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Impacts

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ImpactsImpact

    Impacts

J.Cent.SouthUniv.Techno1.(2008)15:869876

    ;DoI:10.1007/sl1771-008-0159-8Springer

    ;Impactsofflexibleobstructiveworkingenvironmenton

    ;dynamicperformancesofinspectionrobotforpowertransmissionline

    ;XIAOXiao-hui(肖晓晖),WuGongping(吴功平),DUE(杜娥),LISanping(李三平)

    ;(CollegeofPowerandMechanicalEngineering,WuhanUniversity,Wuhan430072,China) ;Abstract:Therigidfexiblecouplingdynamicmodelingandsimulationofaninspectionrobotwereconductedtostudythe

    ;influencesoftheflexibleobstructiveworkingenvironmenti.e.overheadtransmissionlineontherobot’sdynamicperformance.First,

    ;consideringthestructureoftheobstaclesandsymmetricalmechanismoftherobotprototype,fourbasicsubactionswereabstractedto

    ;fulmlfullpathkinematictasks.Then.amulti?rigid-bodydynamicmodeloftherobotwasbuiltwithLagrangeequation,whil~ea

    ;multi.flexible.bodydynamicmodelofaspanof1in~wasobtainedbycombiningfiniteelementmethod(FEM).modalsynthesis

    ;methodandLagrangeequation.Thetwosubsystemmodelswerecoupledunderrollingalongnoobstaclesegmentandovercoming

    ;obstacleposes.andthesesimulationsofthreesubactionsalongdifferentspansoflinewereperformedinADMAS.Thesimulation

    ;results,includingthecouplingvibrationparametersanddrivingmomentofjointmotors,showthedynamicperformancesoftherobot

    ;alongfiexibileobstructiveworkingpath:inflexibleobstructiveworkingenvironment.therobotcanfulfillthepresetmotiongoals;it

    ;responsesslowerinmoreflexiblepath;thefluctuationofrobotaswellasdrivingmomentofthecorrespondingjointinstartupand

    ;brakeregionisgreaterthanthatinrigidenvironment;thefluctuationamplitudeincreaseswithincreasingworkingenvironment

    ;flexibility.

    ;Keywords:inspectionrobot;transmissionline;obstruction;rigid-flexiblecouplingdynamics;finiteelementmethod;simulation

    ;1Introduction

    ;Inspectionrobotisakindofinnovationalmethods

    ;foreffectiveinspectionandmanagementofhigh-voltage

    ;(110and220kV)andextravoltage(500kVandabove)

    ;powertransmissionsystem.Aninspectionrobot

    ;prototypeproposedinthisworkiscapableof

    ;overcomingobstacles(dampers,clamps,suspensionand

    ;tensioningtowers,insulatorchains,etc)alongoverhead

    ;phaselinesandvaryingspansthroughjumperlineto ;carryoutfullpathlivelineinspectionlj.Comparingwith

    ;inspectionworkersandunmannedaerialvehicles(UAV), ;theinspectionrobotcanassurebetterperformances ;includingservicecontinuity,inspectionaccuracyand ;efficiency,andsafetyinsuchsevereconditionsas ;mountainareas,river-crossingandgrasslands. ;Since1980s,anumberofrelativeachievements ;havebeenachieved.Mostoftheresearcheswerefocused ;ontherobotsystemconstructionL2-3J,

    ;mechanism

    ;design[4,

    ;controlsystem[

    ;,

    ;recognitionandnavigation

    ;ofobstaclestlo].

    ;However,fewresearchesconcernedthe

    ;dynamicbehaviorsandvibrationcontrolthatarevery ;importantanddirectlyimpacttheinspection ;performancesofrobots,suchasprecisionoflocationof ;obstaclesandfailuredeteetionofsignals,control ;accuracy,andworkefficiency.In2005,thedynamic ;simulationbasedonmultirigid-bodymodeland

    ;experimentsunderrigidworkingenvironmentwere ;conductedi’”j.Moreover,toimprovetheinspection

    ;speedandeciency,theiointsofrobotwillstar[upand ;stopquicklyduringadjustingposesforovercoming- ;obstaclesandvarying.spans.Akindofactivevibration ;controlalgorithmandanoptimaldesignofdrivingload ;wereproposedforamulti-bOdvrobotL”J.

    ;Theinspectionrobotequippedwithdetection ;instrumentsperformsinspectionalongtheoverhcad ;transmission1ine.whichisakindofflexiblecatenary ;cablewithobstacleslstherigidflexiblecoupling

    ;dynamicbehaviorsshouldbeconsidered.Regardingthe ;robotasamultirigid-bOdvsubsystemandthe

    ;transmissionlineasamulti.flexible_bOdvsubsystem,the ;couplingdynamicsimulationswereconductedunderthe ;workconditionsofno.-obstacleandovercoming-- ;obstacles[2,.Basedontheaboveaccomplishments. ;furthersimulationsandanalysiswereperformedinthis ;worktoexploretheimpactsofobstructiveflexible ;Foundationitem:Project(50575165)supportedbytheNationalNaturalScienceFoundati

    onofChina;Projects(2006AA04Z202,2005AA2006?1)supported

;bytheNationalHigh-TechRese~chandDevelopmentProgramofChina;Project(20813)s

    upportedbytheNaturalScienceFoundation

    ;ofHubeiProvince,China;arojcot(20045006071-28)supportedbytheYouthChenguangP

    rojectofScienceandTechnologyofWuhan

    ;City,China

    ;Receiveddate:2008-0308:Accepteddate:2008-0519

    ;Correspondingauthor:XIAOXiao-hni,Associateprofessor,PhD;Tel:+8627-687722

    49;E-mail:xhxiao@whu.edu?cn

    ;870J.Cent.SouthUniv.Techno1.(2008)15:869876

    ;movingpathontherobot’sperformances

    ;2Inspectionrobotanditsworkingconditions ;2.1Prototypesofinspectionrobot

    ;Since1997.threegenerationprototypesof

    ;inspectionrobot,namelyremotelyoperatedvehicle ;(ROV),autocrawlingrobot(ACR),andauto-rolling/ ;crawlingrobot(ARCR).havebeendevelopedin,vuhan ;University~15J.China.ACRCisabletoautomatically ;fulfillsuchfunctionsasro11ing/crawlingalong ;noobstaclesegment,overcomingobstaclesduring ;tensilesegment,spanningtensioningtowers,detecting ;andidentifyingobstacles,selflocatingrobot,online ;supplyingpowerandmonitoring,detectingfailuresand ;diagnosing,computermanagementoninspectedline ;runningconditionsandinspectiontasks.

    ;Thedynamicstudyinthisworkisbasedonthe

    ;ACRCprototype.AsshowninFig.1.ACRCisdesigned ;intodouble.arlnsymmetricalandsuspendingstructure. ;Thereisonedrivingwheelattheendofeacharm ;enablingtherobottorollalongno.obstaclesegmentof ;line,andapairofclawsenablingtherobottograsp/loose ;thelineduringadjustingposesforovercomingobstacle. ;EacharlTlhastworotationdegreesoffreedom(DOF)to ;realizerotationofrobotarmsontwoverticalaxes. ;Betweenthetwoarms,thereisaninteractivetranslation ;D0Favailablefortheirinteractiveslidingand ;transpositionalongthesliderail.

    ;S1i

    ;Fig.1SymmetricalmechanismstructureofACRCprototype ;Inkinematicanddynamicmodeling,onlysixDOF ;wereconsidered,namely,rotationjoints2and3ofariTl ;I,androtationoints5and6ofarlTlII,translation ;oint1andtranslationjoint4betweentwoarms.Axesof ;ioints2and6arehorizontal,intersectingverticallyto ;thatofioints3and5,respectively.

    ;2.2Characterofinspectionworkingenvironment ;Asmentionedabove,theoverheadlineistheunique ;obstructivemovingpathoftheinspectionrobot.The ;spanbetweentwoadjacentsuspensiontowersisasmuch

    cross, ;ashundredsevenmorethan1kmduringriver

    ;whereasthesagofspanisasmuchasscoresofmeters. ;Theflexibilityoftheoverheadlineisprettyhigh. ;Moreover,windexcitedvibrationsoftheoverhead

    ;linesuchasAeolianvibrationandgalloping【叫canbe

    ;transferredtotherobotbodythroughitsmanipulator ;graspingorrollingwheelcontact.Simultaneously,when ;therobotovercomesobstaclesorvariesmovingpaths,it ;willadjustposesandproduceunbalancedforcedueto ;theinstablityofitsgravitycenter.Thus,thecoupling ;betweentherobotandthetransmissionlinewillmake ;therobotvibrate,furthermore,decreasetherobot’s

    ;performance,includingprecisionofobstacles’location

    ;andfailuresignals’detection,contro1accuracandwork

    ;efficiency,etc.

    ;2.3BarrieIpassingkinematicprogramming

    ;Duetothesymmetricalstructure,themotionsofsix ;D0Fcanbeabstractedintofourbasicsubactions,by ;whichtherobotisabletocarryoutallthethreerequired ;kinematictasks:movingalongnoobstaclesegment,

    ;overcomingobstacleandvaryingspans.Takingdamper- ;overcomingasanexample,thefoursubactionsare ;programmed.asshowninFig.2.

    ;1,Subaction1:Twowheelsrollalongthetrans- ;missionlinewithtwoarmsparallelsuspending. ;21Subaction2:EndmanipulatorofarmI(orarm ;II)clampsthe1ine,whiletherobotrotatesaroundioint2 ;(orioint6)tolift/descendtherobotbodyby30.. ;31Subaction3:EndmanipulatorofarnqI(orariTl ;II1clampstheline,whileanotherarlnrotatesaroundthe ;axisofjoint5(orjoint3)by180..

    ;4,Subaction4:EndmanipulatorofarrnI(orarm ;II)clampsline,whiletheotherarlTltranslatesalong ;joint4totransposetwoarms.

    ;3Couplingdynamicmodeling

    ;Acouplingdynamicmodelwasdevelopedthrough ;combiningrigiddynamicwithflexibledynamictheories. ;Consideringthehighflexibilityoftheoverheadline.it ;wasmodeledasamultiflexible_bodvsubsystem. ;whereastheinspectionrobotasamultirigid.bodysub

    ;system.Themodelingprocedureincludesthreesteps: ;frstly,amulti.rigid.bodydynamicmodelforthe ;inspectionrobotisformedwithLagrangemethod; ;secondly,amultiflexiblebodydynamicmodelof

    rigid.bodymodel ;overheadlineisbuilt;thirdly,themulti

    ;oftherobotandthemultiflexible.bodymodeloftheline ;arecoupledthroughgraspingboundarycouplingor ;roilingcontactcouplingcondition.

    ;Therigidmulti.bodydynamicmodelingof

    ;J.Cent.SouthUniv.Techno1.(2008)15:869876871

    ;inspectionrobotwasdetailedinRef.[111,SOhereareiust ;explanationsonthemodelofflexibleline. ;11Flexiblebodydiscretemethodforoverhead ;transmissionline:commonflexiblediscretemc:thodsare ;Reyleigh.RitzmethOd.FEM.andmodalsynthesis ;method.etct16J.Inthiswork,FEMandmodalsynthesis ;methodwerecombinedtodiscreteaspanofflexibleline. ;Thefornlerwasusedtoobtainthedominantmodal ;vectorsofaspanofline.whereasthelatterwasadopted ;todescribeitsspatialconfiguration.

    ;2,Multiflexiblebodydynamicmodelingmethod

    ;oftransmissionline:commonflexible-bodvdynamic ;modelingmethodsareNewtonEulermethod,Lagrange

    ;method,Guassmethod,Kanemethod,Hustonmethod, ;andHamiltonmethodtl/J’etc.Herein,theLagrange

    ;method,whichcorrespondswiththemethodadoptedin ;Transimission

    ;ADMAS,wasusedtogetthedynamicequations ;3.1Dynamicmodelingofrobot

    ;ConsideringthesixiointsdefinedinCOOrdinatesof ;eachlinkareshowninFig.3,whereafandstandfor ;linklengthandlinkoffset,respectively;standsfor ;iointvariablet”J.BasedonDenavit-Hartenbergmethod,

    ;robotlinkparameterswereobtainedinTlab1e1,wheref ;standsforlinktwistangle.

    ;TheinitialvaluesofthevariablesinTable1are ;listedasfollows:

    ;=

    ;0,d4=/4,02=90.,o5=90.,06----0.(1)

    ;Thenthetransformationmatricesoflinks()Canbe ;obtained.Thegeneraldynamicequationscanbeobtained ;withLagrangemethod:

    ;

    ;(e)(d)

;Fig.2Foursubactionsandcorrespondingposesofinspectionrobotduringovercomingdam

    per:(a)Subactionl;(b)Subaction2;

    ;(c)Subaction3;(d)Subaction4

    ;Fig.3CoordinatessettingforlinksofACRCprototype

    876 ;872J.Cent.SouthUniv.Techno1.(2008)15:869

    ;Table1Links’parametersofACRCprototype

    ;Hn

    ;=

    ;?D腩百+??D4+Gf

    ;k=lk=l,”=1

    ;(2)

    ;wherenisthenumberofrobotIinks;glSthe

    ;generalizedcoordinates;Dikistheaccelerationitem,iff= ;k,Dtiistheeffectiveinertia,otherwiseDiiisthecoupled ;inertiaofointtandjointjDiistheinversetorque ;itemimposingonjointigeneratedbytheaccelerationof ;jointifk=m,Disthecentripetalforcecoefficient ;causedbyvelocityofjointjatjointf,otherwiseDis ;thecoriolisforcecoefficientcausedbyvelocityofjointj ;andkatJoint:Giisthegravityatjointf.

    ;Thedynamicequationsoftherobot,includingitems ;ofinertia,couplinginertia,coriolisacceleration, ;centripetalaccelerationandgravity,werederivedin ;Refs.fll12].

    ;3.2Dynamicmodelingoftransmissionline

    ;Togetthedynamicmodelofthetransmissionline.a ;FEAmodelofaspanoflinebetweentwoadjacent ;suspensiontowerswasbuiltfirst.Forthelargespanof ;flexiblelinebetweentwotowers,therigidityoflinehas ;liRleimpactonitsoverhangingspatialconfiguration. ;Thusassumeitcanonlybeartensileforce.insteadof ;bendingmoment.andthetensiledirectionisalongthe ;line’saxisandsubjectstounifoITndistributionalongline

    ;length.AsshowninFig.4,theshapeofaspanofline ;takeson’’catenarystate’’.andthecoordinatesofa

    ;spanoflinecanbecalculatedbasedonthecatenary ;equation.

    ;ThenthecoordinateswereforwardedtoFEA

    ;soflwareANSYSformodeling.Themodalparameters ;Fig.4Contourcatenaryofspanofoverheadline ;wereobtainedwithsubspacemethod.Thefirstsixorders ;ofmodalfrequenciesandvectorsinXYandXZplanes ;wereadoptedtodescriptthespatialconfigurationof ;overhcad1ine.Thephysicalcoordinate{(,)}ofthe

    ;overhcadlinecanbeindicatedbythesuperpositionof ;dominantsystemmodels,quotaofwhichisrepresented ;bycorrespondingmoda1coordinates.

    ;{(}=[{g(}(3)

    ;where{g(}andIX]arethemodalcoordinateandthe ;selecteddominantmodalmatrixofsystem,respectively. ;3.3Couplingdynamicmodels

    ;BasedontheworkingconditionanalysisinSection ;2.3tyoicalconditionswerechosenforsimulationin ;ADMASsimulationplatform.Themulti.flexiblebody

    ;modeloftherobotandthemulti.flexible-bodvmodelof ;the1inewerecoupledasfollows.

    ;11Condition1--subaction1:Thedynamicmodel ;forinspectionrobotrollingalongnonbarriersegmentof

    ;transmission1inewasconductedwithFEM.Thecontact ;modeloftherigidrobotwheelsandflexiblelinewas ;formedbydiscretizingthecontinuouscontactrea1 ;system.AsADAMS/Viewdidnotsupportcontacton ;FEM.thethreedimensionalcontactforceswere ;simplifiedtotwodimensionalcontactforcesbetween ;eachnodeinFEAmodelofflexiblelineandrigidedge ;circleoftherobotwheels.Adumbobject.ofwhichboth ;qualityandinertiaarezero.isadherestoeachFEMnode ;ThemodeshowninFig.rmI:6Twodimensionalcircle;7--Kinematical ;input;8--Robot;9--Rotationpair;1Coplanerrestraint

    ;2)Condition2--subaction2:Coupleioint1in ;multi??rigid?-bodymodeloftherobotandthegrasping ;pointinmulti.flexible.bodymodeloftheline.namely, ;fixtheendmanipulatorofarmIandtheline.Then ;constrainother4DOFexceptforthatofjoint2. ;31Condition3--subaction4:Couplethegrasping ;pointinthemodelasincondition2.andcons~ainother ;4DOFexceptforthatofioint4.

    ;J.Cent.SouthUniv.Techno1.(2008)15:869876873

    ;4Couplingdynamicsimulation

    ;Thejoint’skinematicalfunctionwasdefinedwith

    ;STEPfunctioninADMAS[1.

    ;TheformofSTEP()is

    ;STEP(t,to,x0,tl,X1)(4)

    ;wheretistheindependentvariable;toandtlarethe ;initialandfinalvaluesoft,respectively;x0andx1arethe ;initialandfinalfunctionvaluesofSTEP(),respectively. ;Accordingtotheparametersoftherobotprototype, ;theiointSTEPfunctionsweresetasfollows.

    ;1,Condition1--subaction1:Taking10sassimula? ;tiontime,and1.0,0,5,and0.3sforaccelerating/ ;deceleratingtime,respectively,thesimulationof ;subaction1wasconductedwiththreedifferentSTEP ;functions.

    ;STEP1:

    ;3×360~[STEP(t,0,0,l,1)STEP(t,4,0,5,1)1

    ;STEP2:

    ;3×360~[STEP(t,0,0,0.5,1)STEP(t,4.5,0,5,

    ;STEP3:

    ;3×360×[STEP(t,0,0,0.3,1)STEP(t,4.7,0,5,

    ;2,Condition2:Taking10sassimulationtime,01

    ;Time/s

    ;sand910sforaccelerating/deceleratingtime, ;respectively,theSTEPfunctionwassetas: ;3×360×[STEP(t,0,0,l,1)STEP(t,9,0,10,1)]

    ;31Condition3:Taking20sforsimulationtime,

    19.6sforaccelerating/decelerating ;00.3sand19.3

    ;time,respectively,theSTEPfunctionwassetas ;28.8×[STEP(t,0,0,0.3,1)-STEP(t,19.3,0,19.6, ;11]

    ;Thefrictionfactorsofioins2and4were0.3,0.2, ;respectively.Theaccelerationtimeofthemotorwas0.5 ;s.whiletherotationvelocitvofthemotorwas270o)Is. ;10m.span,15m-spanand20m-span,were

    ;consideredinConditions2and3toexploretheinfluence ;oftheflexibilityoftheworkingenvironmentonthe ;robot’sdynamics.The10m.spanand30m-spanwere

    ;setincondition1becauseofthehigherrollingspeed. ;Thecounter-dynamicsimulationwasconductedto ;getthedrivingmomentofthejointmotor,andthe ;displacement,velocityandaccelerationofthejoints ;vibration.Mostofthevibrationsoftransmissionlineare ;inplane.whichiscorrespondingwithits ;winddeducedvibrationsJ.Thevibrationdisplacements ;under3conditionsalongaxesXandYareshownin ;Figs68.respectivelyAxesxandYaredefinedasthe ;sameasthoseinFig.4.

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