shaping the digital twin for design and production engineering

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HAL Id: hal-01513846 https://hal.archives-ouvertes.fr/hal-01513846 Submitted on 25 Apr 2017 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Shaping the digital twin for design and production engineering Benjamin Schleich, Nabil Anwer, Luc Mathieu, Sandro Wartzack To cite this version: Benjamin Schleich, Nabil Anwer, Luc Mathieu, Sandro Wartzack. Shaping the digital twin for de- sign and production engineering. CIRP Annals - Manufacturing Technology, Elsevier, 2017, 66 (1), 10.1016/j.cirp.2017.04.040. hal-01513846

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Page 1: Shaping the digital twin for design and production engineering

HAL Id: hal-01513846https://hal.archives-ouvertes.fr/hal-01513846

Submitted on 25 Apr 2017

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

Shaping the digital twin for design and productionengineering

Benjamin Schleich, Nabil Anwer, Luc Mathieu, Sandro Wartzack

To cite this version:Benjamin Schleich, Nabil Anwer, Luc Mathieu, Sandro Wartzack. Shaping the digital twin for de-sign and production engineering. CIRP Annals - Manufacturing Technology, Elsevier, 2017, 66 (1),�10.1016/j.cirp.2017.04.040�. �hal-01513846�

Page 2: Shaping the digital twin for design and production engineering

ShapingtheDigitalTwinforDesignandProductionEngineering

BenjaminSchleicha,NabilAnwerb,LucMathieub,SandroWartzacka

aChairofEngineeringDesign,Friedrich-Alexander-UniversitätErlangen-Nürnberg,

Martensstrasse9,91058Erlangen,Germany.bLURPA,ENSCachan,Univ.Paris-Sud,UniversitéParis-Saclay,

94235Cachan,France.

Abstract:

Thedigitalizationofmanufacturingfuelstheapplicationofsophisticatedvirtualproductmodels,whicharereferredtoasdigitaltwins,throughoutallstagesofproductrealization.Particularly,morerealisticvirtualmodelsofmanufacturedproductsareessentialtobridgethegapbetweendesignandmanufacturingandtomirrortherealandvirtualworlds.Inthispaper,weproposeacomprehensivereferencemodelbasedonthe concept of SkinModel Shapes,which serves as a digital twinof thephysical product in design andmanufacturing. In this regard,model conceptualization, representation, and implementation as well asapplicationsalongtheproductlife-cycleareaddressed.

Keywords:

Design,Tolerancing,DigitalTwin.1.IntroductionIntoday'shighlycompetitivemarkets,theambitionsforshorteningthetimetomarketandforincreasingtheproductdevelopmentperformancefueltheapplicationofsophisticatedvirtualproductmodels,whichare frequentlyreferredtoasdigital twins.Enabledbythedigitalizationofmanufacturing,cyber-physicalproduction systems,model-based systemengineering, anda growingendeavour fordata gatheringandprocessing, thesemodelsare increasinglyenrichedwithproductionandoperationdata.Moreover, theyallowtheefficientpredictionoftheeffectsofproductandprocessdevelopmentaswellasoperatingandservicingdecisionsontheproductbehaviourwithouttheneedforcostlyandtime-expensivephysicalmock-ups[1-3].Particularlyindesign,suchrealisticproductmodelsareessentialtoallowtheearlyandefficientassessmentoftheconsequencesofdesigndecisionsonthequalityandfunctionofmechanicalproducts.However, current approaches to the implementation of digital twins lack of a conceptual basis, whichhinderstheapplicabilityofthedigitaltwinvisiontovariousactivitiesindesignandproductionengineering.Motivatedbythisneed,thispaperproposesacomprehensivereferencemodel,whichservesasadigitaltwin of the physical product in design and production engineering. In this regard, important modelproperties,suchasscalability,interoperability,expansibility,andfidelity,aswellasdifferentoperationsonthis referencemodel along the product life-cycle, such as composition, decomposition, conversion, andevaluation are addressed.Moreover, the application of this referencemodel to geometrical variationsmanagementishighlighted.Thepaper is structuredas follows. In thenext section, thevisionof thedigital twinand itsevolution isreviewed.After that, a comprehensive referencemodel for thedigital twin is introduced,which is thenappliedtogeometricalvariationsmanagement.Finally,aconclusionandanoutlookaregiven.

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2.TheVisionoftheDigitalTwinIthasbeenargued,that“thevisionofthedigitaltwinitselfreferstoacomprehensivephysicalandfunctionaldescriptionofacomponent,productorsystem,whichincludesmoreorlessallinformationwhichcouldbeusefulinall-thecurrentandsubsequent-lifecyclephases”[4].Inthefollowing,theevolutionofthisvisionisbriefly illustrated, recentdefinitionsof thedigital twinarediscussed,andseveralviewpointson itareaddressed.2.1.TheOriginandEvolutionoftheDigitalTwinPriortotheindustrialrevolution,physicalartefactswerepredominantlymanufacturedbyartisansresultinginuniqueinstancesofagiventemplate.However,withtheintroductionoftheconceptofinterchangeablepartsinthe18thcentury,thewayproductsweredesignedandmanufacturedrapidlychangedascompaniesbegantostriveforbuildingcopiesoftheirproducts inmassproduction.Recently,theparadigmofmasscustomizationaimsatcombiningthesetwoestablishedmanufacturingconceptstoachievelowunitcostsforcustomizedproducts.However, thoughsuchmanufacturingparadigmsallow the fabricationof largequantitiesof similar, i.e.customized,partsorproducts,thesemanufacturedinstancesaremereunrelatedcopies.Incontrasttothat,theideaofbuildingatwinreferstoproducingacopyofapartorproductandusingitforreasoningaboutotherinstancesofthesamepartorproduct-thusestablishingarelationbetweenmultiplecopies.ThisideaissaidtooriginatefromNASA’sApolloprogram,“whereatleasttwoidenticalspacevehicleswerebuilttoallowmirroringtheconditionsofthespacevehicleduringthemission”[5].However,overthepastdecades,advancementsincomputertechnologyenabledestablishingincreasinglysophisticated virtual models of physical artefacts as well as the fusion of such models for systemsengineering [6]. Thesemodels notonly serve for thedesign verification and validation [7], but are alsoincreasinglyusedasthemasterproductmodelcomprisingthemodel-baseddefinitionofrequiredproductcharacteristics[8].Moreover,theevolvementsin“microchip,sensorandITtechnologies”[9]pavedthewayfortheadventofsmartproducts,whichtrackandcommunicatetheiroperatingconditionsandthusallowto“feed”theirproductmodelswithdataabouttheirstatus,suchasenvironmentalconditionsandloads.sBesidethis,modernsensingroutines,whichgoevenbeyondgeometricalmeasurementandscanning,allowtheeasy,quick,andreliablecollectionoflargesetsofdatafromphysicalartefacts.Patternrecognition,datamining,deeplearning,reverseengineering,andotherdataanalysisapproachesmakeuseofthesedatasetsandunveildependenciesbetweenproduct,process,andoperationalcharacteristicsthatusedtobehidden.Thevastdevelopments in simulation technologyaswell as the increasingpossibilities forgatheringandexchangingdatafromproductsthusallowedforbuildingvirtualtwinsofphysicalproducts,whichfinallyledtothepresentunderstandingofthe“digitaltwin”vision.ProbablythefirstdefinitionofitwasgivenbyNASAintheirintegratedtechnologyroadmap(TechnologyArea11:Modeling,Simulation,InformationTechnology&ProcessingRoadmap; 2010),whichhasbeen slightly adapted in [10]: “ADigital Twin is an integratedmultiphysics,multiscale,probabilisticsimulationofanas-builtvehicleorsystemthatusesthebestavailablephysicalmodels,sensorupdates,fleethistory,etc.,tomirrorthelifeofitscorrespondingflyingtwin”(Fig.1).Withsomesimilaritytothis,Grievesdefinesthedigitaltwinas“asetofvirtualinformationconstructsthatfullydescribesapotentialoractualphysicalmanufacturedproductfromthemicroatomicleveltothemacrogeometricallevel”[11].

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Fig.1.TheVisionoftheDigitalTwinthroughouttheProductLife-Cyclefollowing[11].

2.2.ViewpointsontheDigitalTwinBasedonthesedefinitions,itcanbefound,thatthereexistdifferentviewpointsonthevisionofthedigitaltwin.Inthiscontext,ithasbeenargued,that“fromasimulationpointofviewthedigitaltwinapproachisthenextwaveinmodelling,simulationandoptimizationtechnology”[5].However,thedigitaltwinisnotonecompletemodelofthephysicalproduct,butasetof linkedoperationdataartefactsandsimulationmodels,whichareofsuitablegranularityfortheirintendedpurposeandevolvethroughouttheproductlife-cycle[4].Thus,thedigitaltwinnotonlyservesrepresentationpurposesbutisalsoapplicableformakingpredictionsabouttheexpectedproductbehaviour[4],whilethegranularityofthesimulationmodelsfitstotheirpurposeandevolvesfromearlydesignstages,wheresimpleproductmodelsareusedtodecideaboutproductconcepts,todetaildesign,wheresophisticatedsimulationmodelssupportthedimensioninganddesignofpartsandsubassemblies.Asaresult,fromaproductlife-cyclemanagementpointofview,thereisastrongneedtointegratealllife-cycledataartefacts intoacomprehensivemanagementsystem,whichcanbeusedbyvariousactors forqueryingdata,suchasthrough-lifeperformance information,andmakingpredictionsaboutthephysicalproductfromthedigitaltwinfordesignoptimizationandmanufacturingsystemimprovement[5].2.3.CurrentIndustrialUnderstandingandApplicationsDifferentunderstandingsof the“digital twin”canbeobserved in industrialpractice,particularlybyPLMsoftwarevendors.Inthisregard,ithasbeenargued,thatPTCisfocusingonestablishingalinkbetweenthevirtualproductmodelandthephysicalparttoincreasethemanufacturingflexibilityandcompetitiveness,while Dassault Systèmes targets the product design performance by creating a platform that enablesdesignerstovirtuallybuildandinteractwithcomplexsystems.Moreover,thedigitaltwinunderstandingofGeneralElectricfocusesonforecastingthehealthandperformanceoftheirproductsoverlifetime,whereasSIEMENS strives for improved efficiency and quality in manufacturing by exploiting the possibilities oftoday’smanufacturingdigitalizationinthecontextofIndustry4.0.TESLAaimsatdevelopingadigitaltwinforeverybuiltcar,henceenablingsynchronousdatatransmissionbetweenthecarandthefactory,whileothercompaniesincreasinglyusecomplexproductmodelstoboosttheimmersioninvirtualandaugmentedrealityapplications.

PhysicalDom

ain

VirtualDom

ainDesign

Manu-

facturing

Use

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2.4.SynthesisandDiscussionAsithasbeenhighlighted,thevisionofthedigitaltwinevolvedduringthelastdecadesanddescribesthevisionofabi-directionalrelationbetweenaphysicalartefactandthesetofitsvirtualmodels.Inthiscontext,the virtual “twinning”, i.e. the establishment of such relations between physical parts and their virtualmodels, enables the efficient execution of product design, manufacturing, servicing, and various otheractivities throughout theproduct life-cycle. Particularly in design, suchdigital twins allow the check forconformanceoftheproductspecificationswiththedesignintentandcustomerrequirements.However, as it has been reported in scientific literature and in practice, current limitations to theimplementationofthevisionofthedigitaltwinareinsufficientpossibilitiesforsynchronizationbetweenthephysicalandthedigitalworldtoestablishclosedloops,themissingofhigh-fidelitymodelsforsimulationandvirtualtestingatmultiplescales,thelackinguncertaintyquantificationforsuchmodels,thedifficultiesinthepredictionofcomplexsystems,aswellasthechallengesforgatheringandprocessinglargedatasets.Indeed, these challenges can only be mastered based on a sound conceptual framework and acomprehensivereferencemodelforthedigitaltwin.3.AReferenceModelfortheDigitalTwinTheneedforrealisticvirtualproductmodelsfordesignandmanufacturingactivitiesisubiquitous.However,current approaches to the implementation of digital twins lack of a conceptual basis. This hinders theapplicabilityoftheimplementationstovariousactivitiesindesignandproductionengineeringandhencehandicaps the efforts for building integrated digital twins of physical artefacts. Motivated by thisshortcoming,weproposeareferencemodelforthedigitaltwin,whichcanbeconsideredasatemplatefortheimplementationofdigitaltwinsforspecificapplicationswhileensuringimportantmodelproperties,suchasmodelscalability,interoperability,expansibility,andfidelity.3.1.BackgroundTheconceptualbackgroundofthereferencemodelisborrowedfromclassicalsolidmodellingandrecentdevelopments in ISO standards for Geometrical Product Specifications (GPS), which offer a widelyacknowledged framework for the modelling, specification, and verification of product geometry. Solidmodellinghas introduced theabstraction-representation schema to conceptualize the idealizedphysicalproduct,andtoimplementitoncomputerswithasuitablerepresentation.ISOGPSstandardsevolvedfromindustrialbest-practicesandexamplestomorerigorousconceptsandalanguagewithconsistentsyntaxandsemanticswiththeaimoftransferringthemintotheageofdigitalization.TheseconceptualizationeffortshaveledtothedevelopmentoftheGeoSpelling“language”[12]whichisbasedonsoundconceptstoallowthe unambiguous definition of geometrical specifications and to mirror specification and verificationoperationsonthegroundsofadualityprinciple.OneofthesebasicconceptsistheSkinModel,whichisanabstractmodelof thephysical interfacebetweenaworkpieceand itsenvironment [13].TheSkinmodelpermitsamentalmodeland thoughtexperiments todevelopa theoretical inspectionprocedure,henceconnecting the specificationworld to thephysicalworld. Furthermore, severalmirroredoperations anduncertainties(ambiguities,methoduncertainty,implementationuncertainty)weredefined[14].

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3.2.ModelAbstractionandRepresentationThe idea behind the comprehensive reference model is to extend and transfer the above conceptualframeworkandtoconveythescientificfundamentalsofthegeometricalproductspecificationlanguagetothevisionofthedigitaltwin.Thenoveltyofthisreferencemodelistheparticularfocusonthe“twinning”betweenthephysicalandthevirtualrealm.Inthisregard,weproposetoendowthedigitaltwinwithanabstractmodelthatcomprisesallcharacteristicsandfullydescribesthephysicaltwinataconceptuallevelthroughout the whole product life-cycle. Based on this abstract model thoughts experiments can beperformed,which allows to capture andunderstand aswell as to clearly describe thephysical twin, itsbehaviouranditsenvironmentatanabstractlevel.TheexperiencesfromGPSstandardizationandrecentresearcheffortsontolerancingledtotheinsightthatonlythedifferentiationbetweentherealworkpiece,itsabstractandconceptualmodel(SkinModel),andthevirtualrepresentationofthisabstractmodelallowsforaclearunderstandingaswellasaforward-lookinglanguageforgeometricalvariationsmanagement.Consequently,theconceptofSkinModelShapeshasbeendeveloped for the virtual representation of the SkinModel based on discrete geometry representationschemes[15].Withsimilaritytothis,weproposeadifferentiationbetweentheabstractionofthedigitaltwinanditsrepresentation(Fig.2).Inthiscontext,themodelrepresentationmaydependontheparticularapplicationandcaninvolvevariousrepresentationandmodellingparadigms.

Fig.2.PhysicalTwinandReferenceModelfortheDigitalTwin(RepresentationandAbstraction).

Thedifferentiationbetweenaconceptualmodelanditsvirtualrepresentationforthedigitaltwinallowsachievingimportantmodelproperties(Table1),suchasmodelscalability,interoperability,expansibility,andfidelity.Inthisregard,theabstractmodeldescriptionenablesthedefinitionofmodeloperationsatdifferentscales,whilemodels for different interfaced parts and subassemblies of a product can be conceptuallyqueriedanddigitalproductmodelscanbeexpandedtosystemmodels.

PhysicalTwin DigitalTwin(Representation) (Abstraction)

Page 7: Shaping the digital twin for design and production engineering

Table1PropertiesoftheReferenceModelfortheDigitalTwin.

Scalab

ility Abilitytoprovideaninsightatdifferent

scales(fromfinedetailstolargesystems).

Interope

rability Abilitytoconvert,tocombine,andto

establishequivalencebetweendifferentmodelrepresentations.

Expa

nsibility Abilitytointegrate,toadd,ortoreplace

models.

Fide

lity

Abilitytodescribetheclosenesstothephysicalproduct.

3.3.OperationsontheReferenceModelBesidetheSkinModel,thedualityprincipleisanchoredintheISOGPSstandards.Itallowsthedifferentiationbetween a specification operator, which covers a set of operations that are used to define certaingeometricalspecificationsontheSkinModel,andtheverificationoperator,whichmirrorsthespecificationoperatorandcomprisestheoperationsthatarerequiredtoverifythespecificationsontherealpart.Thoughtheverificationoperatormirrorsthespecificationoperator,therewillalwaysremainuncertaintieswhethertheverificationoperationsfullycomplywiththespecificationoperator.Thisdualityprincipleaswellastheconceptofuncertaintiesisalsoconveyedtothereferencemodelforthedigital twin. In this regard, theapplicationof adigital twin todifferent scenariosand tasks indesignorproductionengineeringdictatestoapplycertainoperationsonthedigitaltwin.Theseoperationsdependonthe specific application and are backed by physical counterparts (such e.g. manufacturing or assemblyoperations).Theabstractionofthedigitaltwinallowsdescribingtheseoperationsonanabstractlevel,whiletheir virtual “representation” is performed employing specific simulationmodels. Due to the nature ofsimulation models, obviously, uncertainties will remain between the abstract description of a certainoperationanditsrepresentation.Weproposeheretoclassifythesetofoperationsinfourbroadcategories,namelyconversion,composition,decomposition,andevaluation.Moreover, the “twinning” between the physical world and the virtual world can be considered asobservationandpredictionphasesataconceptuallevel(Fig.3).Whiletheinformationtransferfromthephysicaltothedigitaltwinisrelatedtotheobservationandsensingofthephysicaltwin,theinformationtransferfromthedigitaltothephysicaltwinoriginatesfromscientificassumptions,simulationandvirtual

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testing models, with proper handling of uncertainty, used to predict certain characteristics and thebehaviourofthephysicaltwin.

Fig.3.DifferentOperationsonthePhysicalandtheDigitalTwinthroughouttheProductLife-Cycle.4.ADigitalTwinforGeometricalVariationsManagementTheaimofgeometricalvariationsmanagementistoensurethattherequiredgeometricalcharacteristicsoftheproductaremetdespitethepresenceofgeometricalpartdeviations.Theimplementationofadigitaltwin for geometrical variations management hence requires the consideration of all different viewsthroughouttheproductlife-cyclethatrelatetothespecification,generation,verification,andpropagationofgeometricaldeviations.Foreachoftheseviewsandapplications,specificoperationsonthedigitaltwinaredefinedandmirroredbycorrespondingvirtualrepresentations.Forthispurpose,thesetofoperationsdefinedinGPS[16]areexploitedandmappedtothosethatoperateonthereferencemodel.The concept of SkinModel Shapes as a paradigm shift in computer-aided tolerancing and geometricalvariations management [17] serves as a first approach to connect these views and operations in acomprehensivemodelthatincorporatesmanufacturingprocessplanningandinspectionprocessplanning(Fig.4).Thus,animportantsteptowardsthe“twinning”betweenthephysicalworldandavirtualmodelfora digital twin in geometrical variationsmanagement has been taken,which serves as a soundbasis forongoingresearch.

Fig.4.DigitalTwinforGeometricalVariationsManagement

Observation

Prediction

PhysicalTwin

PhysicalOperations- Conversion- Composition- Decomposition- Evaluation

DigitalTwin

Operations- Conversion- Composition- Decomposition- Evaluation

TWINNING

Manufacturing Assembly InspectionDesign …

GenerationofSkinModelShapes

AssemblySimulationfor

SkinModelShapes

MeasurementofSkinModel

Shapes

FunctionalCharacteristicsand

ToleranceSpecifications

Partition FiltrationExtraction

Decomposition

Collection Construction

Composition

Association

Conversion Evaluation

Evaluation

Operations

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5.ConclusionandOutlookTheabilityforassessingtheconsequencesofproduct,process,andservicingdecisionsemployingvirtualmodelsisanimportantcompetitivefactorformodernmanufacturingcompanies.Thevisionofthedigitaltwinreferstoanentangledrelationbetweenaphysicalartefactandthesetofsuchvirtualmodels.Inthispaper,thehistoryandevolvementofthevisionofthedigitaltwinaswellasitscurrentunderstandingandapplicationshavebeenportrayed.Besidethis,currentlimitationstotheimplementationofdigitaltwinshavebeendiscussedandacomprehensivereferencemodelforthedigitaltwinindesignandproductionengineering has been highlighted. Particularly, this reference model enables the clear differentiationbetween a conceptualmodel and its virtual representation for the digital twin. The application of thisreferencemodeltogeometricalvariationsmanagementhasalsobeensketched.Thebenefitofthispaperforresearchaswellasindustrialapplicationsistheprovisionofafirsttheoreticalandconceptualframeworkforthedigitaltwin,which istobeenrichedbythedesignandproductionengineeringcommunity inthefuture and which may lead to a scientific discussion about the vision of the digital twin and itsimplementationthroughouttheproductlife-cycle.References[1] LeuMC,ElMaraghyH,NeeA,OngSK,LanzettaM,PutzM,ZhuW,BernardA(2013)CADmodelbasedvirtualassemblysimulation,planningandtraining.CIRPAnn.62(2):799-822.[2] Roy R, Stark R, Tracht K, Takata S, Mori M (2016) Continuous maintenance and the future –Foundationsandtechnologicalchallenges.CIRPAnn.65(2):667-688.[3] AltintasY,KerstingP,BiermannD,BudakE,DenkenaB,LazogluI(2014)Virtualprocesssystemsforpartmachiningoperations.CIRPAnn.63(2):585-605.[4] BoschertS,RosenR(2016)DigitalTwin–TheSimulationAspect.InHehenbergerP,BradleyD(eds.):Mechatronic Futures: Challenges and Solutions for Mechatronic Systems and their Designers, SpringerInternationalPublishing,2016,59-74.[5] RosenR,vonWichertG, LoG,BettenhausenKD (2015)AboutThe ImportanceofAutonomyandDigitalTwinsfortheFutureofManufacturing,IFAC-PapersOnLine48(3):567-572.[6] Lu SC-Y, Li D, Cheng J,Wu CL (1997) AModel Fusion Approach to Support Negotiations duringComplexEngineeringSystemDesign.CIRPAnn.46(1):89-92.[7] MaropoulosP,CeglarekD(2010)Designverificationandvalidationinproduct lifecycle.CIRPAnn.59(2):740-759.[8] QuintanaV,RivestL,PellerinR,VenneF,KheddouciF(2010)WillModel-basedDefinitionreplaceengineering drawings throughout the product lifecycle? A global perspective from aerospace industry.Comput.Ind.61(5):497-508.[9] AbramoviciM, Göbel JC, Dang HB (2016) Semantic datamanagement for the development andcontinuousreconfigurationofsmartproductsandsystems.CIRPAnn.65(1):185-188.[10] Glaessgen EH, Stargel DS (2012) The Digital Twin Paradigm for Future NASA and U.S. Air ForceVehicles.Proceedingsof the53rdAIAAStructures,StructuralDynamicsandMaterialsConference,2012,Paperno.1818.[11] GrievesM,VickersJ(2017)DigitalTwin:MitigatingUnpredictable,UndesirableEmergentBehaviorinComplexSystems.InKahlenF-J,FlumerfeltS,AlvesA(eds.):TransdisciplinaryPerspectivesonComplexSystems:NewFindingsandApproaches,SpringerInternationalPublishing,2017,85-113.[12] MathieuL,BalluA(2003)GEOSPELLING:acommonlanguageforGeometricalProductSpecificationandVerificationtoexpressmethoduncertainty. InWilhelmR(ed):Proc.ofthe8thCIRPInt.SeminaronComputerAidedTolerancing.70-79.

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[13] Anwer N, Ballu A, Mathieu L (2013) The skin model, a comprehensive geometric model forengineeringdesign.CIRPAnn.62(1):143-146.[14] Nielsen HS (2013) Recent developments in International Organization for Standardizationgeometrical product specification standards and strategic plans for future work. Proceedings of theInstitutionofMechanicalEngineers,PartB:JournalofEngineeringManufacture227(5):643-649.[15] SchleichB,AnwerN,MathieuL,WartzackS (2014)SkinModelShapes:Anewparadigmshift forgeometricvariationsmodellinginmechanicalengineering.Comput.-AidedDes.50:1-15.[16] ISO17450-1:2011,GeometricalProductSpecifications(GPS)—Generalconcepts—Part1:Modelforgeometricalspecificationandverification.[17] SchleichB,AnwerN,MathieuL,WartzackS(2016)StatusandProspectsofSkinModelShapesforGeometricVariationsManagement.ProcediaCIRP43:154-159.