoughforceagainst theball andsocket assembly, thetwo sidesof theassemblymay grind against eachother, potentially destroyingit. The situationis depicted in Figure5.2.

Figure 5.2: Transverseforcespushingagainstthe 576 axle could causethe586 axle to grind anddestroy the magneticball andsocket.

In order to mitigate this possibility, onemayutilize a longaxlewhichhasanattachedwing assemblyfastenedto thetopof themagnetic ball andsocket. ConsiderFigure5.3. In this figure,the lengthof the +2 axle is 9#: andthe wings’ centerof massis located9�; from thetop bearingand 9 � from theaxle.In thiscase,any force < acting on the wings and tending to rotatethe +2 axle around the top bearing will needto overcomeaforce <>=@?�A?CB . What this means is that the longer the axle, theless likely that the force acting on the wings will be able togrind the magnetic ball andsocket assembly. It indicates thatthe axle shouldbe as long aspossiblein a practical design.

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d2

Figure 5.3: The 586 axle is stabilized againstvertical vibrations of the vanesbyopposing tangential forces at the ball and socket. Long axles with large ?CA valuescompareto ? B have mechanicalstability built in.

VI. DISCUSSION AND CONCLUDING REMARKS

One of the big limitations of most kinds of machinery isthat as the machine increasesin sizeandload, the amount ofwearandtearon the various componentsof the machine alsoincreases.This meansthat piecesof the machine which canbe largeandexpensive canbedestroyed by the normal useofthe machine, requiring costly repairs to correct the machine.This is particularly true for wind generatorswhoserepair cancost thousandsof dollarsper repair.

We have introduceda simpleunpoweredmagnetic ball andsocket assemblywhich canbe usedto mitigate the wearandtear of moving machinery. The device is a simple conicalsocket piece which “fits” over a magnetwhich generatesamagnetic ball. This assemblystabilizesitself both verticallyandtangentially, tendingto centerthe conical pieceabove theball piece.Whenusedin an axle, the ball andsocket andbeusedto form what is known as an �2 axle. This axle has asingle assemblyat one end and a solid ball and socket onthe otherside. It is bestusedin a vertical orientation, whichtendsto centerits weighton themagnetic ball andsocket andthereby limit the wear on the non-magnetic ball and socket.When usedin a windmill, the �2 axle is valuable becauseitmitigateswear and allows the windmill to be usedwithoutrequiring repairoften.

The most startlingaspectof this device is that the frictionactually lessenswhen the load increases.As we discussedabove, this happens when the +2 axle is used in a verticalconfiguration,like it is in averticalaxiswindmill. Thisspecificcharacteristic makes the �2 axle ideal for windmills, as itmeansthat the one part of the windmill that is in contactwith a stationaryframe can have a very minimal amount offriction.

This last aspectof the device opens a variety of possi-bilities for future mechanical devices. One device might bean adaptation of Crooke’s radiometer. This device cannotbeusedfor industrial purposesbecause the force generatedbythe solar radiation increasesas the squareroot of the areaofthe vanesin the device while the friction increaseslinearlywith the area of the vanes.One might envision using thisdevice for sucha purpose.Another potentialusemight be for

holding heavy objects which might needto be rotatedarounda basemanually, but held in place once the movement hadbeencompleted. This might be accomplished even with veryheavy objects.Finally onemight explore creatinggyroscopesor motors basedon these platforms. Utilizing the +2 axlemight significantlyincreasethe lifetime andreliability of suchdevices.

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