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.     

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。     

Optimization of injection molding process for contour distortions of polypropylene composite components by a radial basis neural network

This study analyzes the contour distortions of polypropylene (PP) composite components applied to the interior of automobiles. Combining a trained radial basis network (RBN) [1] and a sequential quadratic programming (SQP) method [2], an optimal parameter setting of the injection molding process can be determined. The specimens are prepared under different injection molding conditions by varying melting temperatures, injection speeds and injection pressures of three computer-controlled progressive strokes. Minimizing the contour distortions is the objective of this study. Sixteen experimental runs based on a Taguchi orthogonal array table are utilized to train the RBN and the SQP method is applied to search for an optimal solution. In this study, the proposed algorithm yielded a better performance than the design of experiments (DOE) approach. In addition, the analysis of variance (ANOVA) is conducted to identify the significant factors for the contour distortions of the specimens.     

Study on temperature field for invar alloy during TIG welding

In order to solve the complex multi-objective optimal performance design of large-scale injection molding machines, NSGA-II is used to find a much better spread of design solutions and better convergence near the true Pareto-optimal front. The combination of the design method and the injection molding machine is discussed. Screw diameter performance, stick inside distance performance, mold moving route performance and mold-locked force performance are chosen as the four main performance evaluation indexes. Some related parameters are associated to get a performance indication. And performance optimization design parameter constraints are listed to make the design solutions to have practical significance. The mathematical models of two objectives and the mathematical models of three objectives are analyzed. Finally, the instance of HTF180X1N large-scale injection molding machine is taken as an example to demonstrated that such method is effective and practical.     

Optimization of process variables for improvement of seat-backboard peel strength using response surface design method

With an increased demand for comfortable and aesthetically pleasing automobile interiors, fabric seat covers are being used more widely. Previously, covers were manufactured using adhesives attached to a molding and covered with a skin layer. However, this process releases Volatile organic compounds (VOC), pollutes the air inside the automobile, and leads to peel-strength-related problems. This study examines a multi-component injection molding process that uses residual heat during injection molding to glue the skin layer to the molding, employed in seat-backboard manufacturing. Hence, the VOC emission problem is overcome as adhesives are not employed. To obtain enhanced peel strength the optimal skin material is selected using surface-adhesion length and material peel-strength measurements. The response surface design method is utilized with a design-of-experiments method to determine the process variables that maximize the peel strength for the selected materials. The process variable selection is then confirmed via additional experiments. It is expected that the problems related to VOC emissions and peel strength, which limit current seat-backboard manufacturing techniques, can be resolved through application of the optimal conditions identified in this study to a multi-component injection molding process.

     

红外菲涅尔透镜的注射超声辅助成型优化

为了提升聚合物红外菲涅尔透镜的光学性能,以其表面微沟槽的成型质量为目标,提出了一种高效的注射超声辅助成型方法,并对工艺参数进行了综合质量优化。首先分析了超声振动对聚合物的加热和加压效应,设计了一套一模两腔的对比试验模具;接着以红外菲涅尔透镜的调制传递函数MTF和齿形平均高度h为优化质量目标,设计了四步骤的多目标优化流程,通过试验设计、基于BP神经网络的质量目标与注射工艺参数关系建模、基于NSGA-Ⅱ的多目标优化和试验验证进行工艺参数的综合优化。实验结果表明:该多目标优化流程具有很高的精度,MTF和h的平均预测误差MPE分别为4.16%和3.32%;注射超声辅助成型的菲涅尔透镜微沟槽具有更高的复制质量,其齿沟槽平均高度h增加了15.6%,且h值的波动量随着h值的增大而增大,MTF值受齿高h均匀性的影响大于齿高h对其的影响。     

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.     

Optimal injection molding conditions considering the core shift for a plastic battery case with thin and deep walls

The objective of this paper is to examine the influence of injection molding parameters on the core shift to obtain the optimal injection molding conditions of a plastic battery case with thin and deep walls using numerical analyses and experiments. Unlike conventional injection molding analysis, the flexible parts of the mold were represented by 3-D tetrahedron meshes to consider the core shift in the numerical analysis. The design of experiments (DOE) was used to estimate the proper molding conditions that minimize the core shift and a dominant parameter. The results of the DOE showed that the dominant parameter is the injection pressure, and the core shift decreases when the injection pressure decreases. In addition, it was shown that the initial mold temperature and the injection time hardly affect the core shift. The results of the experiments showed that products without warpage are manufactured when the injection pressure is nearly 32 MPa. Comparing the results of the analyses with those of the experiments, optimal injection molding conditions were determined. In addition, it was shown that the core shift should be considered to simulate the injection molding process of a plastic battery case with thin and deep walls.     

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.     

节能注塑机合模机构多目标优化设计研究

对节能注塑机合模机构进行了运动和动力学分析,以机构行程比较大、力放大比较大和机构尺寸较小为目标函数建立了多目标优化数学模型,使用Matlab优化工具箱对其进行了优化设计,通过实例给出了优化结果并进行比对,验证了优化模型的正确性,为注塑机合模机构的优化设计提供了一定的参考。     

Design of an analytic-hierarchy-process-based expert system for non-traditional machining process selection

The selection of a non-traditional machining (NTM) process is often observed to be a multi-criteria decision-making problem with conflicting and diverse objectives. This paper presents a systematic methodology for selecting the best or optimal non-traditional machining process under constrained material and machining conditions. The paper also includes the design of an analytic-hierarchy-process-based expert system with a graphical user interface to ease the decision-making process. The developed expert system relies on the priority values for different criteria and sub-criteria, as related to a specific non-traditional machining process selection problem. It also depends on the logic table to discover the non-traditional machining processes that lie in the acceptability zone, and then selects the optimal process having the highest acceptability index value. The proposed expert system can automate the selection of a non-traditional machining process and provide artificial intelligence in the multi-criteria decision-making process.     

Multi-objective optimization of the ecm process

Optimization of process parameters is helpful in efficient working of the process and, hence, in lowering the cost of machining. Optimization of ECM process parameters has been achieved by considering only one objective at a time from metal removal rate, geometrical accuracy, and total process cost. From a practical point of view, a solution of the ecm problem satisfying all three objectives simultaneously is highly desirable.In the proposed model, a multi-objective problem involving the ecm process is formulated producing highly nonlinearized equations. These are then linearized by regression analysis and converted into a goal programming format. Finally, the problem is solved by the partitioning algorithm.It is concluded that the tool, or cathode, remains safe at the optimal values of design variables obtained in the examples discussed. The optimal value of voltage when metal removal rate is the only objective, is found to be higher than the case when the geometrical accuracy requirement is also to be satisfied.     

基于BP-NSGA的注塑参数多目标智能优化设计

为获得成型性能最优的注塑参数设计方案,提出了基于BP神经网络和非支配排序遗传算法的注塑参数多目标优化方法。将注塑模结构尺寸参数和注塑工艺参数作为待优化的设计变量,建立了以高质量、低成本、高效率为优化目标的注塑参数优化设计模型。基于非支配排序遗传算法获取给定参数范围内的所有Pareto最优解,并通过建立多输入和多输出的BP神经网络来快速获得非支配排序遗传算法优化进程中所有个体的适应度值。开发了基于BP神经网络与非支配排序遗传算法集成的注塑参数智能优化设计系统,并通过鼠标注塑参数设计实例,验证了其适用性和有效性。     

Trade-off analysis in multi-objective optimization using Chebyshev orthogonal polynomials

In this paper, it is intended to introduce a method to solve multi-objective optimization problems and to evaluate its performance. In order to verify the performance of this method it is applied for a vertical roller mill for Portland cement. A design process is defined with the compromise decision support problem concept and a design process consists of two steps : the design of experiments and mathematical programming. In this process, a designer decides an object that the objective function is going to pursuit and a non-linear optimization is performed composing objective constraints with practical constraints. In this method, response surfaces are used to model objectives (stress, deflection and weight) and the optimization is performed for each of the objectives while handling the remaining ones as constraints. The response surfaces are constructed using orthogonal polynomials, and orthogonal array as design of experiment, with analysis of variance for variable selection. In addition, it establishes the relative influence of the design variables in the objectives variability. The constrained optimization problems are solved using sequential quadratic programming. From the results, it is found that the method in this paper is a very effective and powerful for the multi-objective optimization of various practical design problems. It provides, moreover, a reference of design to judge the amount of excess or shortage from the final object.     

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.     

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.

     

An integrated parameter optimization system for MISO plastic injection molding

This paper presents the development of a parameter optimization system that integrates mold flow analysis, the Taguchi method, analysis of variance (ANOVA), back-propagation neural networks (BPNNs), genetic algorithms (GAs), and the Davidon–Fletcher–Powell (DFP) method to generate optimal process parameter settings for multiple-input single-output plastic injection molding. In the computer-aided engineering simulations, Moldex3D software was employed to determine the preliminary process parameter settings. For process parameter optimization, an L₂₅ orthogonal array experiment was conducted to arrange the number of experimental runs. The injection time, velocity pressure switch position, packing pressure, and injection velocity were employed as process control parameters, with product weight as the target quality. The significant process parameters influencing the product weight and the signal to noise (S/N) ratio were determined using experimental data based on the ANOVA method. Experimental data from the Taguchi method were used to train and test the BPNNs. Then, the BPNN was combined with the DFP method and the GAs to determine the final optimal parameter settings. Three confirmation experiments were performed to verify the effectiveness of the proposed system. Experimental results show that the proposed system not only avoids shortcomings inherent in the commonly used Taguchi method but also produced significant quality and cost advantages.     

Study of injection molding process simulation and mold design of automotive back door panel

Numerical simulation of the injection molding process of the outer panel of the automotive plastic rear door and mold design is presented here. Computer aided three-dimensional interactive application (CATIA) is employed to design the original automotive steel structure, and the modal and thermodynamic properties of the plastic back door outer panel are changed by changing the different injection materials of the back door outer panel. In order to efficiently design the panels, finite element analysis is used to verify whether the designed parts meet the mechanical properties requirements such as light weight, low fuel consumption, short production cycle, strong modeling design, high corrosion resistance and good recovery, the above main parameters have been evaluated, and the above main parameters are carried out evaluate. To simulate the injection molding process, computer aided engineering (CAE) software such as ANSYS and HyperWorks are used to analyze the back door of the selected material. After the numerical analysis, suitable material is selected, so that the modal and thermodynamic properties of the product could be satisfied as well as improved. Unigraphics NX (UG) is employed to design the convex and concave mold for the injection molding of the automobile’s plastic back door panel. Combined with the characteristics of the parts and the design requirements of the injection mold, the multi-scheme design of the pouring and cooling system is carried out. By comparing the effects of different gating and cooling systems on injection molding, the best gating and cooling system is selected. The artificial fish swarm algorithm is used to optimize the process parameters of the injection molding process, and the best combination of the injection molding process parameters of the outer panel of the rear door of the automobile is obtained.

     

基于MATLAB的航空圆弧齿面齿轮的多目标优化设计

基于航空圆弧齿面齿轮的啮合理论,建立了优化设计的目标函数,寻找到了对目标函数构成约束的约束条件。应用线形加权法把目标函数转化为评价函数的基础上,利用MATLAB优化设计工具箱进行了多目标优化设计。     

Performance enhancement of axial fan blade through multi-objective optimization techniques

This paper presents an axial fan blade design optimization method incorporating a hybrid multi-objective evolutionary algorithm (hybrid MOEA). In flow analyses, Reynolds-averaged Navier-Stokes (RANS) equations were solved using the shear stress transport turbulence model. The numerical results for the axial and tangential velocities were validated by comparing them with experimental data. Six design variables relating to the blade lean angle and the blade profile were selected through Latin hypercube sampling of design of experiments (DOE) to generate design points within the selected design space. Two objective functions, namely, total efficiency and torque, were employed, and multi-objective optimization was carried out, to enhance the performance. A surrogate model, Response Surface Approximation (RSA), was constructed for each objective function based on the numerical solutions obtained at the specified design points. The Non-dominated Sorting of Genetic Algorithm (NSGA-II) with local search was used for multi-objective optimization. The Pareto-optimal solutions were obtained, and a trade-off analysis was performed between the two conflicting objectives in view of the design and flow constraints. It was observed that, by the process of multi-objective optimization, the total efficiency was enhanced and the torque reduced. The mechanisms of these performance improvements were elucidated by analysis of the Pareto-optimal solutions.