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CADDM Vol. 15 No.1 (2005) 9 Development of Integrated Simulation System for Plastic Injection Molding CHENG Xue-wen, LI De-qun, ZHOU Hua-min (State Key Laboratory of Plastic Forming Simulation and Die numerical simulation; CAD/CAE/CAM; object-oriented analysis CNC process with CAM tools; check the results and modify the scheme and process circularly till it is satisfied enough. It brings about great disadvantage: the designer can not foresee the possible conflicts of the scheme until it is carried out, and the quality problems of plastic components are common, amongst both the fabricators who produce the components, and the equipment manufacturers who install the components on their equipment2. On the other hand, injection molding CAE systems provide the designer with analysis results regarding the moldability of the design, the cost of the manufacturing process, the quality of the product, and so on. This is to ensure that the plastic part and the mold being designed are manufacture-able by the injection molding process3. The advanced processing with CAD/CAE/CAM can be illustrated as Fig. 1(b). _ Received date: January 15, 2005 Foundation item: Supported by National Natural Science Foundation of China (20490224) Biogrphy: CHENG Xue-wen(1976-), male, born in Guidong contry, Hunan province, Ph.D., main research field is CAD/CAE of plastic injection molding. The basic principle of defect prevention has been overlooked. Quality should be built in from product design and mold design to molding process parameter design. Modern CAE simulation software offered five software modules for analyzing plastic injection molding: filling analysis; packing analysis; cooling analysis; stress analysis; and warpage analysis3. This paper discusses the mathematical formulations for numerical simulation of injection molding filling, packing, cooling, stress and warpage briefly. More 10 CHENG Xue-wen, LI De-qun, ZHOU Hua-min N Y BEGIN CAD CAM OK？ END MODIFY Y Y N N BEGIN CAD CAM OK？ END MODIFY VALID？ CAE (a) Processing with CAD/CAM (b) Processing with CAD/CAE/CAM Fig. 1 The mold design and process with CAD/CAE/CAM tools emphasizes are focused on the development of injection molding CAE system. The commercially available computer simulation packages HsCAE3D is also introduced at the end. 2 System Design 2.1 Modularity The choice of modules for organizing a large system affects understandability, division of labor, modifiability, integratability, and testability. Of these, understandability has the largest impact on the success of a software project. Therefore, modules are important for their role as conceptually coherent chunks of software, and improving coherence through machine-assisted reorganization is an appropriate goal. An integrated injection molding CAE system consists of three basic modules: pre-processing, numerical simulation and post-processing. Pre-processing module offeres four blockettes: mesh generating; feed system designing; cooling circuits designing; and processing parameters designing. Numerical simulation module offeres six blockettes: fast filling analysis; detail filling analysis; packing analysis; cooling analysis; stress analysis; and warpage analysis. Post-processing module offeres three blockettes: display of flow front, weld-line expertise; and report generator. The modularity can be illustrated as Fig. 2. 2.2 Object-Oriented Analysis The injection molding CAE system is a complex product. It should be continuously upgraded and supported in several decades. Advanced analysis and design techniques and methods are necessary for it to improve the quality and reduce the cost. In the software engineering field, object- oriented analysis and design (OOAD) has proven to be a powerful technique with respect to modeling, analysis, and design of complex systems. In such an approach, promoting reuse of software blocks and shortening the software system development time cycle are particularly significant features4. As the advantages of OOAD, it is the preferred approach for developing the injection molding CAE system. And the object model is represented in Fig. 3 (The Development of Integrated Simulation System for Plastic Injection Molding 11 Mesh generating Feed system designing Cooling circuits designing Processing parameters designing Fast filling analysis Filling analysis Packing analysis Cooling analysis Stress analysis Warpage analysis Pre-processing CAE Numerical simulation Flow front displaying Weld-line & air-trap displaying Post-processing Temperature displaying Pressure displaying Shear field displaying Velocity displaying Shrinkage displaying Density displaying Stress displaying Warpage displaying Expertise Report generator Fig. 2 The modularity of the injection molding CAE system topics 1, 2, 3, 4 and 5 in the model are pre-processing, analysis manager, expert system, post-processing and data access manager respectively). 2.3 Key Technologies The following key technologies should be solved felicitously for developing an injection CAE system: (1) Mesh generate: the system must offer the CAE model to analysis manager, that is, after you create or import a CAD model in the CAE system, you must first mesh the model before analyzing. Delauny triangulation is the best method to mesh the CAD model5. (2) Graphics platform: OpenGL is the most popular three-dimensional graphics platform in recent years. As a software interface for graphics hardware, OpenGL renders multidimensional objects into a framebuffer. The Microsoft implementation of OpenGL for the Windows operating system is industry-standard graphics software with which programmers can create high-quality still and animated three-dimensional 12 CHENG Xue-wen, LI De-qun, ZHOU Hua-min 3 3 4 43 4 4 5 5 5 5 1 122 21 2 1 3 Mesh generator CAD model CAE model Import CAD model Generate mesh Configure Output CAE model Processing parameters designer Parameters CAE model Import CAE model Expertise Modify Output parameters Assistant system designer Feed system Cooling circuit Design feed system Design cooling circuit Analysis manager CAE model Processing parameters Analysis result Import CAE model Import parameters Numerical analysis Output result Expert system Rules Initial data Expertise Import initial data Deduce result Output expertise Result display controller Analysis result Import result Display result Report generator Analysis result Report Import result Expertise Generate report Data access manager Data system Access CAD model Access CAE model Access result Access parameters Access expertise Data system Data files Configuration DB Read Write Configuration DB Plastic material DB Molding machine DB Mold material DB Connect to DB Query data from DB Modify DB data Files manager CAD model CAE model Parameters Analysis result Expertise Read Write Fig. 3 Object model of the injection molding CAE system color images. The display can be easily and rapidly manipulated using OpenGL in the CAE system. (3) Data access: it is easy to manage supporting data (e.g. plastic material data, molding machine data and mold material data) using database technology. In the other way, it is more convenient using file system to store project data because the project data is huge and seldom accessed. (4) Expert system: expert system is one of the principal modules to improve technical parameters setting, result analysis and expertise. (5) Numerical simulation: numerical simulation is the principal module of the CAE system. Most of the current numerical solutions are based on finite-element/finite-difference/ boundary-element/volume-control schemes. That is, finite-element/finite-difference/volume-control for Development of Integrated Simulation System for Plastic Injection Molding 13 filling and packing, boundary-element for cooling, finite-difference for stress and finite-element for warpage. And the mathematical formulations for numerical simulation are introduced in the following section. 3 Mathematical Formulations 3.1 Filling The filling equations can be written as 1, 610 0 )()( = + y vb tx ub (1) 0)(= z u zx P (2) 0)(= z v zy P (3) )( z T K zy T v x T u t T p C+ = + + 22 )()( z v z u + (4) where b is half-gap thickness of the cavity, x, y are the planar coordinates in surface of the cavity and z is the gapwise coordinate, whereas u, v and u,vare the velocities and averaged velocities components in the x, y directions and P, T, , , Cp, K represent pressure, temperature, viscosity, density, specific heat and thermal conductivity of polymer melt respectively. In addition, boundary conditions in the gapwise direction can be defined as 1, 610 u=v=0, T=TW at z=0 (5) 0= = z v z u , 0= z T at z=b (6) where TW is the constant wall temperature. 3.2 Packing The packing equations are the same to filling except the continuity equation, and the continuity equation can be written as 48 0)()()(= + + + w z v y u xt (7) We can infer the following governing pressure equation from the Equations（2） （3） and （7） 1, 610 F y P S yx P S xt P G= )()( (8) where z P z P G T b z l T z s d)(d)( 0 + = (9) z T z t T T F P b z l P z s + + = d)(d)( 0 t z zz ls = )( (10) = bz zz z S 00 dd (11) where s, l represent the density of solid and melt of polymer respectively, and is the position at the juncture between melt and solid polymer. z 3.3 Cooling The cooling equation can be written as 11,12 t T c z T y T x T K = + + 2 2 2 2 2 2 (12) where T is the temperature of the mold, x，y，z are the three coordinates of certain point in the mold, t denotes time, and K, , c represent the thermal conductivity, density and heat capacity of the mold respectively. The initial condition and convective boundary condition can be defined as 11,12 )0( 0 =tTT (13) )( c TTh n T K= (14) where T0 is initial temperature, h indicates the heat transfer coefficient, Tc is coolant temperature. 14 CHENG Xue-wen, LI De-qun, ZHOU Hua-min 3.4 Stress The stress analysis equation can be written as 13,14 )(3),( ttRtz t = t t tzTtz y e d ),(),( 0 (15) where , ey are the stress and the strain respectively, t, t is the material time, z is the triplet of coordinates(x, y, z), 0 is the temperature-dependent coefficient of thermal expansion, T is the temperature, R is an auxiliary modulus and can be written as 13,14 )(2)( )( )( 3 4 1 1 tGtRdt t tR ttG K t =+ (16) where K is bulk modulus, G1 is shear relaxation modulus. 3.5 Warpage The warpage analysis equation can be written as 13,14 d e kF= (17) where F is the equivalent load of all nodes, d is the element displacement，ke is the element stiffness matrix and can be written as (18) = V e VBDBkd T where V is the volume of the part, B is the element derivative operator matrix, and D is the elasticity matrix. 4 HsCAE3D Based on the previous mathematical theories and system developing technologies, the authors have successfully developed the commercially available computer simulation packages HsCAE3D (as showed in Fig.4) in the last decades. Notation b thickness x, y, z coordinates u, v, w velocities wvu, averaged velocities P pressure T temperature viscosity density Cp specific heat K thermal conductivity TW wall temperature s, l density of solid and melt of polymer z juncture position between melt and solid polymer t time T0 initial temperature h heat transfer coefficient Tc coolant temperature c heat capacity n normal vector stress ey strain t, t material time 0 temperature-dependent coefficient of thermal expansion R auxiliary modulus G1 shear relaxation modulus F equivalent load d displacement ke stiffness matrix V volume B derivative operator matrix D elasticity matrix Fig.4 HsCAE3D interface References 1 Zhou Huamin, Zhang Yisheng, Li Dequn. Injection Development of Integrated Simulation System for Plastic Injection Molding 15 molding simulation of the filling and post-filling stages based on 3D surface modelJ. China Mechanical Engineering, 2001, 11(3): 288292 (in Chinese). 2 Yeung V W S, Lai K H. 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