中英文翻译几何在机械设计中的作用Word下载.docx

中英文翻译几何在机械设计中的作用Word下载.docx

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学生姓名

学号年级08　

指导教师蔡鹏　

教务处制表

二O一二年五月二十八日

OntheRoleofGeometryinMechanicalDesign

VadimShapiroHerbVoelcker

TheSibleySchoolofMechanicalandAerospaceEngineering,CornellUniversity,Ithaca,NewYork,USA

Acompletedesignusuallyspecifiesamechanicalsystemintermsofcomponentpartsandassemblyrelationships.Eachparthasafullydefinednominaloridealformandwelldefinedmaterialproperties.Tolerancesareusedtopermitvariationsintheformandpropertiesofthecomponents,andareusedalsotopermitvariationsintheassemblyrelationships.Thusthegeometryandmaterialpropertiesofthesystemandallofitspiecesarefullydefined（atleastinprinciple）.Henceforthweshallfocusongeometryand,forreasonsthatwillbecomeevident,willnotdealwithmaterialsdespitetheirobviousimportance.

Mechanicalsystemsspecifiedinthemannerjustdescribedmeetfunctionalspecificationsthatappearedinitiallyasdesigngoals.Theprocessofdesigncanbethoughtofas"

generatingthegeometry"

thebreakdownintocomponentswithcoarselyspecifiedgeometry,andthenthedetailedspecificationofthecomponentformsandfittingrelationships.Designseemstoproceedthroughsimultaneousrefinementofgeometryandfunction[I].Animportantlineofdesignresearchseeksscientificmodelsforthisrefinementprocessandsystematicproceduresforimprovingandperhapsautomatingit.

Atpresentwehavetoolsfordealingwithtwowidelyseparatedstagesoftherefinementprocess.

Forsingleparts,functionisusuallyspecifiedthroughloadsonpiecesofsurface（e.g.aforcedistributionoverasupportsurface,aflowratethroughanorifice,aradiationpatternoveracoolingfin）;

specificationofthesolidmaterialthatpro-videsacarrierforthepiecesofsurfacemaybeviewedasaconstrainedshapeoptimizationprocess.

Atthehigherlevelof"

unitfunctionality,"

whereonedealswithsprings,motors,gearboxes,heatexchangers,andthelike,geometryusuallyisabstractedintorealnumbersifacknowledgedatall,andfunctioniscastintermsofordinarydifferentialoralgebraicequations（forheatflow,motortorqueasafunctionoffieldcurrent,andsoforth）.Systemsofsuchequationsdescribethecompositefunctionalismofnetworksoffunctionalunits.Thereisabiggapbetweenthese"

islandsofunderstanding,"

andintermediatestagesofabstractionareneededwhichacknowledgethepartialgeometryandspatialarrangementtopologyofsubassemblies.Broadlyspeaking,geometryisfaringbadlyincontemporarydesignresearch;

manyinvestigatorseither"

sweepitunderthecarpet"

ordealwithitsyntactically,e.g.through"

features"

definedinadhocways.Clearlyweneedmoresystematicwaystoaddresstherelationshipbetweengeometryandfunction,andwesuggestbelowsomeinitialstepstowardthisgoal.

EnergyExchangeasaMechanismforModelingMechanicalFunction

Mechanicalartifactsinteractwiththeirenvironmentsthroughspatiallydistributedenergyex-changes,andwearguebelowthatmechanicalfunctionalismcanbemodeledintermsoftheseexchanges.TheinitialcastoftheargumentdrawsheavilyonseminalworkbyHenryPaynter[2].Weshallregardmechanicalartifactsassystemsthatrangefromsinglesolidsorfluidstreams,whichusuallyarethelowestlevelofnaturalsystemthatexhibitimportantpropertiesofmechanics,tocomplexassembliesofsolidsandstreams.Aclosedboundary,whichmaybephysicalorconceptual,isadistinguishingcharacteristicofasystem:

thesys-temlieswithin（andpartiallyin）theboundary,theenvironmentliesoutside,andinteractionoccurs

throughtheboundary.Wedistinguishthefollowing:

S:

thephysicalsystemunderdiscussion;

8S:

theboundaryofS;

V:

aspatialregioncontainingSwhosecomplementistheenvironment;

8V:

theboundaryofV.

SmaycoincidewithV,and8Sand8Vareclosedsurfaces（usually2-mainfolds）inE3.WedistinguishSfromVbecauseSmaybepartiallyorwhollyun-known（recallthatthisnoteisaboutdesign）butboundablebyaknownV.Theprincipleofcontinuityofenergyappliestalllevelsofsystemabstraction.Ifnoenergyisgeneratedbythesystem,then

Thesurfaceintegralontheleftdescribesthetotalenergyflux（instantaneouspower）throughtheboundary;

PisageneralizedPoyntingvectordescribingtheinstantaneousrateatwhichenergyistransportedperunitarea,andnisthenormalatapointintheboundary8V.Ontheright,Oe/Otisthe（volumetric）densityofenergystoredinthesystem,andgistherateofenergylossordissipation.Asysteminteractswithitsenvironmentbyex-changingenergythroughitsphysicalboundary:

forexample,byradiatingenergystoredinthesystemoveraportionofitsarea,orbyprovidingsupporttoanexternalmatingpartandtherebyinducingstorageofdeformationenergyinthesystem.Thesub-setsofthephysicalboundaryoverwhichsuchex-changesoccurwillbecalled（followingPaynter）energyports.Ifs~isthephysicalboundarysubset（'

pieceofsurface'

）associatedwiththeituport,then

Thusthetotalenergyfluxthroughtheboundaryisasumofsignedfluxesthroughtheports.Wenotethataboundarysubsetsimaybelongtoseveralports,andthatbodyforces,suchasthoseinducedbygravitationalandmagneticfields,maybeaccommodatedbytaking~Sastheassociatedport.

GeometricalandFunctionalRefinementintheLimit

TheleftsideofEq.（2a）specifiesenergyexchangesthroughthesystem'

sportsandrequiresthatthefluxvector（s）andportgeometriesbeknown.Thetermsontherightcoverinternalenergy（re）distributionand/ordissipation.Thephysicaleffectsimpliedbythesetermsdependontheenergyregime（s）andthegeometryofthesystem;

theremayberigidbodymotion,elasticorplasticdeformation,temperatureredistribution,andsoforth.Mathematicalevaluationrequiresthesolutionof3-Dboundary-and/orinitial-valueproblems.Verymarkedsimplificationsensueifoneassumesthat1）theportsarespatiallylocalizedandidealizedsothattheintegralsontheleftofEq.（2a）maybeevaluatedindividuallytoyieldtermsPi,and2）internalenergystorageanddissipationaresimilarlylocalizedindisjointdiscreteregions,therebypermittingtheright-handintegralstobedecomposedintosumsoflocalintegralswhichmaybeevaluatedindividually.Withtheseassumptions,Eq.（2a）mayberewritten

wherePiisthepowerthroughthediscreteport,Eistheinstantaneousenergystoredinthediscreteregion,andGkisthedissipationrateinthekdiscreteregion.Alimitingformofthisrefinement（inPaynter'

sterminology--reticulation）isa"

Dirac-deltalimit"

whereintheportsshrinktospotsofzeroareaandthevolumetricregionsshrinktopointmasses,idealizedresistors,andthelike.Equation（3）isthebasisforPaynter'

senergybonddiagrams,orbondgraphs.Itdescribesasys-temthatmaytransfer,transform,store,anddissipateenergythroughelementswhosegeometryhasbeenrefinedintoafewrealnumbers--thespatiallpositionsofthediscreteportsandlumpedregions（whichgenerallyarenotcarriedinbond-graphrepresentations）,andintegralcharacterizationsofthediscreteportsandregions（forexamplethe"

value,"

inkilograms,ofapointmass）.Thishigherviewenablesonetoanalyzethedynamicsoftheidealized（discreet）system,butonecandeducelittleaboutthegeometryoffeasibledistributed（i.e.,real）systemsfromsuchanalyses;

essentiallyallgeometrymustbeinduced.Apparentlywehavegonetoofar,i.e.,havethrownawaytoomuchgeometry.

Fig.

（1）Designofsimplebracket

TowardanAppropriateRoleforGeometryWewouldliketostepbackfromthelimitingrefinementjustdiscussed,whereallnotionsofformhavebeenlost,andincludesintheproblemsomecontinuousgeometry--butnotthefull-blownfieldproblemcoveredbyEq.（I）unlessthisisunavoidable.Weshallsuggestbelowthreeprinciplesgoverningtheinteractionofformandfunctionthatwebelievewillyieldgeometricallywelldefined（butnotnecessarilyoptimum）designs.Asimplebutcommonexampledrawnfrompractice--designofabracket—willmotivatethediscussion（Fig.1）.

Thedesignbeginswiththreeholesofknowndiameterandconfigurationthataretobecarriedbyanunknownsolid（Fig.la）;

thesematewithotherparts（twoscrewsandapivotpin）.Bossesarecreatedtocontaintheholes（Fig.lb）becauseofconcernaboutinterferencewithothercomponentspassingbetweentheholes.FinallytheholesandbossesareboundtogetherintoasinglepartasinFigs.lcandld,withthefinalshapebeinggovernedbycriteriaforclearance,strength,weight,andaestheticandmanufacturingsimplicity.Twosimplebutimportantinferencesmaybedrawnfromtheexample.Firstly,theinitialholes（plussomeimpliedconstraintsurfacesinthethirddimension）arethebracket'

senergyports;

theyarefullyspecifiedgeometricallyandspecifybyimplicationwhatthebracketistodo--maintaintherelativepositionofportswhosegeometryadmitsrotationalmotion.Inprincipletheassociatedenergyregimes（force,torque:

elasticity）canbefullyspecifiedaswell,butinpracticetheyareoftenonlyimpliedor"

understood."

Secondly,theremaininggeometryisdiscretionarybutconstrainedbyrequirementsthattheholesbeboundintoaconnectedsolid,thatthesolidnotinterferewithothercomponents,andsoforth.Wenotethat,atthesingle-componentlevelofthebracket,shapeoptimizationusuallydoesrequiresolutionofthefull3-DfieldproblemcoveredbyEq.（2a）.

Fig

（2）position-fixingofthecharacterbracket

Fromthisexamplean