2345 常用小五金零件手柄套的三維參數(shù)化建模及模具設(shè)計(jì)

2345 常用小五金零件手柄套的三維參數(shù)化建模及模具設(shè)計(jì),常用,經(jīng)常使用,小五金,零件,手柄,三維,參數(shù),建模,模具設(shè)計(jì) INTEGRATED NUMERICAL SIMULATION OF INJECTION MOLDING USING TRUE 3D APPROACHWen-Hsien Yang*Allen Peng, Louis Liu and David C.HsuCoreTech System Co.,Ltd., HsinChu, Taiwan, ROCRong-Yeu Chang National Tsing-Hua University, HsinChu, Taiwan 30043, ROCAbstractThe application of true 3D simulation in the injection molding is becoming popular in the recent years. However, a unified CAE analysis based on solid model for the predictions of molding and warpage of the injection-molded part is seldom reported in the literature due to the numerical and hardware limitations. In this paper, an integrated true 3D approach is developed to simulate the filling, packing and cooling stages in injection molding, as well as the part warpage after ejection. All the simulations can be carried out on the same solid model, in which both cavity and mold base are meshed with solid elements of different topologies. Thanks to the highly efficiency of the proposed methodology, a typical integrated 3D analysis of part with hundred thousand elements can usually be finished on a regular PC within one day. Several numerical examples are reported to indicate the success of the present model.IntroductionThe injection molding can be divided into several stages including filling, packing and cooling. Each of these stages can affect the dimension precision and the performance of the molded part after ejection. In the filling stage, the hot polymer melt is injected into the cavity by the applied pressure. After the cavity is completely filled, additional melt is pushed into the cavity at high pressure to compensate the volume shrinkage of the polymer melt during solidification. Usually, once the gated is frozen, the packing phase stops and the cooling phase begin. In the cooling phase, the polymer melt solidifies further until the preset ejected temperature is reached, and then the part is ejected.CAE (Computer-Aided Engineering) has been widely adopted and proved to be an important tool for part and mold designers. Design and process variables of design are evaluated on computer before the mold is actually constructed. In this manner, potential defects are identified and eliminated in the design phase. In addition to this, design can be refined and even be optimized according to the simulation results, this makes concurrent engineering can be implemented in a cost-efficient way. With the advancement of hardware and theoretical modeling, it's possible now to simulate injection molding process in a more realistic way.Conventionally, the 2.5D CAE analysis is used to simulate the injection molding process [4-5]. However, the model simplifications inherent in the 2.5D analysis not only reduces the prediction accuracy but also makes it time consuming to create FEA model. In light of this, true 3D molding simulation becomes increasingly popular in the recent years [6-7]. However, a unified CAE analysis based on solid model for the predictions of molding and warpage of the injection-molded part is seldom reported in the literature due to the numerical and hardware limitations. In this paper, an integrated true 3D approach is developed to simulate the filling, packing and cooling stages in injection molding, as well as the part warpage after ejection. All the simulations can be carried out on the same solid model, in which both cavity and mold base are meshed with solid elements of different topologies.Governing EquationsFilling Phase:The polymer melt is assumed to behave as Generalized Newtonian Fluid (GNF). Hence the non-isothermal 3D flow motion can be mathematically described by the followings:?ρ/ ? t+▽?ρu=0 （1）?（ρu）/ ? t+▽?（ρuu－σ）=ρg （2）σ=﹣pI﹢η(▽u+ ▽u T) （3）ρC p(?T/ ? t+u▽T)= ▽(k▽T)+ηγ 2 （4）where u is the velocity vector, T the temperature, t the time, p the pressure, σ the total stress tensor, ρthe density, η the viscosity, k the thermal conductivity, Cp the specific heat and γ the shear rate. In this work, the modified-Cross model with Arrhenius temperature dependence is employed to describe the viscosity of polymer melt:η（T，γ）=η 0(T)/1+（η 0γ/ τ） 1-n （5）η 0（T）=BExp（T b/T） （6）here n is the power law index, η 0 the zero shear viscosity, τis the parameter that describes the transition region between zero shear rate and the power law region of the viscosity curve. A volume fraction function f is introduced to track the evolution of the melt front. Here, f=0 is defined as the air phase, f=1 as the polymer melt phase, and then the melt front is located within cells with 0blsCooling Phase:During the molding cooling process, a three-dimensional, cyclic, transient heat conduction problem with convective boundary conditions on the cooling channel and mold base surfaces is involved. The overall heat transfer phenomena is governed by a three-dimensional Poisson equation:ρC p ?T/ ? t=k(?2T/ ?x2 + ?2 T/ ?y2 + ?2T/ ?z2)where T is the temperature, t is the time, x, y, and z are the Cartesian coordinates, ρ is the density, Cp is the specific heat, k is the thermal conductivity. Equation (9) holds for both mold base and plastic part with modification on thermal properties:Because mold temperature is fluctuated periodically with time, what we cared is not the actual mold temperature but the effect of the mold temperature on heat transfer of molded part. We can assume there is a cycle-averaged mold temperature that is invariant with time. This cycle-average principle (CAP) is a key concept in the traditional mold-cooling analysis. To reduce the iteration time of the fully transient process, we also introduce the CAP in the calculation of mold temperature. That is, a cycle-averaged temperature distribution of mold base is obtained by solving the following steady-state Laplace equation:km (?2T/ ?x2 + ?2 T/ ?y2 + ?2T/ ?z2)=0 (10)where T is the cycle-averaged mold temperature.Warpage Analysis:After the part is ejected from the mold, a free thermal shrinkage happens due to the temperature difference. Standard three-dimensional solid stress theory can be carried out to simulate the shrinkage and warpage of the molded part as follows.σ=C( ε －ε 0－αΔT ) (11)ε=1/2(▽u+ ▽u T) (12)Where σ is the stress tensor, C is a 4thtensor related to the material mechanical properties, ε is the strain tensor, α is CLET tensor and u is the displace tensor. Also, the simulated result can exported to commercial general purpose stress solver to run more advanced non-linear stress analysis such as buckling analysis.Numerical MethodNumerical Discretization Method: In this paper, a numerical solver based on Finite Volume Method (FVM) is developed to solve the governing equations. The solver has been successfully applied in injection molding filling simulation [8]. Numerical experiments confirm the reliability and efficiency of the solver.Integrated Analysis Procedure:The proposed computation framework is schematically shown in Fig.1. The analysis procedure first reads the input data (including mesh data, material data, and process condition data), performs 3D filling analysis (based on specified uniform mold temperature or mold temperature distribution obtained from previous mold temperature iteration). 3D Cooling analysis is then conducted to obtain part temperature distribution at the end of cooling stage. Cycle-average mold temperature obtained from the cooling analysis fed back to filling modules for improving calculation or serves as an input boundary condition for warpage analysis. The iteration of mold temperature is continued until the mold temperature variation between iterations is small. This integrated analysis ensures a coupling between mold filling and mold cooling results and is of practical value to improve the accuracy of analysis.File inputCool AnalysisFlow/Pack AnalysisTemperature converge?Cool Analysis(Fig 1)ConclusionsIn this paper, an integrated true 3D numerical model for the prediction of Warp AnalysisCheck resultsinjection molding process has been developed. The geometry flexibility and the solution efficiency of the proposed approach have made it a highly reliable CAE tool to aid the designer/engineer to analyze and further optimize the molding process.Reference[1]. E.C.Bernhardt (Ed.), Computer Aided Engineering for Injection Molding, Hanser (1983)[2]. T.Manzione (Ed.), Applications of Computer Aided Engineering in Injection Molding, Hanser (1987)[3]. C.L.Tucker III (Ed.), Fundamentals of Computer Modeling for Polymer Processing, Hanser (1989)[4]. V.W.Wang, C.A.Hieber, and K.K.Wang, J. Polym. Eng., 7, 21, (1986)[5]. P.Kennedy, Flow Analysis Reference Manual, Moldflow Pty. Ltd.,Hanser (1993)[6]. W.B.Young, Polym. Composites, 15, 118 (1994)[7]. J.F.Hetu, D.M.Gao, A.Garcia-Rejon, and G.Salloum, Polym. Eng. Sci., 38, 223 (1998)[8]. R.Y.Chang and W.H.Yang, Int. J. Numer. Methods Fluids, 37, 125-148 (2001)