ImperialCollegeLondonBScProjectComplexProcessesand3DPrintingSupervisor:Author::JoshuaPriceJune10,2013
AcknowledgementIwouldliketoexpressmyspecialgratitudetomysupervisor,,formotivationandguidancethroughouttheproject,aswellasmyprojectpartner,JoshuaPrice,,especiallyThomasClaysonandAksatShah,
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........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................126AchievementsandResults127UnexpectedIssuesandPotentialSolutions148ExtensionsandFutureWork159Conclusion17iii
ListofFigures1Anexampleofemergent3Dprintedart:........................12TheFDMextrusionprocess.......................................23Exampleofathresholdoverhangingangle...............................44Non-manifoldedge............................................45Anexampleofasmalllatticegas....................................56Probabilisticnatureofforestfiremodel................................673Darrayofcubesvisualisation.....................................88Layerswithlittletonooverlap.....................................99Layerswithhalfoverlap.........................................1010Stretchedoverlappingcubes.......................................1011Smoothedoverlappingcubes.......................................1112ExamplesofoptionsavailableintheGUI...............................1313EvolutionofacellularautomatonintheGUI.............................14143Dexampleof2Dlatticegasexpandingintime............................1515Roughandsmooth3Drepresentationsofamodifiedforestfire...................1516Top-downviewofamodifiedforestfire.................................1617Finalprintedmodifiedforestfire....................................1618Undersideofmodelshowsunexpectedoffset..............................17iv
,alsoknownasadditivemanufacturing,,whichremovematerialtocreatefeaturesandareknownassubtractiveprocesses[1].Whilemachininghasbeenusedinfactoriesfordecades,additivemanufacturingtechniquesbringtothetablebenefitssuchaseasyprototyping,increasedgeometriccomplexity,‘Fatherof3Dprinting’[2].In2010,theadditivemanufacturingindustrywasestimatedat$[3].,abletoproducemanygeometriesinawiderangeofmaterials,,inwhichdesignersuseadditivemanufacturingprocessestoquicklyproducescalemodelsofprototypedesignsatreasonablecost[1].Anotheremerginguseforadditivemanufacturingisdirectdigitalmanufacturing,wheremanufacturersuse3Dprintingtoproduceend-userproductswithbenefitsofeasycustomizationandnothavingtoproduceinventoryuntilanorderisplaced[4].,manyexamplesofwhichcanbeseenatthe3DPrintshowwhichtourssomeofthebiggestcitiesintheworld[5].3Darthasalsobeganmakinganappearanceinartmuseums,&AMuseuminLondon,depictedinfigure1[6].Figure1:Anexampleofemergent3Dprintedart,,canbeseenondisplayintheV&.(Imagetakenfrom[6].)1
,eachofwhichhavefundamentallydifferentwaysofbuildinguplayersofmaterial.•ExtrusionDeposition:(FDM),depictedinfigure2,,easytoinstall,.[1][7]Figure2:-Moveableheatedbed.(Imagetakenfrom[8].)•GranularMaterialsBinding:,(SLS),,includingtypesofplastics,metals,ceramics,andglass,’sgranulesize.[1][9]•LaminatedObjectManufacturing(LOM):,,,howeveritspopularityisnowwaningwiththeemergenceofFDMandSLS.[1]•Photo-polymerisation:Thisclassofprocessesexposesphoto-polymerstoradiation(typicallyultravio-let).Theradiationtriggersachemicalreactionwithinthematerial,-lithography(SLA)wasdevelopedinthemid-80s,,manynewtypesofradiationcurablematerialshavebeencommerciallydeveloped,-polymers,andisthemainmethodofbio-printing(whichaimsto3Dprintorgansandtissue).DownsidestoSLAarecostsand2
thechoiceofmaterialsbeinglimitedtophoto-polymermaterials.[1],asmany3Dprintingprocessesarelimitedtoafewtypesofmaterials.•Thermoplastics:Thesesyntheticresinsbecomepliablewhenheated,(PC)aremostoftenused,howeveranumberofblendsandplasticsengineeredforspecificapplications(suchasaerospaceormedical).[1][10]•Metals:Morerecently,,,jewellery,andengineeringsupportstructures.[1]•Photo-polymers:Thisclassofpolymerschangetheirproperties,typicallybychangingfromaliquidstatetoasolid,,-polymersareonlyusedinphoto-polymerisationprocessessuchasSLA,andaretypicallyhybridsofepoxyandacrylicresins.[1][11]•OtherMaterials:,materialssuchasglass,nylons,andpolystyrenehavebeenusedinSLSprinting.[1][9]-terialstothetable,,
Figure3:,.(Imagetakenfrom[13].),conventionallyitwillbedesignedusingacomputer-aided-design(CAD),thematerialrequiredforthepart,
Alimitationofpolygonalmeshesisthattheyhavethepotentialtobenon-manifold,-manifoldmeshesandnon-manifoldmeshesalsodon’tcooperatewellwithpredefinedsmoothingordeformationalgorithms,sowhencreatingmeshesonehastocarefullydesignwiththislimitationinmind.[16],.[17][18]PerhapsthemostwellknownexampleofacellularautomatonisConway’sGameofLife(CGL).CGLisatwodimensionalcellularautomatononasquarelattice,whereeachcelliseither‘alive’or‘dead’.EachcellinCGLupdatesitselfbyconsideringthestateofitselfanditsneighbours:•Anyalivecellwithfewerthantwoorgreaterthanthreealiveneighboursdies.•Anydeadcellwithexactlythreealiveneighbourscomestolife.•’sverysimplerulesandbinarystatevector,itcandisplaycomplexbehaviour,,despitesimplerules,hasdrawntheattentionofthephysicscommunity,especiallyformodellingstatisticalmechanicalprocesses.[18][19]-deterministicinthestateofeachcell;thatisforagivenconfigurationofstates,,theremaybemorethanonestatewhichevolvestoagivenstate.[18]Figure5:Anexampleofasmalllatticegasupdatingaccordingtotherulesdescribedin[20].Noticethatthetwoblackcellsontherightdon’,operatingonthesquarelatticewithtwopossiblestates::5
•,theoccupiedneighbouringcellbecomesempty.•Whenmorethanoneoccupiedneighbouringcellsareattemptingto‘enter’theemptycell,,,asdemonstratedinfigure5,-bodysystems.[20],foreachcell,.[18]Anexampleofaphysicallymotivatedprobabilisticmodelistheforestfiremodel,whichoperatesonasquarelatticeandhasthreepossiblestates:alive,dead,‘trees’:•Aburningcellalwaysdies.•Analivecellstartsburningifoneormoreofitsneighboursisburning.•Adeadcellbecomesalivewithprobabilityp.•Analivecellwithnoburningneighboursstartsburningwithprobabilityf,,asseeninfigure6,asoneinitialstatecanleadtomanysuccessivestates.[20]Figure6:,weseetwo(ofmany)potentialstatesthataforestfirestatemayevolvetowithnon-zeroprobability.(White-Dead,Green-Alive,Red-Burning)6
,bothdeterministicandprobabilistic,’sevolutionisdescribedbylogicalinteractionsbetweenneighbouringcells,,especiallystatisticalmechanics.[17].[17]2MotivationandObjectivesWith3Dprintingemergingasamoreaffordableandcommontechnologyinourworldtoday,creatingprintablephysicscontentmaybeinstructiveeitherintheclassroomortheartmuseum,,,eachconstrainedandconnectedbythedesiredstatisticalmodel,,theresultingobjectshouldbe3Dprintable,inotherwords,theobjectshouldconformtoanumberofstructuralandgeometricconstraintswhicharevaguelydefinedbythespecificprintingprocessandmaterial,,bynature,,manufacturingprocessandhardware,printersettings,,:•,parameters,andupdaterule.•
•,perhapscomposedoftrianglesorhexagons,:•,theslabsofcubeswouldsimplybestackedupononeanother,creatinga3Darrayofcubes,asillustratedinfigure7.•A‘ballandstickmodel’wasalsoconsidered,:Extrudingeachlatticeinthetimeevolutionintoa‘slab’andthenstackingsuccessivetime‘slabs’,().,,,-smoothingalgorithm,,the3Darrayofcubessolutionmustbemodifiedsuchthateachelementoftheoriginalcubearrayisoverlappingaspecifiedamountwitheachofitsneighbouringcubes(inspaceandtime)
Figure8:,whenlookingateachcube-cubeconnection,,thatisthosewhicharecreatedbythelargescaleevolutionofthecellularautomata,,thetime(upward)dimensionofamodelmaybe‘stretched’,bymultiplyingeachofthez-coordinatesbyascalefactor,,themodelasitisnowdefinedstillexhibitsmaximum90◦overhangs(thebottomfacesofeachcube).Todealwiththisproblem,afterthe3Doverlappingcubearray,themodelwillbeimportedintothemesheditorMeshLabandthesmoothingfilter,‘LaplacianSmooth’,◦,++,,aprimarysearchforlibrarieswhichmaybeusefulincomputinggeometricsurfaceswasdoneandwefoundtwowhichseemed9
Figure9:Incontrasttofigure8,:Inordertocontroltheoveralllargescaleangleofthegeometrythemodelmaybestretchedinthetime(z),namelyCGAL[21]andVCG[22].However,aftertinkeringwiththeselibraries,,(),theQTandBoostlibrariesforC++[23]‘cube-y’,NetFabb(aSTLfilerepairandmodificationtool)[24]-printer[25][26]wasusedtoconvertprint-readySTLfilesintoinstructionsforthemovementoftheprinternozzle,
Figure11:Todealwiththeinevitableissueofsmallscaleoverhangsinacubemodel,uptothreeiterationsofa‘LaplacianSmoothing’,howeverifmoredetailedknowledgeisdesiredthesourcecodecanbefoundopen-sourcebynavigatingtotheurlin[27].,,,visualizethecellularautomata,andcreate3Dpolyhedronswithouteditingthesourcecode,,definedonasquarelattice,:Latticewhichdefinesthelatticeofcells,,,,theLatticetypeisdefinedasasquarearrayofLatElem,asimpletypewhichstoresthestateofthecell,aswellaspointerstoeachofitseightneighbouringLatElem(thosewhichshareatleastonevertex).Thestateofeachelementisanenumeratedtype,,,capturingthecellularautomaton’
,storedinaModel,intoa3Dpolyhedron,,,(dependingontheamountofdefinedoverlapbetweenLatElem).TheelementsofaCubeArrayareCubeElem,(emptyoroccupied),theCubeArraymustbeconvertedintoaPolyhedron,,-vectorsdescribingthepositionoftheobject’svertices,,,,,,,,,
Figure12:,,,‘move’,,,:•Burningcellsnolongerbecomeemptycellsimmediately,butratherburnforalengthoftimedefinedbytheuser.•Thechanceforfiretospreadtoadjacentoccupiedcellsisnolonger100%,,ratherthanacompletelydeterministicone,wasinhopeofcreatingmoreaestheticallyinterestingmodels,,youcanseetheexpansionof‘forests’fromseveralindividual‘trees’atthebase,-likeformations,betterseeninfigure16,showwhereandwhen‘lightning’strucka‘tree’.13
Figure13:,whichusesanFDMprintingprocess,◦,,producingthephysical3Dmodeldepictedinfigure17,,,,,itwaslearnedthattheselimitationsarenormallynotwelldefinedandpeoplewhodesignpartstendtohaveexperiencewithdesigningforacertainprocessand,throughtrial-and-error,,,,whohasknowledgeofthequantitativelimitationsoftheprocesss/heintendstouse,
Figure14:,[23].Figure15:,,,-likestructures,seeninsectionsoftheundersideofthemodelinfigure18,iswhathappenswhentheFDMprocessattemptstoprintwithnosupportingstructure,,,peoplefamiliarwiththeReprapprintersuggestedthattheremaybeaneasyfixforthisbychangingsomeoftheprinter’ssettings,,
Figure16:Atopdownviewofamodifiedforestfiremodel,highlightingthe‘pits’:,’srepertoire,-manifoldness,howevernotoolexiststocheckifaSTLfileisactually3Dprintableforagivenprocess/,especiallyfornon-experts(ofwhichthereareboundtobemanymoreduetothegrowthof3Dprinting).16
Figure18:Theundersideoftheprintedmodelshowsthat,earlyintheprintingprocess,,,similartowhatwasdoneinthisproject,,[1]IanGibson,DavidRosen,,2010.[2]://
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