外文翻译输送带的二维动态特性.docx

外文翻译输送带的二维动态特性.docx

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外文翻译输送带的二维动态特性

TheTwo-DimensionalDynamicBehaviorofConveyorBelts

Ir.G.Lodewijks,DelftUniversityofTechnology,TheNetherlands

1.SUMMARY

1--------Inthispaperanewfiniteelementmodelofabelt-conveyorsystemwillbeintroduced.Thismodelhasbeendevelopedinordertobeabletosimulateboththelongitudinalandtransversedynamicresponseofthebeltduringstartingandstopping.Applicationofthemodelinthedesignstageoflongoverlandbelt-conveyorsystemsenablestheengineer,forexample,todesignproperbelt-conveyorcurvesbydetectingprematureliftingofthebeltofftheidlers.Italsoenablesthedesignofoptimalidlerspacingandtroughingconfigurationinordertoensureresonancefreebeltmotionbydetermining（standing）longitudinalandtransversebeltvibrations.Applicationoffeed-backcontroltechniquesenablesthedesignofoptimalstartingandstoppingprocedureswhereasanoptimalbeltcanbeselectedbytakingthedynamicpropertiesofthebeltintoaccount.

2.INTRODUCTION

2--------TheNetherlandshaslongbeenrecognisedasacountryinwhichtransportandtranshipmentplayamajorroleintheeconomy.TheportofRotterdam,inparticularisknownasthegatewaytoEuropeandclaimstohavethelargestharboursystemintheworld.Besidesthelargenumbersofcontainers,alargevolumeofbulkgoodsalsopassesthroughthisport.NotallthesegoodsareintendedfortheDutchmarket,manyhaveotherdestinationsandaretranshippedinRotterdam.Goodexamplesoftypicalbulkgoodsthataretranshippedarecoalandironore,asignificantpartofwhichisintendedfortheGermanmarket.Inordertohandlethebulkmaterialsawiderangeofdifferentmechanicalconveyorsincludingbelt-conveyorsisused.

3--------Thelengthofmostbelt-conveyorsystemserectedintheNetherlandsisrelativelysmall,sincetheyaremainlyusedforin-plantmovementofbulkmaterials.Thelongestbelt-conveyorsystem,whichisabout2kmlong,issituatedontheMaasvlakte,partoftheportofRotterdam,whereitisusedtotransportcoalfromabulkterminaltoanelectricitypowerstation.Inadditiontodomesticprojects,anincreasingnumberofDutchengineeringconsultanciesparticipatesininternationalprojectsforthedevelopmentoflargeoverlandbelt-conveyorsystems.Thisdemandstheunderstandingoftypicaldifficultiesencounteredduringthedevelopmentofthesesystems,whicharestudiedintheDepartmentofTransportTechnologyoftheFacultyofMechanicalEngineering,DelftUniversityofTechnology,oneofthethreeDutchUniversitiesofTechnology.

4--------Theinteractionbetweentheconveyorbeltproperties,thebulksolidsproperties,thebeltconveyorconfigurationandtheenvironmentallinfluencetheleveltowhichtheconveyor-systemmeetsitspredefinedrequirements.Someinteractionscausetroublesomephenomenasoresearchisinitiatedintothosephenomenawhichcausepracticalproblems,[1].Onewaytoclassifytheseproblemsistodividethemintothecategorywhichindicatetheirunderlyingcausesinrelationtothedescriptionofbeltconveyors.

5---------Thetwomostimportantdynamicconsiderationsinthedescriptionofbeltconveyorsarethereductionoftransientstressesinnon-stationarymovingbeltsandthedesignofbelt-conveyorlay-outsforresonance-freeoperation,[2].Inthispaperanewfiniteelementmodelofabelt-conveyorsystemwillbepresentedwhichenablesthesimulationofthebelt'slongitudinalandtransverseresponsetostartingandstoppingproceduresandit'smotionduringsteadystateoperation.It'sbeyondthescopeofthispapertodiscusstheresultsofthesimulationofastart-upprocedureofabelt-conveyorsystem,thereforeanexamplewillbegivenwhichshowsomepossibilitiesofthemodel。

3.FINITEELEMENTMODELSOFBELT-CONVEYORSYSTEMS

6--------Ifthetotalpowersupply,neededtodriveabelt-conveyorsystem,iscalculatedwithdesignstandardslikeDIN22101thenthebeltisassumedtobeaninextensiblebody.ThisimpliesthattheforcesexertedonthebeltduringstartingandstoppingcanbederivedfromNewtonianrigidbodydynamicswhichyieldsthebeltstress.Withthisbeltstressthemaximumextensionofthebeltcanbecalculated.Thiswayofdeterminingtheelasticresponseofthebeltiscalledthequasi-static（design）approach.Forsmallbelt-conveyorsystemsthisleadstoanacceptabledesignandacceptableoperationalbehaviorofthebelt.Forlongbelt-conveyorsystems,however,thismayleadtoapoordesign,highmaintenancecosts,shortconveyor-componentlifeandwellknownoperationalproblemslike:

∙excessivelargedisplacementoftheweightofthegravitytake-updevice

∙prematurecollapseofthebelt,mostlyduetothefailureofthesplices

∙destructionofthepulleysandmajordamageoftheidlers

∙liftingofthebeltofftheidlerswhichcanresultinspillageofbulkmaterial

∙damageandmalfunctioningof（hydrokinetic）drivesystems

Manyresearchersdevelopedmodelsinwhichtheelasticresponseofthebeltistakenintoaccountinordertodeterminethephenomenaresponsiblefortheseproblems.Inmostmodelsthebelt-conveyormodelconsistsoffiniteelementsinordertoaccountforthevariationsoftheresistance'sandforcesexertedonthebelt.Theglobalelasticresponseofthebeltismadeupbytheelasticresponseofallitselements.Thesefiniteelementmodelshavebeenappliedincomputersoftwarewhichcanbeusedinthedesignstageoflongbelt-conveyorsystems.Thisiscalledthedynamic（design）approach.Verificationoftheresultsofsimulationhasshownthatsoftwareprogramsbasedonthesekindofbelt-modelsarequitesuccessfulinpredictingtheelasticresponseofthebeltduringstartingandstopping,seeforexample[3]and[4].

Thefiniteelementmodelsasmentionedabovedetermineonlythelongitudinalelasticresponseofthebelt.Thereforetheyfailintheaccuratedeterminationof:

∙themotionofthebeltovertheidlersandthepulleys

∙thedynamicdrivephenomena

∙thebendingresistanceofthebelt

∙thedevelopmentof（shock）stresswaves

∙theinteractionbetweenthebeltsagandthepropagationoflongitudinalstresswaves

∙theinteractionbetweentheidlerandthebelt

∙theinfluenceofthebeltspeedonthestabilityofmotionofthebelt

∙thedynamicstressesinthebeltduring.passageofthebeltovera（driven）pulley

∙theinfluenceofparametricresonanceofthebeltduetotheinteractionbetweenvibrationsofthetakeupmassoreccentricitiesoftheidlersandthetransversedisplacementsofthebelt

∙thedevelopmentofstandingtransversewaves

∙theinfluenceofthedampingcausedbybulkmaterialandbythedeformationofthecross-sectionalareaofthebeltandbulkmaterialduring,passageofanidler

∙theliftingofthebeltofftheidlersinconvexandconcavecurves

Thetransverseelasticresponseofthebeltisoftenthecauseofbreakdownsinlongbelt-conveyorsystemsandshouldthereforebetakenintoaccount.Thetransverseresponseofabeltcanbedeterminedwithspecialmodelsasproposedin[5]and[6],butitismoreconvenienttoextendthepresentfiniteelementmodelswithspecialelementswhichtakethisresponseintoaccount.

3.1THEBELT

Atypicalbelt-conveyorgeometryconsistingofadrivepulley,atailpulley,averticalgravitytake-up,anumberofidlersandaplatesupportisshowninFigure1.Thisgeometryistakenasanexampletoillustratehowafiniteelementmodelofabeltconveyorcanbedevelopedwhenonlythelongitudinalelasticresponseofthebeltisofinterest.

Sincethelengthofthebeltpartbetweenthedrivepulleyandthetake-uppulley,Is,isnegligiblecomparedtothelengthofthetotalbelt,L,thesepulleyscanmathematicallybecombinedtoonepulleyaslongasthemassinertia'softhepulleysofthetake-upsystemareaccountedfor.Sincetheresistanceforcesencounteredbythebeltduringmotionvaryfromplacetoplacedependingontheexactlocal（maintenance）conditionsandgeometryofthebeltconveyor,theseforcesaredistributedalongthelengthofthebelt.Inordertobeabletodeterminetheinfluenceofthesedistributedforcesonthemotionofthebelt,thebeltisdividedintoanumberoffiniteelementsandtheforceswhichactonthatspecificpartofthebeltareallocatedtothecorresponding,element.Iftheinterestisinthelongitudinalelasticresponseofthebeltonlythenthebeltisnotdiscreditedonthoseplaceswhereitissupportedbyapulleywhichdoesnotforceitsmotion（slippossible）.Thelaststepinbuilding,themodelistoreplacethebelt'sdriveandtensioningsystembytwoforceswhichrepresentthedrivecharacteristicandthetensionforces.

Theexactinterpretationofthefiniteelementsdependsonwhichresistance'sandinfluencesoftheinteractionbetweenthebeltanditssupportingstructurearetakenintoaccountandthemathematicaldescriptionoftheconstitutivebehaviorofthebeltmaterial.Dependingonthisinterpretation,theelementscanberepresentedbyasystemofmasses,springsanddashpotsasisshowninFigure1,[9],wheresuchasystemisgivenforonefiniteelementwithnodalpointscandc+1.ThespringsKanddashpotHrepresentthevisco-elasticbehaviorofthebelt'stensilemember,Grepresentsthebelt'svariablelongitudinalgeometricstiffnessproducedbytheverticalactingforcesonthebelt'scrosssectionbetweentwoidlers,Vrepresentthebeltsvelocitydependentresistance's.

Figure1:

Fiveelementcompositemodel[9].

3.1.1NONLINEARTRUSSELEMENT

Ifonlythelongitudinaldeformationofthebeltisofinterestthenatrusselementcanbeusedtomodeltheelasticresponseofthebelt.AtrusselementasshowninFigure2hastwon