A systematic computer-aided approach to cooling system optimal design in plastic injection molding

Cooling system design is of great importance for plastic injection molding because it significantly affects the productivity and quality of the final products. In this paper, a systematic computer-aided approach is developed to achieve the cooling system optimal design. This approach expiates the trial and error process normally practiced in conventional cooling system design based on the designer's experience and intuition. Various aspects of the optimization process for cooling system design are investigated including cooling analysis using boundary element method (BEM), a perturbation-based approach to design sensitivity analysis, optimization problem formulation, and a novel hybrid optimizer based on Davidon–Fletcher–Powell (DFP) method and simulated annealing (SA). A case study shows that the proposed methodology for cooling system optimal design is efficient, robust and practical.     

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.     

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.     

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.     

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.     

基于宽容分层序列法的飞机装配公差稳健设计技术

飞机制造中由于工序能力指数和公差等设计变量存在变差,可能导致无法满足飞机装配质量要求以及制造成本波动较大的问题。运用稳健设计方法建立了飞机装配公差的可行稳健性和敏感稳健性两类设计模型。可行稳健设计考虑了公差等设计变量对装配可行性的影响,使其变差不影响装配功能的实现;敏感稳健性设计则考虑了公差等设计变量对制造成本和装配质量的影响,在目标成本较小的前提下使得目标成本和装配质量受设计变量变差的影响最小。提出了针对飞机装配公差可行敏感稳健设计的多目标优化问题的宽容分层序列求解算法。将公差设计中制造成本、装配质量波动、制造成本波动多个设计目标按照重要性依次排序。首先求解成本最小情况下的公差一般优化解,然后在成本最小值的宽容约束下,求得具有装配质量波动最小值的公差,最后在上述两个优化目标的宽容约束下,求得成本波动最小的最优公差。应用实例和分析结果表明了方法的有效性。       

A response surface based sequential approximate optimization using constraint-shifting analogy

When a traditional response surface method (RSM) is used as a meta-model for inequality constraint functions, an approximate optimal solution is sometimes actually infeasible in a case where it is active at the constraint boundary. The paper proposes a new RSM that ensures the constraint feasibility with respect to an approximate optimal solution. Constraint-shifting is suggested in order to secure the constraint feasibility during the sequential approximate optimization process. A central composite design is used as a tool for design of experiments. The proposed approach is verified through a mathematical function problem and engineering optimization problems to support the proposed strategies.     

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.     

基于性能稳健偏差的区间型参数稳健设计优化

提出了基于系统性能稳健偏差的稳健设计优化方法。该方法针对区间型参数非梯度性能函数的稳健设计问题，应用性能稳健偏差概念评估目标性能函数和约束性能函数的稳健性，形成了三层次稳健设计优化模型：①搜索优化设计点；②迭代策略搜索设计点的目标函数和约束函数的稳健偏差；③优化寻求给定性能偏差所对应的稳健性指数。该方法可获得同时满足约束条件和目标值稳健性要求的优化设计，并输出目标值及其稳健偏差。用三杆桁架结构稳健设计优化说明了该方法的用法和特点。     

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.     

Selection of machining datum and allocation of tolerance through tolerance charting technique

Tolerance charting is an effective tool to determine the optimal allocation of working dimensions and working tolerances such that the blueprint dimensions and tolerances can be achieved to accomplish the cost objectives.The selection of machining datum and allocation of tolerances are critical in any machining process planning as they directly affect any setup methods/machine tools selection and machining time.This paper mainly focuses on the selection of optimum machining datums and machining tolerances simultaneously in process planning.A dynamic tolerance charting constraint scheme is developed and implemented in the optimization procedure.An optimization model is formulated for selecting machining datum and tolerances and implemented with an algorithm namely Elitist Non-Dominated Sorting Genetic Algorithm(NSGA-II).The computational results indicate that the proposed methodology is capable and robust in finding the optimal machining datum set and tolerances.     

Cyber-enabled concurrent material and process selection in a flexible design for manufacture paradigm

This paper presents a cyber design for manufacturing (DFM) framework for concurrent material and process selections. An internet-of-things (IoT) interface is developed wherein design, material, and process databases are accessed in a cloud-based environment. Digital designs are processed to extract dimensional features and functional requirements. A Node-RED IoT simulator is developed to provide seamless interconnectivity to translate design specifications with material and process databases via web sockets. The output from the cloud system is incorporated within a decision-making algorithm. The analytical hierarchy process (AHP) is implemented where alternatives are hierarchically compared to generate weights based on combinatorial order ranking of the designer preferences. A material-process index (MPI) is developed that integrates the material and process generated weights with material-process compatibility for selecting the optimal material and process combination. The proposed methodology is applied to an electrical power distribution interchangeable fuse cutout system to validate the approach. Material and processes are selected on a standalone basis without considering their compatibilities. Further, the MPI function is implemented that integrates functional preferences for material, process, and their compatibilities to contrast against standalone material and process selections. The material-process combination with the highest MPI was chosen as the optimal solution for a product design. The cyber DFM methodology developed in this research can be extended to different application domains based on flexible user chosen criteria.     

Non-probabilistic Robust Optimal Design Method

For the purpose of dealing with uncertainty factors in engineering optimization problems, this paper presents a new non-probabilistic robust optimal design method based on maximum variation estimation. The method analyzes the effect of uncertain factors to objective and constraints functions, and then the maximal variations to a solution are calculated. In order to guarantee robust feasibility the maximal variations of constraints are added to original constraints as penalty term; the maximal variation of objective function is taken as a robust index to a solution; linear physical programming is used to adjust the values of quality characteristic and quality variation, and then a bi-level mathematical robust optimal model is coustructed. The method does not require presumed probability distribution of uncertain factors or continuous and differentiable of objective and constraints functions. To demonstrate the proposed method, the design of the two-bar structure acted by concentrated load is presented. In the example the robustness of the normal stress, feasibility of the total volume and the buckling stress are studied. The robust optimal design results show that in the condition of maintaining feasibility robustness, the proposed approach can obtain a robust solution which the designer is satisfied with the value of objective function and its variation.     

Optimization techniques applied to single point incremental forming process for biomedical application

Single point incremental forming (SPIF) process has the potential to replace conventional sheet forming process in industrial applications. For this, its major defects, especially poor geometrical accuracy, should be overcome. This process is influenced by many factors such as step size, tool diameter, and friction coefficient. The optimum selection of these process parameters plays a significant role to ensure the quality of the product. This paper presents the optimization aspects of SPIF parameters for titanium denture plate. The optimization strategy is determined by numerical simulation based on Box–Behnken design of experiments and response surface methodology. The Multi-Objective Genetic Algorithm and the Global Optimum Determination by Linking and Interchanging Kindred Evaluators algorithm have been proposed for application to find the optimum solutions. Minimizing the sheet thickness, the final achieved depth and the maximum forming force were considered as objectives. For results evaluation, the denture plate was manufactured using SPIF with the optimum process parameters. The comparison of the final geometry with the target geometry was conducted using an optical measurement system. It is shown that the applied method provides a robust way for the selection of optimum parameters in SPIF.     

Robust Collaborative Optimization Method Based on Dual-response Surface

A novel method for robust collaborative design of complex products based on dual-response surface (DRS-RCO) is proposed to solve multidisciplinary design optimization (MDO) problems under uncertainty. Collaborative optimization (CO) which decomposes the whole system into a double-level nonlinear optimization problem is widely Accepted as an efficient method to solve MDO problems. In order to improve the quality of complex product in design process, robust collaborative optimization (RCO) is developed to solve those problems under uncertain conditions. RCO does opfmiTation on the linear sum of mean and standard deviation of objective function and gets an optimal solution with high robustnmess. Response surfaces method is an important way to do approximation in robust design. DRS-RCO is an improved RCO method in which dual-response surface replaces system uncertainty analysis module of CO. The dual-response surface is the approximate model of mean and standard deviation of objective function respectively. In DRS-RCO, All the information of subsystems is included in dual-response surfaces. As an additional item, the standard deviation of objective function is added to the subsystem optimization. This item guarantee both the mean and standard deviation of this subsystem is reaching the minima at the same time. Finally, a test problem with two coupled subsystems is conducted to verify the feasibility and effectiveness of DRS-RCO.     

基于动态序列响应面方法的钣金成形过程参数优化

为得到钣金成形最佳工艺方案，结合有限元方法将设计转化为特定目标和约束的待优化问题；针对成形模拟易受干扰和强非线性特点，提出采用逐次逼近模型，分解复杂设计函数为显式简单函数组合，进行递进全局寻优，避免出现局部最优解和过程发散现象；并利用动态多项式序列响应面方法构造目标和约束的简单近似响应面，用以去除噪声干扰及最大程度减少精确分析计算量。该方法无需求解复杂函数敏度，经实例验证具有很高的精度和效能。     

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.

     

Analysis of shrinkage and warpage in an injection-molded part with a thin shell feature using the response surface methodology

This paper presents a systematic methodology to analyze the shrinkage and warpage in an injection-molded part with a thin shell feature during the injection molding process. The systematic experimental design based on the response surface methodology (RSM) is applied to identify the effects of machining parameters on the performance of shrinkage and warpage. The experiment plan adopts the centered central composite design (CCD). The quadratic model of RSM associated sequential approximation optimization (SAO) method is used to find the optimum value of machining parameters. One real case study in the injection molding process of polycarbonate/acrylonitrile butadiene styrene (PC/ABS) cell phone shell has been performed to verify the proposed optimum procedure. The mold temperature (M _T), packing time (P _t), packing pressure (P _P) and cooling time (C _t) in the packing stage are considered as machining parameters. The results of analysis of variance (ANOVA) and conducting confirmation experiments demonstrate that the quadratic models of the shrinkage and warpage are fairly well fitted with the experimental values. The individual influences of all machining parameters on the shrinkage and warpage have been analyzed and predicted by the obtained mathematical models. For the manufacture of PC/ABS cell phone shell, the values of shrinkage and warpage present the reduction of 37.8 and 53.9%, respectively, using this optimal procedure.     

Robust optimization of the energy efficiency of the cold roll forming process

This paper proposes a hybrid modeling methodology for the robust optimization of cold roll forming process parameters. Energy efficiency is considered with the utilization of both analytical and computational models. A robust design algorithm is developed for the calculation of the optimized energy efficiency indicator through an analytical model at a low computational cost. The calculated optimum energy efficient solution is validated by a finite elements model (FEM) under specific quality constraints: the mapping of longitudinal strains, along a roll forming direction and a cross-sectional distribution, major strains on FLD, profile thickness reduction, and cross-sectional dimensional error. A robust design optimization towards the energy efficiency of a U-channel profile is demonstrated, and the effect of process parameters on the energy efficiency indicator is calculated. The paper arrived at the conclusion that the factors with the dominant effect on energy efficiency are roll gap, roller radius, and bending angle concept, with 30.96, 24.77, and 23.62 % contribution, respectively. Verification of the quality constraints over FEM has proven the feasibility of the optimum solution.     

Multi-objective optimization and sensitivity analysis of tube hydroforming

Tube hydroforming is a manufacturing process used to produce structural components in cars and trucks, and the success of this process largely depends on the careful control of parameters such as internal pressure and end-feed force. The objective of this work was to establish a methodology, and demonstrate its effectiveness, to determine the optimal process parameters for a tube hydroformed in a die with a square cross section. The Taguchi method was used to establish a design of virtual hydroforming experiments, and numerical simulations were carried out with the finite element code LS-DYNA®. A sensitivity analysis was also carried out with analysis of variance. Multi-objective functions that consider necking/fracture, wrinkling, and thinning were formulated, and the response surface methodology was used with the most sensitive factors to obtain a defect-free part. An objective function, based on the final corner radius in the part, was also included in the optimization model. The forming severity of virtual hydroformed parts was evaluated using the forming limit stress diagram and the forming limit (strain) diagram. Finally, the normal-boundary intersection method and the L ₂ norm were used to obtain the Pareto-optimal solution set and the optimal solution within this set, respectively. The hydroforming process for this part was also optimized using the commercial optimization software LS-OPT®, with two different single-objective algorithms. However, the optimum load path predicted with the proposed methodology was shown to achieve a smaller corner radius. The proposed optimization technique helped to define a process window that leads to a robust manufacturing process and improved part quality.