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1、Integrated simulation of the injection molding process withstereolithography moldsAbstract Functional parts are needed for design veri?cation testing, ?eld trials ， customer evaluation, and production planning. By eliminating multiple steps， the creation of the injection mold directly by a rapid pro

2、totyping (RP ) process holds the best promise of reducing the time and cost needed to mold low volume quantities of parts. The potential of this integration of injection molding with RP has been demonstrated many times. What is missing is the fundamental understanding of how the modi?cations to the

3、mold material and RP manufacturing process impact both the mold design and the injection molding process. In addition, numerical simulation techniques have now become helpful tools of mold designers and process engineers for traditional injection molding. But all current simulation packages for conv

4、entional injection molding are no longer applicable to this new type of injection molds， mainly becausethe property of the mold material changes greatly。 In this paper, an integrated approach to accomplish a numerical simulation of injection molding into rapid prototyped molds is established and a c

5、orresponding simulation system is developed. Comparisons with experimental results are employed for veri?cation, which show that the present scheme is well suited to handle RP fabricated stereolithography (SL) molds。Keywords Injection molding Numerical simulation Rapid prototyping1 IntroductionIn in

6、jection molding ， the polymer melt at high temperature is injected into the mold under 1high pressure 1 。 Thus, the mold material needs to have thermal and mechanical properties capable of withstanding the temperatures and pressures of the molding cycle. The focus of many studies has been to create

7、theinjection mold directly by a rapid prototyping (RP) process. By eliminating multiple steps, this method of tooling holds the best promise of reducing the time and cost needed to create low-volume quantities of parts in a production material. The potential of integrating injection moldi ng with RP

8、 tech no logies has bee n dem on strated many times The properties of RP molds are very different from those of traditional metal molds. The key differences are the properties of thermal conductivity and elastic modulus (rigidity). For example， the polymers used in RPfabricated stereolithography (SL

9、) molds have a thermal conductivity that is less than one thousandth that of an aluminum tool. In using RP technologies to create molds, the entire mold design and injection-molding process parameters need to be modi?ed and optimized from traditional methodologies due to the completely different too

10、l material. However ， there is still not a fundamental understanding of how the modi?cations to the mold tooling method and material impact both the mold desig n and the injectio n moldi ng process parameters。ne cannot obtain reasonable results by simply changing a few material properties in current

11、 models. Als，o using traditional approaches when making actual parts may be generating sub-optimal results. So there is a dire need to study the interaction between the rapid tooling(RT) process and material and injection molding, so as to establish the mold design criteria and techniques for an RT-

12、oriented injection molding process. 个人收集整理 ,勿做商业用途本文为互联网收集 , 请勿用作商业用途In addition， computer simulation is an effective approach for predicting the quality of molded partsr Commercially available simulation packages of the traditional injection molding process have now become routine tools of the mold

13、 designer and process engineer 2r Unfortunately, current simulation programs for conventional injection molding are no longer applicable to RP molds, because of the dramatically dissimilar tool material. For instance ， in using the existing simulation software with aluminum and SL molds and comparin

14、g with experimental results， though the simulation values of part distortion are reasonable for the aluminum mold, results are unacceptabl，e with the error exceeding 50%r The distortion during injection molding is due to shrinkage and warpage of the plastic par，t as well as the mold. For ordinarily

15、molds， the main factor is the shrinkage and warpage of the plastic part, which is modeled accurately in current simulations. But for RP molds, the distortion of the mold has potentially more in?uence， which have been neglected in current moderls For instance， 3 used a simple threestep simulation pro

16、cess to consider the mold distortion ， which had too much deviationr 文档为个人收集整理，来源于网络文档为个人收集整理，来源于网络In this paper， based on the above analysis， a new simulation system for RP molds is developed. The proposed system focuses on predicting part distortion, which is dominating defect in RP-molded parts.

17、The developed simulation can be applied as an evaluation tool for RP mold design and process optimizationr Our simulation system is veri?ed by an experimental example.Although many materials are available for use in RP technologies, we concentrate on using stereolithography (SL), the original RP tec

18、hnology， to create polymer moldsr The SL process uses photopolymer and laser energy to build a part layer by layrer Using SL takes advantage of both the commercial dominance of SL in the RP industry and the subsequent expertise base that has been developed for creating accurate， highquality partsr U

19、ntil recently， SL was primarily used to create physical models for visual inspection and form-?t studies with very limited functional applicationsr However ， the newer generation stereolithographic photopolymers have improved dimensional, mechanical and thermal properties making itpossible to use th

20、em for actual functional molds.本文为互联网收集，请勿用作商业用途个人收集整理，勿做商业用 途2 Integrated simulation of the molding process2.1 MethodologyIn order to simulate the use of an SL mold in the injection molding process， an iterative method is proposed。 Different software modules have been developed and used to accompli

21、sh this task。 The main assumption is that temperature and load boundary conditions cause signi?cant distortions in the SL mold. The simulation steps are as follows:1 The part geometry is modeled as a solid mode，l which is translated to a ?le readable by the ?ow analysis package。2 Simulate the mold?l

22、ling process of the melt into a photopolymer mold, which will output the resulting temperature and pressure pro?les.3 Structural analysis is then performed on the photopolymer mold model using the thermal and load boundary conditions obtained from the previous step, which calculates the distorti on

23、that the mold un dergo duri ng the in jecti on process4 If the distortion of the mold converges， move to the next step. Otherwise， the distorted mold cavity is then modeled(changes in the dimensions of the cavity after distortion), and returns to the sec ond step to simulate the melt injectio n into

24、 the distorted mold5 The shrinkage and warpage simulation of the injection molded part is then applied， which calculates the ?nal distortions of the molded part.In above simulation ?ow， there are three basic simulation modules.2。 2 Filling simulation of the melt2。2.1 Mathematical modelingIn order to

25、 simulate the use of an SL mold in the injection molding process， an iterative method is proposed。 Different software modules have been developed and used to accomplish this task。 The main assumption is that temperature and load boundary conditions cause significant distortions in the SL mold。 The s

26、imulation steps are as follows:1. The part geometry is modeled as a solid model, which is translated to a file readable by the flow analysis package。2。Simulate the mold-filling process of the melt into a photopolymer mold ， which willoutput the resulting temperature and pressure profiles3. Structura

27、l analysis is then performed on the photopolymer mold model using the thermal and load boun dary con diti ons obta ined from the previous step, which calculates the distorti on that the mold un dergo duri ng the in jecti on process.4. If the distortio n of the mold con verges, move to the n ext step

28、o Otherwise, the distorted mold cavity is then modeled (changes in the dimensions of the cavity after distortion ), and returns to the sec ond step to simulate the melt injectio n into the distorted mold.5. The shri nkage and warpage simulati on of the inject ion molded part is the n applied, which

29、calculates the final distortions of the molded partIn above simulation flow, there are three basic simulation modules.2o 2 Filling simulation of the melt2.2。1 Mathematical model ingComputer simulation techniques have had success in predicting filling behavior in extremely complicated geometries. How

30、ever, most of the curre nt nu merical impleme ntati on is based on a hybrid finite-element/finite differenee solution with the middleplane model。 The application process of simulation packagesbased on this model is illustrated in Fig。2 1.However, uni ike the surface/solid model in molddesig n CAD sy

31、stems,the so calledmiddle-plane (as shown in Fig. 2-1b) is an imaginary arbitrary planar geometry at the middle of the cavity in the gap wise direct ion, which should bring about great inconvenience in applications。For example, surface models are commonly used in current RP systems (generally STL fi

32、le format), so sec on dary modeli ng is un avoidable when using simulati on packages because the models in the RP and simulation systems are different Considering these defects the surface model of the cavity is in troduced as datum pla nes in the simulation,in stead of themiddlepla ne.个人收集整理，勿做商业用途

33、文档为个人收集整理，来源于网络According to the previous investigations 4 -6,fillinggoverning equations for the flowand temperature field can be writte n aswhere x, y are the planar coordinates in the middleplane, and z is the gap wise coord in ate； u, v,w are the velocity comp onents in the x, y, z directi ons; u,

34、 v are the average whole-gap thicknesses and n p, CP (T) , K(T) represent viscosity density, specific heat and thermal con ductivity of polymer melt, respectively.Fig.2-1 a -d. Schematic procedure of the simulation with middle-plane model 。 a The 3-D surface model bThe middle-plane model c The meshe

35、d middle-plane model d The display of the simulation resultIn additi on, boun dary con diti ons in the gap-wise directi on can be defi ned asti = = v = 0. T = Tw &E Z =(5)=0 = = Oa nr =Q atZ= 0(6)where TW is the constant wall temperature (shown in Fig. 2a。Combining Eqs. 1 with Eqs。5 -6, it follo

36、ws that the distributions of the u, v, T, P at zcoord in ates should be symmetrical with the mirror axis being z = 0, and con seque ntly theu， v averaged in half gap thick ness is equal to that averaged in wholegap thick ness. Based on this characteristic, we can divide the whole cavity into two equ

37、al parts in the gap-wise direction as described by Part I and Part II in Fig. 2b. At the same time, triangular finite elements are gen erated in the surface(s) of the cavity (az = 0 in Fig。 2b)， in stead of the middle-pla ne (at z = 0 in Fig. 2a). Accord in gly， fin ite-differe nee in creme nts in t

38、he gapwise directi on are employed on ly in the in side of the surface (s)( wall to middle/ce nter line), which， in Fig.2b， means from z = 0 to z = b。This is sin gle sided in stead of two sided with respect to the middlepla ne (i。e. from the middle-li ne to two walls)。In additi on, the coord in ate

39、system ischa nged from Fig. 2a to Fig= 2b to alter the fin ite-eleme nt/fini tediffere nee scheme, as show n in Fig. 2b. With the above adjustment, governing equations are still Eqs。1 F. However, theorig inal boun dary con diti ons in the gapwise direct ion are rewritte n as文 档为个人收集整理，来源于网络文 档为个人收集整

40、理，来源于网络yr=0. U1 = 0 at= fr uZh =如=匕=r = 7V机匚=oiK)Mean while, additi onal boun dary con diti ons must be employed az = b in order to keep the flows at the jun cture of the two parts at the same secti on coord in ate 7:w； = uti V/ - r； - Tn. Pi - Pu m= If(?)Cm -i = Cm-1 £(10)where subscripts 1,11

41、 represe nt the parameters OP art I and Part II respectively, and Cm-I and Cm-II indicate the moving free melt-fronts of the surfaces of the divided two parts in the filling stage.It should be no ted tha, un like con diti ons Eqs. 7 and 8, en suri ng con diti ons Eqs 9 and 10 are upheld in numerical

42、 implementations becomes more difficult due to the following reasons:1。The surfaces at the same sect ion have bee n meshed respectively, which leads to a disti nctive pattern of fin ite eleme nts at the same secti on。 Thus, an in terpolatio n operati on should be employed for u, v, T, P during the c

43、omparison between the two parts at the juncture。2。Because the two parts have respective flow fields with respect to the no des at point A and point C (as show n in Fig. 2 b) at the same sect ion, it is possible to have either both filled or one filled (and one empty) . These two cases should be hand

44、led separately, averaging the operati on for the former, whereas assig ning operati on for the latter3。 It follows that a small difference between the melt fronts is permissible。 That allowance can be implemented by time allowance control or preferable location allowance con trol of the meltfront no

45、 des。4。The boundaries of the flow field expand by each meltfront advancement so it is necessary to check the condition Eq. 10 after each change in the mtfront.5。 In view of above men ti oned an alysis, the physical parameters at the no des of the same secti on should be compared and adjusted so the

46、in formati on describ ing fin ite eleme nts of the same secti on should be prepared before simulation that is, the match ing operati on among the eleme nts should be preformed.Fig. 2a,b。 Illustrative of boun dary con diti ons in the gap-wise direct iona of the middle-pla ne model b of thesurface mod

47、el2。2.2 Numerical implementationPressure field。 In modeling viscosity n which is a function of shear rate, temperature and pressure of melt, the shear-th inning behavior can be well represe nted by a cross-type model such as:机认 T,P)- "' ' " T -7(H)】+(浙Jwhere n corresp onds to the p

48、owelaw in dex, and T characterizes the shear stress level of the tran siti on regi on betwee n the Newt onian and powelaw asymptotic limits. I n terms of anArrhe ni us-type temperature sen sitivity and exp onen tial pressure depe ndence n(T, P) can be represe nted with reas on able accuracy as follo

49、ws:HO匾巧=庆时""(12)Equations 11 and 12 constitute a five-constant (n,T , B, Tb, B) representation forviscosity。 The shear rate for viscosity calculati onis obta ined by:Based on the above, we can infer the following filling pressure equation from the governing Eqs. 14V= 0(14)where S is calcul

50、ated by S = b0( (b- z)2 qdz。Applying the Galerkin method, the pressure finite-element equation is deduced aswhere l_ traverses all eleme nts in cludi ng node N, and where I and j represe nt the local node number in element l_ corresponding to the node number N and N_ in the whole, respectively. The

51、D (l_) ij is calculated as follows：where A( l_) represents triangular finite elements, and L ( l_) i is the pressure trial function in finite elements.Temperature field. To determ ine the temperature profile across the gap， each tria ngular finite element at the surface is further divided intoNZ lay

52、ers for the finitedifference grid.The left item of the energy equation (Eq. 4) can be expressed as:where TN, j,t representsthe temperatureof the j layer of node N at time t。 The heat conduction item is calculated by:where l traverses all elements,including node N, and i and j represent the local nod

53、enu mber in eleme ntl corresp onding to the node nu mbeN and N_ in the whole, respectively.The heat conv ecti on item is calculated by:心(忖薯十曙)Iohixl(-?)们(晋)昭环上屮For viscous heat, it follows that:| xp+iJ- U 加(20JSubstitut ing Eqs。 17-20 into the en ergy equatio n (Eq。 4), the temperature equati on bec

54、omesMl二2.3 Structural an alysis of the moldThe purpose of structural analysis is to predict the deformation occurring in the photopolymer mold due to the thermal and mecha ni cal loads of the filli ng process This model is based on a thredimensional thermoelastic boundary element method (BEM。The BEM

55、 is ideally suited for this application because only the deformation of the mold surfaces is of interest. Moreover, the BEM has an advantage over other techniques in that computing effort is not wasted on calculating deformation within the mold。文档为个人收集整理，来源于网络文档为个人收集整理，来源于网络The stresses resulting fr

56、om the process loads are well within the elastic range of the mold material. Therefore, the mold deformati on model is based on a thermoelastic formulatio n. The thermal and mechanical properties of the mold are assumed to be isotropic and temperature in depe ndent.Although the process is cyclic, ti

57、me-averaged values of temperature and heat flux are used for calculat ing the mold deformati on. Typically, tran sie nt temperature variatio ns within a mold have been restricted to regions local to the cavity surface and the nozzle tip 8。 The transients decay sharply with dista nce from the cavity

58、surface and gen erally little variati on is observed beyond distances as small as 2 5 mm. This suggests that the contribution from the transients to the deformati on at the mold block in terface is small and therefore it is reas on able to n eglect the transient effect® The steady state temperature field satisfieLaplace ' s equation 2 0 and the time-averaged boundary conditions。 The boundary conditions on the mold surfaces are described in detail by Tang et al. 9 . As for the mechanical boundary conditions, the cavity surface is subjected to the melt pressure the surfaces