中英文翻译几何在机械设计中的作用.docx
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中英文翻译几何在机械设计中的作用.docx
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中英文翻译几何在机械设计中的作用
本科毕业论文(设计)翻译
题目新型超声波洗碗机
学院制造科学与工程学院
专业机械设计及其自动化
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
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