滅火器端蓋塑料注射模設(shè)計(jì)【高度100】

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Whatismissingisthe fundamental understanding of howthe modifications to the mold material and RP manufacturing process impact both themold design and the injection mold ing process. In addition, numerical simulationtechniques have now become helpful tools of mold designers and process engi neersfor traditional injection molding. Butallcurrent simulation packages for conventionalinjection molding are no longer ap plicable to this new typeofinjection molds,mainly because the propertyofthe mold material changes greatly.Inthis paper, anintegrated approach to accomplish a numerical simulation of in jection molding intorapid-prototyped moldsisestablished and a corresponding simulation systemisdeveloped. Comparisonswithexperimental results are employed for verification,which show that the present schemeiswellsuited to handle RP fabri catedstereolithography (SL) molds.KeywordsKeywordsKeywordsKeywordsInjection moldingNumerical simulationRapid prototyping1 1 1 1 IntroductionIntroductionIntroductionIntroductionIn injection molding, the polymer melt at high temperatureisinjected into themold under high pressure 1. Thus, the mold material needs to have thermal andmechanical properties capa bleofwithstanding the temperatures and pressures ofthe mold ing cycle. The focus of many studies has been to create theinjection mold directly by a rapid prototyping (RP) process. By eliminatingmultiple steps, this method of tooling holds the best promise of reducing the time andcost needed to create low-volume quantities of parts in a production material. ThepotentialofintegratinginjectionmoldingwithRPtechnologieshasbeendemonstrated many times. The properties of RP molds are very different from thoseof traditional metal molds. The key differ ences are the properties of thermalconductivity and elastic mod ulus (rigidity). For example, the polymers used inRP-fabricated stereolithography (SL) molds have a thermal conductivity thatislessthan one thousandth that of an aluminum tool. In using RP technologies to createmolds, the entire mold design and injection-molding process parameters need to bemodified and optimized from traditional methodologies due to the completelydifferent tool material. However, thereisstillnota fundamen tal understanding ofhow the modifications to the mold tooling method and material impact both the molddesign and the injec tion molding process parameters. One cannot obtain reasonableresultsbysimply changing a few material properties in current models. Also, usingtraditional approaches when making actual parts may be generating sub-optimalresults. So thereisa dire need to study the interaction between the rapid tooling (RT)pro cess and material and injection molding, so as to establish the mold designcriteria and techniques for an RT-oriented injection molding process.In addition, computer simulationisaneffective approach for predicting thequality of moldedparts. Commerciallyavailablesimulation packages of thetraditional injection molding process have now become routine toolsofthe molddesigner and pro cess engineer 2. Unfortunately, current simulation programs forconventional injection molding arenolonger applicable to RP molds, because of thedramatically dissimilar tool material. For instance, in using the existing simulationsoftware with alu minum and SL molds and comparing with experimental results,though the simulation values of part distortion are reasonable for the aluminum mold,results are unacceptable, with the error exceeding 50%. The distortion duringinjection moldingisdue to shrinkage and warpage of the plastic part, aswellas themold. For ordinarily molds, the main factoristhe shrinkage and warpage of theplastic part, whichismodeled accurately in cur rent simulations. But for RP molds,the distortion of the mold has potentially more influence, which have been neglectedin current models. For instance, 3 used a simple three-step simulation process toconsider the mold distortion, which had too much deviation.In this paper, based on the above analysis, a new simula tion system for RPmoldsisdeveloped. The proposed system focuses on predicting part distortion, whichisdominating defect in RP-molded parts. The developed simulationcanbe applied asan evaluation tool for RP mold design and process opti mization. Our simulationsystemisverifiedbyan experimental example.Although many materials are available for use in RP tech nologies, weconcentrateonusing stereolithography (SL), the original RP technology, to createpolymer molds. The SL pro cess uses photopolymer and laser energy to build a partlayerbylayer. Using SL takes advantage of both the commercial domi nanceofSLin the RP industry and the subsequent expertise base that has been developed forcreating accurate, high-quality parts.Untilrecently, SL was primarily used to createphysical models for visual inspection and form-fitstudieswithvery limitedfunc tional applications. However,thenewer generationstereolitho graphicphotopolymers have improved dimensional,mechanical and thermal propertiesmakingitpossible to use them for actual functional molds.2 2 2 2 IntegratedIntegratedIntegratedIntegrated simulationsimulationsimulationsimulation ofofofof thethethethe moldingmoldingmoldingmolding processprocessprocessprocess2.1 MethodologyIn order to simulate the use of an SL mold in the injection molding process, aniterative methodisproposed. Different soft ware modules have been developed andused to accomplish this task. The main assumptionisthat temperature and loadbound ary conditions cause significant distortions in the SL mold. The simulationsteps are as follows:1The part geometryismodeled as a solid model, whichistranslated to afilereadable by theflow analysis package.2Simulate the mold-fillingprocess of the melt into a pho topolymer mold,whichwilloutput the resulting temperature and pressure profiles.3Structural analysisisthen performed on the photopolymer mold modelusing the thermal and load boundary conditions obtained from the previous step,which calculates the distor tion that the mold undergo during the injection process.4Ifthe distortion of the mold converges, move to the next step. Otherwise,the distorted mold cavityisthen modeled (changes in the dimensions of the cavityafter distortion), and returns to the second step to simulate the melt injection into thedistorted mold.5The shrinkage and warpage simulation of the injection molded partisthenapplied, which calculates thefinaldistor tions of the molded part.In above simulationflow, there are three basic simulation mod ules.2.2Filling simulationof themelt2.2.1 Mathematical modelingIn order to simulate the use of an SL mold in the injection molding process, aniterative methodisproposed. Different software modules have been developed andused to accomplish this task. The main assumptionisthat temperature and loadboundary conditions cause significant distortionsinthe SL mold. The simulation stepsare as follows:1. The part geometryismodeled as a solid model, whichistranslated to a filereadable by the flow analysis package.2. Simulate the mold-filling process of the melt into a photopolymer mold, whichwilloutput the resulting temperature and pressure profiles.3. Structural analysisisthen performedonthe photopolymer mold model usingthe thermal and load boundary conditions obtained from the previous step, whichcalculates the distortion that the mold undergo during the injection process.4.Ifthe distortion of the mold converges, move to the next step. Otherwise, thedistorted mold cavityisthen modeled (changesinthe dimensions of the cavity afterdistortion), and returns to the second step to simulate the melt injection into thedistorted mold.5. The shrinkage and warpage simulationofthe injection molded partisthenapplied, which calculates the final distortionsofthe molded part.In above simulation flow, there are three basic simulation modules.2.2 Filling simulation ofthe melt2.2.1 Mathematical modelingComputer simulation techniques have had success in predictingfillingbehaviorin extremely complicated geometries. However, most of the current numericalimplementationisbasedona hybrid finite-element/finite-difference solution with themiddleplane model. The application processofsimulation packages basedonthismodelisillustrated in Fig. 2-1. However, unlike the surface/solidmodel inmold-design CAD systems, the so-called middle-plane (as shown in Fig. 2-1b)isanimaginary arbitrary planar geometry at the middle of the cavity in the gap-wisedirection, which should bring about great inconvenience in applications. For example,surface models are commonly used in current RP systems (generally STL file format),so secondary modelingisunavoidable when using simulation packages because themodels in the RP and simulation systems are different. Considering these defects, thesurface model of the cavityisintroduced as datum planes in the simulation, instead ofthe middle-plane.According to the previous investigations 46, fillinggoverning equations for theflow and temperature field can be written as:wherex, yare the planar coordinates in the middle-plane, andzisthe gap-wisecoordinate;u, v,ware the velocity componentsinthex, y, zdirections;u, vare theaverage whole-gap thicknesses; and, ,CP(T), K(T)represent viscosity, density,specific heat and thermal conductivity of polymer melt, respectively.Fig.2-1Fig.2-1Fig.2-1Fig.2-1 a a a a d. d. d. d. Schematic procedure of thesimulation with middle-plane model. a a a aThe3-D surfacemodelb b b bThemiddle-plane model c c c c Themeshed middle-plane modeld d d dThedisplay of thesimulation resultIn addition, boundary conditions in the gap-wise direction can be defined as:whereTWisthe constantwalltemperature (shown in Fig. 2a).Combining Eqs. 14 with Eqs. 56,itfollows that the distributions of theu, v, T,Patzcoordinates should be symmetrical, with the mirror axis beingz= 0, andconsequently theu, vaveraged in half-gap thicknessisequal to that averaged inwholegap thickness. Basedonthis characteristic, we can divide the whole cavity intotwo equal parts in the gap-wise direction, as described byPartIandPartIIin Fig. 2b.At the same time, triangular finite elements are generatedinthe surface(s) of thecavity(atz= 0 in Fig. 2b), insteadofthe middle-plane(atz= 0 in Fig. 2a).Accordingly, finite-difference increments in the gapwise direction are employed onlyin the inside of the surface(s)(wallto middle/center-line), which, in Fig. 2b, meansfromz= 0 toz=b. Thisissingle-sided instead of two-sided with respect to themiddle-plane (i.e. from the middle-line to two walls).Inaddition, the coordinatesystemischanged from Fig. 2a toFig.2b to alter the finite-element/finite-differencescheme, as shown in Fig. 2b. With the above adjustment, governing equations are stillEqs. 14. However, the original boundary conditionsinthe gapwise direction arerewritten as:Meanwhile, additional boundary conditions must be employed atz=bin orderto keep the flows at the juncture of the two parts at the same section coordinate 7:where subscripts I,IIrepresent the parametersofPartIandPartII, respectively,and Cm-I and Cm-II indicate the moving free melt-fronts of the surfaces of thedivided two parts in the filling stage.Itshould be noted that, unlike conditions Eqs. 7 and 8, ensuring conditions Eqs.9 and 10 are upheld in numerical implementations becomes more difficult due to thefollowing reasons:1. The surfaces at the same section have been meshed respectively, which leadsto a distinctive pattern of finite elements at the same section. Thus, an interpolationoperation should be employed foru, v, T, Pduring the comparison between the twoparts at the juncture.2. Because the two parts have respective flow fields with respect to the nodes atpoint A and point C (as shown in Fig. 2b) at the same section,itispossible to haveeither both filled or one filled (and one empty). These two cases should be handledseparately, averaging the operation for the former, whereas assigning operation for thelatter.3.Itfollows that a small difference between the melt-frontsispermissible. Thatallowance can be implementedbytime allowance control or preferable locationallowance control of the melt-front nodes.4. The boundaries of the flow field expandbyeach melt-front advancement, soitisnecessary to check the condition Eq. 10 after each change in the melt-front.5. In view of above-mentioned analysis, the physical parameters at the nodes ofthe same section should be compared and adjusted, so the information describingfinite elements of the same section should be prepared before simulation, that is, thematching operation among the elements should be preformed.Fig.Fig.Fig.Fig. 2a,b.2a,b.2a,b.2a,b. Illustrative of boundary conditionsinthe gap-wise direction a a a aof themiddle-planemodelb b b bof thesurfacemodel2.2.2 Numerical implementationPressure field.In modeling viscosity, whichisa functionofshear rate,temperature and pressureofmelt, the shear-thinning behavior can bewellrepresentedby a cross-type model such as:wherencorresponds to the power-law index, and*characterizes the shearstress level of the transition region between the Newtonian and power-law asymptoticlimits. In terms ofanArrhenius-type temperature sensitivity and exponential pressure dependence,0(T, P)can be represented with reasonable accuracy as follows:Equations 11 and 12 constitute a five-constant(n,* ,B,Tb,)representationfor viscosity. The shear rate for viscosity calculationisobtainedby:Based on the above, we can infer the following filling pressure equation from thegoverning Eqs. 14:whereSiscalculatedbyS=b0/(bz)2dz. Applying the Galerkin method, thepressure finite-element equationisdeduced as:wherel_ traversesallelements, including nodeN, and whereIandjrepresent thelocal node number in elementl_ corresponding to the node number N andN_ in thewhole, respectively. TheD(l_)ijiscalculated as follows:whereA(l_)represents triangular finite elements, andL(l_)iisthe pressure trialfunction in finite elements.Temperature field.To determine the temperature profile across the gap, eachtriangular finite element at the surfaceisfurther divided intoNZlayers for thefinite-difference grid.The leftitemofthe energy equation (Eq. 4)canbe expressed as:whereTN, j,trepresents the temperature of thejlayerofnodeNat timet. Theheat conductionitemiscalculatedby:whereltraversesallelements, including nodeN, andiandjrepresent the localnode number in elementlcorresponding to the node numberNandN_ in the whole,respectively.The heat convectionitemiscalculatedby:For viscous heat,itfollowsthat:Substituting Eqs. 1720 into the energy equation (Eq. 4), the temperatureequation becomes:2.3 Structural analysis ofthemoldThe purpose of structural analysisisto predict the deformation occurring in thephotopolymer mold due to the thermal and mechanical loads of the filling process.This modelisbased on a three-dimensional thermoelastic boundary element method(BEM). The BEMisideally suited for this application becauseonlythe deformationof the mold surfacesisof interest. Moreover, the BEMhasan advantage over othertechniques in that computing effortisnot wasted on calculating deformation withinthe mold.The stresses resulting from the process loads arewellwithin the elastic rangeofthe mold material. Therefore, the mold deformation modelisbasedona thermoelasticformulation. The thermal and mechanical properties of the mold are assumed to beisotropic and temperature independent.Although the processiscyclic, time-averaged values of temperature and heatflux are used for calculating the mold deformation. Typically, transient temperaturevariations within a mold have been restricted to regions local to the cavity surface andthe nozzletip8. The transients decay sharply with distance from the cavity surfaceand generally little variationisobserved beyond distances as small as 2.5 mm. Thissuggests that the contribution from the transients to the deformation at the mold blockinterfaceissmall, and thereforeitisreasonable to neglect the transient effects. Thesteadystatetemperaturefieldsatisfies Laplaces equation2T=0 andthetime-averaged boundary conditions. The boundary conditions on the mold surfacesare describedindetail by Tang et al. 9. As for the mechanical boundary conditions,the cavity surfaceissubjected to the melt pressure, the surfaces of the mold connectedto the worktable are fixed in space, and other external surfaces are assumed to bestress free.The derivation of the thermoelastic boundary integral formulationiswellknown10.Itisgivenby:whereuk,pkandTare the displacement, traction and temperature,representthe thermal expansion coefficient and Poissons ratio of the material, andr=|yx|.clk(x)isthe surface coefficient which dependsonthe local geometry atx, theorientation of the coordinate frame and Poissons ratio for the domain 11. Thefundamental displacementulkat a pointyin thexkdirection, in a three-dimensionalinfinite isotropic elastic domain, results from a unit load concentrated at a pointxacting in thexldirection andisof the form:wherelkisthe Kronecker delta function andisthe shear modulus of the moldmaterial.The fundamental tractionplk, measured at the pointyon a surface with unitnormaln n n n,is:Discretizing the surface of the mold into atotalofNelements transforms Eq. 22to:wherenrefers to thenthsurface elementonthe domain.Substituting the appropriate linear shape functions into Eq. 25, the linearboundary element formulation for the mold deformation modelisobtained. Theequationisapplied at each node on the discretized mold surface, thus giving a systemof 3Nlinear equations, whereNisthetotalnumber of nodes. Each node has eightassociated quantities: three components of displacement, three components of traction,a temperature and a heat flux. The steady state thermal model supplies temperatureand flux values as known quantities for each node, and of the remaining six quantities,three must be specified. Moreover, the displacement values specified at a certainnumber of nodes must eliminate the possibility of a rigid-body motion or rigid-bodyrotation to ensure a non-singular system of equations. The resulting system ofequationsisassembled into a integrated matrix, whichissolved withaniterativesolver.2.4 Shrinkage and warpage simulation ofthemoldedpartInternal stresses in injection-molded components are the principal cause ofshrinkage and warpage. These residual stresses are mainly frozen-in thermal stressesdue to inhomogeneous cooling, when surface layers stiffen sooner than the coreregion, as in free quenching. Based on the assumption of the linear thermo-elastic andlinearthermo-viscoelasticcompressiblebehaviorofthepolymericmaterials,shrinkage and warpage are obtained implicitly using displacement formulations, andthe governing equationscanbe solved numerically using a finite element method.With the basic assumptionsofinjection molding 12, the components of stressand strain are givenby:The deviatoric components of stress and strain, respectively, are given byUsing a similar approach developedbyLee and Rogers 13 for predicting theresidual stresses in the tempering of glass, an integral form of the viscoelasticconstitutive relationshipsisused, and the in-plane stresses can be related to the strainsby the following equation:WhereG1isthe r