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毕业设计（论文）中期检查表（指导教师）指导教师姓名： 填表日期： 年 4 月 7 日学生学号 学生姓名 题目名称打印机上盖的注塑模设计已完成内容 完成开题报告和外文翻译，完成塑件的绘制，开始撰写说明书。 检查日期：完成情况全部完成按进度完成滞后进度安排存在困难在准备三维建模中遇阻，之前对于SolidWorks掌握得并不是很好，所以建模过程并不顺利。且塑件结构尺寸比较多，在绘制三维图时也比较耽误时间。解决办法借阅图书馆里有关于SolidWorks注塑模的设计的书籍，网上查找学习视频。预期成绩优 秀良 好中 等及 格不及格建议 教师签名： 教务处实践教学科制表说明：1、本表由检查毕业设计的指导教师如实填写；2、此表要放入毕业设计（论文）档案袋中；3、各院(系)分类汇总后报教务处实践教学科备案。编号： 毕业设计(论文)外文翻译（原文）学 院： 机电工程学院 专 业： 机械设计制造及其自动化 学生姓名： 学 号： 指导教师单位： 姓 名： 职 称： 年 3 月 20 日Abstract Today, the time-to-market for plastic products is becoming shorter, thus the lead time available for making the injection mould is decreasing. There is potential for timesaving in the mould design stage because a design process that is repeatable for every mould design can be standardised. This paper presents a methodology for designing the cavity layout for plastic injection moulds by controlling the geometrical para-meters using a standardisation template. The standardisation template for the cavity layout design consists of the configurations for the possible layouts. Each configuration of the layout design has its own layout design table of all the geometrical parameters. This standardisation template is predefined at the layout design level of the mould assembly design. This ensures that the required configuration can be loaded into the mould assembly design very quickly, without the need to redesign the layout. This makes it useful in technical discussions between the product designers and mould designers prior to the manufacture of the mould. Changes can be made to the 3D cavity layout design immediately during the discussions, thus saving time and avoiding miscommunication. This standardisation template for the cavity layout design can be customised easily for each mould making company to their own standards.Keywords: Cavity layout design; Geometrical parameters; Mould assembly; Plastic injection mould design; Standardisation template1 Introduction Plastic injection moulding is a common method for the mass production of plastic parts with good tolerances. There are two main items that are required for plastic injection moulding. They are the injection-moulding machine and the injection mould. The injection-moulding machine has the mould mounted on it and provides the mechanism for molten plastic transfer from the machine to the mould, clamping the mould by the application of pressure and the ejection of the formed plastic part. The injection mould is a tool for transforming the molten plastic into the final shape and dimensional details of the plastic part. Today, as the time-to-market for plastic parts is becoming shorter, it is essential to produce the injection mould in a shorter time. Much work had been done on applying computer technologies to injection mould design and the related field. Knowledge-based systems (KBS) such as IMOLD 1,2, IKMOULD 3, ESMOLD 4, the KBS of the National Cheng Kang University, Taiwan 5, the KBS of Drexel University 6, etc. were developed for injection mould design. Systems such as HyperQ/Plastic 7, CIMP 8, FIT 9, etc. are developed for the selection of plastic materials using a knowledge-based approach. Techniques have also been developed for parting design in injection moulding 1012. It has been observed that although mould-making industries are using 3D CAD software for mould design, much time is wasted in going through the same design processes for every project. There is great potential for timesaving at the mould design stage if the repeatable design processes can be standardised to avoid routine tasks. A well-organised hierarchical design tree in the mould assembly is also an important factor 13,14. However, little work has been done in controlling the parameters in the cavity layout design; thus this area will be our main focus. Although there are many ways of designing the cavity layout 15,16, mould designers tend to use only conventional designs, thus there is a need to apply standardisation at the cavity layout design level. This paper presents a methodology for designing the cavity layout for plastic injection moulds by controlling the parameters based on a standardisation template. First, a well-organised mould assembly hierarchy design tree had to be established. Then, the classification of the cavity layout configuration had to be made to differentiate between those with standard configurations and those with non-standard configurations. The standard configurations will be listed in a configuration database and each configuration has its own layout design table that controls its own geometrical parameters. This standardisation template is pre-defined at the layout design level of the mould assembly design.2 Cavity Layout Design for a Plastic Injection Mould An injection mould is a tool for transforming molten plastic into the final shape and dimensional details of a plastic part. Thus, a mould contains an inverse impression of the final part. Most of the moulds are built up of two halves: the front insert and the back insert. In certain mould-making industries, the front insert is also known as the cavity and the back insert is known as the core. Figure 1 shows a front insert (cavity) and a back insert (core). Molten plastic is injected into the impression to fill it. Solidification of the molten plastic then forms the part. Figure 2 shows a simple two-plate mould assembly.Fig. 1. Front insert (cavity) and back insert (core).Fig. 2. A simple mould assembly.2.1Difference Between a Single-Cavity and a Multi-Cavity Mould Very often, the impression in which molten plastic is being filled is also called the cavity. The arrangement of the cavities is called the cavity layout. When a mould contains more than one cavity, it is referred to as a multi-cavity mould. Figures 3(a) and 3(b) shows a single-cavity mould and a multi-cavity mould. A single-cavity mould is normally designed for fairly large parts such as plotter covers and television housings. For smaller parts such as hand phone covers and gears, it is always more economical to design a multi-cavity mould so that more parts can be produced per moulding cycle. Customers usually determine the number of cavities, as they have to balance the investment in the tooling against the part cost. Fig. 3. (a) A single cavity mould. (b) A multi-cavity mould.2.2Multi-Cavity Layout A multi-cavity mould that produces different products at the same time is known as a family mould. However, it is not usual to design a mould with different cavities, as the cavities may not all be filled at the same time with molten plastic of the same temperature.On the other hand, a multi-cavity mould that produces the same product throughout the moulding cycle can have a balanced layout or an unbalanced layout. A balanced layout is one in which the cavities are all uniformly filled at the same time under the same melt conditions 15,16. Short moulding can occur if an unbalanced layout is being used, but this can be overcome by modifying the length and cross-section of the runners (passageways for the molten plastic flow from the sprue to the cavity). Since this is not an efficient method, it is avoided where possible. Figure 4 shows a short moulding situation due to an unbalanced layout. A balanced layout can be further classified into two categories: linear and circular. A balanced linear layout can accommodate 2, 4, 8, 16, 32 etc. cavities, i.e. it follows a 2n series. A balanced circular layout can have 3, 4, 5, 6 or more cavities, but there is a limit to the number of cavities that can be accommodated in a balanced circular layout because of space constraints. Figure 5 shows the multi-cavity layouts that have been discussed. Fig. 4. Short moulding in an unbalanced layout. Fig. 5. Multi-cavity layouts.3 The Design Approach This section presents an overview of the design approach for the development of a parametric-controlled cavity layout design systemforplasticinjection moulds. An effective working method of mould design involves organising the various subassemblies and components into the most appropriate hierarchy design tree. Figure 6 shows the mould assemblyhierarchy design tree for the first level subassembly and components.Other subassemblies and components are assembled from the second level onwards to the nth level of the mould assembly hierarchy design tree. For this system, the focus will be made only on the “cavity layout design”. Fig. 6. Mould assembly hierarchical design tree.3.1 Standardisation Procedure In order to save time in the mould design process, it is necessary to identify the features of the design that are commonly used. The design processes that are repeatable for every mould design can then be standardised. It can be seen from Fig. 7 that there are two sections that interplay in the standardisation procedure for the “cavity layout design”: component assembly standardisation and cavity layout configuration standardisation.Fig. 7. Interplay in the standardization procedure.3.1.1 Component Assembly Standardisation Before the cavity layout configuration can be standardised, there is a need to recognise the components and subassemblies that are repeated throughout the various cavities in the cavity layout. Figure 8 shows a detailed “cavity layout design” hierarchy design tree. The main insert subassembly (cavity) in the second level of the hierarchy design tree has a number of subassemblies and components that are assembled directly to it from the third level onwards of the hierarchy design tree. They can be viewed as primary components and secondary components. Primary components are present in every mould design. The secondary components are dependent on the plastic part that is to be produced, so they may or may not be present in the mould designs.Fig. 8. Detailed “cavity layout design” hierarchical design tree. As a result, putting these components and subassemblies directly under the main insert subassembly, ensures that every repeatable main insert (cavity) will inherit the same subassemblies and components from the third level onwards of the hierarchy design tree. Thus, there is no need to redesign similar subassemblies and components for every cavity in the cavity layout.3.1.2 Cavity Layout Configuration Standardisation It is necessary to study and classify the cavity layout configurations into those that are standard and those that are non-standard. Figure 9 shows the standardisation procedure of the cavity layout configuration.Fig. 9. Standardisation procedure of the cavity layout configuration. A cavity layout design, can be undertaken either as a multi-cavity layout or a single-cavity layout, but the customers always determine this decision. A single-cavity layout is always considered as having a standard configuration. A multi-cavity mould can produce different products at the same time or the same products at the same time. A mould that produces different products at the same time is known as a family mould, which is a non-conventional design. Thus, a multi-cavity family mould has a non-standard configuration. A multi-cavity mould that produces the same product can contain either a balanced layout design or an unbalanced layout design. An unbalanced layout design is seldom used and, as a result, it is considered to possess a non-standard configuration. However, a balanced layout design can also encompass either a linear layout design or a circular layout design. This depends on the number of cavities that are required by the customers. It must be noted, however, that a layout design that has any other non-standard number of cavities is also classified as having a non-standard configuration. After classifying those layout designs that are standard, their detailed information can then be listed into a standardisation template. This standardisation template is pre-defined in the cavity layout design level of the mould assembly design and supports all the standard configurations. This ensures that the required configuration can be loaded very quickly into the mould assembly design without the need to redesign the layout.3.2 Standardisation Template It can be seen from Fig. 10 that there are two parts in the standardisation template: a configuration database and a layout design table. The configuration database consists of all the standard layout configurations, and each layout configuration has its own layout design table that carries the geometrical parameters. As mould-making industries have their own standards, the configuration database can be customised to take into account those designs that are previously considered as non-standard. Fig. 10. The standardization template.3.2.1 Configuration Database A database can be used to contain the list of all the different standard configurations. The total number of configurations in this database corresponds to the number of layout configurations available in the cavity layout design level of the mould design assembly. The information listed in the database is the configuration number, type, and the number of cavities. Table 1 shows an example of a configuration database. The configuration number is the name of each of the available layout configurations with the corresponding type and number of cavities. When a particular type of layout and number of cavities is called for, the appropriate layout configuration will be loaded into the cavity layout design.Table 1. Sample of the configuration database. 3.2.2 Layout Design Table Each standard configuration listed in the configuration database has its own layout design table. The layout design table contains the geometrical parameters of the layout configuration and is independent for every configuration. A more complex layout configuration will have more geometrical parameters to control the cavity layout. Figures 11(a) and 11(b) show the back mould plate (core plate) with a big pocket and four small pockets for assembling the same four-cavity layout. It is always more economical and easier to machine a large pocket than to machine individual smaller pockets in a block of steel. The advantages of machining a large pocket are: Fig. 11. The back mould plate with pocketing.1. More space between the cavities can be saved, thus a smaller block of steel can be used.2. Machining time is faster for creating one large pocket compared to machining multiple small pockets.3. Higher accuracy can be achieved for a large pocket than for multiple smaller pockets. As a result, the default values of the geometrical parameters in the layout design table results in there being no gap between the cavities. However, to make the system more flexible, the default values of the geometrical parameters can be modified to suit each mould design where necessary.3.3 Geometrical Parameters There are three variables that establish the geometrical parameters: 1. Distances between the cavities (flexible). The distances between the cavities are listed in the layout design table and they can be controlled or modified by the user. The default values of the distances are such that there are no gaps between the cavities. 2. Angle of orientation of the individual cavity (flexible). The angle of orientation of the individual cavity is also listed in the layout design table which the user can change. For a multi-cavity layout, all the cavities have to be at the same angle of orientation as indicated in the layout design table.If the angle of orientation is modified, all the cavities will be rotated by the same angle of orientation without affecting the layout configuration. 3. Assembly mating relationship between each cavities (fixed).The orientation of the cavities with respect to each other is pre-defined for each individual layout configuration and is controlled by the assembly mating relationship between cavities. This is fixed for every layout configuration unless it is customised. Figure 12 shows an example of a single-cavity layout configuration and its geometrical parameters. The origin of the main insert/cavity is at the centre. The default values of X1 and Y1 are zero so that the cavity is at the centre of the layout (both origins overlap each other). The user can change the values of X1 and Y1, so that the cavity can be offset appropriately. Figure 13 shows an example of an eight-cavity layout configuration and its geometrical parameters. The values of X and Y are the dimensions of the main insert/cavity. By default, the values of X1 and X2 are equal to X, the value of Y1 is equal to Y, and thus there is no gap between the cavities. The values of X1, X2, and Y1 can be increased to take into account the gaps between the cavities in the design. These values are listed in the layout design table. If one of the cavities has to be oriented by 90, the rest of the cavities will be rotated by the same angle, but the layout design remains the same. The user is able to rotate the cavities by changing the parameter in the layout design table. The resultant layout is shown in Fig. 14. A complex cavity layout configuration, which has more geometrical parameters, must make use of equation to relate the parameters. Fig. 12. Single-cavity layout configuration and geometrical parameters.Fig. 13. Eight-cavity layout configuration and geometrical parameters without cavity rotation.Fig. 14. Eight-cavity layout configuration and geometrical parameters with cavity rotation.4 System Implementation A prototype of the parametric-controlled cavity layout design system for a plastic injection mould has been implemented using aIII PC-compatible as the hardware. This prototype system uses a commercial CAD system (SolidWorks 2001) and a commercial database system (Microsoft ) as the software. The prototype system is developed using the Microsoft Visual C+ V6.0 programming language and the SolidWorks API (Application Programming Interface) in a Windows environment. SolidWorks is chosen primarily for two reasons:1. The increasing trend in the CAD/CAM industry is to move towards the use of Windows-based PCs instead of UNIX workstations mainly because of the cost involved in purchasing the hardware.2. The 3D CAD software is fully Windows-compatible, thus it is capable of integrating information from Microsoft Excel files into the CAD files (part, assembly, and drawing) smoothly 17. This prototype system has a configuration database of eight standard layout configurations that are listed in an Excel file.This is shown in Fig. 15(a). Corresponding to this configuration database, the layout design level, which is an assembly file in SolidWorks (layout.sldasm), has the same set of layout configurations. The configuration name in the Excel file corresponds to the name of the configurations in the layout assembly file, which is shown in Fig. 15(b). Every cavity layout assembly file (layout.sldasm) for each project will be pre-loaded with these layout configurations. When a required layout configuration is requested via the user interface, the layout configuration will be loaded. The user interface shown in Fig. 16 is prior to the loading of the requested layout configuration. Upon loading the requested layout configuration, the current layout configuration information will be listed in the list box. The user is then able to change the current layout configuration to any other available layout configurations that are found in the configuration database. This is illustrated in Fig. 17. The layout design table for the current layout configuration that contains the geometrical parameters can be activated when the user triggers the push button at the bottom of the user interface. When the values of the geometrical parameters are changed, the cavity layout design will be updated accordingly. Figure 18 shows the activation of the layout design table of the current layout configuration.Fig. 15. The configuration database and layout template for prototype system.Fig. 16. The user interface prior to loading of the requested configuration.Fig. 17. The user interface after loading of the requested configuration.Fig. 18. The user interface with the layout design table.5 A Case Study A CAD model of a hand phone cover, is used in the following case study. Prior to the cavity layout design stage, the original CA model has to be scaled according to the shrinkage value of the moulding resin to be used. The main insert is then created to encapsulate the shrunk part. This entire subassembly is known as the main insert subassembly (xxx cavity.sldasm),where “xxx” is the project name. After the main insert subassembly is created, the cavity layout design system can be used to prepare the cavity layout of the mould assembly.5.1 Scenario 1: Initial Cavity Layout Design In a mould design, the number of cavities to be built in a mould is always suggested by the customers, as they have to balance the investment in the tooling against the part cost. Initially, the customers had requested a two-cavity mould to be designed for this hand phone cover. After the creation of the main insert subassembly, the mould designer loads a layout configuration that is of a linear type which has two cavities using this cavity layout design system. The corresponding configuration name is L02 and is listed in the user interface as shown in Fig. 21.Fig. 21. A linear two-cavity configuration.5.2 Scenario 2: Modification in the Cavity Layout Design Technical discussion sessions between the customers and mould designers are common. This enables changes to be made to the 3D CAD files of both the product and mould as soon as possible, prior to mould manufacture. Changes are almost always inevitable and mould designers are never given any extension in the lead time. In this case, during a technical discussion session, the customers changed their minds and needed a linear four-cavity mould instead of a two-cavity mould so that the production rate of the hand phone covers can be increased. The mould designer can use the cavity layout design system to modify the existing cavity layout design to a linear four-cavity mould. The required new layout configuration can be selected from the available layout configurations that are listed in the configuration database. This is shown in Fig. 22.Fig. 22. A linear, four-cavity layout configuration (after a change in the layout configuration).5.3 Scenario 3: Gap is Required Between Cavities Finally, in another technical discussion session, the mould designer is required to introduce a gap of 20 mm between the cavities in the longitudinal direction, as shown in Fig. 23. In the cavity layout subassembly level, the mould designer uses the cavity layout system to activate the layout design table of the current layout configuration. The value of Y1 is changed from 50 mm to 70 mm to introduce a gap of 20 mm between the cavities in the longitudinal direction. Figure 24 shows the change of the value of Y1 in the layout design table. The result of the final design, after addition of the gap, is shown in Fig. 25.Fig. 23. The introduction of a gap between the cavities.Fig. 24. Modifying the value of Y1 in the layout design table.Fig. 25. The final design after the addition of the gap.6 Conclusions In this paper, an approach using a standardisation template is proposed for the development of a parametric-controlled cavity layout design system. Since this approach makes use of standardisation, it can be further applied to other components for mould assembly design if their design processes are repeatable or they have features that are commonly used for every mould design. The advantages of the developed cavity layout system are as follows:1. The developed system has user-friendly interfaces.2. Since it makes use of databases, it is highly flexible, and mould-making industries that have their own standards can customise the databases to suit their needs.3. Because a pre-defined standardisation template is available in the layout design level of the mould assembly design, the required layout configuration can be loaded very quickly into the mould assembly design without the need to redesign the layout.4. This system enables product designers and mould designers to have more useful technical discussions prior to mould manufacture as changes to the layout can be made immediately during the discussions.5. This system saves time in the mould design process because it removes redundant work. This is very important for the mould-making industries since the lead time for mould making is decreasing. The developed system has some limitations. Although the databases and layout design tables can be customised, customisation will be more difficult for more complex non-standard configurations because the correct geometrical parameters have to be determined. We are currently working on applying a standardisation template for other components in mould design. Abstract Plastic injection molding is widely used for manufacturing a variety of parts. Molding conditions or process parameters play a decisive role that affects the quality and productivity of plastic products. This work reviews the state-of-the-art of the process parameter optimization for plastic injection molding. The characteristics, advantages, disadvantages, and scope of application of all of the common optimization approaches such as response surface model, Kriging model, artificial neural network, genetic algorithms, and hybrid approaches are addressed. In addition, two general frameworks for simulation-based optimization of injection molding process parameter, including direct optimization and meta-modeling optimization, are proposed as recommended paradigms. Two case studies are illustrated in order to demonstrate the implementation of the suggested frameworks and to compare among these optimization methods. This work is intended as a contribution to facilitate the optimization of plastic injection molding process parameter.Keywords: Injection molding ;Process parameter optimization;Optimization methods; Simulation-based optimization1 IntroductionMolding conditions or process parameters play an important role for the plastic injection molding. The quality of the molded part including strength, warpage, and residual stress is greatly influenced by the conditions under which it is processed. Molding conditions also affect the productivity, cycle time, and energy consumption of the molding process. Molding conditions have a close relationship with other factors such as materials, part design, and tooling, which determine the quality of the plastic products. Molding conditions comprise the following important parameters 1: melt temperature, mold temperature, fill time, packing time, and packing pressure.The quality of a given molded part depends not only on the plastic material properties but also on the process parameters. Optimum process parameters reduce the cycle time and increase the quality of the product. In practice, setting the process parameters is mainly based on the experience of the plastic engineer. This method does not always ensure appropriate values of process parameters. Because the plastic exhibits a complex thermo-viscoelastic property, setting a proper molding condition that obtains a desired product quality is a challenge. As the result, the process parameters are often selected from hand books and are then adjusted subsequently by the trial-and-error method. It can be seen that trial-and-error method is costly and time-consuming. For the analytical approach, a number of mathematical equations have been developed for deriving proper process parameters of injection molding 2. However, they generally cannot always satisfy a reliable solution due to the complexity of the injection process when many simplifications are involved in the analytical equations. Therefore, many researchers have made great effort to find the methods for optimizing molding process parameters. Although there is a considerable amount of publications that focused on injection molding process parameters optimization, some of them still sound academic and are difficult to apply to practice. Furthermore, there have been no comparisons, assessment about the scope of application as well as review of the strong points and weaknesses of optimization methods. The selection of optimization method mainly depends on experience and subjective choice of each author. Therefore, analyzing the characteristics and the scope of application of existent optimization methods is a significant task. Moreover, finding appropriate general frameworks that facilitate the optimization of process parameters in injection molding is necessary.2 Theoretical background and survey of the injection molding process parameter optimization2.1 Optimization techniques If we classify the numerical optimization technique, which is based on the way of improving the design point after each iteration, there are three kinds of optimization techniques: non-gradient-based, gradient-based, and hybrid optimization techniques. They are described briefly as follows: Non-gradient based optimization techniques do not require an objective function, f(x), to be differentiable because the algorithms do not use derivatives of f(x). Examples of non-gradient-based optimization techniques are adaptive simulated annealing, Hooke-Jeeves direct search, and genetic algorithm (GA). These optimization techniques tend to reach a global optimum but require the huge number of function evaluations. GA is a well-known non-gradient based optimization technique. It is a stochastic search or optimization algorithm that mimics Darwins theory of biological evolution. Gradient-based techniques define the search directions by the gradient of the function at the current point. In practice, there are many kinds of gradient-based optimization techniques such as generalized reduced gradient, conjugate gradient, method of feasible directions, mix integer optimization, sequential linear programming, sequential quadratic programming, and DavidonFletcherPowell. Gradient-based techniques, in general, give a quick convergence, but they may require a long run when the number of variables increases. Gradient-based techniques can also get risk of local extremum for high nonlinear optimization problem.Hybrid optimization techniques use the combination of both non-gradient based and gradient-based techniques subsequently in order to take the advantages and reduce the disadvantages of single optimization technique. Presenting all of these optimization techniques is beyond the scope of this paper.2.2 The common optimization methodsThe terminology optimization method used in this paper refers to whether or not the explicit objective functions are formulated. For simulation-based optimization, the objective functions are often in the form of implicit equations. The value of the objective function is unknown until simulation results are obtained. There are two approaches that are used to resolve the optimization problem including direct optimization and metamodel-based optimization methods as shown in Fig. 1. The detail of these two optimization methods is described as follows.Fig. 1. Classification of optimization methods.2.2.1Direct optimization methods Direct numerical optimization is an approach that explicit objective functions are not required. Both gradient-based optimization techniques and non-gradient based optimization techniques can be applied to solve the optimization problem. Sometimes, direct optimization methods combine the GA and other optimization techniques. It is well known that GA tends to reach a global extremum, but this method requires a large number of function evaluations. On the contrary, gradient-based methods are efficient to guarantee a local extremum. If these two algorithms are combined as a hybrid system, they can strengthen the advantages and remove the disadvantages.2.2.2Metamodel-based optimization methodMetamodel-based optimization methods is an approach that objective functions are frequently approximated into the explicit form of low order polynomials with acceptable accuracy. Once the metamodel mathematically renders the process with minimum error, the optimization problem is easy to tackle by applying appropriate optimization techniques. Metamodel-based optimization methods are widely used compared to direct optimization. The common metamodels are response surface methodology (RSM), artificial neural network (ANN), radial basis function (RBF), Kriging, and hybrid model. The review of metamodeling technique for computer-based engineering design and optimization can be found in the survey of Simpson et al. 3 and the work of Wang and Shan 4. This optimization method has some benefits such as being easy to connect to simulation program, to render a view of entire design space as well as computational efficiency as claimed by Papalambros 5, Wang and Shan 4, and Park and Dang 6.2.3 Review of process parameter optimization in injection molding Direct optimization method is not often used in injection molding. This method requires a complex integration between simulation tool and optimization code. There are several authors who have used this approach. Lam et al. 7 proposed a GA/ gradient hybrid approach for injection molding conditions optimization. GA method optimization approach requires a huge number of function evaluations or an enormous number of simulation cycles. Parallel computing can reduce the simulation time when some computers run simultaneously. Wu et al. adopted an enhanced genetic algorithm, referred to distributed multi-population genetic algorithm. Their approach combined an optimization algorithm and commercial Moldflow software with a dominance-based constraint-handling technique and a masterslave distributed architecture 8. Direct optimization method can also be carried out using only gradient-based optimization technique. This approach sometimes converges quickly when the optimization problem is low nonlinear.Metamodel-based optimization methods are widely used in injection molding. Most of the common metamodeling techniques such as RSM, ANN, RBF, and Kriging model are applied. The application of metamodel-based optimization methods depends on particular cases and on the preferred use of the researchers. Following are the common optimization methods appeared in the literature in the field of plastic injection molding.2.3.1RSM model RSM is one of the metamodeling techniques in which the relationship between input and output is often expressed in the form of quadratic polynomial. Although this is a traditional method, it is widely used by many authors due to its maturity and the ease of use. Orthogonal array is often used as the design of experiment (DOE) method for this approach. RSM is used in conjunction with GA optimization algorithms to minimize the warpage, sink-mark or shrinkage 913. In fact, we can use any optimization techniques to resolve the optimization problem expressed in terms of RSM model. However, most of the authors used GA because they thought that GA is a global optimization. GA can avoid being trapped in local extremum. Other authors used RSM in conjunction with gradient-based optimization techniques, or they applied RSM to predict the effects of process parameters on the quality of molded parts 11,1417.2.3.2Artificial neural network model ANN that mimics some basic aspects of the functionality of human brain is an emerging approach because ANN is a powerful tool for predicting high nonlinear responses via function approximation. There are many authors who used ANN as a predictor model showing the relationship between process parameters and quality index. Kwak et al. 18, Yarlagadda and Teck Khong 19, and Yarlagadda 20 stated that the neural network predictor using learning data extracted by CAE analysis agrees well with the experimental results. Kenig et al. 21, Mok and Kwong 22, Chen et al. 23, and Altan 24 claimed that the neural network model can accurately predict the product quality, and this approach is usable and efficient tool for quality criteria prediction (shrinkage, weight, or tensile strength). ANN is considered as a robust model to predict the relationship between process parameters and the quality of molded parts. The process parameter optimization can be carried out based on this approximate relation. ANN model is preferred to use in conjunction with GA optimization technique. Shen et al. 25 optimized injection molding process parameters using a combination of artificial neural network and GA method. Chen et al. 26,27 optimized process parameters for multi-input multi-output (MIMO) and multi-input single-output (MISO) plastic injection molding via soft computing with ANN and GA. Ozcelik and Erzurumlu 28 compared the warpage optimization in the plastic injection molding using ANOVA, ANN and GA. Other authors 2934 also used ANN and GA for optimizing process parameter in injection molding in order to improve the quality of molded part. Most of these authors concluded that ANN and GA hybrid strategy is a robust approach. However, most of them did not mention the way to select the number of experiments which is used to obtain training data for ANN model. The number of input parameters varies from 4 to 6 in most of these studies, but the number of experiment changes in a large range (from 27 28 to 252 25). It is clear that if the number of experiments is too high, the simulation or physical experiment cost is extremely elevated.2.3.3Kriging model Kriging, a kind of metamodel, is considered as an appropriate model for deterministic and high nonlinear when the number of process parameters is moderate 3,35. However, this method has low attraction to the researchers in the field of injection molding because of its complexity compared with RSM or because of its reputation in comparison with ANN. Very few studies used Kriging method. Gao and Wang 36,37 introduced an effective warpage optimization method in injection molding based on the Kriging model.2.3.4Radial basis function model RBF is also a common metamodel, but it is not widely used in process parameters compared to other models. Li et al. applied the radial basis function to optimize the packing profile of the injection molding process 38. They used the gradient-based optimization algorithm namely sequential quadratic programming. The Latin hyper cube sampling technique was used for DOE. This technique offers the designer a freedom for choosing the number of experiment. Although a large amount of works that devoted effort to process parameters optimization, there are still some consider-able issues. The existence of many approaches shows that the process parameters optimization for injection molding is quite complex and diverse. The level of complication depends on the optimization objective, the geometry of the molded part, materials, and the number of design variables. In addition, the selection of optimization techniques and optimization methods mainly depends on the experience and subjective choice of researchers. In the literature, there is no guideline or a generalization of the optimization method that is used to optimize injection molding process parameters. Thus, general frameworks for simulation-based optimization applied to injection molding are proposed in order to facilitate and accelerate the design and optimization process.3 Proposed frameworks for optimizing molding parameters3.1 Optimization method for optimizing molding parameters using direct numerical optimization models A framework for optimizing molding parameters using direct numerical optimization model includes a framework for automated simulation and a schematic procedure of the direct simulation-based optimization. The optimization process is based on the direct numerical optimization method. Both gradient based and non-gradient based optimization techniques can be used to find the optimum solution. Numerical optimization is a searching process in which the optimization loop is terminated when the convergence is reached (optimum solution is found), or the termination criteria are active. Because the computing cost of CAE simulation is usually expensive for large and complex parts, the common termination criterion is the predefined maximum number of simulations. The process of simulation-based optimization using direct numerical optimization models should be automatic in order to accelerate the optimization process. A framework for automated simulation applied to direct numerical optimization methods is proposed in Fig. 2. This framework includes two components: optimizer and CAE (computer aided engineering) components. The simulation result obtained from CAE component is sent directly to the optimizer. Subsequently, the optimizer evaluates the result and modifies the input parameters (design variables) in every iteration based on a selected optimization technique. If the gradient-based optimization technique is used, finite difference method is applied to determine the gradient and search direction. If non-gradient based optimization technique is selected, for example GA, the design variables are modified according the strategy of this optimization technique. All the tasks in this framework are absolutely automatic without the intervention of the user (namely designer) at any stage during the optimization process.Fig. 2. A framework for automated simulation applied to direct numerical optimization methods. To build the proposed framework, it is necessary to couple the two tools: plastic injection molding simulation tool (CAE software) and a programing tool (or integration software) that is used to connect two tools and to solve the optimization problem. The selection of implementing software depends on the available tools and individual choices of the designer. They can use any standard programming languages such as Visual Basic, Visual C, MATLAB, or process integration and design optimization tools such as iSight and PIAnO to connect the CAE components and the optimizer, control the integration loop, and resolve the optimization problem. How the optimizer component works in the proposed framework is also important. The schematic procedure for optimizing injection process parameters in conjunction with direct simulation-based optimization is described in Fig. 3. Firstly, the objective functions such as warpage, shrinkage, or residual stress are determined. Secondly, the designer identifies the design variables such as melt temperature (Ti), mold temperature (Tm), fill time (ti), packing time (tp), and packing pressure (Pp) as well as constraints. The constraints are usually the range of design variables and some boundary conditions related to the specification of the molding machine. Thirdly, the simulation is carried out in order to obtain the values of the objective functions. The loop of evaluating the simulation results, modifying design variables, and running simulation in Fig. 3 is terminated when the stop criteria or the convergence of the optimization process is met. Finally, the optimum solution is obtained after the optimization search is stopped.Fig. 3. Schematic procedure of the direct simulation-based optimization for optimizing injection molding process parameters.The quality of optimum solution depends on some factors in which an initial start point of the numerical search is important. The number of iteration sometimes depends on an arbitrary initial starting point. However, no one knows what the best initial point is when he starts the searching process. Another problem is that the local optimum can be reached in-stead of global optimum when gradient-based optimization technique is used. When the behavior of the response of the out-put is high nonlinear, the optimization process may be trapped in a local optimum. In addition, if the number of design variables increases, direct optimization method requires a lot of iterations and the total simulation cost may be high. Assuming that the flow and warpage simulation take an hour to complete and the optimization process terminates after 240 iterations, it takes 10 days to finish the optimization process. These problems are the disadvantages of direct simulation-based optimization method.The optimization method for optimizing molding parameters using direct numerical optimization model is suitable for problems with low simulation cost. High performance computer nowadays can facilitate the application of this optimization method. In addition, hybrid optimization techniques which combine non-gradient based and gradient-based algorithm can ensure a global optimum with a moderate number of simulations for high nonlinear problems.3.2 Optimization method for optimizing molding parameters using metamodelsA framework for optimizing molding parameters using metamodel-based optimization approach is comprised of two components: a CAE component and an integration controller as shown in Fig. 4. The CAE component is responsible for simulating and calculating the values of the objective functions. The integration controller reads the results obtained from CAE simulation and stores them in an output file, controls the number of simulation and organizes the combination of process parameters for every run based on a chosen DOE technique. The number of simulations is predetermined by the certain DOE strategy. All the tasks in the framework should be automatic using application programming interface (API) language.After the last simulation is completed, a metamodel in the form of explicit equation is built, and we can optimize the process parameters based on the metamodel.Fig. 4. A framework for automated simulation applied to metamodel-based optimization Method.The schematic procedure of simulation-based in conjunction with metamodeling techniques is presented in Fig. 5 in which the selection of metamodel type should be elaborate. The popular metamodels are RSM, ANN, RBF, and Kriging model. Second order RSM is suitable for low or moderate nonlinear responses. It requires less number of simulations compared to other models. RBF, ANN, and Kriging model are different from RSM and RBF because they interpolate the sample data points, and their response surface is not as smooth as those of RSM. RBF, ANN, and Kriging model are suitable for high nonlinear problems, but they require an adequate set of sample data obtained from experiment or simulation.Fig. 5. Schematic procedure of simulation-based and metamodel-based optimization strategy for optimizing process parameters.After selecting the metamodel type, DOE or space sampling technique is an important step when using metamodel-based optimization approach. The common DOE or space sampling techniques include full factorial, D-optimal design, central composite design, orthogonal array, Latin hypercube, and optimal Latin hypercube. The right choice of sampling technique can be referenced from the work of Wang and Shan 4. After running a predefined number of simulations according to the DOE strategy, the approximation process is carried out, and the metamodel is then built. The accuracy or the goodness of fit of the metamodel is often assessed by four error measures: averages absolute error, maximum error, root mean square error, and R-squared. If the metamodel is adequate, the optimization process is then performed based on this model. Otherwise, it is necessary to improve or change the metamodel type. Any optimization techniques (gradient-based optimization techniques or non-gradient based optimization techniques) can be used to solve optimization problem. Because the objective and constraint functions are in the form of explicit equation, the computing cost of optimization is ignored compared to the total simulation cost.Because metamodeling technique is an approximate technology, there are errors between the predicted values obtained by the regression model and the true values obtained by simulation/experiment at the “optimum” point. Therefore, evaluating optimum design point is required. This is a remarkable difference between direct simulation-based optimization method and metamodel-based optimization method. If the error between the predicted and actual values at the optimum point is acceptable, the optimization process is finished successfully. The advantage of metamodel-based optimization approach is that the designer can initiatively choose the numbers of experiment or simulations. This advantage is extremely important when optimizing process parameter for molding complex and large parts with many elements.A comparison between the two proposed optimization methods in terms of simulation cost, number of iterations or simulation time, response nonlinearity, molded part geometry, and the accuracy of optimization result is summarized in Table 1 in order to make a guideline for selecting the appropriate optimization framework.Table 1 Comparison between direct optimization and metamodel-based optimization methods.4 Case studies To show the feasibility of the proposed optimization frameworks, two examples of application are implemented. This section also investigates the characteristics of some of optimization methods.4.1 Case study 1: highly nonlinear response problemThe molded part is a tray made by PP material as shown in Fig. 6. We used Moldflow software for flow and warpage simulation. The molded part was modeled by CAD software, imported to Moldflow environment, and meshed with triangular elements. An API program was coded in order to automatically perform the simulation task. The integration between optimization controller and flow simulation was implemented using iSight software.The problem is finding the optimum values of five important process parameters including mold temperature (Tm ), melt temperature (Ti ), injection time (ti ), packing pressure (Pp ), and packing time (tp ). The value ranges of these parameters are determined from the recommended ranges given by the plastic manufacturer (Table 2). Table 2 Comparison of optimization results obtained from different optimization approaches. One of the local optimum.The optimization problem is stated as follows:- Minimize the warpage (1)- Subject to: (2)Both the previously mentioned optimization methods that cover gradient-based, non-gradient based, and hybrid optimization techniques are adopted. The first method applies the indirect or metamodel-based optimization approaches including RSM, RBF, and ANN. The second method applies the direct optimization approaches including GA, gradient-based optimization technique, and hybrid of GA and gradient-based optimization technique. For gradient-based optimization, firstly, the RSM metamodel was used with 36 numerical experiments organized by L36 orthogonal array. The fitness plot of the RSM model shows a very good prediction of cooling time ( = 1.0); however, the warpage response is too low ( = 0.62, see Fig. 7). The low value of R 2 for the response of warpage is caused by a highly non-linear behavior of warpage due to low stiffness and corner effect of the molded part. Therefore, RSM method is inadequate metamodel for this example. RBF is subsequently used instead of RSM model. The value of R-squared of RBF model is higher than those of RSM (0.72 compared to 0.62, Figs. 7 and 8) because RBF model can fit the non-linearity better. ANN model was also applied in this example. The quality of ANN model depends on the quality of training data set. In this case study, training data-set is 60 design points sampled by Latin hypercube technique. The columns marked with (1) and (2) in Table 2 show the optimization results obtained by RBF and ANN approaches.Fig. 7. Fitness plot of RSM metamodel with 36 design points.Fig. 8. Fitness plot of RBF metamodel with 36 experiments.The direct simulation-based optimization methods were tested with non-gradient based GA, gradient based and hybrid optimization techniques. Non-gradient based GA method gives a relatively significant result, in general, because it gives low values of considered outputs (2.93 mm of warpage and 11.7 s of cooling time). The history plot of optimization process using direct GA optimization method is shown in Fig. 9. However, the number of simulations is confined in a predetermined value of 200 runs for this case study due to the computing cost of each simulation and the budget of time. Therefore, the real optimum point is not always guaranteed. The evidence is that the value of objective function of GA method is 2.93 meanwhile this value continues to be improved when applying gradient-based optimization method subsequently (2.93 compared to 2.72, Table 2). The starting point for searching the optimum point of gradient-based optimization method is the optimum point obtained by GA.Fig. 9. History plot of optimization process using direct GA optimization method. When we applied the direct gradient-based optimization method using sequential quadratic programming, the convergence is reached very fast, just after 50 iterations. However, the optimum result is worse than other methods. The evidence is that the value of the warpage is 3.54 mm. The history plot of the optimization process using direct gradient-based approach is shown in Fig. 10. Trying other starting points may improve the final optimum result but the simulation cost will increase.Fig. 10. History plot of optimization process using direct gradient-based method The efficiency of the optimization method depends on the number of simulations and on the fidelity of optimum point. Table 3 compares the number of simulations of the optimization methods that have been used. Direct GA optimization method requires a lot of simulations compared to other methods. The combination of coarse GA and gradient-based fine search has a moderate number of simulations gives the best optimum solution. Gradient-based methods require less iteration, but they are easy being trapped in a local minimum. RBF and ANN metamodel-based optimization methods reduce the number of simulations; however, the error at the optimization point is high. We found that using rough GA search followed by a gradient-based optimization technique is a good choice that ensures an expected optimum point for the high nonlinear response problem.Table 3 The number of simulations of different optimization method.4.2 Case study 2: low nonlinear response problem This case study investigates the proposed optimization methods when the behavior of objective functions is low nonlinear. Multi-objective optimization is considered instead of single objective optimization. Warpage, cooling time, and residual stress were minimized simultaneously.The molded part is a deep tray with 2.5 mm thickness as shown in Fig. 11. Due to the g