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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 equipment 2 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 process 3 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 analysis 3 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 features 4 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 model 5 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 6 10 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 6 10 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 4 8 0 w z v y u xt 7 We can infer the following governing pressure equation from the Equations 2 3 and 7 1 6 10 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 k e 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 k e 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 model J China Mechanical Engineering 2001 11 3 288 292 in Chinese 2 Yeung V W S Lai K H Injection moulding C MOLD CAE package process parameter design and quality function deployment a case study of intelligent materials processing J Journal of Materials Processing Technology 1997 63 481 487 3 Deng Y M Lam Y C Tor S B Britton G A A CAD CAE integrated injection molding design system J Engineering with Computers 2002 18 80 92 4 Shao Weizhong Yang Fuqing Object oriented analysis design M Beijing Tsinghua University Press 1998 in Chinese 5 Cheng Xuewen Li Dequn Zhou Huamin Pretreatment system of injection mould CAE with STL J Plastic Science Technology 2002 1 11 13 in Chinese 6 Chen Xing Li Dequn Hu Junqiao Integrated simulation of overall process in injection molding J China Mechanical Engineering 1997 8 3 46 49