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DesignforAdditiveManufacturingBasedonAxiomaticDesignMethodKonstantinosSalonitis

ManufacturingDepartment,CranfieldUniversity,Bedford,UK

k.salonitis@cranfield.ac.uk

AbstractAdditive manufacturing technology promises to revolutionize the way products are

manufacturedandsuppliedtothecustomer.Existingdesignmethodshoweverdonottake

full advantageof theadditivemanufacturingprocesses capabilities. Thispaperpresents a

framework to improve the current design approach for additive manufacturing using an

axiomaticdesignapproach.Theproposedframework isusedbothforthedevelopmentof

newproductsandthere-designingofexistingproductsthataredesignedforconventional

manufacturing.Acasestudyispresentedforthevalidationoftheframeworkthathighlights

howthismethodcanbeusedfordesignvalidationanddecisionmaking.

Keywords:Productdevelopment;designmethod;additivemanufacturing

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1.IntroductionConventional manufacturing processes, such as machining, pose limitations on the

component geometries that can be produced. These limitations often result in structures

that are inefficient, asmany areas of a component have excessmaterial that cannot be

removed physically or in a cost effective way through conventional methods. Additive

Manufacturing (AM) processes provide the opportunity to address the problem of

inefficientstructures.Theyallowcomponentstobemanufacturedinabottom-upapproach

withlayingmaterialonlywhereitisrequired.Oneofthekeyadvantagesofsuchprocesses

isthefabricationofcomponentsandevencompleteassembliesdirectlyderivedfroma3D

CADmodel without the need for process planning in advance ofmanufacturing. Various

methods that allow the “building” of three-dimensional objects in sequence by adding

layersovereachotherhavebeendeveloped[1].

AMtechnologyhasarelativeshorthistoryofabout25yearsandithasgrownlargelysince

itsinvention:accordingtoWohlersReport[2],theAMprojectedvaluefor2015is$4bn,and

willreach$6bnin2017andalmost$11bnin2021.However,althoughitisbecomingmore

andmoremature,oftenclaimedasthe“nextindustrialrevolution”,therearestillanumber

ofchallengesforthesuccessfulcommercialisation.AMtechnologychallengesarerelatedto

the materials, the available CAD software, the data management, the sustainability, the

affordability, the process speed, the process reliability, the intellectual property, and the

standardstonamefew[3].ThedesignforAMhasbeenalsoidentifiedasakeychallenge,

highlightingthatforexploitingthecapabilitiesthatAMprocessesoffer,thedesignershave

to adapt their approach to the AM technology, not replicating the existingmethods and

philosophiesestablishedforconventionalprocesses.

AMprocesses canbeclassified into threedifferent categoriesdependingon the statusof

thematerialusedtocreatethepartduringtheprocesssuchaspowderbased,liquidbased

andsolidbased(Figure1).AlargenumberofdifferentAMprocesseshavebeendeveloped

intheshorthistoryofAM;fewofthemthoughsurvivedovertime.Commonmaterialsare

aluminium, steel alloys, precious metals, plastics used in a powder form and paper; but

wood,wax,paper,clay,concrete,sugarandchocolatearepossibletobeusedasfilament.

Selective laser sintering (SLS), electron beammelting (EBM), laser powder forming (LPF),

binder jetting (BJ) are applicable formetals, for prototype and direct partmanufacturing

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purposes.LPFisapplicableforrepairofpartsandcanthusextendthelifetimeofaproduct

even further. BJ’s ability to produce complex sand casting moulds has the potential of

designoptimisation,where lessmaterialwouldbeused in themould.Ultrasonic additive

manufacturing (UAM) and laminated object manufacturing (LOM) are suitable for metal

artefacts, whereas LOM is additionally considered suited for paper and plastic artefacts.

UAM’sabilityforinterchangeablemetalsduringthelayeringprocessoffersopportunitiesfor

theproductionandrepairofmetalmaterialofmorethanonetype,suchasbimetalswhere

differentcoefficientofthermalexpansionarerequired.Fuseddepositionmodelling(FDM)

with polymer basedmaterial and using stereolithography (SL) and digital light processing

(DLP)withphotopolymerbasedmaterialareusedmainlyforprototypesmanufacturing.

Figure1.Additivemanufacturingprocessesclassification(updatedfromKruthetal.[1])

The 3D model of a product is traditionally generated via computer-aided design (CAD).

Materialisaddedlayerbylayer,derivedasthincross-sectionfromthe3Dmodel.Thelayer

thicknessdeterminestheresolutionofthemanufacturedproduct.

Components optimised to exploit the benefits provided by additive manufacturing

techniques can look very different from those designed to suit conventional production

methods.It ishoweverchallengingforengineersaccustomedtodesigningcomponentsfor

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conventionalmanufacturing to adapt their thinking to exploit the additivemanufacturing

capabilities.

2.DesignforadditivemanufacturingAMtechnologiesallowforthecreationofmodelsandproductsthatareintricateinnature

andmadeofcompositematerialswhichcanbecustomised.Suchprocessescanbedefined

as the ones in which physical objects are made through layer by layer selective fusion,

polymerisationorsinteringofmaterials,dependingontheunderlineprincipleoftheprocess

[4].Afterthedesignhasbeenfinalized,thedesignerhastofollowanumberofsteps(such

as slicing, support generation etc.) that are required for the additivemanufacturing of a

part;thesestepsmayvarywiththetechnologyused.

Sinceadditivemethodsremovemostofthelimitationsofconventionalmanufacturing,any

complex design can be directly transformed into the final product. Conventional

manufacturing design constraints, such as avoidance of sharp corners, minimising weld

lines, draft angles and constant wall thickness are obsolete in that case. This allows

designerstocloselyadheretotheinitialconceptdesignandspecification.

Design methodologies that have been developed for manufacturing are attempting to

constrain designer’s imagination based on the manufacturing processes capabilities. For

example limitations due to the use of tooling are not relevant to additivemanufacturing

processes. For the conventional processes, a numberof designmethodologies havebeen

presented such as design for manufacturing and design for assembly with a number of

variationsforspecificprocessesandindustrialsectors.

However,withregardstothedesignframeworksforusingAMprocesses,fewstudieshave

been published. Indicatively Rodrigue and Rivette [5] developed a design methodology

based on design for assembly notion, borrowing ideas from TRIZ analysis, for the

optimizationofthealternativedesigns.Vayreetal.[6]presentedamethodologycomposed

of four steps. Podshivalov et al. [7] focused on the design for additivemanufacturing in

medical applications.Poncheetal. [8] took into consideration thepartorientationduring

building, the functional optimization and the optimization of the manufacturing paths.

AdamandZimmer[9]documentedanumberofdesignrulesforadditivemanufacturingthat

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can be integrated in a design framework. Salonitis and Saeed [10] presented a decision

supportmethodfortheredesignofexistingproductsusingadditivemanufacturing.

A common characteristic of all the studies reviewed is that the additive manufacturing

capabilities are not considered early enough on the design phase. Among the different

design theories andmethodologies, axiomatic design theory considers and assesses good

designideasevenfromtheconceptdesignphase,andthuslooksasapromisingapproach.

Axiomaticdesign[11],[12]wasintroducedinanattempttoscientificallydefinethedesign

process.Sinceitsintroductionnumerouspapershavebeenpresentedapplyingthemethod

for the development of new products none though on the design for AM. Recently a

thorough literature reviewwaspresented indicating thatmostof the relevant studiesare

applicationbasedusingmostlytheindependenceaxiom[13].

The objective of the present paper is to investigate the idea of using axiomatic design

method for the conceptual design of a component to be manufactured using additive

manufacturing.

3.ProposedframeworkAxiomaticdesign isbasedonmapping thecustomerneedson functions that theobject is

expected to perform (defined as functional requirements - FRs), then derive design

parameters (DPs) indicating how the object can satisfy such FRs and finally describe the

process variables (PVs) for the manufacturing of the object. This process is usually

implementedthroughzigzagdecompositionhavinginmindtwofundamentaldesignaxioms,

the independence axiom (each functional requirement should be independent) and the

informationaxiom(selectthedesignalternativewiththeminimuminformationcontent).

Themethodisidealfordevelopingnewproductdesignsandassessingthedesignsearlyin

the process. However, the manufacturing process constraints and capabilities are not

considered directly during the transition from the functional to the physical domain. The

mappingisfocusedontwoadjacentdomainsinordertointerlink“whatwewant”and“how

toachievewhatwewant”[12].Axiomaticdesignthusconsidersthemanufacturingofthe

componentafterthedesignhasbeendefinedinthephysicaldomainandit isdescribedin

theprocessdomainthroughtheprocessvariables.

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Nevertheless,anumberoftheoremsandcorollariesthathavebeenpresentedbySuh[12]

consider themanufacturability of a product. For example the third corollary suggests the

integrationofphysicalparts,withadditivemanufacturingprovidinglargecapabilitiesinsuch

design approach. Suh discussed in detail how axiomatic design can be used for assisting

manufacturing[14].

The proposed approach for taking into consideration the manufacturing capabilities and

limitations is depicted in Figure 2. The coreof theproposed framework is the axiomatic

design decomposition of the design space into domains (shown as ellipses in Figure 2),

however in order for themanufacturability of the design to be improved from the early

design phases, in addition to the theorems and corollaries, information such as

manufacturingguidelinesneedtobefedintothefunctionalandphysicaldomainduringthe

decompositionofthesedomains.

Figure2.Axiomaticdesignframeworktailoredfortheadditivemanufacturing

Therefore, in order for themanufacturing capabilities to be taken into consideration, the

zigzagdecompositionshouldnottakeplaceonlybetweentwoadjacentdomains(Figure3),

but through the threemain domains (functional, physical and process) as can be seen in

Figure4.Suchwiderdecompositioncanbeassistedbyguidelinesformanufacturingthatcan

be obtained by the practitioners and the literature review. Additionally, simulation and

Market

Needs

Customerdomain

{CNs}

Functionaldomain

Physicaldomain

Processdomain

• Manufacturingguidelines• ADcorollaries&theorems

VOCQFDKano

{FRs} {DPs} {PVs}

CADdetaileddesign

CAM

Manufa-cturing

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processmodellingcanassistinthedecisionoftheprocessvariablesaswillbeshowninthe

casestudy.

Figure3.Traditionalaxiomaticdesignmappingbetweentwoadjacentdomains.

Figure4.Axiomaticdesignmappingforconsideringmanufacturingprocesscapabilitiesduringtheearlydesignphases.

Improving themanufacturability of the design from such an early stage allows the direct

linkingof theaxiomaticdesignwith theCADsoftwareandsubsequently theCAMtool for

theplanningofthemanufacturing,ascanbeseeninFigure2.

3.1AdditiveManufacturingGuidelines

Asmentioned,thecurrentpracticewithregardstheassessmentofthemanufacturabilityof

a component takes place after the design phase has been almost finalized. In order

however, for these constraints to be considered early in the design process, even at the

conceptualphaseofthedesign,asetofrulesorguidelinesareneeded.Inordertocollect

suchdesignguidelines,furthertothethoroughliteraturereview,questionnaireswereused

tocapturethepractitioners’views.Theliteraturereviewwasperformedinordertoidentify

such guidelines from academic papers and simultaneously additive manufacturing OEMs

FR

FR1

FR1.1 FR1.2

FR2

DP

DP1

DP1.1 DP1.2

DP2

12

3

4

FR

FR1

FR1.1 FR1.2

FR2

DP

DP1

DP1.1 DP1.2

DP2

PV

PV1

PV1.1 PV1.2

PV2

1 2

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6

5

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were contacted (either by direct personal communication, or through the available

informationintheirwebsites).However,sincethegoalwastobetterunderstandhowthese

constraintsare“interpreted”bytheendusers, thequestionnairewasdevelopedforrapid

manufacturingbureausbasedontheinitial literaturereviewandinternetfindingsinorder

toassesstheusebythem.Theconstraintsidentifiedwererankedbytherespondentsand

exampleswererequestedforeachoftheseconstraints.

35 rapid manufacturing bureaus with expertise in both metallic and plastic additive

manufacturing technologywere contactedwithin theUK,with 22 responds received in a

periodof threemonths.Theconstraints thatwerecollectedareapplicabletomostof the

additivemanufacturingtechniques,andcanbegroupedintothefollowingdesignguidelines

andlimitations:

• Avoidanceofenclosedhollowvolumes

• Selectionofproperclearances.

• Minimumfeaturesize.

• Considerationofsurfacefinish.

• Selectionofmaterialsandresultingmechanicalproperties.

• Considerationofthemaximumworkingvolume.

• Buildingtimeandcost.

Thefirstthreeguidelinesarespecifiedduringthedesignphaseofthecomponent,whereas

theremainingonesarefunctionofthespecifictechnologyusedandtheprocessparameters

selection and decisions. Indicatively, enclosed hollow volumes might be desirable for

reducingtheweightofacomponent,butingeneraltheywillbefilledwithsupportmaterial

thatisdifficulttoremoveafterthefinishingprocess.Suchproblemscanbeaddressedinthe

designphaseby including gates to such areas.With regards the clearances, the standard

achievabletolerancesformostoftheadditivemanufacturingmachinesareintherangeof±

0.005”[15].Thesurfacefinishofadditivemanufacturedpartscanbecontrolledthroughthe

properselectionofprocessparameters,partorientationandmaterialselection.

Furthermore,asindicatedbyKlahnetal.[16],additivemanufacturingcannotbeconsidered

to replace conventional manufacturing processes, but should be considered when the

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designgoal is todevelopproducts thatpresenteitherof the followingcriteria: integrated

design,individualization,lightweightdesignandefficiency.

4.CaseStudyForthevalidationoftheproposedframework,abracketthattraditionallyismanufactured

throughmillingofanaluminiumalloy6082-T6block(Figure5),wasselectedasacasestudy.

Thebracketiscomposedofthreesmallrecessesonthetopsurfacethatareusedtoposition

and secure the bracket using three screws. The bracket needs to operate using existing

clamping components. It must be also compatible with the interfaces of the existing

mountingrailinthebottomofthebracket.Thebracketissubjecttothreeorthogonal,non-

concurrentshockloads.Thefinalpartneedstobeaslightaspossibleandshouldbeeasily

cleaned.

Figure5.Casestudydesignformanufacturingusingmachining

4.1Decomposition

In adopting the axiomatic design methodology, the first step is to define the Functional

Requirements(FRs)basedonthecustomerneeds.Thehighest-levelfunctionalrequirement,

whichservesasthemissionstatementisshownasFR0inTable1.Thepreviousparagraph

canbeconsideredasthedesignbrief,andthusthedesignparameter(DP)thatwillsatisfy

the functional requirement is considered to be surface topology optimization and can be

denoted as DP0. The design that will result from such a design parameter can be

manufactured using additivemanufacturing and thus this is considered to be the highest

level process variable (PV0). Fewmoredecompositionswill lead to theDPs andPVswith

more specific details, as can be shown in Table 1. The corresponding DPs and PVs are

derivedfollowingtheextendedzigzaggingmethodproposedintheprevioussection.

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Table1.Highlevelfunctionalrequirements,designparametersandprocessvariablesandfirstleveldecomposition

FRs FR0:Lightweightbracket

FR1:Supportloads

FR2:Easytoclean

DPs DP0:Surfacetopologyoptimization

DP1:Materialstrength

DP2:Surfaceroughness

PVs PV0:Additivemanufacturingprocess

PV1:Processparameters

PV2:Partorientationduringbuilding

DP0hasbeenidentifiedassurfacetopologyoptimization.Sincethefunctionalrequirement

is a lightweight bracket, the structure of the bracket needs to be optimized. Topology

optimisationisasystematicmethod,basedonfiniteelementanalysis,toproduceastrong

part with minimum use of material, exhibiting an organic looking structure. Stress

distributionanddeformationsarecalculatedtroughfiniteelementsimulationoftheexisting

model,inordertodecidewherematerialisredundant.Theinitialgeometryfiniteelement

analysis and the resulted organic shape of the bracket are shown in Figure 6. The only

technology that can replicate with detail such organic structures is the additive

manufacturing.

Figure6.(a)FEAappliedtotheoriginalbracketdesignand(b)Optimisedshapeusingtopologyoptimisation

a) b)a) b)

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Thedecompositiontolowerlevelsisachievedusingthezigzaggingmethod.Forexamplethe

secondlevelofFRshavebeenidentifiedastherequirementforthebrackettosupportthe

operating loads (FR1)and the requirement for the component tobeeasily cleaned (FR2).

The design parameters that can achieve such requirements, keeping in mind the

manufacturingguidelines,wereconsideredtobethestrengthofthematerial(DP1)andthe

surfaceroughness(DP2).Byproperselectionoftheprocessparameters(PV1)bothstrength

andsurfaceroughnessofthecomponentcanbecontrolled.Additionally,theorientationof

the component (PV2) during “building” will affect the surface quality. The functional

requirements, the design parameters and the process parameters can be further

decomposed; indicatively DP1 could be decomposed into DP1.1 “static loads” and DP1.2

“dynamicloads”.However,usuallythedecompositionisterminated,whenalevelisreached

wheretheFRscanbefullysatisfiedbytheselectedsetofDPs,andsubsequentlysuchDPs

can be fully controlled by the selected PVs. The integrated product and process

decompositiondiagramcanhelpinvisualizingthezigzaggingprocess[17],andispresented

inFigure7.

Figure7.Integratedproductandprocessdecomposition(rectanglesdenoteFRs,lozengesDPsandellipsesPVs)

Supportloads Easytoclean

Surfacetopology

MaterialStrength

Additivemanufacturing

Processparameters

Processparameters

LightweightBracket

Surfaceroughness

PartOrientation

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4.2Independenceaxiom

Suh [11], [12] has presented themathematical background of the axiomatic design. The

mappingofthefunctionalrequirementstothedesignparameters(throughthehierarchical

decompositionandthezigzagging)isdescribedbythefollowingequation:

!"# = % &'# (1)

where {FRs} and {DPs} are the functional requirements and design parameters vectors

respectivelyand [A] is thedesignmatrix. Similarly themappingbetween thephysicaland

theprocessdomainsisdenotedby:

&'# = ( ')# (2)

where{PVs} is theprocessvariablesvectorand[B]thematrix linkingthephysicalandthe

processdomain.Followingthewiderdecompositionproposed inFigure4,eqs. (1)and(2)

canbecombinedintothefollowingequation:

!"# = * ')# (3)

where[C]=[A]⨯[B]isthematrixlinkingtherequirementstotheprocessvariables.

The independenceaxiom isassessedby the shapeand thecontentof thematrix. Asper

Suh’s notation, when the matrix is diagonal then the design is considered to be

“uncoupled”, when triangular then it is classified as “decoupled”, otherwise it is

characterizedas“coupled”.Anuncoupleddesignistheidealwhereasthedecoupleddesign

is also acceptable when the DPs (and subsequently the PVs) are selected in the correct

order. Therefore, in thepresentapproachall threematrices ([A], [B]and [C])need tobe

checked,andthevariousvectorsmustbeoptimizedinordertoachieveatleastdecoupled

solutions. For the proposed solution the three matrices are presented in the following

equations,withX indicatingstrong influencewhereas0 indicatesweak influencebetween

theFRandDP:

!"1!"2 = . 0

0 .&'1&'2 (4)

&'1&'2 = . 0

. .')1')2 (5)

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!"1!"2 = . 0

. .')1')2 (6)

Eqs.(4)to(6)indicatethatthedesignisacceptablefromtheindependenceaxiompointof

view,asdesignmatrix[A]isdiagonal,whereasmatrices[B]and[C]aretriangular.Figure7is

alsoconveyingthesamemessage.Thustheresultofthisanalysisindicatesthattheinitial

decompositionproposedisfeasible,andthedesignsthatadheretosuchdecompositionare

acceptable.Anumberofconceptdesignscanthusbedevelopedandproposed,asshownin

Figure8.

Figure8.Alternativeconceptsthatcomplywiththefirstaxiom

4.3Informationaxiom:comparisonofdifferentsolutions

The comparison of the different acceptable solutions that conform to the independence

axiomisperformedbasedontheinformationaxiom.Theinformationaxiomwasdefinedby

Suh [12] with regards the information content needed for satisfying a given functional

requirement.Foreachfunctionalrequirementtheinformationcontentcanbecalculatedas:

01 = log5 678

(7)

wherepi is the probability for achieving the functional requirement FRi. In literature, the

probability is given in terms of design range (the tolerances that the designerwishes his

designtomeet)andthesystemrange(whatthesystemiscapableofdelivering).Inthelast

fewyearsanumberofapproacheshavebeenpresentedwheretheinformationisexpressed

infuzzylogictermsinordertoaccountforqualitativeinformation[13].

Forthecasediscussedinthepresentstudy,theinformationcontentneedstobedefinedfor

the two functional requirements. Since the support load is specified through the design

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specifications,all thealternativedesignswillbeabletosupportthis.Furthermore,wecan

safelyassumethatallconceptswillmeetFR1(support load),as thesamematerialwillbe

usedwith the same technology (thus the influencing process variables do not affect this

functionalrequirement).Thusonlythe“easetoofcleaning”willbeconsideredhere.High

values of surface roughness can result in accumulation of dust and dirt, thus surface

roughnessneedstobeminimizedwithamaximumallowablevalue.Processmodelscanbe

employedforthisreasontoquantitativelydescribethecapabilityoftheprocess.

Figure9.(a)Surfaceroughnessasafunctionofsurfaceangleand(b)thesystemanddesignrangeandthecommonrange

Figure9.apresentstheresultsofsuchmodelsconnectingtheangleof inclinationwiththe

resulting surface roughness for the case of stereolithography. The average surface

roughnessofSLA-producedpartswasestimatedasafunctionofthelayerthicknessandthe

angle of the inclined surface [18], [19]. Modelling was based on simplistic trigonometry

assumptions, while the surface roughness (Ra) could be calculated according to the

followingequation:

WhereDp isthedepthofpenetration,PL isthenominal laserpower,W0 isthelaserbeam

spot diameter,VS is the laser scanning speed, EC is the critical exposure time,OC is the

overcureandθistheinclinationangle.

0.00

1.00

2.00

3.00

0 30 60 90

Sufacero

ughness(μm)

SurfaceAngle(degrees)

AMsystemrange

Designrange

SurfaceRoughness

Probabilitydensityfunctio

n

Common rangea) b)

Basedon:[18],[19][20]

via a genetic algorithm model in order to determine the opti-mal process parameters (which include layer thickness, hatchspacing and hatch overcure) that would yield the minimumpart build error. Chryssolouris et al. [25] has estimated theaverage surface roughness of SLA-produced parts as a func-tion of the layer thickness and the angle of the inclined surface(Fig. 10). Modelling was based on simplistic trigonometryassumptions, while the surface roughness could be calculatedaccording to the following equation:

Ra ¼ Dp⋅lnffiffiffiffi2π

rPL

W 0VSEC

sinθ4tanθ

" #

−OCsinθ4tanθ

ð1Þ

where:

Dp depth of penetrationPL laser powerW0 laser beam spot diameterVS laser scanning speedEC critical exposure timeOC overcure

Reeves and Cobb in [26] and [49] presented an analyticalmodel for SLA surface roughness that took into considerationthe layer profile as well whether the plane was up-facing ordown-facing, which was verified with experimental data.Podshivalovab et al. [35] has used a 3D model to verify thedimensional accuracy of scaffold-like structures used in bonereplacement via CAD and FEA. Part dimensional stability hasbeen experimentally studied by a number of researchers.Rahmati [43] studied dimensional stability in SLA as a resultof resin shrinkage; Wang et al. [44] studied the effect of thepost-curing duration, the laser power and the layer pitch on thepost-cure shrinkage and empirical relations were establishedon the basis of the least squares method. The shrinkage strainswere investigated by Karalekas and Aggelopoulos [45] basedon a simple experimental setup and the elastic lamination the-ory. Narakahara et al. [46, 90] studied the relationship betweenthe initial linear shrinkage and resin temperature in a minute

volume built by SLA. Flach et al. [27] integrated an analyticalresin shrinkage model into the general SLA process modeldeveloped in [28], to have a theoretic prediction of the dimen-sional stability due to resin shrinkage, concluding that fastershrinking resins should result in lower overall shrinkagevalues. It has been found that the overall linear shrinkage,due to cure for a line of plastic, was estimated to have beengiven by the equation:

FC ¼ 1=LZL

0

f r Yð Þdy ð2Þ

where:

fr(y) residual fractional linear shrinkage at position yFC overall fractional linear shrinkage due to cureL length of strand of plastic (cm)t time (sec)ts time for laser to scan from position y to L (sec)

Chryssolouris [25], Jelley [29] and Jacobs [30] investigatedthe polymerization process that occurs during SLAmanufacturing, based on the modelling of the laser source,the modelling of the photo-initiated free radical polymeriza-tion and the modelling of the heat transfer involved in theprocess. A few have dealt with modelling the build time inthe SLA process. Chen [31], Giannatsis [91] and Kechagias[32] have calculated the process time analytically. Kechagias[32] has presented a method where the total distance travelledby the laser beam is directly calculated from the part geometry(STL file). The time required for each layer to be produced isthen calculated analytically on the basis of the laser velocity,keeping in mind whether the laser is performing border draw-ing, hatching or filling. Furthermore, the time required for allthe auxiliary steps is estimated. Contouring and hatching ve-locities were calculated by:

Cv ið Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2π

PL

W 0ECeCd ið Þ

.Dp

" # ;vuut ð3Þ

Hv ið Þ ¼ mPL

hsECeCd ið Þ

.Dp

" # ð4Þ

where:

PL laser powerW0 laser beam half widthCd curing depthhs hatching space (distance between neighbour scanning

vectors)m number of times the slice area is hatchedEc critical energyDp penetration depthFig. 10 Trigonometry used by Chryssolouris [25]

Int J Adv Manuf Technol

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AnanalyticalmodelpresentedfromReevesandCobbin[20]forSLAsurfaceroughnessthat

tookintoconsiderationthelayerprofileaswellwhethertheplanewasup-facingordown-

facingwasalsousedinthepresentstudyandpresentedinfigure9.a.Similartrendscanbe

observedbetweenthetwomodels.

Similar models can be derived for other additive processes as well (indicatively fused

depositionmodellinghasbeenmodelledin[21]and[22],SelectiveLaserMeltingin[23],3D

printingin[81],Laminatedobjectmanufacturingin[33],etc.).

Consideringuniformprobabilityfunctions,asshowninFigure9.b,theinformationcontent

ofeachapproachcanberelatedtotheamountofinclinedfeaturesintheselecteddesign,

withthedesignshavingmoreinclinedsurfacestopresenthigherinformationcontent.The

designthatexhibitedtheminimuminformationcontentwasselected(Figure10).

Figure10.CasestudydesignformanufacturingusingAM

5.ConclusionsDesign for additive manufacturing is limited by the use of methods and approaches

developed for conventional manufacturing. In the present work, the axiomatic design

theorywasadaptedandzigzaggingdecompositionwasexpandedtotakeintoconsideration

the manufacturing limitations and capabilities from the early phases of design. For this

reason manufacturing guidelines and constraints were captured from additive

manufacturing practitioners. The method was validated for the case of additive

manufacturingofacomponent.Theaxiomaticdesignwascombinedwithsurfacetopology

optimizationforthehigh leveldecompositionandwaspresented inthepresentpaper for

the first time. Basedonsuchacombinedapproach,designers can takeadvantageof the

processescapabilitiesinordertodesigncomplexdesignsbyusingunexploredregionsofthe

designspaceandassesstheircreativityusingthetwoaxiomaticdesigntheorems.

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