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Comp. Part. Mech. (2014) 1:229243DOI 10.1007/s40571-014-0025-4Flow analysis and validation of numerical modelling for a thinwalled high pressure die casting using SPHPaul W. Cleary Gary Savage Joseph Ha Mahesh PrakashReceived: 22 December 2013 / Revised: 1 April 2014 / Accepted: 12 May 2014 / Published online: 28 May 2014 OWZ 2014Abstract High pressure die casting (HPDC) is an impor-tant process for high throughput manufacturing of complexshaped metallic components. The flow involves significantfragmentation and spray formation as the high pressure liq-uid jets into the die from the gate system. An important classof die cast components is one with large areas of thin walls.An example of this is the chassis of the laptop computer.Computational modelling provides an opportunity to bothbetter understand the filling process and to optimize the run-ner, gates, flash overs and venting systems for the die. SPHhas previously been found to be very suitable for predictingHPDC for bulkier automotive components. The modellingchallenges arising from the very thin sections and the manyflow paths in a laptop chassis require careful validation. Awateranalogueexperimentisusedtovalidatethepredictionsof the SPH model for this representative thin walled casting.SPH predictions are used to understand and characterise thefillingprocess.Finally,comparison offlowlinesvisibleinanetched finished casting with the high speed flow paths in thefinalfilledSPHmodelshowverystrongagreement.Togetherthese demonstrate that such an SPH model is able to capturesubstantial detail from both the water analogue system andthe actual casting process and is very suitable for simulatingthese types of complex thin walled castings.Keywords High pressure die casting HPDC Smoothedparticle hydrodynamics SPH Validation Thin walls water analogueP. W. Cleary (B) J. Ha M. PrakashCSIRO Mathematics, Informatics and Statistics, Private Bag 33,Clayton South, VIC 3168, Australiae-mail: paul.clearycsiro.auG. SavageCSIRO Materials Science and Engineering,Clayton South, VIC 3168, Australia1 IntroductionHigh pressure die casting (HPDC) is an important process inthe manufacturing of high volume and low cost metal com-ponents for the automotive, household products and elec-tronics industries. Liquid metal (generally aluminium, mag-nesium or zinc) is injected into the die at high speed (30100 m/s) and under high pressure through complex gate andrunner systems. The geometric complexity of the dies leadsto strongly three dimensional fluid flow with significant freesurface fragmentation and splashing. The order in which thevariouspartsofthediefillandthepositioningoftheairventsare crucial to forming homogeneous cast components withminimal entrapped voids. This is influenced by the designof the gating system and the geometry of the die. Numericalsimulation offers a powerful and cost effective way to studytheeffectivenessofdifferentdiedesignsandfillingprocesses,ultimately leading to improvements in both product qualityand process productivity, including more effective control ofthe die filling and die thermal performance.A simulation technique that has proven to be very effec-tive at modelling these HPDC flows is smoothed particlehydrodynamic (SPH). See Monaghan 2123forareviewof the basic method and Cleary et al. 9forareviewofitsuse in industrial applications, such as die casting. SPH is aLagrangian (grid-free) method for modelling heat and massflows and is well suited to simulating the complex splashingfree surface flows found here. In SPH, materials are approxi-matedbyparticlesthatarefreetomovearoundratherthanbyfixed grids or meshes. The particles are moving interpolationpoints that carry with them physical properties, such as themass of the fluid, its temperature, enthalpy, density and anyotherpropertiesthatarerelevant.Theinter-particleforcesarecalculated by smoothing the information from nearby parti-cles in a way that ensures that the resultant particle motion is123230 Comp. Part. Mech. (2014) 1:229243consistent with the motion of a corresponding real fluid, asdetermined by the NavierStokes equations.SPH has the following advantages for modelling variousdie casting processes: Complex free surface and material interface behaviour,including fragmentation, can be modelled easily and nat-urally. The Lagrangian framework means that there is no non-linear term in the momentum equation, thus the methodhandles momentum dominated flows very well. Ability to include thermal shrinkage. Ability to easily track microstructure and compositioninformation. Ability to predict oxide formation and gas entrapmentdirectly as part of the simulations.Complicated physics such as multiple phases, realistic equa-tions of state, compressibility, solidification, fracturing,porousmediaflow,electromagneticsandhistorydependenceof material properties are also easier to implement than inEulerian methods. SPH was introduced for modelling highpressure die casting by Cleary et al. 3. Ha 14 applied thisfor the first time to modelling HPDC in three dimensionsfor a simple machine component. Cleary et al. 5,6 sug-gested improved methods of visualizing the 3D HPDC SPHsimulations and also compared SPH simulations of gravitydie casting with experimental and MAGMAsoft simulatedresults. In 16 the effect of Reynolds number and resolu-tion of the SPH solution were analysed for the HPDC of amachine component. Cleary et al. 7,8 applied SPH to pre-dicting HPDC in a range of automotive products. Cleary etal. 11 then applied SPH to a broader range of product typesincluding house hold products (such as door handles castfrom zinc) and housings for electronic components.Validation has so far been mainly performed using wateranalogue experiments. Ha and Cleary 4 used existing pub-lishedwateranalogueexperimentsinasimplequasi-2Dcon-figuration to show the advantages of SPH in capturing criti-cal thin films and small scale flow features. Good quantita-tiveagreementbetweenSPHsimulationsandwateranalogueexperiments was also obtained for gravity die casting in Haet al. 15. Cleary et al. 7,8 performed detailed comparisonbetween SPH, MagmaSoft simulations and water analogueexperiments forarelativelycompact automotive component.Thisshowedmuchbetteragreement fortheSPHpredictions.Cleary et al. 11 also explored the impact of a range of ther-mal operating conditions on the filling of a thin wall coasterusing SPH. The simulations included heat transfer and solid-ification coupled to the fluid flow and were compared withexperimental short shots showing good agreement.DuetoitsabilitytotrackhistorydependentpropertiesSPHhas also been used to evaluate and optimize oxide levels inAl re-melt ingot casting by Prakash et al. 27 and duringfurnace tipping operations in Prakash et al. 2830. It hasbeen used for metal forming operations such as forging byBonetandKulasegaram1andClearyetal.7,8,10.Cleary2extendedtheSPHmethodtopredictfeeding,freezinganddefectcreationinlowpressurediecastingapplications.Morerecently, Pineau and DAmours 26 used SPH to predictskininclusionsinsemi-solidmetalcastings.Vijaykumar35also used SPH to investigate its ability to model continuouscasting of steel.Other methods sometimes used for modelling castinginclude the finite element method (using FIDAP) by Schnei-derandGrun34whomodelledflowandtemperatureduringdirect chill (DC) casting table filling. Hu et al. 18usedthefinite difference based MAGMAsoft to design and optimizethe runner and gating system for the die-casting of a thinwalled magnesium telecommunication component. Pellikaand Wendt 25 used the finite element based software Pro-CASTtodemonstratetheadvantagesofnumericalsimulationin modeling the HPDC of a simple aluminium coaster withheat transfer and solidification. Helenius et al. 17alsousedMAGMAsoft to predict the heat transfer and flow during thefilling of a HPDC shot sleeve. Rai et al. 31 used ProCASTin combination with an artificial neural network model topredict the filling time, solidification time and porosity in asimple HPDC component by setting an optimality criterionon four industrially relevant process parameters. Kerman-pur et al. 19 simulated the metal flow and solidification ina multi-cavity mould for automotive components using thefinite volume code FLOW-3D. As described in this paper,conventional grid based methods find it difficult to gener-ate good quality meshes for complex geometries when usingthe finite element method. Lee et al. 20 used the 3D finiteelement code DEFORM-3D to analyse internal void defectsduring open die forging of large ingots into wrought ironcomponents.Gunasegaram et al. 13 used the finite difference basedMAGMAsoft in conjunction with the concept of designof experiments (DOE) to limit the number of simulationsrequired for optimizing a given set of process parameters.Forfinitedifferenceandfinitevolumemethods,withoutcare-ful special treatments, one typically encounters a“stair-step”representation of curved geometries which leads to artificialnumerical resistance to flow and flow artifacts if the surfacesare not resolved at a very fine resolution.Pang et al. 24 used a particle level set method to simu-late two phase flows of cast filling process. This is the firstattempt at numerically evaluating back pressure effects dur-ing die casting processes. However, the simulations wereperformed only for low pressure die casting applications forsimple geometries.The use of a grid free method such as SPH means thatissues relating to the numerical representation of the geome-123Comp. Part. Mech. (2014) 1:229243 231tryareabletobeavoidedaswellasthedifficultiesincreatinghigh quality meshes for geometrically very complex compo-nents.TheabilityofSPHtonaturallyresolvethefreesurfaceshape without use of surface tracking methods such as theones described in Rudman 33 and Rider and Kothe 32, isalso strongly advantageous.In this paper, the use of SPH is extended to modellingHPDC flow in castings with large areas of thin walls. Theindicative example used is that of casting a laptop chas-sis. The flow is characterised by a central location of theshot sleeve, radial runners and divergent radial flow out-wardsthroughthethinwalledbaseplatewithorthogonalthinwalledstructures.Thisisaverychallengingcastinggeometrywithproportionallylargerareasofsectionsthatarerelativelythinner than in previous studies. Since economic pressuresandrequirementsforlightweighting(inbothautomotiveandmobile devices) are towards ever thinner walls, it is impor-tant that numerical simulation also be tested and validatedfor these types of casting geometries. So here we comparethe detailed isothermal filling pattern predicted by SPH towater analogue experiment. We also compare the predictedflow lines during feeding to the frozen flow lines that are vis-ible in etched examples of the laptop casting. Both forms ofexperimental comparison demonstrate that the prediction ofthin walled HPDC by SPH has good accuracy.2 The SPH methodology2.1 SPH function and gradient estimationHere, we provide only a brief summary of the method. Formore comprehensive details on the method see Monaghan21,22 and Cleary et al. 9. The interpolated value of afunction A at any position r can be expressed using SPHsmoothing as:A(r) =summationdisplaybmbAbbW(r rb, h) (1)where mband rbarethemassanddensityofparticlebandthesumisoverallparticlesbwithinaradius2hofr.HereW(r,h)is a C2spline based interpolation or smoothing kernel withradius2h,thatapproximatestheshapeofaGaussianfunctionbut has compact support. The gradient of the function A isgiven by differentiating the interpolation Eq. (1)togive: A(r) =summationdisplaybmbAbb W(r rb, h) (2)Using these interpolation formula and suitable finite differ-enceapproximationsforsecondorderderivatives,oneisableto convert parabolic partial differential equations into ordi-nary differential equations for the motion of the particles andthe rates of change of their properties.2.2 Continuity equationFrom Monaghan 21, our preferred form of the SPH conti-nuity equation is:dadt=summationdisplaybmb(va vb) Wab(3)where rais the density of particle a with velocity vaandmbis the mass of particle b. We denote the position vec-tor from particle b to particle a by rab= ra rband letWab= W(rab,h) be the interpolation kernel with smoothinglengthhevaluatedforthedistance|rab|.Thisformofthecon-tinuity equation is Galilean invariant (since the positions andvelocities appear only as differences), has good numericalconservation properties and is not affected by free surfacesor density discontinuities. The use of this form of the conti-nuity equation is very important for predicting free surfaceflows such as those occurring in die casting 4.2.3 Equation of stateThe SPH method used here is compressible and is used nearthe incompressible limit by choosing a sound speed that ismuchlargerthanthevelocityscalesintheflow.Theequationof state, giving the relationship between particle density andfluid pressure, is:P = P0bracketleftbiggparenleftbigg0parenrightbigg 1bracketrightbigg(4)where P0is the magnitude of the pressure and0is the ref-erence density. For water or liquid metals we use = 7. Thepressure scale factor P0is given by: P00= 100V2= c2s(5)where V isthecharacteristicormaximumfluidvelocity.Thisensuresthatthedensityvariationislessthan1%andtheflowcan be regarded as incompressible.2.4 Momentum equationThe SPH momentum equation used here, using the pressurefrom Eq. (4), to predict the particle motion:dvadt= g summationdisplaybmbbracketleftBiggparenleftBiggPb2b+Pa2aparenrightBiggab4ab(a+ b)vab.rabr2ab+ 2bracketrightBiggaWab(6)123232 Comp. Part. Mech. (2014) 1:229243where Paand aare pressure and viscosity of particle a andvab= va vb. Here h is a small parameter used to smoothout the singularity at rab= 0 and g is the gravity vector. Thefirst two terms involving the pressure correspond to the pres-sure gradient term of the NavierStokes equation. The nextterm involving viscosities is the Newtonian viscous stressterm. This form ensures that stress is automatically continu-ous across material interfaces and allows the viscosity to bevariableordiscontinuous.Multiplematerialswithviscositiesvarying by up to five orders of magnitude can be accuratelysimulated.The nature of the interaction between these SPH equa-tions can be understood by considering two particles. Asthey approach each other, their relative velocity is negativeso that there is a positive contribution to da/dt causing ato rise, leading to a positive pressure that pushes the parti-cles apart again. As two particles move apart their densitiesdecrease creating a negative pressure that pulls the particlesback towards each other. This interplay of velocity and den-sity/pressure ensures that the particles remain on averageequallyspacedandthatthedensityisclosetouniformsothatthe fluid is close to incompressible.3 Water analogue experimental apparatusWater analogue methods for the validation of high pres-surecastingsimulationmodelshavebeenwidelyadoptedformanyyearswithoneofthefirstsuchattemptsmadebyDavieset al. 12. This is based on the similarity of the kinematicviscosity of water to that of liquid metals such as aluminiumand magnesium, so that the Reynolds number for the waterandmetalsystemsarecomparableleadingtosimilarityintheflow behaviour.A perspex mould was manufactured from 3D CAD dataderived from an actual casting of the laptop cover, completewith sprue, runners, gates and overflows as shown in Fig. 1.The casting is 277 mm wide by 216 mm high by 20 deep.The main wall section thickness for the chassis was 1.6 mm.The perimeter of the gate is 175 mm and the gate thicknessis 0.9 mm. The weight of the casting and overflows was 223g and the gate area was 156 mm2. The sprue diameter at thevisible top of the finished casting is around 30 mm.The water analogue experimental setup consisted of apressurized accumulator, partially filled with coloured waterat 6 bar pressure, which was connected to the perspex mouldthroughavalve.Theperspexmouldwasbacklitthroughadif-fuserandfillingwascapturedusingaKodakSR1000MotionCorder Analyser high speed digital camera. This configura-tion was chosen to provide a constant pressure water deliv-ery system and a cavity fill time of approximately 37 ms.The cavity fill time was chosen to provide good resolutionof the early stages of cavity filling, based on the maximumallowable camera frame rate of 1,000 fps.Fig. 1 Perspex model of the laptop cover used for water analogue flowexperiments4 Modelling assumptions and setupThe simulation was set up to exactly match the water ana-logue experiment with the geometry specified from the sameCAD model used for making the perspex mould. The basicfluid properties used were density = 1,000 kg/m3and viscos-ity = 0.01 Pa s. This viscosity represents an estimate of theturbulent viscosity which is estimated to be around ten timeshigher than the kinematic viscosity of water. This viscositylevel was found suitable in earlier validation work by Ha etal. 15 and Cleary et al. 7,8 leading to very good matchesto the water analogue flow patterns. Previous testing has alsoshown low sensitivity of the flow predictions to the specificchoice of viscosity in this range.Sincethewateranalogueflowratewaspressurecontrolledit varied moderately throughout the shot. We therefore usedan estimated peak fluid speed in the shot sleeve of 3 m/swhich leads to maximum fluid speeds through the gate ofaround 33 m/s to match the average experimental flow rate.Sensitivity of the predicted flow to the injection speed wasalso tested to estimate the error arising from this assump-tion. The choice of injection speed does not appear to affectthe nature of the flow pattern but simply linearly scales thetime for filling the die. These simulations used a resolutionof0.64mmgivingamaximumof1.32millionSPHfluidpar-ticles when the die was completely filled. This w
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