University of Groningen
Design and fabrication of conformal cooling channels in molds
Feng, Shaochuan; Kamat, Amar M; Pei, Yutao T.
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International Journal of Heat and Mass Transfer
DOI:
10.1016/j.ijheatmasstransfer.2021.121082
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Feng, S., Kamat, A. M., & Pei, Y. T. (2021). Design and fabrication of conformal cooling channels in molds:
Review and progress updates. International Journal of Heat and Mass Transfer, 171, [121082].
https://doi.org/10.1016/j.ijheatmasstransfer.2021.121082
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International Journal of Heat and Mass Transfer 171 (2021) 121082
ContentslistsavailableatScienceDirect
International
Journal
of
Heat
and
Mass
Transfer
journalhomepage:www.elsevier.com/locate/hmt
Review
Design
and
fabrication
of
conformal
cooling
channels
in
molds:
Review
and
progress
updates
Shaochuan
Feng
a,b,∗,
Amar
M.
Kamat
a,
Yutao
Pei
aa Department of Advanced Production Engineering, Engineering and Technology Institute Groningen, Faculty of Science and Engineering, University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands
b School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 10 0 083, China
a
r
t
i
c
l
e
i
n
f
o
Article history: Received 24 December 2020 Revised 28 January 2021 Accepted 8 February 2021 Keywords:Conformal cooling channels Injection molding Structural design Additive manufacturing
Hybrid additive/subtractive manufacturing
a
b
s
t
r
a
c
t
Conformalcooling(CC)channelsareaseriesofcoolingchannelsthatareequidistantfromthemold cav-itysurfaces.CCsystemsshow greatpromisetosubstituteconventionalstraight-drilledcooling systems astheformercanprovidemoreuniformandefficientcoolingeffects andthusimprovetheproduction quality and efficiency significantly.Although thedesign and manufacturing of CCsystemsaregetting increasingattention,acomprehensiveand systematicclassification,comparison,andevaluationarestill missing.Thedesign,manufacturing,andapplicationsofCCchannelsarereviewedandevaluated system-aticallyand comprehensively inthisreviewpaper. To achieve auniform andrapid cooling,somekey designparametersofCCchannelsrelatedtoshape,size,andlocationofthechannelhavetobe calcu-latedandchosencarefullytakingintoaccountthecoolingperformance,mechanicalstrength,andcoolant pressuredrop.CClayoutsareclassifiedintoeighttypes.Thebasictype,morecomplextypes,andhybrid straight-drilled-CCmoldsaresuitableforsimply-shapedparts,complex-shapedparts,andlocallycomplex parts,respectively.ByusingCCchannels,thecycletimecanbereducedupto70%,andtheshape devi-ationscanbeimprovedsignificantly.Epoxycastingandlaserpowderbedfusion(L-PBF)show thebest applicabilitytoaluminum(Al)-epoxymoldsandmetalmolds,respectively,becauseofthehighforming flexibility andfidelity. Meanwhile,laserpowder deposition (LPD)hasan exclusiveadvantageto fabri-catemulti-materialsmolds althoughitcannotprintoverhangregions directly.Hybrid L-PBF/computer-numerical-control(CNC)millingpointedoutthefuturedirectionforthefabricationofhigh dimensional-accuracyCCmolds,althoughthereisstillalongwaytoreducethecostand raiseefficiency.CCmolds areexpectedtosubstitutestraight-drilledcoolingmoldsinthefuture,asitcansignificantlyimprovepart quality,raiseproductionrateandreduceproductioncost.Inadditiontothis,theuseofCCchannelscan beexpandedtosomeadvancedproductsthatrequirehigh-performanceself-cooling,suchasgasturbine engines,photoinjectorsandgears,improvingworkingconditionsandextendinglifetime.
© 2021 The Author(s). Published by Elsevier Ltd. ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/)
1. Introduction
The thermoforming process plays a key role in manufac-turing, where a molten or thermally softened material is in-jected/compressedintomoldsandthencooledtoresolidifyinthe form of the designed shape. Almost all the plastic products and some metal products are fabricated by thermoformingprocesses. Accordingtothetypeofformingprocess,thermoformingisfurther classifiedinto severalspecific methodssuch asinjectionmolding, diecasting,andhotextrusion,all ofwhichinvolvea common
re-∗Corresponding author.
E-mail addresses: [email protected] , [email protected] (S. Feng).
quirementonmolds,namely,theircoolingability.Forinstance,the injectionmoldingprocess can be divided intofour stages:filling, packing,cooling,andejection[1].Ininjectionmolding,part qual-ityandcycletime depend stronglyon thecooling stage, because the cooling stage accountsfor up to 80% of the total cycle time anddirectlyaffectsshape deviations(e.g.duetoshrinkage,bend, andwarpage)oftheresultedplasticpart[2,3].
Coolingchannelsare mandatoryinmoldstoforcetheinjected materialstocooldown,andusuallyconsistofaseriesof straight-drilled channels. Although they are machined easily and eco-nomically,straight-drilledchannelscannotprovideoptimalcooling sincetheir layoutsare limitedbythecavityshape(to prevent in-terference betweenthe cavity andchannels) and drillingprocess (onlystraightholescanbedrilled).Therefore,inasense,
straight-https://doi.org/10.1016/j.ijheatmasstransfer.2021.121082
Nomenclature
A surfacearea(m2) Cf surfacefrictionfactor Cp specificheat(JKg− 1K− 1) d coolingchanneldiameter(m)
hC contactheattransfercoefficient(Wm− 2K− 1) kst thermalconductivityofmold(Wm− 1K− 1) L coolingchannellength(m)
Ra surfaceroughnessofthechannelwall(m) Re Reynoldsnumber
s partthickness(m) TC coolanttemperature(K) TE ejectiontemperature(K)
Ti initialtemperatureofthecavity(K) TM melttemperature(K)
TS averagetemperatureoftoolsurface(K) TW moldtemperature(K)
tC coolingtime(s)
V volumeofthecavity(m3)
x pitchoftwoneighboringcoolingchannels(m) y distance from cavity surface to center of cooling
channel(m)
P pressuredrop(Pa)
δ
distance from cavity surface to conformal cooling line(m,equalstoyinvalue)ν
viscosity(m2/s)ρ
density(kg/m3) Acronyms3D threedimensional AM additivemanufacturing BEM boundaryelementmethod CC conformalcooling
CFD computationalfluiddynamics CNC computernumericalcontrol DOE designofexperiments EBM electronbeammelting FEM finiteelementmethod GMAW gasmetalarcwelding L-PBF laserpowderbedfusion LPD laserpowderdeposition Chemicalsymbols
Al aluminum
Cu copper
drilledcircularchannelsaredictatedbymanufacturingconstraints butmaynot be optimallysuitedforthe mostefficientcooling of themold.
Consider astraight-drilledchannelthat ismeanttocooldown a curvedcavityasshowninFig.1a[4].Thedistancebetweenthe straight channelandthecurvedsurfaceofthecavityvariesalong the channel, inducing differential cooling rates atthe cavity sur-face andthusa temperaturenonuniformitythat consequently re-sults in differential shrinkage and warpage in the manufactured part[5].Moreover,becausethepartcanbeejectedfromthemold only when the cavity temperature entirely cools down to below theejectiontemperature,thecoolingtimedependsonthe highest-temperature point inthe cavityas well asits local cooling rate. Thus, in the situation shown in Fig. 1a, the cooling time is de-termined by the temperature and cooling rate of the most left andmostrightofthecavitysurface(wherehavethelongest dis-tance to the cooling channel) but not the middle of the cavity surface (where hasthe shortestdistanceto the cooling channel).
Fig. 1. Schematic of (a) a straight-drilled cooling channel, (b) a conformal cooling channel and (c) cross-sectional view of cooling channels ( d – channel diameter, x – pitch of two neighboring channels, y – offset distance from cavity surface to channel center) (Subfigures a and b are reprinted by permission from [4] , Copyright 2010 KSPE and Springer).
Therefore,coolingefficiencyisnot ashighasdesiredwhenusing straight-drilledcooling molds. Onthe other hand, sharpturns at theconnectionoftwoadjacentstraight-drilledchannels(asshown inFigs.2aandb[6])impedethecoolantmobility,leadingtoa sud-denpressuredropthat weakensthecoolingcapacitydownstream andfurtherenhancestheunevencooling[2].
Inmostcases,thepartsproducedbythermoformingpossessa thinshell,complexcurvedsurface,and/ordeephollowfeatures[7]. Insuchcases,differentialshrinkageandwarpageare moresevere andthecoolingratesare muchlower, sincethedeephollow fea-turetendstoinducelocalheataccumulation[8].Thismayrequire expensiverectificationofthe moldtoensurethe dimensional ac-curacyofthepart[9].Tomitigatethewarpageandshorten cool-ing times,conformal cooling(CC) channelswere proposed in the 1990s.TheCCchannelisdesignedasacurvedchannelwitha con-stantdistanceto the cavitysurface, asshowninFig. 1b[4].This ensuresauniformcoolingratealongthechannelandshortensthe distancebetweenthechannelandthecavitysurface.TheuseofCC channelscan thus enhance thecooling performance ofthe mold significantlybyreducingtemperaturedifferentialsandtheinduced warpage[10]andincreasing thecoolingefficiency(reducing both thestart-up time andcooling time)[11,12] considerably.In some cases,withpropercoolingchanneldesigns,CCchannelscanreduce thecoolingtimebyasmuchas80%[3]andthecycletimeby60– 70%[11,13].
It is thus evident that an optimal design of CC channel net-worksisimportanttoproducepartsquickly,reliably,andmore ef-ficiently. Some basicdesign rules needto be obeyed tomeet re-quirementson cooling performance, mechanicalstrength, coolant fluidity,andsoon.Severalpivotaldesignparameterssuchas cross-sectional shape, size (that specifically refers to the diameter for circularchannels), offsetdistanceto thecavity surface, andpitch betweentwoadjacentchannels(Fig.1c),mustbechosencarefully inlight of therules. Manymethodologiesandalgorithms for
de-S. Feng, A.M. Kamat and Y. Pei International Journal of Heat and Mass Transfer 171 (2021) 121082
Fig. 2. Comparison of straight-drilled cooling channels and CC channels: straight-drilled cooling channels in cavity insert (a) and in core insert (b), and CC channels in cavity insert (c) and in core insert (d) (Adapted from [6] with permission from the authors).
signingCC channelshavebeenproposedby researcherstoenable theintelligentandoptimaldesignofCCsystems[14–16],and cool-ing channel layoutssuch as spiral[17],zigzag [18], profiled [19], andvascularized[20]havebeenproposed.However,inspiteofthe progressmadeinCCdesign,severalobstaclesstillexistinfrontof molddesignersandengineers,mainlybecausethereexistsno stan-dardanduniformtaxonomyandframeworkforCCsystemdesigns (ofwhichthereexistmany).
While the design of CC channels is an important problem in itself, manufacturing the internal channelsposes its own unique challenges. Most CC network designs, optimized forcooling effi-ciency, possess complex three-dimensional shapes (as shown in
Figs. 2c and d [6]) that are difficult (or impossible) to be real-izedusingconventionalmachiningtechniquessuchasdrilling. De-signers thus need to turn to modern technologies such as addi-tive manufacturing (AM) to build molds containingCC channels. Inthepasttwodecades,theemergence ofavarietyofnewmetal AM technologies(e.g. powder bed fusion, binder jetting, and di-rect energydeposition)hasenabledthefabricationofmoldswith complex-shaped CC channels. Although the technology readiness level ofAMislower thanthatofconventional methods(with re-specttofactorssuchascost,efficiency,anddimensionalaccuracy), additively manufactured CC molds show considerablepromise to compete with andfinally substitutestraight-drilled moldsdueto the potential oflong-termsavings dueto moreefficientand uni-formcoolingofthemold.
Although some review papers on the design and manufactur-ingofCCchannelsexist[21–23],acomprehensiveandsystematic classification,comparison,andevaluationofthedesign methodol-ogyandmanufacturingtechniquesarestillmissing.Inthisreview paper,straight-drilled cooling channelswill be introduced briefly inSection2.Then,thedesignmethodsandlayoutsofCCchannels willbeclassifiedandreviewedsystematicallyinSection3.Features andadvantagesof eight typesof CC channel layoutswill be dis-cussedindetailandevaluatedaccordingtosimulationand experi-mentalresultsoftheresultingcoolingperformanceinthemold.In
Section4,manufacturingtechniquesusedhistoricallyandcurrently to fabricate CC molds will be discussed and compared in detail. Finally,theapplications ofCC channelsinplasticandmetal ther-moformingandfabricatingotheradvancedproductswillbebriefly summarizedinSection5.
2. Straight-drilledcoolingchannels
2.1. Conventionalstraight-drilledcoolingchannels 2.1.1. Straightserialcoolingchannels
Conventional straight-drilled cooling channels are the most widely usedchannel systems inmoldsanddies up tonow. They are broadly classified into two types, i.e. serial and parallel, as shownin Fig.3 [24].Practically, a straight serial cooling channel network(Fig.3a)isthesimplestandmostcommonlyusedcooling
Fig. 3. Two types of conventional straight-drilled cooling channel networks: (a) straight serial cooling channel network and (b) straight parallel cooling channel net- work (Adapted from [24] ).
channelsystemwhereinallthecoolingchannelsinthesystemare connected endtoendtoforma singleloopwithan inletandan outlet.
2.1.2. Straightparallelcoolingchannels
Astraightparallelcoolingchannelnetwork(Fig.3b)consistsof a setofcooling channelsthat areconnectedtoasupplymanifold and a collection manifold but not connected directly with each other. Forthestraight parallel cooling channels,the coolantdoes not flowthroughevery channelby orderandthe coolant,aswell asitsflow characteristicssuchasflowrateandflow resistancein eachchannelareindependentofeachother.Thus,comparedtothe straight serialcoolingchannels,thestraight parallelcooling chan-nels are moreflexible inconfiguringthecooling rateandcoolant temperature. Forlargemoldsanddies,morethan onesetof con-ventionalstraight-drilledcoolingchannelsmaybeemployedto im-plementamoreefficientandmoreuniformcoolanteffect. 2.2. Straight-drilledcoolingchannelswithbaffles
Conventionalstraight-drilledcoolingchannelsdonotrepresent an ideal design,leavingmuch room forimprovementtowards an optimalcoolingsystem. BeforethedevelopmentoflaserAM, baf-fles in straight-drilled cooling channels were used as a compro-misebetweenthemanufacturingabilityandtheefficacyofcooling channels[25].Bafflesareaseriesoftubesinstalledonthe straight-drilled channels,andtheir endpoints are inside the space where thestraightcoolingchannelsarenotconvenienttobedrilled,such asthesemi-enclosedconvexspaceinacoreinsertshowninFig.2b (the greentubes inside thecoreinsertarethe baffles).As shown inSection 2.1,both twoendsofastraight-drilledcoolingchannel areconnectedtootherchannels.Forabaffle,onlyoneendis con-nectedtoanotherchannelwhiletheotherend(far-end)isnot con-nectedwithanychannels,withawallinsidethebaffleforcingthe coolantflowthroughthebaffle,asshowninFig.4[4].Thefar-ends of a series ofbaffles are equidistant from the cavitysurface and muchclosertothecavitysurfacecomparedtothestraight-drilled
Fig. 4. The array of baffles (Reprinted by permission from [4] , Copyright 2010 KSPE and Springer).
Fig. 5. Schematic of bubbler cooling (Reprinted by permission from [10] , Copyright 2015 Elsevier).
channel,sothatthebafflescanenhancethecoolingefficiencyand uniformity.
2.3. Straight-drilledcoolingchannelswithbubblers
Another approach to enhance the cooling effect in straight-drilledcoolingchannelsisbubblers,whicharesimilartobaffles.A bubblerisatubular cavitywithalargerdiameterthan a straight-drilledcoolingchannel.Aconcentrictubeisnestedinsidethe bub-bler, asthe inlet, supplying coolant to the innermost endof the bubbler.Meanwhile,astraight-drilledcoolingchannelisconnected to the outermost end of the bubbler as the outlet, as shown in
Fig.5 [10], makingit an effectivewayto ensurethat the cooling channelsreachtheconcaveareas[26].
3. Structuraldesignofconformalcoolingchannels
3.1. Physicalandmathematicalprinciplesinstructuraldesignof conformalcoolingchannels
The goals in the design and optimization of CC channels are to ensure uniformity in the temperaturedistribution, reduce the coolingtime neededtoreachtheejectiontemperature, and mini-mizeshrinkageandpartwarpage[27,28].CC is,atitscore,aheat andmasstransferprocesswherethecoolantflowsthroughtheCC channelstakingaway theheat fromthe moldcavityand cooling downtheinjectedpolymer.Thephysicsofthisprocessisdescribed bythecouplingoftheNavier-Stokesequationsandthe convection-diffusionequation[29,30].
In injection molding, most of the heat is taken away by the coolantinCCchannelswhilelessthan5%oftheheatlossesoccur throughtheexteriorsurfacesofthemold[31].Afterseveralcycles, the moldingprocess reaches asteady state in whichthe average temperatureofthemoldisconstant.Theenergybalanceprinciple isapplicable to thisheattransfer process accordingtowhich the
S. Feng, A.M. Kamat and Y. Pei International Journal of Heat and Mass Transfer 171 (2021) 121082
Fig. 6. A CC design window defined by the cooling channel diameter and the cool- ing line length (Adapted by permission from [35] , Copyright 2001 Society of Plastics Engineers).
heat transfer ratefrom the cavity to the tools is assumed to be equal tothatfromthetoolstothecoolant[32].The coolingtime iscalculatedby[31]: tC = [Cp
(
TM− TE)
]ρ
2sx Tw− TC 1 2π
kst ln 2xsinh2π
yxπ
d + 1 0.03139π
Re0.8 (1) where,tC,TM,TE,TW,TC,Cp,ρ
,s,x,y,kst,d,andRearethecooling time, melt temperature, ejection temperature, mold temperature, coolanttemperature,specificheat,density,partthickness,pitchof two neighboringcoolingchannels,distancefromcavitysurfaceto centerofthecoolingchannel,thermalconductivityofmold, cool-ingchannel diameterandtheReynoldsnumber,respectively. Sim-ilarly,asimplerrelationshipbetweentheaveragetemperatureofa toolsurfaceandthecoolingtimeisgivenby[33]:TS= Ti· exp
−AhC ρCpV tC − TE exp−
AhC ρCpV tC − 1 (2)
where,TS,Ti,A,hC,andVaretheaveragetemperatureoftool sur-face,theinitialtemperatureofthecavity,surfacearea,contactheat transfer coefficient, and volume of the cavity, respectively. More practically, an empirical formula to rapidly estimate the cooling timeaccordingtothedistancefromthecavitysurfacetothecenter ofacoolingchannelwasproposedas[34]:
tC=141.49ln[y
(
mm)
]+733.03 (3)Some constraintsandlimitationsshould betakenintoaccount when designing a CC system, e.g. geometric constraints, manu-facturingconstraints,coolanttemperatureuniformity,andcoolant pressuredrop,asshowninFig.6[35].Theoretically,decreasingthe distance fromthe cavitysurfaceto the centerof acooling chan-nelisnecessaryforreducingthecoolingtime.However,thereisa lowerlimittothiscavity-channeldistancetomaintainthestrength of the wall, with the recommended values being 1× d for steel, 1.5× dforberyllium,and2× dforaluminum(Al)[36] wheredis the cooling channel diameter. Moreover, the increasing tempera-tureandthe pressuredropofthecoolantalong thechannel pas-sage weakenits heat-carrying ability and causethe temperature nonuniformity in the cavity surface. Better cooling performance can beachievedby usingvariableoffsetdistancesand/orvariable channel diameters (Fig. 7) to compensate for this nonuniformity
Fig. 7. A design of a variable diameter CC channel. Table 1
General recommendations for the cooling channel diameter depending upon cavity thickness [40] .
Cavity thickness, s (mm) Cooling channel diameter, d (mm)
s ≤ 2 8 ≤ d ≤ 10
2 < s ≤ 4 10 < d ≤ 12 4 < s ≤ 6 12 < d ≤ 14
[37,38]. The pitch oftwo neighboring coolingchannels is recom-mendedtobe 3–5timesd[39].Thecoolingchannel diameter(d) isusually8–14mmdependingonthecavitythickness,aslistedin
Table1[40].
InEq.(1),itcan beobserved thatthe Reynoldsnumberis in-verselyrelatedtothecoolingtime.ThegreatertheReynolds num-ber(indicatingahigherdegreeofturbulenceinthecoolantflow), thelowertheaveragetemperatureinthemolds[41].Nevertheless, whentheReynoldsnumberoftheturbulentcoolantflowisgreater than 10,000,the rate of pressure drop increasesrapidly, but the rateofthermalconvectionincreasesslowly,resultinginadecrease ofthetotalheattransferrate.TheReynoldsnumberisthus recom-mendedtobeintherangeof4,000–10,000with10,000beingthe optimalvalue[32,42,43].
Thepressuredropdependsupontheflowconditionsasfollows [44,45]:
P= L 2d
ρν
2C
f (4)
where,
P, L,
ν
and Cf are the pressure drop, cooling channel length,viscosity,andsurfacefrictionfactor,respectively.For lami-narflow,CfiscalculatedbyCf=
16
Re (5)
Theincreaseofsurfaceroughnessleadstotheincrease of con-tactareaandtheenhancementofconvectionbetweenthecoolant andchannelsurface[46].Whenthecoolantexperiences turbulent flow, however, the surface roughness of the channel wall affects thepressuredropbydeterminingCf:
Cf= 0.25 1.82
log10R a 3.7d 1.11 +6.9 Re −2 (6) whereRa isthe surfaceroughnessof thechannel wall. It can be concludedthattherougherthewall,thelargerthepressuredrop, andthesmallertheflowrate,especiallywhenthecoolantflowis completelyturbulent[34,47].
Althoughahighercoolantflowrateisbeneficialtoreduce the maximumandaveragetemperatures,italsoinducesahigher pres-sure drop and thus requires a stronger coolant pumping system (meaning a higher financial investment) [48]. Reducing the re-quiredflowratewillnotonlysavecostsrelatedtothecoolant sup-plysystembutwillalsoensureadequatecoolingofthemolds, es-peciallyformulti-cavity molds.Finiteelementmethod(FEM) sim-ulationresultshaveshownthatalthough thecoolantflowratein CCchannelsislessthanhalfofthatforstraightcoolingchannels, the cycle time achieved by the former method can be less than
two-thirds of thelatter because ofmuch higher cooling efficien-cies[8].
3.2. Methodologyforstructuraldesignandoptimizationofconformal coolingchannels
3.2.1. Experimentalbaseddesign
Design of experiments (DOE) is a convenient and well-established methodology to correlatedesign parameters and pro-cess parameters withthe cooling performance ofa CC system. A number of DOEtechniques, such asfull factorial design [48], or-thogonal design [49], Taguchi method [50–52], response surface methodology [53–55],and optimalLatin hypercubemethod [53], have beenadoptedto designandoptimize CC systems.Here,the experimentscanbe conductedeitherphysicallyornumerically.In additiontoinjectionmoldingtrials,FEMorcomputationalfluid dy-namics (CFD) simulations are more economical and efficient ap-proachestoevaluatethecoolingperformancethaninjection mold-ing trialsduetothehighcostsofmoneyandtimeinmold man-ufacturingalthoughthefidelityofsimulationneedstobeverified. Based onthesimulation result,a formulawasproposed to calcu-latethesize(diameterandlength)andpositionofspiralCC chan-nels forinjectionmoldsofplasticcupsinalldimensionswith up-perlimitof5mmonthickness[56].Anoptimizationindicator,viz. theratioofproductcoolingratesandcoolantpumpingenergy,was employedtoyieldthemostadvantageousoutcomefromthe view-pointsofbothcoolingperformanceandeconomy.
Combiningorthogonal experimentwithrangeanalysis, Lietal. proposed an optimized parameter combination with a cooling channel diameter of 4mm, an offset-diameter ratio (the ratio of the distance of cavity wall from the center of cooling channel and the cooling channel diameter) of 2.2, a cooling water tem-peratureof25°C,andasurfaceroughnessofcoolingchannelwall of 0.05
μ
m [49].However, thisoptimized parameter combination was obtained from the numerical simulation results. It can be noted that the required wall roughness of 0.05μ
m is very diffi-culttoachievepractically.Jahanetal.proposedanoptimumdesign configuration in thermal-mechanical performance andprovided a guideline chart that is visual andpractical for molddesignersto choose design parameters by using DOEcombined with a trade-off technique[57,58]. DOEisa simpleapproachsince itdoesnot need any specialized optimizationalgorithms. However, a limita-tion is that the design parameters can only be chosen fromthe experimental rangesandcannot beexpandedtoa widerrange.If adesigndoesnotfallintotherangeoftheexperimentaldata,the guidelinechartwillberenderedimpractical.3.2.2. Designandoptimizationbasedontheconformalcoolingline CC lines (or CC surfaces in 3D) are the most widely used approach to design and optimize the CC channels [6,59,60]. CC lines/surfaces area seriesofcurves/curvedsurfaces(
3 inFig.8) offsetfromthecavityprofile(
2inFig.8)[61].ByusingCClines, the procedures to design CC channels are generally divided into two steps:(a) extracting the conformal loops based on the geo-metriccontourofthepart,and(b)blendingtheseloopsto gener-atespiralCCchannels,asshowninFig.9[17].
Some methods havebeenproposed to determinethe arrange-mentoftheCCchannels,e.g.theoffsetofthechannelwithrespect tothecavityandthespacingbetweentheadjacentchannels.A tri-angularmethodwasproposedbasedontheenergybalance princi-ples,asshowninFig.10[32].Boundary-distancemapswere intro-ducedtogenerateevenlydistributedchannels[62].Intheworkof Agazzi etal., thefluid temperaturewasoptimizedby minimizing an objectivefunction relatedto thelevelandsurfacedistribution oftheparttemperature[59].
Fig. 8. Schematic of CC line/surface (Reprinted by permission from [61] , Copyright 2012 Elsevier).
Foracomplexshapedpart,apracticalmethodistodecompose thecomplexsurfaceintosimplersub-surfacesanddesign individ-ualsub-coolingchannelsystemsforthesesub-surfaces[17,63,64], asshowninFig.11.Thesesub-coolingchannelsystemsmayhave individualinletandoutletorshareaninletandoutletby connect-ingwitheachother.
3.2.3. Optimizationusingexpertalgorithms
The design approaches based on experiments and experi-ence are not adequate when designing molds and dies for parts with more complex geometric shapes. Some automatic methods have been developed to design and optimize the layout of the (straight-drilled)coolingchannels,suchasconfigurationspace (C-space) methodcombined withheuristics geneticalgorithms [65], two-stageautomaticdesignmethodwithaheuristic-search-based graph traversal algorithm [66],boundary element method (BEM)
[9],andtwo-phaseevolutionaryalgorithm[67].
InlightofthedesignprinciplesandproceduresforCCchannels, anincreasingnumberofresearchgroupsreportedtheirapproaches andstrategiesofstructuraloptimizationforCCchannels.Inrecent years,theautomatedandintelligentimplementationinthedesign andoptimizationofCCchannelsby employingsophisticated algo-rithmshasbeengainingtraction.Abottom-up approachwas pro-posed to generate automatically cooling channel systems follow-ingthedesignprocedureofpreliminarydesign,layoutdesignand detaileddesign[14].Multi-objectiveoptimizationforCC channels is usually employed to shorten the cooling time andreduce the warpage[68].Objective functionswerecorrespondingly proposed toincreasethecooling rateandhomogenizethetemperature dis-tributiononcavitysurfaces[69].Anumberofmethods/algorithms were developed to solve these objective functionsand findtheir Paretooptimalfrontiers[53,69,70],e.g. aconjugategradient algo-rithm coupledwitha Lagrangian approach[69],Voronoidiagram algorithms[71,72],andageneticalgorithm[73].
Recently, gradient-based algorithms (GBA) and robust genetic algorithms (RGA)were respectivelycombinedwithCOMSOL Mul-tiphysics software to optimize the geometric layout of spiral CC channels[15].ThesimulationresultshowsthatbothGBAandRGA providedbetter designs ascompared toconventional designwith significantimprovementsinthe coolingtime,temperature unifor-mity,andwarpage,withtheRGA-optimizeddesignproving supe-riortotheGBA-optimizeddesign.
Cycle-averagedapproachandBEMwere adoptedtodesignand optimize the meshy-topological CC channel systems [74]. By us-ing thesemethods, thenodes ofthechannel network were opti-mized and the topology wassimplified andsmoothed. For
cool-S. Feng, A.M. Kamat and Y. Pei International Journal of Heat and Mass Transfer 171 (2021) 121082
Fig. 9. A two-step method to generate CC channels: (a) geometric shape of a part to be injected, (b) generation of conformal loops, (c) generation of spiral curve, and (d) generation of the CC channel (Adapted from [17] ).
Fig. 10. Triangular method for arranging cross-sections of cooling channels on a CC line ( δis the offset of the CC line) (Reprinted by permission from [32] , Copyright 2013 Springer-Verlag London).
Fig. 11. A design consisting of two sub-CC channel systems (Reprinted by permis- sion from [64] , Copyright 2009 KSAE and Springer).
ingsystemswithamorecomplextopology,aLagrangemultipliers methodwasemployed bydefining ageometric parameter, svelte-ness (equals to external length scale divided by internal length scale),tominimizethelocalpressuredropandalong-channel pres-suredrop[16].Besides,avisibilitytechniquewasproposedto gen-erate automaticallyCC channelsfora complex-shaped cavity sur-facewithoutrequiringtheengineertohaveexperienceinthe de-signofconventionalstraight-drilledcoolingchannels[75]. 3.2.4. Modular/parametricaldesignofconformalcoolingchannels
Modularandparametricdesignresemblesablockbuilding pro-cess. The CC channelsystemis rapidlybuiltbylocating and con-necting severalstandardcells. Thebasicsteps are (i)determining
the space for cooling channels, e.g. to determine the CC surface by offsettingthecavity surface;(ii)dividing thespace intosmall units such that each unit corresponds to a cooling cell; and(iii) connecting (sub-) channels in each cell and setting coolant inlet andoutlet. The procedure ofdesigning a 2D modular CC system is schematically illustrated in Fig. 12 [76].The offsettingmethod
[77]anddualityprinciple [76]wereemployed respectivelyasthe main design methodand principle formodular CC channels. De-tailsonmodularly/parametricallydesignedCCchannelswillbe re-viewedinSection3.3.5.
3.2.5. Solidmodelingbasedontopologyoptimization
Inaddition totheabove methods, anotherapproachto design CC channels is based on topology optimization. This is typically usedforheterogeneous(dual-materials)modelingandlightweight designs. Usingthisapproach, thechannel positionproblemis re-placed withatopology optimizationproblemtakingintoaccount flow resistance, heat conduction, and forced/natural convection
[78]. Shinproposed a heterogeneoussolid modeling approachfor CC channels made of functionally graded materials [79]. In this model,a weighting function wasdefined to specifythe distribu-tion(volumefraction)ofeachmaterialcomposition,withan expo-nentbeingusedtocontroltheformoftheweightingfunction (lin-ear,parabolic,etc.). In thework ofHuang andFadel[80],a two-stepmethod wasdevised forbi-objective optimizationof hetero-geneous cooling channels.Thisisa generic methodfordesigning bothstraight-drilledandCCchannels.Inthefirststep,asingle fun-damentalmoldmaterial wasassumed, andoptimalcooling chan-nelsizes,locations,andcoolantflowrateswereobtainedthrougha gradient-basedoptimizationmethod.Basedontheoptimalresults fromthefirststep,thesecondstepwastofindsensitiveareasand distributeboth fundamentalandsecondarymaterials inthese ar-easthroughageneticalgorithm.Further,theauthors[80]also pro-posedthreedesign rulesregardingmaterials selectionfor hetero-geneous cooling channels:a) thedifference betweenthe thermal diffusivities of the two moldmaterials mustbe large enough, b) thefundamentalmoldmaterialmustbeametaloralloywith suf-ficientstrengthandhardness,andc)ceramics,metal,oralloywith reasonablestrengthandhardnesscanbeselectedasthesecondary moldmaterial.
The problem of weight minimization is solved by gradient-basedoptimizationafteranalyticallyderivingthesensitivityofthe
Fig. 12. Procedures of designing a 2D modular CC system (Adapted by permission from [76] , Copyright 2011 Elsevier).
coupled thermo-fluid model using the adjoint method [30]. The gradient-based solver can also be used to solve the polynomial interpolation ofthe homogenization properties seeking the most lightweightsolutionsatisfyingtheconstraintconditions[81].A2D conceptualmodelforthegenerationofthermal-mechanicalporous structureswasproposedtodesignthelightweightCCchannelsfor the purposeofreducing weight, savingmaterial and manufactur-ing cost, and enhancing thermal performance [82]. In this two-objectiveoptimizationmodel,theoptimizedtopologyoptimization forbothsteadyheatconductionandstructuralstabilitywas calcu-lated by assigningthem linearweight factors. This work showed the potential of efficientlyreducing the materials between cavity and coolants withoutsignificantly decreasingthe performance of thecomponents.Themaximumvolumereductionofthematerials wasexpectedtobeashighas60%.
3.3. Typesandlayoutsofconformalcoolingchannels 3.3.1. Conformalcoolingchannelswithbasictopology
The spiral shape is one of the simplest and most common basic topologies for CC channels, as shown in Fig. 9d [17] and
Fig. 11 [64]. Besides spiral, the linear shape (zigzag type) is an-other popularoptionforthetopology ofCCchannels,asshownin
Fig.13[18].It mustbe notedthat ascomparedtothespiraltype, thezigzagshapehasmanysuddenturnsthatincreasethepressure drop,therebyslowingdowntheflowrateandconsequently weak-ening the cooling efficiency [41]. According to the kind of con-nection betweeneach channel,CC channelscan alsobe classified intoeitherseriesorparalleltypes[28,48],similartoconventional straight-drilledcoolingchannels(Fig.3).Forinstance,thespiralCC channelsystemcanbeclassifiedas:(i)asinglespiralinseries con-nection, (ii) double(multiple)spirals inseriesconnection, or(iii) spiralsinparallelconnection[17].
3.3.2. Meshy-topological conformalcoolingchannels
TheapplicabilityofspiralCCchannelsreducesasthe complex-ityofthegeometricshapeofthepartincreases.Comparedtospiral CC channels,meshy-topologicalCC channelsaremoresuitable for this situation,as shownin Fig. 14[71]. The vascularized CC sys-tem, inspired by the design of blood vessels, is another meshy-topologicallayout [83].Thisbiomimeticdesign[16]wasproposed
Fig. 13. Two zigzag CC system designs (Reprinted from [18] with permission from the authors).
Fig. 14. Design of a meshy-topological CC channel system: (a) injected part and (b) layout of CC channels (Adapted by permission from [71] , Copyright 2011 Elsevier).
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Fig. 15. Vascularized CC system (Adapted from [20] with permission from the au- thors).
toaddressthehotspotsincomplex-shapedpartswithnarrowand deep hollow areas, such as an automotive oil filter housing, as showninFig.15[20].Inthisdesign,themajorarterybranchesinto sub-arteries, whichcould further divideintocapillarytubes, thus eliminating local heat accumulation and achieving uniform tem-peraturedistribution.
The two main characteristics ofmeshy-topological CC channel systems are the complex topology and the non-uniform diame-ter, as shownin Fig. 16 [74]. Consequently, the flow distribution andpressuredropshouldbepaidmoreattentiontowhen design-ing a meshy-topological CC system, since the usual design rules are derived for simpler topologies with uniform channel diame-ters andshapes. Further,corresponding tothe allowablepressure drop,there existsa minimumchannel diameterbelowwhichthe channelcannotbefurtherdividedintosub-branches[72]. 3.3.3. Conformalcoolingchannelswithnon-circularcross-sections
Although circular cross-sections are the most commonin the design ofCC channels(sincetraditionallydrilledholes are neces-sarilycircularinshape),someattemptshavealsobeenmadeto de-velopCCchannelswithnon-circularcross-sectionssuchassquare, rectangular, diamond, trapezoidal, elliptical, and other polygons [51,84–86].Thisisincreasinglyviableduetotherecentprogressin metal AMwhich doesnot imposeanyconstraintson thechannel shape.Althoughthestiffnessofa rectangularchannel islessthan that of its circular counterpart, the former is more efficient and homogeneous incoolingbecauseits effectivecoolingsurfacearea is largerthan thelatterforthesamecross-sectional area[87,88]. The widthofthemaingrooves(lw)is recommendedtobe inthe range of10–20mm, andtherecommended valuesfor thegroove depth, the pitch between two neighboringgroove walls, andthe grooveoffsetfromthecavitysurfaceare(0.3–0.4)lw,(1–1.5)lw and (0.7–1.5)lw,respectively[8].Toenhanceitscoolingeffectby
enlarg-Fig. 16. Two instances of meshy-topological CC channel systems (Adapted by per- mission from [74] , Copyright 2017 Springer-Verlag London).
ingthecontactarea,Kamarudinetal.proposed amodifieddesign by addingsub-groovesto thesquare-shapedCC channels [89],as showninFig.17.
In addition to sub-grooves, ribbed channel designs, wherein ribs (inclined [90], wavy [91,92], V-shaped [92], rod array [93], etc.) were designed on the inner surface of the channel (shown inFig.18), canalsoenlargethecontactareabetweencoolantand channel surface. Similarly, a design with fins in the circular or square channelswasproposed tofurtherenlargethe surfacearea ofCCchannels(thusleveragingthepotential ofAM) asshownin
Figs.19a-d[94].TheCFDsimulationresult(Figs.19eandf)showed thattheheattransfertothecoolantwassignificantlyenhancedby addingfins [94]. However, manufacturing thiscomplex fin shape willbe aconsiderable challengeto AM(especiallyconsideringits printingaccuracy) becauseofthesmallthicknessofthefins(0.2– 0.6mm).Moreover, before thisproposalcould be realistically im-plementedusingAM,severalpracticalissuesneedtobeaddressed, e.g.howtoremove themetalpowder(in thecaseofpowderbed fusion)fromthenarrowandcurvedslit-likechannels.
To avoidshape deviation (or even collapse) at the top of the horizontalcircularchannel [95],a self-supportingteardrop profile wasproposed inwhichthe upperhalfof thecircularprofilewas modifiedtoa“triangularroof” withtwo40°–45° inclines,asshown
Fig. 17. The cross-sectional shape of a square-shaped CC channel with sub-grooves (Adapted by permission from [89] , Copyright 2017 AIP Publishing).
inFig.20[96].Althoughthedesignmodificationreducedtheshape deviationoftheadditively manufacturedchannel,thiswasan un-desiredcompromisesincethemodificationwasnotnecessarily op-timal fromthe coolingefficiencypoint of view butrathera con-cessionformanufacturability.Furthermore,theteardropshape fea-turesastressconcentratoratthesharpcorner,reducingitsfatigue resistance.
Circular cooling channels can induce uneven heat dissipation justbyvirtueoftheirshape;e.g.,considerthesituationinFig.21a where,eventhoughthechannel isconformalwiththecavity sur-face intheaxial direction,thedistancefromtheedgesofthe cir-cularcross-sectionalprofiletothecavity(namelyintheradial di-rection) is not constant. The issue can be resolved by employing aprofiled(semicircular)CCchanneltofurtherenhancethe unifor-mityofheatdissipation[50,97].Themodifiedcross-sectional con-tour consistsof two parts, i.e. a half-circularpart and a straight part,withthestraightpartbeingparalleltothecavitycontour,as
shownin Fig. 21b. The profiled CC channel is more in linewith theconceptofCC.The simulationresultsshowedthatthecooling timeusingtheprofiledCCchannelisshorterthanusingthe circu-larCC channel dueto betterthermal dissipation (in thestudyof Altafetal.,theheatflowincreaseandcoolingtimereductionwere 14.6% [97]and22% [19],respectively).However, the sharpcorner atthejunctionofthehalf-circularpartandthestraightpartmay inducestressconcentrationandcrackpropagation.Thisstress con-centrationwasfoundintheworkofHopkinsonandDickens,who fabricatedCC channelswithstar-shapedcross-sectionsusinglaser AM[98].Fromthepointofviewoffracturemechanics,3Deffects nearsharply-V-notches play an importantrole incrack initiation andrapidpropagation,finallyleadingtobrittlefailure[99–101].
Therefore, the profiled CC channel raises the difficulty of de-signandmanufacturing.Itisnecessarytofindabalancebetween the cooling effect and the cost by further investigation. Further, CC channels with varying cross-sections have been proposed to achieve more efficient and homogenous cooling. An example is shownin Fig. 22 where the channelsare locallywidened at the hotspotstoincreaseheattransferwhereneeded[61].
3.3.4. Conformalcoolingbubbler
ACC bubblerisachamberinthethinwallmoldthatdoesnot look like a tubular channel butis essentially a CC channel with varying diameterand/or profiledcross-sectional shape[102].In a conformal bubbler cooling mold, the wall thickness is kept con-stantandweb or ribsare added to themold construction in or-derto withstandpressureonthemoldsurfaceandtoprevent its deflection duringthe plastic injectioncycle, asshown in Fig. 23 [10]. This strengthening of the structures may, however, lead to additionalpressure dropinthecoolantflow, anda tradeoff must be maintained between pressure drop and mechanical strength throughcarefulcalculationswhendesigningCCbubblers.
3.3.5. Modularly/parametricallydesignedconformalcoolingchannels Mercado-Colmeneroetal.designeda coolingcellconsistingof sixhexagonal-distributedinletchannelsanda singleoutlet chan-neltorealizetheCCsystem,asshowninFig.24a[73].Using para-metricdesignmethodologyreducestherequirementsforexpertise andexperienceofdesigners. Thissimplifies thedesignprocess of complex CC channel systems andreduces the developmentcosts
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Fig. 19. Designs of fins in CC channels (a-d), and heat flux of (e) a normal circular channel and (f) a channel with fins (Adapted from [94] ).
Fig. 20. (a) Design of self-supporting profile and (b) comparison of printed circular and self-supporting profiles (Adapted by permission from [96] , Copyright 2016 Emerald Publishing Limited).
Fig. 21. (a) Circular (conformal) cooling channel and (b) profiled (conformal) cool- ing channel.
andcycles.However,duetothe denselydistributedchannelsand their complextopologyinside themolds,some importantfactors, suchaspressuredrop,mechanicalstrength,andmanufacturability, should also be taken intoconsideration when conducting modu-larandparametricdesign.Particularly,forthedesignof Mercado-Colmeneroetal.showninFig.24b[73],theremaybespatial inter-ference betweeninlet andoutletchannelsinthecaseofcomplex partgeometries.
3.3.6. Lattice/porousstructureinconformalcoolingchannels
Latticestructural CC channels are a specialtype ofmodularly and parametrically designed CC channels. A scaffolding architec-turewithcubicbasiccells, developedby AuandYu, representsa typicalcaseofmodulardesignforCCchannels,asshowninFig.25
[76,77]. By using the orthogonal support structures in the scaf-foldingarchitecture,thevolumeofcoolingchannelsisgreatly ex-panded.Thesupportstructuresstrengthenthemechanicalstrength andheightenthemanufacturabilityofAMbyreducingthespanof theoverhangregions.Further,supportstructuresprovidethe pos-sibility of integrating numerous parallel CC channels into an in-terconnected layer. Therefore,these lattice cooling structures are moreoften referred toasCC layers (asopposed tosimply ‘chan-nels’).
CubiclatticeswithorthogonalstrutslimittheoutlineoftheCC layertostep-like,asshowninFig.25c.TomaketheCClayermore conformal,a modifiedscaffolding layoutwasproposed, asshown
Fig. 22. A design of CC system with varying cross-sections (quarter of the part) (Reprinted by permission from [61] , Copyright 2012 Elsevier).
Fig. 23. Conformal bubbler cooling in a mold core (Reprinted by permission from
[10] , Copyright 2015 Elsevier).
in Fig. 26. The size and shape of each unit cell were varied ac-cordingtotheshapeofaninjectionmoldedpart,providingamore flexiblelayout(occurring,however,atthecostofacomplicated de-signprocedure)[103].Attemptswere alsomadetobuild the sup-portstructures inother forms,suchascross-typeandN-typeunit cells, asshowninFig.27[104].Somedesignprincipleswere pro-posed, such as:(a) thestrutsare ideallyover 45° fromthe hori-zontal andwithlow enough aspect ratios,(b)the overhangspan should be assmall aspossible while not impeding flow, and (c) theunitcellsneedabaselevelofsymmetry.
The lattices enhance the heat transfer dueto increased inter-facial surface areas and fluid vorticity [104,105]. The simulation results, however, indicated that only the average mold tempera-ture decreased to some extent by using the CC layers as
com-Fig. 24. Parametric CC channels designed by Mercado-Colmenero et al.: (a) de- sign of a cooling cell and (b) cooling channel system combined by cooling cells (Reprinted by permission from [73] , Copyright 2019 Springer-Verlag London).
Fig. 25. CC channels with scaffolding architecture: (a) basic cells of design I, (b) basic cells of design II, and (c) channel distribution in a mold (Subfigures a and c are adapted by permission from [77], Copyright 2006 Springer-Verlag London; subfigure b is adapted by permission from [76], Copyright 2011 Elsevier).
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Fig. 26. A modified CC layer with variable unit cells.
paredto circularcoolingchannels.Therewasnostatistical differ-encebetweenthetwoCClayoutsonthereductionofcoolingtime, warpage, andsink marks. At present, it seems that the costs in-curred in fabricating and using a CC layer are much more than their benefits.Besidesthepressuredrop,mechanicalstrengthcan alsobeaconsiderableconcern.Therefore,moreeffortsneedtobe madeoninvestigatingthecompetitivenessofCClayers.
Another lattice structural CC channel layout, similar to the scaffolding architecture, wasproposed tominimize the weight of moldswhilesatisfyingtheCCperformancerequirements[81].This design differed from its predecessors in that the cubic cells in the lattice structurallayout hadvariable volume fraction (poros-ity)whilethecubiccellsinthescaffoldingarchitecturewere uni-formly sized. In this design,weight reduction of17.25% and 37% were achieved for the cavity insert and coreinsert, respectively. Moreover, the thermal performance was improved 30% by using this porosity-varied lattice structural layout as compared to the uniform-porosityscaffoldinglayout[106].
Besides employing the lattice structure as a CC layer, a lightweight lattice (porous) structure was also employed to con-struct the main body ofmold inserts (core andcavity) [82,107], asshownin Fig.28.Thiswasan interesting attemptbecausethe buildingofCCsystemhaddevelopedfromchanneltolattice struc-tures.Apreliminarydesignwasproposedbasedonsimulation re-sultstoreducetheweights ofthecavityinsertandcoreinsertby
Fig. 28. Porus lightweight design of a mold core (a and c) and a mold cavity (b and d) (Adapted by permission from [107] , Copyright 2016 The Authors, Published by Elsevier).
40% and50%, respectively. Thoughthe heat conductivity andthe stiffnessreducedinsuchadesign,itstill showcasedthepotential toapplythisdesignininjectionmolding.However,more investiga-tionswill havetobeconductedondetailedstructuraldesignand experimentalvalidationinthefuture.
3.3.7. Dual-materialconformalcoolingchannels
Toolsteel isthemost commonlyusedmaterial formoldsand dies due to its highstrength andwear resistance. However, due to its low thermal conductivity, it is not an ideal option from the point ofview ofheat transfer efficiency. Althoughincreasing the coolantflow rate could raise the cooling efficiency, thismay be limited by the mold layout, and may lead to higher coolant pumpingcosts [8].Amorefeasible solutionis tofabricateCC in-serts using materials with higher thermal conductivity such as copper (Cu). A simulation study showed that molds made ofCu or its alloys(e.g. beryllium copper) reduced the cooling time by 25–30% as compared to molds made of tool steel [108]. How-ever, Cu molds may not fulfill strength requirements. The adop-tion of multi-material CC channels combines the advantages of tool steel withthat of other well thermallyconductive materials andpresentsamoredesirablecoolingeffect.Incontrastto single-materialmolds,multi-materialsmoldsaremadeofmorethanone material(usuallytwo,suchastoolsteel/Cu[109],although triple-materialmoldshavealsobeenproposed[110,111]).Onesolutionto the dual-materialmold isto sinter a steel/Cu alloy[112]; on the other hand,amore popularsolutionisto makethe mainpartof
Fig. 27. CC layer and its unit cells proposed by Brooks and Brigden: (a) overview of the CC layer and (b) unit cells: cross (left) and N (right) (Reprinted by permission from
Fig. 29. A design of dual-materials CC channel made of P21/Cu graded materials (Reprinted by permission from [79] , Copyright 2019 KSME & Springer).
themoldoutoftoolsteelandtheCCchannelsoutofCu.By insert-ingCutubes,notonlythecoolingefficiencybutalsothelongevity ofthecoolingchannelswasincreased[113,114].
To minimize the thermalstresses causedby the mismatch of thermal expansion coefficients, there is usually an intermediate layer (referredto as‘functionallygraded material’) that smoothly transitions thematerial propertiesfromone toanotherone. Shin designed CC channels madeof linear-graded orparabolic-graded P21 tool steel/Cu layers [79,115], as shown in Fig. 29. A P21/Cu graded layer was designed to join two materials, achieving a smooth transition in material structure (related to strength) and function (thermalconductivity). FEManalysisresultsshowedthat the graded P21/Cu layered cooling channel exhibited faster cool-ingratesandsimilarthermalstresslevelscomparedtothe single-material(P21)coolingchannel.
Huang andFadel designedsteel/ceramic andsteel/bronze het-erogeneous cooling channels [80]. Their FEM analysis showed interesting results: for thermal-stress-resistant polymers, a sec-ondary mold material with highthermal diffusivity (e.g. bronze) waspreferredforobtainingfastcooling,whileasecondmold ma-terial with very low thermal diffusivity (e.g. ceramics) was pre-ferred forobtaining uniformcooling. Thisrepresentedan innova-tive attempt to apply ceramics in mold fabrication. However, it mustbenotedthatlaserAMforceramicsisstillachallengingtask at present. Similarly, Al insert wasemployed between the cavity andCCchannelsinepoxymoldstoenhance thethermal diffusiv-ity,achievingacoolingtimereductionofapproximately66%[116].
3.3.8. Combinationofconformalcoolingchannelswithother cooling/heatingtechniques
CombiningCCchannelswithother techniquesisanother inter-estingwaytoachieveabettercoolingeffect.Thisideaderivesfrom the combination of straight-drilled cooling channels with other cooling/heatingtechniques(suchasbafflesorbubblers).A combi-nation ofCC channels withheat sinks (heat thermocouples) was proposed to improve the cooling rateand shorten the solidifica-tion time forspace-limited situations [117,118]. This is an effec-tive but costly solution since it highly increases the complexity of manufacturing. Atwo-step manufacturing processinginvolving laserAMandconventionalmachiningwasemployedtorealizethis
Fig. 30. Local CC channels combining with straight-drilled cooling channels and baffles (Reprinted by permission from [41] , Copyright 2017 The Authors, Published by Elsevier).
combinedmold.Therefore,itisnotapreferredoptionforgeneral situations.
AlthoughCCchannelswere proposed asa substitutionof con-ventionalstraight-drilledcoolingchannels,somecaseswarrantthe useof thetwo designs together. CC channelsandstraight-drilled cooling channelscan be combinedin two ways. The first wayis tolocally(partially) useCCchannelsforproducingparts with lo-cally complexstructures, whileconventional straight-drilled cool-ing channelsand/or baffleswere employed forregions with rela-tivelysimplestructures[41,53],asshowninFig.30.ThelocallyCC channelsmayhave individual coolantinlet/outlet,orbe (serially) connectedwithstraight-drilledcooling channels.This designwas proposedtocontroltheproductioncostofthemolds.However,the coolingperformance wasalsoreducedcomparedto afullCC sys-tem.Thesecond wayistodesigna mixed full-conformal/straight-drilled coolingsystem[119].Inthis design,some straight cooling channelswereadditionallydrilledonafullCCmoldtofurther in-creasethecoolingperformance.
Inadditiontobeingusedinthecoolingstage,CCchannelscan alsobeusedinrapidheatcyclemolding(alsoknownasdynamic temperaturecontrol)wherethecavityisrapidlyheatedtoahigh temperaturebeforeplasticmeltinjection[120,121].Therapidheat cyclemoldingtechnique, inwhichheatingisimplementedby the CC/heatingchannelsorextraelectricresistancebuiltinthemolds, isusedto improvethe fluidityofmoltenpolymerduringthe fill-ing stage, especially in the case of complex geometric cavities. The combinationof the rapidheat cyclemolding techniquewith CC channels is expectedto further enhance the part quality and shortenthecycletimes.
3.4. Performanceevaluationofconformalcoolingchannels 3.4.1. Numericalsimulation
Althoughthe heatandmass transfertakingplace inCC chan-nelscan beclearlydescribedby physicalandmathematical equa-tions,itisadifficultchallengetosolvetheseequationsduetotheir highcomplexity and nonlinearity.Numerical simulation methods
such as FEM [122] and CFD [123] are commonly used tools to
obtainsolutions fortheseproblems.Variouscommercialsoftware packages, suchasMoldflow® [124,125],Ansys [126]and COMSOL Multiphysics®[127],havebeen employed to conductsimulations onthermal[128],mechanical[73] andfluid flow[30] analysis.In some simple cases, it is reasonable to approximate the 3D heat transferproblemasa2DonebecausetheCCchannelsare equidis-tantfromthecavitysurfaces[120].Forcomplexandcriticalparts,
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Fig. 31. Simulated results comparing the performance of normal straight-drilled cooling channels, CC channels with baffles, combined straight-drilled and CC channels and fully CC channels: (a) time to reach ejection time and maximum temperature and (b) volumetric shrinkage, sink mark and warpage (Reprinted from [27] ).
a full3D thermalstress analysisandwarpage predictionare nec-essaryformoreaccurateresults[8].
To obtain higher-fidelity simulation results, hot plate method and differential scanning calorimetry were employed to respec-tivelydeterminethethermalconductivityandspecificheat,which arethetwomostimportantthermalparameters usinginthe sim-ulation [129]. Maximum temperature, average temperature, tem-perature uniformity,coolingtime (time toreach ejection temper-ature), pressure drop, warpage, residual stresses, and length of weld lines are some ofthe main indicators usedto evaluate the cooling performance ofa cooling channel system[48,70,130]. Al-though many simulations have been performed in the literature underdifferentprocessparameters andconditions,alloftheir re-sults pointed to similar conclusions, viz. the CC systems showed bettercoolingperformancethanconventionalstraight-drilled cool-ingsystems.Arepresentativesimulationresult,isshowninFig.31 [27],wherethe fullyCC channelsystemwasseentobe themost suitable one ascompared to other cooling channel systemssince it provided the lowest volumetric shrinkage, sink mark percent-age,andtimetoreachtheejectiontemperature,resultingin near-uniform cooling and lesscooling time. Weld lines were also re-duced when usinga CC channel system [70]. The more complex thecoremold,themoredifficultitistocoolbyconventional cool-ing channels, and the greater the potential for cooling time re-duction withCCchannels[131].The efficiencyofthethermal ex-change in the cooling phase is particularly improved for plastic
parts with large concavities, slender details, internal turrets, and housings[73].3D simulationresultsshowingtheaverage temper-atureofmoldsandtimetoreachejectiontemperatureinmolding acomplexautomotivepartareillustratedinFig.32[41].Boththe average temperatureandthe temperature difference can be seen to be significantly reducedby using CC channel systems [41,64]. Moreover,itis moreeffectivetoapplyCC channelstotheconvex corewheremoreheatisaccumulatedthantheconcaveside [72]. Also, itisexpected thata bettercooling performance isachieved bycombiningCCchannelswithpulsecooling[130].
The cooling performance is affected by the flow behavior of coolant. As expected, a lower coolant temperature (indicating a greater temperaturegradient betweencoolant andcavity) results in more heat transfer and lower warpage defects, while a lower coolant flow rate enhances the temperature rise at the coolant outlet(indicatingagreater temperaturegradientofcoolant along thepassage,andthusinducingunevencooling)[132].Further,the flow front ofthe molten plastic is mainlydetermined by its vis-cosity,andthemorethemolten plasticis cooleddown themore ittends tobeviscous andsolidifies.Ascomparedto onlyone in-jection point,multiple injection pointsreduce the filling time as wellastheinjectionpressure,althoughnotdrastically[133]. How-ever, multiple injection points lead to weld lines between each flowfrontinadditiontoairbubbles,thusweakeningthe continu-ityandthestrengthofthemoldedpart/material.Fromthisaspect, asingleinjectiongatearrangedinthecenterofthemoldisa
pre-Fig. 32. Simulated results comparing the average temperature and time to reach ejection temperature of straight-drilled cooling channels and CC channels: (a) average temperature, straight-drilled cooling channels, (b) average temperature, CC channels, (c) time to reach ejection temperature, straight-drilled cooling channels, and (d) time to reach ejection temperature, CC channels (Reprinted by permission from [41] , Copyright 2017 The Authors, Published by Elsevier).
ferred optiontoobtain apropergeometrywithnodefectscaused byairbubbles,weldlines,ordifferentialshrinkage[133,134].
By comparing the CC channels with different cross-sectional shapes,circular,semicircular,elliptical,andrectangular,itisfound by Shinde and Ashtankar [135] that surface area of CC channels is theimportantparameterforreductionofcoolingtime and im-provement ofpartqualityirrespective ofcross-sectionalshape.In thecaseofaconstantvolumeofCCchannels,moreover, rectangu-larCCchannelsgivebetterresultsonaccountofthelargersurface areaascomparedtoCCchannelswithothercross-sectionalshapes
[135].Further,thecoolingperformance isaffectedby thechannel connectionpattern.Numericalsimulationshaveshownthatthe se-ries CC channelsperform better than the parallel ones in reduc-ingaveragetemperatures(indicatinghighercoolingrates)and im-proving temperatureuniformity,especiallyforpartswithcomplex shapes[42,48].Thisisbecausetheflowrateisinsufficientto main-tain theturbulenceintheparallelCCchannels,especiallyin com-plex channel layouts. Moreover, acombination ofseries and par-allel patterns is superior to the series pattern in cooling ability, although thismay increase the complexityin design and manu-facturing [136].However, in the caseofan improperdesign ofa CC system, e.g. the presence of deadflow zonesin the channels whichleadto increaseinpressuredropanddecreaseinflowrate
[72],thecoolingtimemaynotbelessenedevenifthesurfacearea and/or volume oftheCCsystemis/are largerthan aconventional coolingsystem[12,42,117].
3.4.2. Molding/castingexperiments
Although there exist several articles in the literature numer-ically evaluating the performance of CC channels, experimental studies are comparatively lower due to the capital intensity re-quiredformanufacturing injectionmoldsinthelab.Although nu-mericalsimulationsareimportantforqualitativevalidationof con-ceptsand/orpredictivemodeling,molding/castingexperimentsand prototyping are crucial for proof of concepts and validation. In some cases,asverifiedby Norwood etal.in theirdie casting
ex-Fig. 33. Comparison of mold temperature in CC mold and conventional cooling mold (data from [137] ).
periments,therecouldbeaconsiderabledifferencebetween simu-latedand experimental results[12]. Bˇehálek andDobránsky con-ducted injection molding by additively manufacturing CC molds
[137]. The mold was made of maraging steel 1.2709 and fabri-catedbylaserpowderbedfusion(L-PBF),oneofthelaserAM ap-proachesthatwillbediscussedinSection4.5.2.Theinjected mate-rialwaspolypropylene(MostenMT230)withgoodflowproperties (e.g.lowviscosity)thataresuitableforinjectingthin-walledparts. From the temperaturefield distribution in the injection mold, it wasconcludedthatincomparisonwithconventionalcooling sys-tems,the CC channelsrevealeda higherrateofheat removal in-tensityandhighertemperatureuniformity,asshowninFig.33.
The reductionof thecycletime strongly dependson the con-formabilityofthecoolingchannelsandthecomplexityofthepart. ForalocallyCCchannel system, 30%ofthecycletimecan be re-duced[41].Meanwhile, whenusinga fullCC channelsystem, the reduction ofthecycletime can bemore than50% forpartswith complex shapesand structures [131], or even be as highas 70%
S. Feng, A.M. Kamat and Y. Pei International Journal of Heat and Mass Transfer 171 (2021) 121082
Fig. 34. Fabricating procedures of an epoxy CC mold by epoxy casting: (a) preparing the master model (pattern of the molded part), (b) preparing the pattern of CC channels, (c) pouring Al-filled epoxy resins, (d) curing the mold and removing the frame, (e) removing master model, and (f) removing cooling channels (Adapted by permission from [142] , Copyright 2016 Springer-Verlag London).
for some specific cases[11,138]. Also, it isfound that the proper topologicaldesign couldresultinahighercoolingefficiencyeven ifmoldswithalowerheatconductivityareused[20].
4. Manufactureofconformalcoolingchannels
Inadditiontoaproperdesigntomeettherequirementof cool-ing performance, there is an equally important concern pertain-ing to theCC channel system, namely its manufacturability [66]. Due to the complex 3D internal structures that are characteris-tic ofoptimalCC designs,it’s impossibletomachine CC channels usingconventional mechanicalcuttingmethods(subtractive man-ufacturing). Several methods have been proposed to fabricate CC moldssincethelate1990s[139–141].Thesemethodscanbe sum-marized asfollows: casting [142], welding [10], U-groovemilling
[143],laminatedtooling[12],andpowder-basedAM(binderjetting
[139],laserpowder bedfusion[144,145],laser powderdeposition
[146], andelectron beammelting). Moreover, surfacequality and dimensionalaccuracyofcoolingchannelsaffectthecooling perfor-mance.Thus,surfacefinishing[138]usingmechanicalmethodsand the combinationofadditive/subtractivemanufacturing [141]were alsoproposed toimprovethesurfacequality anddimensional ac-curacy of the additively manufactured moldinserts. More details aboutthesemethodsareprovidedinthesubsectionsbelow. 4.1. Casting
4.1.1. Epoxycasting
Injection molds can be classified into two typesaccording to thematerials ofthemold,i.e.metalmoldandepoxymold. Metal molds,madeoftoolsteeland/orCu asexplainedinSection3.3.7, representthe mainstreamandareusually fabricated by mechani-cal machining and/ormetal AM.Onthe otherhand,epoxymolds are fabricatedusingepoxycasting,whereinaseriesofprocedures are undertaken to produce epoxy molds,as schematically shown inFig.34[142].Thefirststepistopreparethemastermodel(i.e. thepatternofthemoldedpart,whichcan bemadeofeitherwax
[147] or other materials, such as acrylonitrile butadiene styrene, ABS[148])andthewaxpatternofCCchannels[149].Then,the Al-filled epoxyresin powdersare pouredinto an Al frame inwhich the waxpattern waspre-located by designedsupports [150,151]. Thesupporttolocateandfixthepatternscanbemadeofthesame materialasthemold,i.e.Al-filledepoxy,sothat thereisnoneed toremove the supportin thefollowingprocess [151].During the finalcuringphase,thewaxpatternismeltedawayfromtheepoxy mold,leavingbehindthecavityandCCchannels[116,147].
The wax patternof CC channels is usually madeusing rapid-prototyping techniques such as 3D wax printing [147,152], fused deposition modeling [153], or wax injection molding [154]. The wax filament should be prepared before 3D printing [155]. The as-printed wax patternis usually subjected to post-printing pro-cesses such as polishing (10s immersion in 85°C water) to ob-tainhighsurfacequality,whichdetermines thesurfaceroughness of the final epoxy channels [156]. In the curing stage, both the epoxy andwax are heated wherein the formeris cured and the latterismelted.However, thewaxpatterncannot bemelted ear-lierthantheepoxybeingcuredtoenoughstrengthotherwisethe moldwoulddeviateorcollapse.Therefore,thetypeofwaxhasto bechosen specificallyto ensurethemelt temperatureofthewax not lower thanthe curing temperatureofthe epoxy[157]. As an alternativetowaxpatterns,Kuoetal.proposedacrylonitrile buta-dienestyrene(ABS) patternswhichcan be eithersolid orhollow andremovedbyacetoneliquid[148,158].
Metalmoldsarecompatiblewithbatchproductionduetotheir robustness, long lifetime, and mechanical strength. On the other hand,epoxymolds(knownas“soft” molds[159])aremoresuitable forsampletrialproduction orsmall-batch (short-run)production due to their weaker mechanical strength and lifetime [147,155]. The advantagesofepoxymolds includehigh-qualitychannel sur-faces and ease of post-processing using mechanical approaches (duetothelower mechanicalstrengthandhardnesscompared to atoolsteelmold),althoughtheproceduresoffabricatinganepoxy moldarecomplexandconsistofmanysteps[154].Moreover, pre-cisionmoldswithmicrofeaturescanbefabricated[160].However, thecoolingtimeismuchlongercomparedtometallictoolsdueto thepoorerthermalconductivityofepoxy, despitethepresenceof Alparticles[116,142].
4.1.2. Metalcasting
Metalcasting[161]andsprayforming[162]aretwoother pro-cesses tofabricate metallicmolds withCC channels.Theremoval ofthemastermodeland/orpatternsofCCchannelscanbe accom-plishedintwoways:(a)usingacetoneliquidandpressurized wa-ter to remove sand-filledepoxy masterandpatterns (metal cast-ing) [161],or (b) heatingup to melt away the patterns madeof low-melting-temperature metal such asCu (sprayforming) [162]. Byusingtheseimprovedfabricationmethods,boththemechanical strengthandlifetimeofthemoldcanbeimprovedascomparedto thatoftheAl-filledepoxymold.
4.2. Milledgroovemethod
The milled groovemethod is apractical approach to fabricate CCchannelsasanalternativetolaserAM[163,164].Inthismethod, thedesignedmoldinsert(cavity,coreorboth,dependingonwhere themilled-groove isdesigned) isdivided intotwo halves so that one half is used to mill grooves and the other half is used to cover (seal) the grooves. The grooves are usually milled on the sideclosedtothecavitysurface(i.e.thehalfwithcavitysurfaces) to improvethe cooling effect, asshown inFig. 35[87]. The two halves can be joined by bolts [165] or vacuum diffusion bond-ing[166].Forboltedconjunction, sealingisan importantconcern toprevent coolant leakage,requiring theuse ofsealants, gaskets,
Fig. 35. Design of a CC mold with milling-grooved channels (Reprinted by permis- sion from [87] , Copyright 2015 Wiley Periodicals, Inc.).
Fig. 36. Another design of milling-grooved CC mold proposed by Hughes (Reprinted from [167] ).
and O-rings between the halves, in ejector pinholes, and screw holes, andsurroundingthe milledgrooves[8,87,165].Forvacuum diffusion bonding,additionalsealingis notneeded. However, this methodiscostlyinspiteofbeingeffective.Aninnovativeapproach to fabricate milling-grooved CC molds was proposed by Hughes whereinthegroovesaremilled directlyonthecavitysurfaceand thensealedbywelding,asshowninFig.36[167].
Inthemilledgroovemethod,thecross-sectionalshapedepends on theshape ofthe millingtool used, e.g.square, rectangular, or U-shaped[165].Somenon-conventional machiningmethods,such aselectrical dischargemachining, serveasauxiliary processes for machining corners or other intricate geometries that are difficult formilling[8].
4.3. Laminatedtooling
Laminatedtoolingisalayer-by-layermanufacturingprocessand essentially a non-powder AM approachemployed to fabricate in-jectionmoldsanddies[12].Inlaminatedtoolingofinjectionmolds and dies, thegeometry design ofa mold/die isfirstly sliced into layers. The thickness of the layers (usually several millimeters) is determined by thetradeoff betweendimensional accuracy and processing costs [168,169]. Thus,the layerthicknessof laminated toolingismuchlargerthanthatofpowder-basedAM(usuallytens to hundreds of microns), so that it is more applicable to fabri-catelargerCCmolds[170].After theslicing, thelaminatesarecut by laser cutting [12,171] or abrasive waterjet [170] according to the slicedprofile.Finally,thelaminatesare bondedandsealedto complete the CC mold. There are severalways to bond the lam-inates, the most popular being to braze the laminates. For tool steel, nickelalloyisthepreferredchoiceasthefillermetaldueto its appropriate melting temperatureandmachinability. Toensure a good bond between the laminates, the laminates are required to be processed to remove burrs, oxide layers and grease before
Fig. 37. Stair-stepping channel surface after laminated tooling (Reprinted by per- mission from [173] , Copyright 2007 Emerald Publishing Limited).
Fig. 38. Schematic of manufacturing equipment for GMAW deposition (Reprinted by permission from [10] , Copyright 2015 Elsevier).
brazing [12].Bolting isanother waythat can bond thelaminates rapidlyandinexpensively.However, thejoininginterfacebetween twoadjacentlaminates,especiallyaroundtheholeofcooling chan-nels,hastobewellsealedusingadhesivetopreventleakageofthe coolant[170,172].
Laminatedtoolingisapractical approachtofabricateCC chan-nels. However, its cross-sectional profile is step-likewhose accu-racyis limitedbythe thicknessofthelamina sheet,asshownin
Fig.37 [173].Therefore,some post-processingmaybe requiredto remove the stair-stepping effectin the channel profile [169]. Be-sides,somemeasuresneedtobetakentoensurethebondingand sealingquality satisfiesrequirements onmechanical strengthand thermalconductivity.
4.4. Welding
Eiamsa-ard andWannissornproposed a metal deposition pro-cess by gas metal arcwelding (GMAW) to fabricate CC bubblers
[10]. In principle, this was essentially an AM approach wherein the weld bead was deposited track by track and layer by layer. A machine setup was built by attaching a GMAW torch onto a computer-numerical-control(CNC)machine,asschematically illus-trated inFig. 38.ER70S-6 wire(Ø 1.2mm)wasused inthis ma-chine setup. By minimizing weld splash, an optimal set of pro-cessparameters were proposed includinga 19Vvoltage,a 100 A current, a 10mm standoff distance,a 15L/min shielding gas flow rate, anda 300mm/min travel speed. Underthisoptimal param-eter set, samples with an average hardness of 19.16 in the HRC scaleandanaveragegrainsizeof11.1± 3.1μmwereobtained.Out of thetwo deposition paths tested by the authorsi.e. offsetand