外文翻译输送带的二维动态特性.doc

TheTwo-DimensionalDynamicBehaviorofConveyorBeltsIr.G.Lodewijks,DelftUniversityofTechnology,TheNetherlands1.SUMMARY1-Inthispaperanewfiniteelementmodelofabelt-conveyorsystemwillbeintroduced.Thismodelhasbeendevelopedinordertobeabletosimulateboththelongitudinalandtransversedynamicresponseofthebeltduringstartingandstopping.Applicationofthemodelinthedesignstageoflongoverlandbelt-conveyorsystemsenablestheengineer,forexample,todesignproperbelt-conveyorcurvesbydetectingprematureliftingofthebeltofftheidlers.Italsoenablesthedesignofoptimalidlerspacingandtroughingconfigurationinordertoensureresonancefreebeltmotionbydetermining(standing)longitudinalandtransversebeltvibrations.Applicationoffeed-backcontroltechniquesenablesthedesignofoptimalstartingandstoppingprocedureswhereasanoptimalbeltcanbeselectedbytakingthedynamicpropertiesofthebeltintoaccount.2.INTRODUCTION2-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-conveyorsystemwillbepresentedwhichenablesthesimulationofthebeltslongitudinalandtransverseresponsetostartingandstoppingproceduresanditsmotionduringsteadystateoperation.Itsbeyondthescopeofthispapertodiscusstheresultsofthesimulationofastart-upprocedureofabelt-conveyorsystem,thereforeanexamplewillbegivenwhichshowsomepossibilitiesofthemodel。3.FINITEELEMENTMODELSOFBELT-CONVEYORSYSTEMS6-Ifthetotalpowersupply,neededtodriveabelt-conveyorsystem,iscalculatedwithdesignstandardslikeDIN22101thenthebeltisassumedtobeaninextensiblebody.ThisimpliesthattheforcesexertedonthebeltduringstartingandstoppingcanbederivedfromNewtonianrigidbodydynamicswhichyieldsthebeltstress.Withthisbeltstressthemaximumextensionofthebeltcanbecalculated.Thiswayofdeterminingtheelasticresponseofthebeltiscalledthequasi-static(design)approach.Forsmallbelt-conveyorsystemsthisleadstoanacceptabledesignandacceptableoperationalbehaviorofthebelt.Forlongbelt-conveyorsystems,however,thismayleadtoapoordesign,highmaintenancecosts,shortconveyor-componentlifeandwellknownoperationalproblemslike:excessivelargedisplacementoftheweightofthegravitytake-updeviceprematurecollapseofthebelt,mostlyduetothefailureofthesplicesdestructionofthepulleysandmajordamageoftheidlersliftingofthebeltofftheidlerswhichcanresultinspillageofbulkmaterialdamageandmalfunctioningof(hydrokinetic)drivesystemsManyresearchersdevelopedmodelsinwhichtheelasticresponseofthebeltistakenintoaccountinordertodeterminethephenomenaresponsiblefortheseproblems.Inmostmodelsthebelt-conveyormodelconsistsoffiniteelementsinordertoaccountforthevariationsoftheresistancesandforcesexertedonthebelt.Theglobalelasticresponseofthebeltismadeupbytheelasticresponseofallitselements.Thesefiniteelementmodelshavebeenappliedincomputersoftwarewhichcanbeusedinthedesignstageoflongbelt-conveyorsystems.Thisiscalledthedynamic(design)approach.Verificationoftheresultsofsimulationhasshownthatsoftwareprogramsbasedonthesekindofbelt-modelsarequitesuccessfulinpredictingtheelasticresponseofthebeltduringstartingandstopping,seeforexample3and4.Thefiniteelementmodelsasmentionedabovedetermineonlythelongitudinalelasticresponseofthebelt.Thereforetheyfailintheaccuratedeterminationof:themotionofthebeltovertheidlersandthepulleysthedynamicdrivephenomenathebendingresistanceofthebeltthedevelopmentof(shock)stresswavestheinteractionbetweenthebeltsagandthepropagationoflongitudinalstresswavestheinteractionbetweentheidlerandthebelttheinfluenceofthebeltspeedonthestabilityofmotionofthebeltthedynamicstressesinthebeltduring.passageofthebeltovera(driven)pulleytheinfluenceofparametricresonanceofthebeltduetotheinteractionbetweenvibrationsofthetakeupmassoreccentricitiesoftheidlersandthetransversedisplacementsofthebeltthedevelopmentofstandingtransversewavestheinfluenceofthedampingcausedbybulkmaterialandbythedeformationofthecross-sectionalareaofthebeltandbulkmaterialduring,passageofanidlertheliftingofthebeltofftheidlersinconvexandconcavecurvesThetransverseelasticresponseofthebeltisoftenthecauseofbreakdownsinlongbelt-conveyorsystemsandshouldthereforebetakenintoaccount.Thetransverseresponseofabeltcanbedeterminedwithspecialmodelsasproposedin5and6,butitismoreconvenienttoextendthepresentfiniteelementmodelswithspecialelementswhichtakethisresponseintoaccount.3.1THEBELTAtypicalbelt-conveyorgeometryconsistingofadrivepulley,atailpulley,averticalgravitytake-up,anumberofidlersandaplatesupportisshowninFigure1.Thisgeometryistakenasanexampletoillustratehowafiniteelementmodelofabeltconveyorcanbedevelopedwhenonlythelongitudinalelasticresponseofthebeltisofinterest.Sincethelengthofthebeltpartbetweenthedrivepulleyandthetake-uppulley,Is,isnegligiblecomparedtothelengthofthetotalbelt,L,thesepulleyscanmathematicallybecombinedtoonepulleyaslongasthemassinertiasofthepulleysofthetake-upsystemareaccountedfor.Sincetheresistanceforcesencounteredbythebeltduringmotionvaryfromplacetoplacedependingontheexactlocal(maintenance)conditionsandgeometryofthebeltconveyor,theseforcesaredistributedalongthelengthofthebelt.Inordertobeabletodeterminetheinfluenceofthesedistributedforcesonthemotionofthebelt,thebeltisdividedintoanumberoffiniteelementsandtheforceswhichactonthatspecificpartofthebeltareallocatedtothecorresponding,element.Iftheinterestisinthelongitudinalelasticresponseofthebeltonlythenthebeltisnotdiscreditedonthoseplaceswhereitissupportedbyapulleywhichdoesnotforceitsmotion(slippossible).Thelaststepinbuilding,themodelistoreplacethebeltsdriveandtensioningsystembytwoforceswhichrepresentthedrivecharacteristicandthetensionforces.Theexactinterpretationofthefiniteelementsdependsonwhichresistancesandinfluencesoftheinteractionbetweenthebeltanditssupportingstructurearetakenintoaccountandthemathematicaldescriptionoftheconstitutivebehaviorofthebeltmaterial.Dependingonthisinterpretation,theelementscanberepresentedbyasystemofmasses,springsanddashpotsasisshowninFigure1,9,wheresuchasystemisgivenforonefiniteelementwithnodalpointscandc+1.ThespringsKanddashpotHrepresentthevisco-elasticbehaviorofthebeltstensilemember,Grepresentsthebeltsvariablelongitudinalgeometricstiffnessproducedbytheverticalactingforcesonthebeltscrosssectionbetweentwoidlers,Vrepresentthebeltsvelocitydependentresistances.Figure1:Fiveelementcompositemodel9.3.1.1NONLINEARTRUSSELEMENTIfonlythelongitudinaldeformationofthebeltisofinterestthenatrusselementcanbeusedtomodeltheelasticresponseofthebelt.AtrusselementasshowninFigure2hastwonodalpoints,pandq,andfourdisplacementparameterswhichdeterminethecomponentvectorx: