高架起重机桥架的建模与有限元分析外文文献翻译中英文翻译外文翻译.docx
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高架起重机桥架的建模与有限元分析外文文献翻译中英文翻译外文翻译.docx
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高架起重机桥架的建模与有限元分析外文文献翻译中英文翻译外文翻译
SolidModelingandFiniteElementAnalysisofanOverheadCraneBridge
C.Alkin,C.E.Imrak,H.Kocabas
Abstract
Thedesignofanoverheadcranebridgewithadoubleboxgirderhasbeeninvestigatedandacasestudyofacranewith35toncapacityand13mspanlengthhasbeenconducted.Intheinitialphaseofthecasestudy,conventionaldesigncalculationsproposedbyF.E.MRulesandDINstandardswereperformedtoverifythestressanddeflectionlevels.Thecranedesignwasmodeledusingbothsolidsandsurfaces.Finiteelementmesheswith4-nodetetrahedraland4-nodequadrilateralshellelementsweregeneratedfromthesolidandshellmodels,respectively.Afteracomparisonofthefiniteelementanalyses,theconventionalcalculationsandperformanceoftheexistingcrane,theanalysiswithquadraticshellelementswasfoundtogivethemostrealisticresults.Asaresultofthisstudy,adesignoptimizationmethodforanoverheadcraneisproposed.
Keywords:
overheadcrane,finiteelementmethod,solidmodeling,boxgirder.
Notation
bdistancebetweentwosideplates
bkwidthoflowerplate
FAAstaticloadduetothetrolley
FYloadduetotheworkingload
h0heightofthegirderend
h2heightofthesideplates
LAdistancebetweentrolleywheels
LKspanofcranegirder
LPdistancebetweentwoadjacentsupports
qweightofonemeterplatform
qKweightofonemetermaintenanceplatform
qPuniformlydistributedmassunitsofbridge
t1thicknessoftheupperandlowerplates
t2thicknessofthesideplates
x2distancebetweencenterofgravityandthemidpointoftheleftsideplate
x4distancebetweencenterofgravityandthemidpointoftherail
y1distancebetweenneutralaxisandthemidpointoftherail
y3distancebetweencenterofgravityandthemidpointofthetopplate
y5distancebetweenneutralaxisandthemidpointofthetopplate
WX1momentofresistanceonx-axis
WY1momentofresistanceony-axis
amplifyingcoefficient
dynamiccoefficient
1Introduction
Cranesarethebestwayofprovidingaheavyliftingfacilitycoveringvirtuallythewholeareaofabuilding.Anoverheadcraneisthemostimportantmaterialshandlingsystemforheavygoods.Theprimarytaskoftheoverheadcraneistohandleandtransferheavypayloadsfromonepositiontoanother.Thustheyareusedinareassuchasautomobileplantsandshipyards[1,2].Theirdesignfeaturesvarywidelyaccordingtotheirmajoroperationalspecifications,suchas:
typeofmotionofthecranestructure,weightandtypeoftheload,locationofthecrane,geometricfeaturesandenvironmentalconditions.Sincethecranedesignproceduresarehighlystandardizedwiththesecomponents,mosteffortandtimearespentoninterpretingandimplementingtheavailabledesignstandards[3].
Therearemanypublishedstudiesonstructuralandcomponentstresses,safetyunderstaticloadinganddynamicbehaviorofcranes[5–16].SolidmodelingofbridgestructuresandfiniteelementanalysistofindthedisplacementsandstressvalueshasbeeninvestigatedbyDemirsoy[17].Solidmodelingtechniquesappliedforroadbridgestructures,andananalysisofthesestructuresusingthefiniteelementmethodareprovidedin[18].Inthisstudy,stressanddisplacementswerefoundusingFEM90software.Solidmodelingofacranebridge,theloadingatdifferentpointsonthebridgeandthenapplicationofthefiniteelementmethodhavebeenstudiedbyCeliktas[19].Shepresentedtheresultsoffiniteelementmethodsforanoverheadcrane.
DIN-TaschenbuchandF.E.M.(FederationEuropéennedelaManutention)Rulesofferdesignmethodsandempiricalapproachesandequationsthatarebasedonpreviousdesignexperienceandwidelyaccepteddesignprocedures.DIN--Taschenbuch44and185areacollectionofstandardsrelatedtocranedesign.DINnormsgenerallystatestandardvaluesofdesignparameters.F.E.MRulesaremainlyanacceptedcollectionofrulestoguidecranedesigners.Itincludescriteriafordecidingontheexternalloadstoselectcranecomponents[3,20].
Inthisstudy,thecalculationsapplytheF.E.M.rulesandDINstandards,whichareusedforboxgirdercranebridges.ThecalculationoftheboxgirderusestheCESANInc.standardbridgetables.Thenasolidmodelofthecranebridgeisgeneratedwiththesamedimensionsasinthecalculationresults.Thenstaticanalysisisperformed,usingtheFiniteElementMethod.Beforestartingthesolution,theboundaryconditionsareappliedasinpractice.
2Overheadcraneswithadoubleboxgirder
Overheadtravellingcraneswithadoubleboxgirdernotonlyhoistloadsbutalsocarrythemhorizontally.Adoublebeamoverheadcraneisbuiltofatrolleytravellingonbridges,andbridgestravellingonrails.Thetrolleyhoistsorlowerstheloadsandcarriesthemonthebridgestructure.Thebridgescarrytheloadsonarail.Asaresult,threeperpendicularmovementsareperformed.ThesystemisdepictedinFig.1,wherethepayloadofthemassisattachedtothebridgewithwireropes[21,22].
Thedoubleboxgirdersaresubjectedtoverticalandhorizontalloadsbytheweightofthecrane,theworking(hook)loadandthedynamicloads.Withadoubleboxgirderconstruction,thetrolleyrunsaboveorbetweenthegirders.TheacceptableconstructionrequirementsandvaluesforaboxgirderbridgestructureareshowninFig.2.
Fig.1:
Overallviewofanoverheadcrane
Fig.2:
Constructionrequirementsforaboxgirderbridge
3ApplicationofFEMtoanoverheadcrane
Amongnumericaltechniques,thefiniteelementmethodiswidelyusedduetotheavailabilityofmanyuser-friendlycommercialsoftwares.Thefiniteelementmethodcananalyseanygeometry,andsolvesbothstressesanddisplacements[23].FEMapproximatesthesolutionoftheentiredomainunderstudyasanassemblageofdiscretefiniteelementsinterconnectedatnodalpointsontheelementboundaries.Theapproximatesolutionisformulatedovereachelementmatrixandthereafterassembledtoobtainthestiffnessmatrix,anddisplacementandforcevectorsoftheentiredomain.InthisstudyfiniteelementmodelingiscarriedoutbymeansoftheCosmosWorksandMSCcommercialpackage.Patranand4-nodetetrahedralelementsand4-nodequadrilateralshellelementshavebeenusedformodelingtheoverheadcranebridge.
Thefour-nodetetrahedralelementisthesimplestthree--dimensionalelementusedintheanalysisofsolidmechanicsproblemssuchasbracketstressanalysis.Thiselementhasfournodes,witheachnodehavingthreetranslationalandthreerotationaldegreesoffreedomonthex,y,andz-axes.Ashellelementmaybedefined,whichallowsintheplaneorcurvedsurfaceoftheelementandpossesbothlength.It
widthandmayonlybeusedin3-Dsimulations.Thefour--nodeshellelementisobtainedbyassemblingthebendingelementtotheappropriatedegreesoffreedom.Thisissufficientaslongastheshellelementdeflectioniswithinthepredefinedratioofshellthickness,otherwisethesystemworksasalargedeflection.
Atypicalfour-nodetetrahedralelementandfour-nodequadraticshellelement,andtheircoordinatesystemsareillustratedinFig.3[24].Thefour-nodetetrahedralelementchosenhassixdegreesoffreedomateachnode:
translationinthenodalx,y,andzdirectionsandrotationsaboutthenodalx,y,andzdirections.Forthefour-nodequadraticshellelementusedtomodeltheoverheadcranegirder,randsdenotethenaturalcoordinatesandδisthethicknessoftheelement.
Thissystemdoesnothaveanyhorizontalforce.Theaxialdisplacementsandrotationsofthefirstandlastfacesareequaltozero.Inaddition,thetransversedisplacementiszeroatthefirstandlastfacenodes.
Theexternalforcesactingonthesystemarethemassofthemaingirderofthecrane(distributedload)andtheforcesactingonthewheelsofthetrolleyalongthecrane(activeload).Theforcesactingonthetrolleywheelsarecausedbythemassofthetrolley,antheliftingloadwhichwillbemovedonthecrane.
4-nodetetrahedralelement
4-nodequadraticshellelement
Fig.3:
Elementsusedtomodelanoverheadcranegirder
4Solidandfiniteelementmodelingofanoverheadcranebridge
Thefiniteelementmethodisanumericalprocedurethatcanbeappliedtoobtainsolutionstoavarietyofproblemsinengineering.Steady,transient,linearornonlinearproblemsinstressanalysis,heattransfer,fluidflowandelectromechanismproblemsmaybeanalysedwithfiniteelementmethods.Thebasicstepsinthefiniteelementmethodaredefinedasfollows:
preprocessingphase,solutionphase,andpostprocessingphase.
RealcranedatawasgatheredfromCESANInc.,aTurkishcompanyinvolvedinmassproductionofoverheadcranes.First,thecranebridgeismodeledasasurface.Bridgegeometryissuitableforthis,andlongandthinpartsshouldalsobemodeledasasurface.Later,ameshiscreated.Inthisstudy,aquadraticelementtypeisused.SolidmodelingisgeneratedforthecalculatedcranebridgeandthesolidmodelisshowninFig.4[20].
SolidmodelofacranebridgeWireframeviewofacranebridge
Fig.4:
Modelsofanoverheadcranebridge
5Numericalexampleofanoverheadcrane
A35-ton-capacityoverheadcraneofoveralllength13mandtotalweight22.5tonswasselectedasastudyobject.TheconfigurationoftheoverheadcraneisshowninFig.1.Theoverheadcraneconsistsoftwogirders,twosaddlestoconnectthem,andatrolleymovinginthelongitudinaldirectionoftheoverheadcraneandwheels.Thedrivingunitisinstalledinoneofthetwogirders.Theoverheadcraneissupportedbytworailsandtherunwaygirdersinstalledinbuilding.
Inordertocalculatethestre
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