活塞连杆机构的外文和翻译综述Word文档格式.docx

活塞连杆机构的外文和翻译综述Word文档格式.docx

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Abstract

Thispaperdealswithmodelingandsimulationofthedynamicsoftwocommonlyusedmechanisms,

（1）theCrankshaft–Connectingrod–Piston–Cylindersystem,and

（2）theUniversalJointsystem,usingtheBondGraphApproach.Thisalternativemethodofformulationofsystemdynamics,usingBondGraphs,offersarichsetoffeaturesthatinclude,pictorialrepresentationofthedynamicsoftranslationandrotationforeachlinkofthemechanismintheinertialframe,representationandhandlingofconstraintsatjoints,depictionofcausality,obtainingdynamicreactionforcesandmomentsatvariouslocationsinthemechanism,algorithmicderivationofsystemequationsinthefirstorderstate-spaceorcauseandeffectform,codingforsimulationdirectlyfromtheBondGraphwithoutderivingsystemequations,andsoon.

Keywords:

BondGraph,Modeling,Simulation,Mechanisms.

1Modeling

Dynamicsoftwocommonlyusedmechanisms,

（1）theCrankshaft–Connectingrod–Piston–Cylindersystem,and

（2）theUniversalJointsystem,aremodeledandsimulatedusingtheBondGraphApproach.Thisalternativemethodofformulationofsystemdynamics,usingBondGraphs,offersarichsetoffeatures[1,2].Theseinclude,pictorialrepresentationofthedynamicsoftranslationandrotationforeachlinkofthemechanismintheinertialframe,depictionofcauseandeffectrelationship,representationandhandlingofconstraintsatjoints,obtainingthedynamicreactionforcesandmomentsatvariouslocationsinthemechanism,derivationofsystemequationsinthefirstorderstate-spaceorcauseandeffectform,codingforsimulationdirectlyfromtheBondGraphwithoutderivingsystemequations.Usuallythelinksofmechanismsaremodeledasrigidbodies.

Inthiswork,wedevelopandapplyamultibondgraphmodelrepresentingbothtranslationandrotationofarigidbodyforeachlink.Thelinksarethencoupledatjointsbasedonthenatureofconstraint[3-5].Bothtranslationalandrotationalcouplingsforjointsaredevelopedandintegratedwiththedynamicsoftheconnectinglinks.Aproblemofdifferentialcausalityatlinkjointsariseswhilemodeling.Thisisrectifiedusingadditionalstiffnessanddampingelements.Itmakesthemodelmorerealistic,bringingineffectsofcomplianceanddissipationatjoints,withindefinabletolerancelimits.MultibondGraphmodelsfortheCrankshaft–Connectingrod–Piston–Cylindersystem,and,theUniversalJointsystem[6],aredevelopedusingtheBondGraphApproach.ReferenceframesarefixedoneachrigidlinkofthemechanismsusingtheDenavit-Hartenbergconvention[7].Thetranslationaleffectisconcentratedatthecenterofmassforeachrigidlink.Rotationaleffectisconsideredintheinertialframeitself,byconsideringtheinertiatensorforeachlinkaboutitsrespectivecenterofmass,andexpressedintheinertialframe.Themultibondgraphisthencausaledandcoding

inMATLAB,forsimulation,iscarriedoutdirectlyfromtheBondGraph.AsketchofthecrankshaftmechanismisshowninFig.1,anditsmultibondgraphmodelisshowninFig.2.AsketchoftheUniversaljointsystemisshowninFig.3,anditsmultibondgraphmodelisshowninFig.4.Resultsobtainedfromsimulationofthedynamicsofthesemechanismsarethenpresented.

1.1Crankshaft-ConnectingRod-Piston-CylinderMechanism

Fig.1showsthesketchofthe“Crankshaft–Connectingrod–Piston–Cylindersystem.”

Fig.1:

Crankshaft-ConnectingRod-Piston-CylinderMechanism.

Theindividualcomponentsareconsideredasrigidlinks,connectedatjoints.Thefirstmovinglinkisthecrank,thesecondlinkistheconnectingrodandthethirdlinkisthepiston.Aframeisfixedoneachlink.Thusframe1isfixedonlink1,frame2onlink2,andframe3onlink3.Afixedinertialframe0,whoseorigincoincideswithframe1,ischosen.However,itwillneitherrotatenortranslate.C1,C2andC3arecentresofmassofrespectivelinks.TheframesarefixedonrespectivelinksusingtheDenavit-Hartenbergconvention[4].

DynamicsofthesystemofFig.1ismodeledinthemultibondgraphshowninFig.2.Themodeldepictsrotationaswellastranslationforeachlinkinthesystem.Theleftsideofthebondgraphshowstherotationalpartandrightpartshowsthetranslationalpart.WerestrictanymotionbetweentheoriginofinertialframeOandpointonthelink1thatisO1byapplyingsourceofflowSfaszero.SimilarlywerestrictanyrelativemotionatpointA,distinguishedbyA1onlink1andA2onlink2,byapplyingsourceofflowSfaszero.Thepistonwhichislink3,isconstrainedtotranslateonlyalongtheX0direction.TranslationalongY0andZ0directionisconstrainedbyapplyingsourceofflowSfaszeroforthesecomponents.DifferentialcausalityiseliminatedbymakingtheK（1,1）elementofthestiffnessmatrix[K]betweenlink2andlink3aszero.

Additionalstiffnessanddampingelementsusedforeliminatingdifferentialcausalitymakethemodelmorerealistic,bringingineffectsofcomplianceanddissipationatjoints,withindefinabletolerancelimits.TheseviscoelasticelementsarerepresentedinthebondgraphbyusingCandRelements.

WehaveasourceofeffortSeatlink3,whichisthepressureforceactingonthepiston,althoughthisforceisalsoactingonlyinXdirection.

Fig.2:

MultibondgraphmodelfortheCrankshaft–Connectingrod–Piston–CylindersystemofFig.1.

1.2UniversalJointMechanism

TheFig.3showsthesketchofthe“UniversalJoint”mechanism.

Fig.3:

UniversalJointMechanism.

Ithasthreerigidlinks,twoareyokeswhichareattachedtorotatingshaftsandthemiddleoneisthecrossconnectingthetwoyokes.Theinertialframeisnumbered0,anditisfixed.Frame1isonlink1,frame2onthecrosswhichislink2,andframe3ontherightyokewhichislink3.Originoftheinertialframecoincideswiththatofframe1oflink1.Thelinks1and2areconnectedwitheachotherattwocoincidentendpointspointsA-A1onlink1andA2onlink2,andB-B1onlink1andB2onlink2.Similarlylinks2and3areconnectedattwopointsD-D2onlink2andD3onlink3,andE-E2onlink2andE3onlink3.

Link1rotatesaboutZaxiswithrespecttotheinertialframe.Theframe2islocatedatthecentreofmassofthelink2.Link2rotateswithrespecttothelink1indirectionZ2asshowninFig.3.Frame3alsocoincideswithframe2butitislocatedonthelink2.Theframe3onlink3rotateswithrespecttothelink2,aboutZ3,asshowninFig.3.ThebondgraphforthissystemisshowninFig.4.

Fig.4:

MultibondgraphfortheUniversalJointsystemofFig.

Theissueofdifferentialcausalityarisesforthismechanismalso.Itiseliminatedusingadditionalstiffnessanddampingelements.Asdiscussedearlier,thismakesthemodelmorerealistic,bringingineffectsofcomplianceanddissipationatjoints,withindefinabletolerancelimits.Therelativemotionbetweenthelinksatjoints,alongcertaindirections,isrestrainedbyapplyingthesourceofflowSfaszero.Theconstraintrelaxationistunedbychangingthevaluesofstiffnessanddampingatcorrespondingjoints.Herewerestrictthemotionofthelink3intwodirectionsYandZ,andallowmotioninXdirectionbyresolvingthesourceofflowinthreepartsandbyputtingSfaszeroinYandZdirectionsonly.Forthesimulation,anexcitationtorqueisappliedtolink1abouttheZdirection

2Simulation

TheresultsofcomputersimulationforthecrankshaftmechanismofFig.1arediscussedfirst.Theinitialpositionofthecrankshaftisat1θ=60owiththeX0axis.Itisthenreleasedundertheeffectofgravity.Theforceofgravityalsoactsontheconnectingrod.Noforceduetogaspressureisconsideredforthesimulationasitisnotthemainissueunderfocusforthispaper.TheupperrowinFig.5showsthedisplacementofthecentreofmassC1,asobservedandexpressedinFrame0.ItmovesinacirculararcabouttheZ0axis.ThefirstfigureinthelowerrowofFig.5showstheoscillationofthecrankshaft

abouttheZ0axisthroughchangeinorientationoftheunitvectorsofFrame1.ThesecondfigureinthesecondrowshowstheoscillationofthecentreofmassC1withtime.Thiscouldperhapsbeascribedtothenonlinearityimposedduetocouplingwiththeconnectingrod.

SimulationresultsfortheUniversaljointsystemarepresentedinFig.8.Aconstanttorqueisappliedtothedrivingshaftaboutitsaxis.Thedrivenshaftmakesanangleof5°

withtheaxisofthedrivingshaft.TheFirstrowshowstheresponseofthedrivingshaftwhichisthefirstlink.Thecomponentofangularmomentumofthedrivingshaftaboutitsaxisincreaseslinearly,whichisasexpected.Thefirsttwofiguresofthesecondrowshowthechangeinorientationofthecross,whichislink2.Angularmotionaboutallthreeaxesisclearlyvisible.ThedrivenshaftfollowsthemotionofthedrivershaftasisclearfromthethirdrowinFig.8.

3Conclusions

TheBondGraphapproachisusedtomodeldynamicsoftwocommonlyusedmechanisms,

（1）theCrankshaft–Connectingrod–Piston–Cylindersystem,and

（2）theUniversalJointsystem.Pictorialrepresentationofthedynamicsoftranslationandrotationforeachlinkofthemechanismintheinertialframe,representationandhandlingofconstraintsatjoints,depictionofcauseandeffectrelationships,codingforsimulationdirectlyfromtheBondGraphwithoutderivingsystemequations,havebeenexplainedinthiswork.MATLABbasedsimulationshavebeenpresentedandinterpretedforbo