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1、Keywords Injection molding Numerical simulation Rapid prototyping 1 IntroductionIn injection molding, the polymer melt at high temperature is injected into the mold under high pressure 1. Thus, the mold material needs to have thermal and mechanical properties capable of withstanding the temperatures

2、 and pressures of the molding cycle. The focus of many studies has been to create the injection 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 part

3、s in a production material. The potential of integrating injection molding with RP technologies has been demonstrated 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 （r

4、igidity）. For example, the polymers used in RP-fabricated stereolithography （SL） 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 modied an

5、d optimized from traditional methodologies due to the completely different tool material. However, there is still not a fundamental understanding of how the modications to the mold tooling method and material impact both the mold design and the injection molding process parameters. One cannot obtain

6、 reasonable results by simply changing a few material properties in current models. Also, 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 mo

7、lding, so as to establish the mold design criteria and techniques for an RT-oriented injection molding process. In addition, computer simulation is an effective approach for predicting the quality of molded parts. Commercially available simulation packages of the traditional injection molding proces

8、s have now become routine tools of the mold designer and process engineer 2. Unfortunately, current simulation programs for conventional injection molding are no longer applicable to RP molds, because of the dramatically dissimilar tool material.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 softwa

9、re with aluminum 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 during injection molding is due to shrinkage and warpage of the plastic

10、part, as well as the mold. For ordinarily 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 inuence, which have been neglected in current models. For instance,

11、 3 used a simple three-step simulation process to consider the mold distortion, which had too much deviation. 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-mol

12、ded parts. The developed simulation can be applied as an evaluation tool for RP mold design and process optimization. Our simulation system is veried by an experimental example.Although many materials are available for use in RP technologies, we concentrate on using stereolithography （SL）, the origi

13、nal RP technology, to create polymer molds. The SL process uses photopolymer and laser energy to build a part layer by layer. 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, high-quali

14、ty parts. Until recently, SL was primarily 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

15、 to use them for actual functional molds. 2 Integrated simulation of the molding process 2.1 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 accomplish this task. The

16、main assumption is that temperature and load boundary conditions cause signicant 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

17、 melt into a photopolymer mold, which will output the resulting temperature and pressure proles. 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 underg

18、o 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

19、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 2.2.1 Mathematical modeling In order to simulate the use o

20、f 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 simulation steps are

21、 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 will output the resulting temperature and pressure profiles.3. Structural analysis is the

22、n 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 mo

23、ld 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

24、the molded part.In above simulation flow, there are three basic simulation modules.2.2 Filling simulation of the melt2.2.1 Mathematical modelingComputer simulation techniques have had success in predicting filling behavior in extremely complicated geometries. However, most of the current numerical i

25、mplementation is based on a hybrid finite-element/finite-difference solution with the middleplane model. The application process of simulation packages based on this model is illustrated in Fig. 2-1. However, unlike the surface/solid model in mold-design CAD systems, the so-called middle-plane （as s

26、hown in Fig. 2-1b） is an imaginary arbitrary planar geometry at the middle of the cavity in the gap-wise direction, 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 modeling is

27、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 middle-plane.According to the previous investigations 46, fillinggo

28、verning equations for the flow and temperature field can be written as:where x, y are the planar coordinates in the middle-plane, and z is the gap-wise coordinate; u, v,w are the velocity components in the x, y, z directions; u, v are the average whole-gap thicknesses; and , ,CP （T）, K（T） represent viscosity, density, specific heat and thermal conductivity of polymer melt, respecti