A method for calculating static conditions of a dr

F_ISEVIERAvailableonlineat¢IENCE~OIREOTCOMPUTERMODELLINGMathematicalandComputerModelling40(2004)233-247(ReceivedNovember2003;revisedandacceptedMarch2004)Abstract--Atechniquetonumericallyobtainthestaticequilibriumstateofaconventionaldraglineexcavationsystemisreported,includingstaticposeofthebucketaswellasinternalloadsactingonelementsoftheexcavationsystem.Equilibriumconditionsaregeneratedbynumericallyintegratingthedynamicequationsofmotionwiththehoistanddragropelengthsfixed.Itisshownthatthismethodcanbegreatlyacceleratedwiththeapplicationofartificialforcesandmomentsproportionaltothevelocityofthebodiesthatcomprisethedraglineexcavationsystem.Thebenefitsofappendingartificialforcesandmomentsaredemonstratedonanexemplarconventionaldraglineexcavationsystemusingacomplexthree-dimensionaldynamicsimulationmodel.Inthismodel,thebucket,spreaderbar,hoistcluster,anddragclusteraremodeledasrigidbodieswith6degreesoffree-domapiecewhilethedragrope,hoistrope,dumprope,hoistchains,anddragchainsarediscretizedintoafinitenumberofvisco-elasticelements.Resultsgeneratedfromthenumericalstaticposesim-ulationarecomparedagainstmeasuredstaticposedataandagreefavorably.©2004ElsevierLtd.Allrightsreserved.Keywords--staticpose,Draglineexcavator,Dynamicsimulation.NOMENCLATUREXB,YB,ZBcomponentsofthepositionuR~,ve~,wa~vectorofthecenterofmassofabodyinaninertialreferenceframecomponentsofthepositionPB,qB,rBvectoroftheithparticleonaropesegmentinaninertialreferenceframeEulerroll,pitch,andyawanglesofabodyxzrQ,YFQ~zRidPB,OB,%bBXB,YB,ZBcomponentsofthevelocityvectoroftheithparticleonaropesegmentinaninertialreferenceframecomponentsoftheangularvelocityvectorofabodyinthebodyreferenceframetotalappliedforcecompo-nentsonabodyinaninertialreferenceframe0895-7177/04/$-seefrontmatter(~)2004ElsevierLtd.Allrightsreserved.doi:10.1016/j.mcm.2004.03.001TypesetbyJtA&S-TEX234M.COSTELLOANDJ.KYLExr~,Yr,,zr,LB,MB,NBfTV,fRYelasticforceintheithsegmentofaropeelementintheinertialbodyreferenceframetotalappliedmomentsonabodyaboutitsmasscenterexpressedinthebodyreferenceframeartificialforceandmomentfactorsproportionaltotrans-lationalvelocityandrotationalvelocityXA,YA,ZALA,MA,NAcomponentsofartificialforceinaninertialreferenceframecomponentsofartificialmomentappliedtoabodyaboutitsmasscenterexpressedinthebodyreferenceframeINTRODUCTIONRemovalofoverburdeninsurfaceminingoperationsiseffectivelyaccomplishedbydraglineexcavationsystems.AtypicaldraglineexcavationsystemisshowninFigures1and2.Anopenbucketandriggingcomponentsaresupportedfromabovebyacableroutedoveralongboomwhichextendsabovethemine.Overburdenisremovedbydraggingthebucketalongthegroundbyacable,anddumpingitelsewhere.Thebucketisindirectlycontrolledbyanoperatorintheexcavatorthroughrotationoftheboomaboutaverticalaxisandpayoutandwindupofthehoistanddragropes.Forslowlyoperatingdraglineexcavationsystems,staticsystemmodelsprovideasatisfactoryestimateofloadsthatisutilizedinstructuralsizingofcomponents.Staticsystemmodelsalsoprovidebucketpositionandorientationinformationforvarioushoistanddragropelengthsandi,'[KIBucketFigure1.Draglineexcavationsystemschematic.AMethodforCalculatingStaticConditions!LHoistl~e235°7°Dm~HoistChaiuRichtDr-~Bar_.~$~.~HoistChai.DragCouplerLeftDragChai~Figure2.Draglinebucketschematic.variousbucketriggingsthatisusefulforsiteexcavationplanning.Incaseswhererelativelyrapidmaneuveringofthedraglinesystemisencountered,theuseofadynamicdraglineexcavationmodelismoreappropriateforestimatingbucketorientationexcursionsandmaximumloadsondifferentcomponents.Sincebothstaticanddynamicmodelsofadraglineexcavationsystemprovehelpfulinthedesignandanalysisofthesesystems,acomprehensivemethodcapableofperformingbothtypesofanalysisisdesirable.Severalresearchgroupshavedevelopeddraglineexcavationsystemmodelsatvariouslevelsofsophisticationfordifferentanalyticalpurposes.McCoyandCrowgey[1]investigatedstaticanddynamicdraglinebuckettightlinecontrol.Usingsimplegeometricanalysis,theyconstructedbothstaticanddynamictightlinelimitsbasedonthelengthofthedragandhoistropesandsubsequentlyusedtheselimitsaspartofanantitightlinecontrolsystem.Haneman,ttayesandLumley[2]reportedondraglineperformanceevaluationsusingphysicalmodeling.Riggingge-ometryandbucketsizewereoptimizedusingphysicalmodelingandcomparedagainstfielddata.Pathak,DasguptaandChattopadhyay[3]generatedamethodtocomputetheworkingzoneofadraglinebucket.Agraphicalapproachfordeterminationofthebucketpathprofileofastandarddraglinewasindicated~consideringathreeperioddutycycleineachoperation.Hainsworth,CorkeandWinstanley[4]usedmachinevisiontechniquestoremotelymeasurethelocationofadraglinebucketinspace.Usingonlyasinglecamera,animagesegmentationprocessisusedtoclassifythebucketandtoidentifyitspositioninthescene.RidleyandCorke[5]developedatechniquetoestimatedraglinebucketposeundergravityloa