An enhanced optimization approach based on Gaussian process surrogate model for process control in injection molding

A stepwise optimization approach based on Gaussian process (GP) surrogate model is proposed to determine the process parameters and improve the quality control for injection molding. In order to improve the global performance in this optimization, an enhanced probability of improvement criterion is also introduced. Firstly, GP surrogate model is constructed with the initial samples which are obtained from an optimal design of experiment method. GP is capable of giving both a prediction and an estimate of the confidence for the prediction simultaneously. Secondly, an enhanced probability of improvement criterion is used to find the direction of adding training samples and optimize the surrogate model. Since the global optimal region of the model become accurate efficiently after steps of optimizing the surrogate model, the proposed enhanced probability of improvement criterion can switch more swiftly to global optima compared with other improvement criterion. Finally, an auto front grille molding process is taken as an example to illustrate the method. The results show that the proposed optimization method can effectively decrease the warpage of injection-molded parts.     

Optimal design of medium channels for water-assisted rapid thermal cycle mold using multi-objective evolutionary algorithm and multi-attribute decision-making method

Rapid heat cycle molding technology developed recently is a novel polymer injection molding process. In this study, a new water-assisted rapid heat cycle molding (WRHCM) mold used for producing a large-size air-conditioning plastic panel was investigated. Aiming at improving heating efficiency and temperature distribution uniformity of the mold cavity surface, a two-stage optimization approach was proposed to determine the optimal design parameters of medium channels for the WRHCM mold. First of all, the non-dominated sorting genetic algorithm-II (NSGA-II) combined with surrogate models was employed to search the Pareto-optimal solutions. Subsequently, the Technique for Order Preference by Similarity to Ideal Solution was adopted as a multi-attribute decision-making method to determine the best compromise solution from the Pareto set. Then, the layout of the medium channels for this air-conditioning panel WRHCM mold was optimized based on the developed optimization method. It was indicated that the heating efficiency and temperature distribution uniformity on the mold cavity surface were greatly improved by using the optimal design results. Furthermore, the effectiveness of the optimization method proposed in this study was validated by an industrial application.     

Optimization of injection molding process parameters using integrated artificial neural network model and expected improvement function method

In this study, an adaptive optimization method based on artificial neural network model is proposed to optimize the injection molding process. The optimization process aims at minimizing the warpage of the injection molding parts in which process parameters are design variables. Moldflow Plastic Insight software is used to analyze the warpage of the injection molding parts. The mold temperature, melt temperature, injection time, packing pressure, packing time, and cooling time are regarded as process parameters. A combination of artificial neural network and design of experiment (DOE) method is used to build an approximate function relationship between warpage and the process parameters, replacing the expensive simulation analysis in the optimization iterations. The adaptive process is implemented by expected improvement which is an infilling sampling criterion. Although the DOE size is small, this criterion can balance local and global search and tend to the global optimal solution. As examples, a cellular phone cover and a scanner are investigated. The results show that the proposed adaptive optimization method can effectively reduce the warpage of the injection molding parts.     

基于神经网络和遗传算法的薄壳件注塑成型工艺参数优化

建立基于神经网络和遗传算法并结合正交试验的薄壳件注塑成型工艺参数优化系统.正交试验法用来设计神经网络的训练样本,人工神经网络有效创建翘曲预测模型;遗传算法完成对影响薄壳塑件翘曲变形的工艺参数(模具温度、注射温度、注射压力、保压时间、保压压力和冷却时间等)的优化,并计算出其优化值.按该参数进行试验,效果良好,可以有效地减小薄壳塑件翘曲变形,其试验数值与计算数值基本相符,说明所提出的方法是可行的.     

智能注射成形中工艺参数的多目标自学习优化

注射成形工艺参数是保障产品质量的关键因素。传统试错法严重依赖工艺人员的试模经验,随着注射成形工艺广泛应用于电子、航空航天等国家战略领域,产品的高端化对工艺参数智能化设置水平提出更高的要求。由于成形产品存在多方面的质量要求,且不同质量指标间可能相互制约,因此亟需一种工艺参数多目标智能优化方法,以获得不同优化目标间的帕累托最优。已有学者利用智能优化方法,如非支配排序遗传算法等,对多目标优化问题进行求解,但是此类方法需大量样本数据对质量-参数关系进行建模,存在试验次数多、且对不同材料及模具的适应性较差等问题。为解决上述问题,提出一种注射成形工艺参数多目标自学习优化方法,在优化过程中实时计算并更新各个工艺参数的梯度,并由不同质量指标的多梯度下降算法对多个目标函数进行优化,在优化过程中实现各工艺参数对产品质量影响程度的自主学习,省去了采集大量数据来建立多个质量模型的过程,实现了注射成形工艺参数的高效智能优化。在基准测试函数实验中,所提方法的优化结果与理论解的相对误差小于2%。同时数值仿真与注射成形实验结果表明,所提方法能高效获得多个优化目标的帕累托最优。     

Experimental-based optimization of polymer injection molding process parameters using anfis-ga method

Compared with ordinary injection-molded parts, the slender, cantilevered, and thin-walled plastic parts are harsh on the injection molding process conditions. For complexity and particularity, it is difficult to form such parts. It is also more likely to cause excessive warpage deformation, affecting the molding quality and performance. The automobile audio shell is a typical slender, cantilevered, thin-walled plastic part. When the mold structure and material are determined, optimizing its injection molding process is the most economical and effective method to manufacture the products with the optimum properties. In order to minimize the warpage deformation, the adaptive network based fuzzy inference system (ANFIS) and genetic algorithm (GA) were adopted to optimize the injection molding process parameters. In particular, considering the high-dimensional nonlinear relationship between the process parameters and the warpage, the ANFIS is constructed as the prediction model of the warpage. Then, the GA is used to globally optimize the prediction model to determine the optimal process parameters. The results show that the optimization method based on ANFIS-GA has a good performance. The warpage is reduced to 0.0925 mm while reduced by 88.25 %. The optimal injection molding process parameters are used for simulation and manufacture, verifying the effectiveness and reliability of the optimization method.

     

Multiobjective optimization of injection molding parameters based on soft computing and variable complexity method

The objective of this study is to propose an intelligent methodology for efficiently optimizing the injection molding parameters when multiple constraints and multiple objectives are involved. Multiple objective functions reflecting the product quality, manufacturing cost and molding efficiency were constructed for the optimization model of injection molding parameters while multiple constraint functions reflecting the requirements of clients and the restrictions in the capacity of injection molding machines were established as well. A novel methodology integrating variable complexity methods (VCMs), constrained non-dominated sorted genetic algorithm (CNSGA), back propagation neural networks (BPNNs) and Moldflow analyses was put forward to locate the Pareto optimal solutions to the constrained multiobjective optimization problem. The VCMs enabled both the knowledge-based simplification of the optimization model and the variable-precision flow analyses of different injection molding parameter schemes. The Moldflow analyses were applied to collect the precise sample data for developing BPNNs and to fine-tune the Pareto-optimal solutions after the CNSGA-based optimization while the approximate BPNNs were utilized to efficiently compute the fitness of every individual during the evolution of CNSGA. The case study of optimizing the mold and process parameters for manufacturing mice with a compound-cavity mold demonstrated the feasibility and intelligence of proposed methodology.     

Optimization of conformal cooling channels with array of baffles for plastic injection mold

Cooling system has an important role in the injection molding process in terms of not only productivity and quality, but also mold-making cost. In this paper, a conformal cooling channel with an array of baffles is proposed for obtaining uniform cooling over the entire free-form surface of molded parts. A new algorithm for calculating temperature distribution through molding thickness, mold surface temperature and cooling time was presented. The relation among cooling channels’ configuration, process parameters, mold material, molding thickness and temperature distribution in the mold for a given polymer is expressed by a system of approximate equations. This relation was established by the design of experiment and response surface methodology based on an adequate physical-mathematical model, finite difference method and numerical simulation. By applying this approximate mathematical relation, the optimization process for obtaining target mold temperature, uniform temperature distribution and minimizing the cooling time becomes more effective. Two case studies were carried out to test and validate the proposed method. The results show that present approach improves the cooling performance and facilitates the mold design process in comparison to the trial-and-error simulation-based method.     

塑料注射成型工艺参数优化的模糊规则网络模型

注射成型是塑料产品成型的最主要工艺,工艺参数是影响成型产品外观、尺寸与性能的关键因素之一。工艺参数的设置与优化属于弱理论、强经验的问题,迫切需要发展科学化、系统化的方法。针对产品缺陷修正中人工经验依赖性强的问题,构建知识的统一模糊化规则形式,建立工艺优化知识表示和推理于一体的Takagi-Sugeno-Kang(TSK)模糊规则网络模型。进一步,提出从工艺数据集自动发现工艺参数优化规则的学习方法,采用Dropout策略与Bagging集成学习策略缓解高维工艺数据下工艺知识库增长出现的规则数量爆炸等问题。分析了模糊规则网络参数、结构对知识表示和推理的影响,建立模型的参数学习与结构优化的双重进化方法。提出基于经验回放的工艺数据增量学习方法,建立数据的增量学习策略。在注射成型工艺数据集上的结果表明,模型的规则数量和长度降低了50%,具有高可解释性以及增量学习稳定性。     

A study of optimization of injection molding process parameters for SGF and PTFE reinforced PC composites using neural network and response surface methodology

This study analyzed variations of mechanical characteristics that depend on the injection molding techniques during the blending of short glass fiber and polytetrafluoroethylene reinforced polycarbonate composites. A hybrid method including back-propagation neural network (BPNN), genetic algorithm (GA), and response surface methodology (RSM) are proposed to determine an optimal parameter setting of the injection molding process. The specimens are prepared under different injection molding processing conditions based on a Taguchi orthogonal array table. The results of 18 experimental runs were utilized to train the BPNN predicting ultimate strength, flexural strength, and impact resistance. Simultaneously, the RSM and GA approaches were individually applied to search for an optimal setting. In addition, the analysis of variance was implemented to identify significant factors for the injection molding process parameters and the result of BPNN integrating GA was also compared with RSM approach. The results show that the RSM and BPNN/GA methods are both effective tools for the optimization of injection molding process parameters.     

A modified global optimization method based on surrogate model and its application in packing profile optimization of injection molding process

This article introduces a step-by-step optimization method based on the radial basis function (RBF) surrogate model and proposes an improved expected improvement selection criterion to better the global performance of this optimization method. Then it is applied to the optimization of packing profile of injection molding process for obtaining best shrinkage evenness of molded part. The idea is first, to establish an approximation function relationship between shrinkage evenness and process parameters by a small size of design of experiment with RBF surrogate model to alleviate the expensive computational expense in the optimization iterations. And then, an improved criterion is used to provide direction in which additional training samples could be added to better the surrogate model. Two test functions are investigated and the results show that stronger global exploration performance and more precise optimal solution could be obtained with the improved method at the expense of increasing the infill data properly. Furthermore the optimal solution of packing profile is obtained for the first time which indicates that the type of optimal packing profile should be first constant and then ramp-down. Subsequently, the discussion of this result is given to explain why the optimal profile is like that.     

熔融沉积制造高能效工艺参数优化方法

为降低熔融沉积制造过程中能量消耗,提高能量利用率,针对熔融沉积制造参数优化问题进行了研究。建立了熔融沉积制造过程能量效率函数,以喷嘴温度、成型层高、空走速度和打印速度为优化变量,以最大能量效率为优化目标,利用田口法设计正交实验,得出能量效率较高的工艺参数组合。在此基础上,利用BP神经网络建立能效优化模型,采用自适应小生境遗传算法对模型求解。研究结果表明,要实现熔融沉积的高能效制造,需在较高的喷嘴温度和成型层高的情况下,采用较低的空走速度和打印速度。     

<Emphasis Type="Bold">Optimisation of Plastic Injection Moulding Process with Soft Computing</Emphasis>

The paper presents a hybrid strategy in a soft computing paradigm for the optimisation of the plastic injection moulding process. Various plastic injection molding process parameters, such as mold temperature, melt temperature, injection time and injection pressure are considered. The hybrid strategy combines numerical simulation software, a genetic algorithm and a multilayer neural network to optimise the process parameters. An approximate analysis model is developed using a Back-propagation neural network in order to avoid the expensive computation resulting from the numerical simulation software. According to the characteristic of the optimisation problem, a nonbinary genetic algorithm is applied to solve the optimisation model. The effectiveness of the improved strategy is shown by an example.     

Multi-objective optimization of MIMO plastic injection molding process conditions based on particle swarm optimization

Determining optimal process parameter settings critically influences productivity, quality, and cost of production in the plastic injection molding industry. Selecting the proper process conditions for the injection molding process is treated as a multi-objective optimization problem, where different objectives, such as minimizing product weight, volumetric shrinkage, or flash present trade-off behaviors. As such, various optima may exist in the objective space. This paper presents the development of an experiment-based optimization system for the process parameter optimization of multiple-input multiple-output plastic injection molding process. The development integrates Taguchi’s parameter design method, neural networks based on PSO (PSONN model), multi-objective particle swarm optimization algorithm, engineering optimization concepts, and automatically search for the Pareto-optimal solutions for different objectives. According to the illustrative applications, the research results indicate that the proposed approach can effectively help engineers identify optimal process conditions and achieve competitive advantages of product quality and costs.     

Minimization of sink mark depth in injection-molded thermoplastic through design of experiments and genetic algorithm

This paper deals with minimization of sink marks occurring behind the rib in plastic injection molding. In terms of rib structure and injection processing parameters, a theoretical analysis model was created. Meanwhile, finite element flow analysis with design of experiments (DOE) and genetic algorithm (GA) was integrated. Values of sink mark depth depend on design variables and technological parameters. Out of all, the four most influential variables, viz., rib thickness, mold temperature, melt temperature, and coolant temperature, were selected for optimization. The mathematic relation between sink mark depth and variables was established by conducting a set of FE analyses at various combinations of variables based on central composite design (CCD). Furthermore, the influence incidence of each factor and interaction between each variable on sink marks were investigated. The prediction model of sink marks was effectively coupled with GA for optimization of variables to minimize the sink depth. Results of the contrast analysis indicated that the proposed methodology could be used effectively in minimizing sink mark depth and parameter optimization design.     

Quality control of the injection molding process using an EWMA predictor and minimum–variance controller

This study presents an exponentially weighted moving average predictor and minimum–variance controller for the quality control of plastic injection molding processes. This is a slow drifting problem of quality control during plastic injection molding processes. In order to have good product quality for plastic injection molding process, a proposed approach was applied to achieve the desired process control quality during the control process. To simplify the process model and reduce system loads, design of experiments technique was adopted to analyze the important factors that had significant effects on the product quality and their relative correlations. The results of this research showed that the proposed approach was effective for a quality control of plastic injection molding process. This cannot only steadily control the manufacturing process to reduce product loss and maintenance time due to unforeseen malfunctions, but they can also increase the efficiency of the equipment and the process.     

Mold design and forming process parameters optimization for passenger vehicle front wing plate

The main objective of the present article is to solve the problems of poor molding quality, large warpage, inadequate cooling effect and unsuitable selection of process parameters, in the injection molding process for passenger vehicle front-end plastic wing plate. The thickness and parting surface of the vehicle front-end fender were determined, the injection mold and its cooling system were designed. The relevant process parameters, affecting the product molding quality, were tested, according to orthogonal experimental approach, while their influence on the warpage was obtained, by analyzing the data. Finally, the BP neural network of warpage model was established and globally optimized using genetic algorithm. The optimal parameter combination of the injection molding process was derived as: melt temperature 236 °C, mold temperature 51 °C, cooling time 32 s, packing pressure 97 MPa and packing time 16 s.

     

基于组合优化策略的动车组悬挂参数优化设计

为快速获得改善车辆横向平稳性的最优悬挂参数,提出基于自适应模拟退火算法和非线性序列二次规划算法的组合优化策略对动车组悬挂参数进行优化设计。建立动车组动力学模型,利用最优拉丁超立方抽样方法选取对横向平稳性影响较大的悬挂参数作为设计变量;以横向平稳性为目标函数构建Kriging代理模型,并利用可决系数检验代理模型精度;采用自适应模拟退火算法对代理模型进行全局范围内初步寻优,在初步最优解的基础上采用非线性序列二次规划算法进行局部空间精确求解。研究结果表明,基于Kriging代理模型和组合优化策略的优化效率明显提高,车辆横向平稳性得到显著改善,并且优化前后运行稳定性均满足要求。     

Multi-objective optimization of injection molding process parameters in two stages for multiple quality characteristics and energy efficiency using Taguchi method and NSGA-II

In this paper, the parameters optimization of plastic injection molding (PIM) process was obtained in systematic optimization methodologies by two stages. In the first stage, the parameters, such as melt temperature, injection velocity, packing pressure, packing time, and cooling time, were selected by simulation method in widely range. The simulation experiment was performed under Taguchi method, and the quality characteristics (product length and warpage) of PIM process were obtained by the computer aided engineering (CAE) method. Then, the Taguchi method was utilized for the simulation experiments and data analysis, followed by the S/N ratio method and ANOVA, which were used to identify the most significant process parameters for the initial optimal combinations. Therefore, the range of these parameters can be narrowed for the second stage by this analysis. The Taguchi orthogonal array table was also arranged in the second stage. And, the Taguchi method was utilized for the experiments and data analysis. The experimental data formed the basis for the RSM analysis via the multi regression models and combined with NSGS-II to determine the optimal process parameter combinations in compliance with multi-objective product quality characteristics and energy efficiency. The confirmation results show that the proposed model not only enhances the stability in the injection molding process, including the quality in product length deviation, but also reduces the product weight and energy consuming in the PIM process. It is an emerging trend that the multi-objective optimization of product length deviation and warpage, product weight, and energy efficiency should be emphasized for green manufacturing.     

An effective warpage optimization method in injection molding based on the Kriging model

In this paper, an effective optimization method using the Kriging model is proposed to minimize the warpage in injection molding. The warpage deformations are nonlinear, implicit functions of the process conditions, which are typically evaluated by the solution of finite element (FE) equations, a complicated task which often involves huge computational effort. The Kriging model can build an approximate function relationship between warpage and the process conditions, replacing the expensive FE reanalysis of warpage in the optimization. In addition, a “space-filing” sampling strategy for the Kriging model, named rectangular grid, is modified. Moldflow Corporation’s Plastics Insight software is used to analyze the warpage deformations of the injection-molded parts. As an example, the warpage of a cellular phone cover is investigated, where the mold temperature, melt temperature, injection time, and packing pressure are regarded as the design variables. The result shows that the proposed optimization method can effectively decrease the warpage deformations of the cellular phone cover and that the injection time has the most important influence on warpage in the chosen range.