【正文】 nalysis, a new simulation system for RP molds is developed. The proposed system focuses on predicting part distortion, which is dominating defect in RPmolded parts. The developed simulation can be applied as an evaluation tool for RP mold design and process optimization. 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 technology, to create polymer molds. The SL pro cess uses photopolymer and laser energy to build a part layer by layer. Using SL takes advantage of both the mercial dominance of SL in the RP industry and the subsequent expertise base that has been developed for creating accurate, highquality parts. Until recently, SL was primarily 3 used to create physical models for visual inspection and form?t studies with very limited functional applications. However, the newer generation stereolithographic photopolymers have improved dimensional, mechanical and thermal properties making it possible to use them for actual functional molds. 2 Integrated simulation of the molding process Methodology In 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 acplish 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 model, which is translated to a ?le readable by the ?ow analysis package. 2 Simulate the mold?lling 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 distortion that the mold undergo during the injection process. 4 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 second step to simulate the melt injection into the distorted mold. 5 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 melt Mathematical modeling In 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 acplish this task. The main assumption is that temperature and load boundary conditions cause significant distortions in the SL mold. The simulation steps are as follows: 4 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 moldfilling process of the melt into a photopolymer mold, which will output the resulting temperature and pressure profiles. 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 distortion that the mold undergo during the injection process. 4. 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 second step to simulate the melt injection into the distorted mold. 5. The shrinkage and warpage simulation of the injection molded part is then applied, which calculates the final distortions of the molded part. In above simulation flow, there are three basic simulation modules. Filling simulation of the melt Mathematical modeling Computer simulation techniques have had success in predicting filling behavior in extremely plicated geometries. However, most of the current numerical implementation is based on a hybrid finiteelement/finitedifference solution with the middleplane model. The application process of simulation packages based on this model is illustrated in Fig. 21. However, unlike the surface/solid model in molddesign CAD systems, the socalled middleplane (as shown in Fig. 21b) is an imaginary arbitrary planar geometry at the middle of the cavity in the gapwise direction, which should bring about great inconvenience in applications. For example, surface models are monly used in current RP syste ms (generally STL file format), so secondary modeling is unavoidable when using simulation packages because the models in the RP and simulation systems are different. Considering these defects, the surface model of the cavity is introduced as datum planes in the simulation, instead of the middleplane. According to the previous investigations [4–6], fillinggoverning equations for the flow and temperature field can be written as: 5 where x, y are the planar coordinates in the middleplane, and z is the gapwise coordinate。 u, v,w are the velocity ponents in the x, y, z directions。 and η, ρ,CP (T), K(T) represent viscosity, density, specific heat and thermal conductivity of polymer melt, respectively. a–d. Schematic procedure of the simulation with middleplane model. a The 3D surface model b The middleplane model c The meshed middleplane model d The display of the simulation result In addition, boundary conditions in the gapwise direction can be defined as: where TW is the constant wall temperature (shown in Fig. 2a). Combining Eqs. 1–4 with Eqs. 5–6, it follows that the distributions of the u, v, T, P at z coordinates should be symmetrical, with the mirror axis being z