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New Method to Measure the Fill Level of the Ball Mill I Theoretical Analysis and DEM Simulation

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New Method to Measure the Fill Level of the Ball Mill I Theoretical Analysis and DEM Simulationof,I,to,the,Fill,Level,Ball,Mill,New,The

    New Method to Measure the Fill Level of the Ball Mill I Theoretical Analysis and

    DEM Simulation

    ?460?

    CHINESEJOURNALOFMECHANICALENGINEERING

    Vo1.23,No.4,2010

    DOI:10.3901/CJME.2010.04.460,availableonlineatwww.cjmenet.com;?|,n?

    cjmenet.corn.cn

    NewMethodtoMeasurethe

    TheoreticalAnalysis

    FillLeveloftheBallMill

    andDEMSimulation

    HUANGPeng

    ,JIAMinping,andZHONGBinglin

    SchoolofMechanicalEngineering,SoutheastUniversity,Nanjing211189,China ReceivedOctober3,2009;revisedMay24,2010;acceptedJane10,2010;publishedelectronicallyJune11,2010

    Abstract:Theaccuratemeasurementofthefil1leve

    jnthebal1millhasnotbeenresolvedbecauseoftheinterplayofmanyvariable factors,whichledthemilltobeoperatedundertheuneconomicalconditionandlostalotofenergy.Atpresent,somemethods,suchas

    vibrationmethodandacousticmethod,havebeenappliedformeasuringthefilllevelbytheresearchers.Aimingattheproblemofthe

    traditionalmethodsformeasuringthefillleve1.thatis.thefeaturevariablesofthefillleve1suffertheinfluencesoftheballloadandthe

    watercontentofthecoa1.anovelmethodtomeasurethefilllevelisproposedandapossiblerela

tionbetweenthefilllevelandthe

    angularpositionofthemaximumvibrationpointonthemillshellisinvestigated.Theangularpositionsofthemaximumvibrationpoint

    onthemillshellfordifferent151lleve1casesarecalculatedtheoreticallyundertwoassumptions.respectively.Meanwhilethecharge

    motionsofthemillfordifferentfill

    evelcasesaresimulatedwiththediscreteelementmethod(DEM,.Andthesimulationresultsare

    verifiedbycomparingthemotiontrajectoriesofsteelballsandpowerdraftofthemil1.Thesimulatedmovementtrajectoriesofthe

    outmostlayersteelballsintheraillaremonitoredandanabrzedtoobtaintheangularpositionsofthemaximumvibrationpointonthe

    millshel1.Boththeresultsofthetheoreticalcalculationandthe3DDEMsimulationshowthatthepositionofthemaximumvibration

    pointonthemillshellmovestoalowerangularpositionsasthefillleveldecreasing,whichprovidesanewideaformeasuringthefill

    leveaccurately.,

    Keywords:ballmill,filllevel,discreteelementmethod(DEM),simulation 1Intr0ducti0n

    Theballmillpulverizingsystemhastheadvanmgesof

    goodadaptabilityfordifferenttypesofcoalandeasy

    maintenance,andhasbeenappliedwidelyforcomminuting

    anddryingcoalincoa1.firedpowerplant.Atthesametime

    thissystemconsumeshighenergythatmakesupabout20

    percentofallelectricityconsumptionofpowerplant.So

    makingthemilloperationsafelyandhavinghighefficiency

    areimportantgoalsforpowerplant.Becausetheballmill

    pulverizingsystemisnonlinearity,longtimedelayand

    timevarying.the6Uleve1ofcoalpowdercannotbe

    measuredaccurately,whichleadsthemil1tobeoperated

    usuallyundertheveryuneconomicalconditiontoprevent thecoa1blockage.Furthermoreitisdif.ficultforthe automaticconffolsystemtoaccomplishthesteady operationofthemil1.Thereforetheexactmeasurementof thefil11evelisakeyandbasicfactorforrealizing automatic.reliableandemcientoperationofthemill systern.

    Manymethodshavebeenappliedformeasuringthet511 leve1.Oneoftraditionalmethodswasthatthefil11eve1 Correspondingauthor.Email:feihonghp@163.com

    ThisprojectissupposedbyNationalNaturalScienceFoundationof China(GrantNo.50775035),andNewDoctorTeacherFoundationof SoutheastUniversityofChina(GrantNo.9202000024) canbemeasuredasafunctionofthedifferential pressurebetweentheinletandtheoutletofthemil1.Asthe fill1evelincreases.morecoalpowderisexposedtotheair flowthroughthemill,airdragforcesarehigh,andthe differentialpressureincreases.Thesamerelationship concernstheoppositecondition.asthefillleveldecreases. ZHANGstudiedthefi11leve1bymeasuringthepower consumptionofthemillmotor.K0LACZputforwarda

    methodtomeasurethefill1evelbyusingastrain transducert.Thetransducerwasinstalledatthemiddleof themillshel1.Whenthetransducerwasinthetopposition oftherail1shel1compressionwasmeasuredbythe transducer.Whenthetransducerreachedthebottomofthe millshellalongwiththerotationofthemill,tensionwas measuredbythetransducer.Bytakingthedifference betweenthereadingscorrespondingtocompressionand tension.itwaspossibletocalculatethetotalstrain

    variationsthataredirectlyproportionaltothefil1leve1. Recentlythemeasurementandcontro1ofthefill1eve1in theraillhavealsobeenaccomplishedbyanalyzingthe acousticsignalsofthemillt3-5J.Togetherwilhtheincrement ofthefillleve1.theacousticsignalpresentsadecreasing trendandviceversa.Sincethevibrationstrengthofthe rail1shel1andthebearinghousingscanreflectthe informationofthefillleve1.vibrationmethodshave recentlybeencarriedouttodeveloptechniquesfor monitoringthefil11eve1.Amongthesevibrationmethods. CHINESEJOURNALOFMECHANICALENGINEERING?461? thefilllevelcanbemeasuredthroughextractingsome characteristicvaluesfromthevibrationsignalsofthe bearinghousings,suchasamplitude,energy,powerand rootmeansquarerRMS)[.

    Tosumupaboveworks,somefactorsandvariables,such asthesteelbal1load.coalpropertyandthedisturbanceof othernoisenearthemillcanaffectthemainvariables correctivetothefill1evelandthemeasuredresult.For example,theamplitudeofacousticandvibrationsignalof themillhasagreaterdifierenceunderthesamefilllevel conditionbythevariationoftheballloadandthewater contentofcoa1.andthepowerofthemillisalsoinfluenced seriouslybythechangeofsteelballload.Themaingoalof thispaperistoputupanewmethodformeasuringthefill levelthroughstudyingtherelationbetweenthefillleve1 andthepositionofthemaximumvibrationpointonthemil1 shel1.Inthispaper,thisrelationisresearchedbytwo approaches.0neistheoreticalanalysismethod.andanother istheDEMsimulationmethod.Atthesametinetheresults

    ofthetheoreticalcalculationandtheDEMsimulationare comparedanddiscussed.Finally,inthesecondpart(II)of thisresearch,thevibrationsignalsthataredirectly collectedoffofthemillshellundervariousexperiment conditionsareanalyzedtoveilfytheresultsand conclusionsofthefirstpartfI1ofthisresearch. 2TheoreticalCalculation

    Comparedwithstee1ballsinotherlayers.thesteelballs intheoutmostlayerhavethegreatestimpulseandkinetic energyinthecourseoffalling,andthemaximumvibration pointonthemillshellisgeneratedbythefallingimpactof stee1ballsinthislayer.Thepositionsoftheoutmostlayer steelballscanbeseeninFig.1.

    Z

    b

    o

    s

    105o|ooo

    Ioooo

    Ver

    S

    Fig.1.Schematicdiagramofmotionofthesteelbails inmanylayersinthemill

    Whentheoutmostlayersteel

    millwall,thecollisionpoint

    ballimpactsdirectlyonthe

    isthemaximumvibration

    pointofthemillshel1.Whenthesteelballintheoutmost layerimpactsoncoalparticles,theimpactenergyis deliveredtothemillshell,whichalsoleadstoamaximum

    vibrationpointonthemillshel1.Inthisresearch,the relationshipbetweenthefilllevelandthepositionofthe maximumvibrationpointofthemillshellistriedtostudy onthefirsttime.Ifthisrelationshipcanshowcertain regularity,thefilllevelcanbestudiedbythispoint. Inthisresearch.thefilllevelisdefinedasfollows: :×100%.

    i11ll

    '

    whereVmillistheeffectivevolumeofthemill,m;1is

    theaccumulatedvolumeofthestee1ballsinsidethemil1. m;0aistheaccumulationvolumeofthecoa1particles andpowderinsidethemil1.m.

    Thepositionofthemaximumvibrationpointofthemil1 shelliscalculatedtheoreticallyundertwoassumptions describedasfollows.

    (1)Duringtheworkprocessofthemill,exceptforasteel ballintheoutmostlayer,asshowninFig.2.thecoal particlesandothersteelballsareaccumulatedatthebottom oftherolleratstaticstate.InFig.2.thelengthoflineC denotestheaccumulatedheightofthecoalparticlesand steelballsinthemil1.andthelineAErepresentsthe accumulationsurface.

    f2)InFig.2thereisnodisplacementinthexdirection forthemovementtrajectoryoftheballintheoutmostlayer, andxcoordinateofthisballisalwaysequaltozero. Z

    luu

    \?O

    0.

    Fig.2.Schematicdiagramofmotiontrajectory oftheoutmoststeelballinthemill

    WhentheballreachesthedetachmentpointG,asshown inFig.2,thisballbeginsaparabolicmovement.The intersectionpoint(collisionpoint)betweenthisparabolic trajectoryandaccumulationsurfaceispointD(0,a,6).In thefallingcourse,whenthesteelballsimpactsonthecoal particles,thepartofimpactenergyofsteelballsis absorbedbycoalparticlestorealizethegrindingand comminutingofcoal,andanotherpartofimpactenergyis deliveredfromthecollisionpointtothemillshelland causesthevibrationoftheshel1.Sothepositionofthe maximumvibrationpointonthemillshellisataminimum distancefromthecollisionpoint,andpointB(0,Y,z)(see Fig.21denotesthemaximumvibrationpoint.Herethe minimumdistanceisobtainedwitharestrictivecondition. whichisexpressedby

    HUANGPeng,etal:NewMethodtoMeasuretheFil1LeveloftheBallMillI--

    Theoretica1AnalysisandDEMSimulation

    {:_)+(6z),(2)I+z=R,

    wheremisthedistancebetweenpointBandpointD.InEq. (2),theminimumvalueof"isneeded,andthefollowing formulacanbeobtainedbytherestrictivecondition: z:一腑

    Thenparameterucanbecalculatedas%llows

    ":(a-)+(6+)

    (3)

    (4)

    Eq.(4)takingthederivativeofYatbothitsendscanbe determinedby

:

    2+?一

    thepositionofpointBlocatesat331.7.onthemillshel1. andthisangle(331.7o)representstheangularpositionof themaximumvibrationpointonthemillshel1.Thisangular positionisdenotedbytheparameter0inthispaper.Bya similarprinciple,thecoordinatesofpointDandpointB, andtheangularpositionsofpointBfor0%.5%and10% filllevelcasescanbecalculated.andthecalculatedresults areshowninTlable1.

    Table1.CoordinatesofpointsDandtheangular positionsofpointBforfourlevelsoffilllevel (5)AsevidentfromFig.3,

    maximumvibrationpointon

    ZerovalueisgiventheleftendofEq.(5),andY coordinateofpointBcanbeobtainedby

    

    AndthenzcoordinateofpointBcanalsobeobtainedby bR(7)

    InFig.2,pointDistheintersectionpointofthe parabolictrajectoryGFandtheaccumulationsurfaceAE, andthisparabolictrajectoryandaccumulationsurfacecan bedescribedbythefollowingequations:

    {y::=-Rc.sina++tvincosa,..5g,

    z:C?

    (8)

    (9)

    ThecoordinatesofpointDcallbegainedbytheEqs.(8) and(9).Intheonsitetests,a3.5mdiameterby6.0mlong industrialtubularballmillwasoperatedat17.57r/min

theangularpositionofthe

    themil1shelldecreaseswith

    theincreaseinthefi11leve1.Howeverthisresultisobtained undertheidealconditions.Manyfactors.suchasthe collisionbetweenballandballorthemillwal1.themotion ofcoalandsteelballs,havenotbeenconsidered,sothis conclusionneedstobeverifiedfurtherbyotherapproaches. Oncethisconclusioncanbevalidated,whichcanprovidea newtheoryandmethodformeasuringthefil1leve1.Inthe nextcontent.the3dimensionaIDEMsimulationsare performedtopredictthe1oadbehaviour,motiontrajectory oftheoutmostlayersteelballsandthemillpowerdraw. AndtheDEMsimulatedresultswillbecomparedand discussedwiththeresultsofthetheoreticalcalculation. Fig.3.VibrationintheangularpositionofpointB(themaximum vibrationpoint)onthemillshellwiththefilllevel (77%ofcriticalspeed),andthismillfilledby38tsteel ballswithdiameterfrom0.04mto0.06m.WhenthemiIl isoperatedwith15%fil1leve1.thecoordinatesofpointD33DDEMSimulationofChargeMo

    tion

    (0,O.35m,0.65n1)canbecalculated,andthentheoftheMill coordinatesofpointB(0,0.83m,?1.54m)canbe

    obtainedeasilybymeansofEqs.(6)and(7).Atthesame timethevalueofZBOC(seeFig.21canbecalculatedby thecoordinatesofpointBandisequalto28.3..InFig.2, 3.1Disereteelementmethod

    TheDEMwasoriginatedin1971byCUNDALLforthe

    analysisofrockmechanicsproblemsandthenwasapplied .\c0暮?o(IJ.c

    CHlNESEJoURNALOFMECHANICALENGINEERING?463?

    tomodelthebehaviorofsoilparticlesunderdynamic loadingconditionsbyCUDALLandSTRACKJ.The

    DEMreferstoanumericalschemethatallowsfinite rotationsanddisplacementofrigidbodies,wherecomplete lossofcontactsandformationofnewcontactsbetween bodiestakeplaceasthecalculationcycleprogresses.And theDEMisbasicallyanumericalmethodbywhichthe dynamicbehaviouroftheparticlesorbodiesinaphysica1 systemissimulatedwiththeparticlesbeingeatedas

    distinctbutinteractingelement.Accordingtotheadvantage oftheDEMandtheworkmechanismofthemill,theDEM suitstoresolvetheproblemofthemil1.SincetheDEMwas firstlyusedinthemillingbvMISHRAandRAJAMANI. thereweresomesuccessfulapplicationsoftheDEMin solvingvarioustumblingmillproblems[11-14J.Thetheory andprincipleofDEMcanbeacquiredindetai1fromRefs. [1517],itisonlyintroducedbrieflyinthispaper.Inthe DEMmode1.thesteelballsandcoalparticlesaresimulated asthesmoothroundsphereandcontactsbythemwithother ballsandwallsareconsideredtobedistinctsingle.point contacts.Thebal1.to.ballandbal1.to.wallcollisionsare modeledbytheDEMwitha1inearspringanddashpot.The springprovidestherepulsiveforce,andthedashpot dissipatesaportionoftherelativekineticenergV.Inthe following.thebal1.ballcollisionmode1isillustratedto introducethemotionandforceofthebal1.Thebal1.wall collisionissimulatedinasimilarmanner.Fig.4isa schematicdiagramofbal1AandballBincollision. 2

    3

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