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.     

基于改进自适应模糊推理系统的YG3硬质合金精密外圆磨削表面质量预测

为提高硬质合金材料精密外圆磨削的表面完整性和加工质量,研究其表面质量的预测技术,建立了基于自适应模糊推理系统(ANFIS)的YG3硬质合金精密外圆磨削表面粗糙度预测模型,并引入混合田口遗传算法(HTGA)对预测模型进行了改进。采用工艺试验中所用的磨削参数及相应条件下测得的表面粗糙度数据作为训练样本和测试样本,通过对BP神经网络模型、传统ANFIS预测模型及改进ANFIS预测模型的预测结果进行对比分析,对三种模型的有效性和预测精度进行了验证。结果表明,所提出的改进ANFIS预测模型从预测值相对误差Er的分布及均方根相对误差EMSRE的大小来看,均优于其他两种预测模型,预测精度较高,是一种有效的表面质量预测方法。      

面齿轮磨削加工工艺参数的优化

基于磨削面齿轮工艺参数的分析,在满足产品质量要求和磨削加工条件等设计约束的前提下,建立了以磨齿效率和表面质量为目标函数的多目标优化数学模型。将内点罚函数法与遗传算法相结合用于该数学模型的优化计算,获得了三组最优的磨削用量方案且三组方案均能使磨齿效率和表面质量得到较大提高。根据优化后的结果设计并完成了工艺实验,实验结果也验证了该方法的正确性、有效性和实用性。     

Optimization and modeling of spot welding parameters with simultaneous multiple response consideration using multi-objective Taguchi method and RSM

This paper presents an alternative method to optimize process parameters of resistance spot welding (RSW) towards weld zone development. The optimization approach attempts to consider simultaneously the multiple quality characteristics, namely weld nugget and heat affected zone (HAZ), using multi-objective Taguchi method (MTM). The experimental study was conducted for plate thickness of 1.5 mm under different welding current, weld time and hold time. The optimum welding parameters were investigated using the Taguchi method with L₉ orthogonal array. The optimum value was analyzed by means of MTM, which involved the calculation of total normalized quality loss (TNQL) and multi signal to noise ratio (MSNR). A significant level of the welding parameters was further obtained by using analysis of variance (ANOVA). Furthermore, the first order model for predicting the weld zone development is derived by using response surface methodology (RSM). Based on the experimental confirmation test, the proposed method can be effectively applied to estimate the size of weld zone, which can be used to enhance and optimized the welding performance in RSW or other application.     

Development of a hybrid particle swarm optimization algorithm for multi-pass roller grinding process optimization

In the field of metal rolling, the quality of steel roller’s surface is significant for the final rolling products, e.g., metal sheets or foils. The surface roughness of steel rollers must fall into a stringent range to guarantee the proper rolling force between the sheet and the roller. To achieve the surface roughness requirement, multiple grinding passes have to be implemented. The current process parameter design for multi-pass roller grinding mainly relies on the knowledge of the experienced engineers. This always requires time tedious “trial and error” and is insufficient to work out cases: (1) multi-pass with complex interaction for one pass with its neighboring passes; (2) large number of process parameters setup; (3) multiple process objectives and constrains. In this paper, a process planning method for multi-objective optimization is proposed with a hybrid particle swarm optimization while incorporating the response surface model of the surface roughness evolution. The hybrid particle swarm optimization regards the entire grinding process parameters (from rough grinding, semi-finish grinding, finish grinding to spark-out grinding) as a whole, and realizes the parameter optimization by considering multiple objectives and constrains. The establishment of the response surface model of surface roughness evolution is capable to incorporate the inter-correlation of neighboring passes into the multi-pass parameter optimization. Finally, the experimental verification was implemented to verify the effectiveness of the proposed method. The error between predicted roughness and experimental roughness is less than 16.53%, and the grinding efficiency is improved by 17.00% compared with the empirical optimal process parameters.     

Robust parameter design and multi-objective optimization of laser beam cutting for aluminium alloy sheet

The application of laser beam for precise cutting of sheet metals, in general, and reflective sheet metals, like aluminium, in particular, has become of interest in the recent past. The optimum choice of the cutting parameters is essential for the economic and efficient cutting of difficult to cut materials with laser beams. In this paper, a robust design and quality optimization tool called the Taguchi methodology has been applied to find the optimal cutting parameters for cutting of a reflective sheet made of aluminium alloy with a Nd:YAG laser beam. All the steps of the Taguchi method, such as a selection of orthogonal array, computation of signal-to-noise ratio, decision of optimum setting of parameters, and the analysis of variance (ANOVA), have been done by a self-developed software called computer aided robust parameter design (CARPD). A considerable improvement in the kerf taper (KT) and material removal rate (MRR) has been found by using Taguchi method-based predicted results. Confirmatory experimental results have shown good agreement with predicted results. Further, the Taguchi quality loss function has also been used for multi-objective optimization of laser beam cutting of Al-alloy sheet. The results of multi-objective optimization are compared with the single-objective optimization and it has been found that the kerf taper was increased by 1.60% in multi-objective optimization while the MRR was same in both cases.     

Multi-objective optimization of process parameters for the helical gear precision forging by using Taguchi method

Precision forging of the helical gear is a complex metal forming process under coupled effects with multi-factors. The various process parameters such as deformation temperature, punch velocity and friction conditions affect the forming process differently, thus the optimization design of process parameters is necessary to obtain a good product. In this paper, an optimization method for the helical gear precision forging is proposed based on the finite element method (FEM) and Taguchi method with multi-objective design. The maximum forging force and the die-fill quality are considered as the optimal objectives. The optimal parameters combination is obtained through S/N analysis and the analysis of variance (ANOVA). It is shown that, for helical gears precision forging, the most significant parameters affecting the maximum forging force and the die-fill quality are deformation temperature and friction coefficient. The verified experimental result agrees with the predictive value well, which demonstrates the effectiveness of the proposed optimization method.     

Application of grey-based Taguchi method for simultaneous optimization of multiple quality characteristics in laser transmission welding process of thermoplastics

In the present work, Taguchi method in combination with grey relational analysis is applied for solving multi-criteria optimization problems in laser transmission welding processes. The welding parameters, namely laser power, welding speed and defocal position are optimized with respect to weld strength and weld width. Using the Taguchi quality design concept, an L16 orthogonal array table is chosen for the experiments. Grey relational analysis is applied to convert the multiple quality characteristics to a single performance characteristic called grey relational grade. Optimal welding parameters are then determined by the Taguchi method using grey relational grade as the quality index. Furthermore, analysis of variance is carried out to identify the most significant factor for the overall output feature of the laser transmission welding process. The results of the confirmation experiment show that the optimal laser transmission welding parameters can be determined effectively so as to improve multiple quality characteristics through this approach.     

Optimization of the dressing operation using load cells and the Taguchi method in the centerless grinding process

The finishing processes of industrial components use grinding due to the elevated quality generated by this method. Centerless grinding is among the main manufacturing processes due to its high flexibility, accuracy, and great volume of production that is necessary in modern industry. However, the dressing operation has been a pronounced bottleneck in the centerless grinding process due to the time lost to make the corrections in the grinding wheel. This work presents an optimization of the dressing operation in centerless grinding using load cells and the Taguchi method. The experimental tests were carried out on the shop floor of a manufacturer of shock absorbers. The input parameters were the depth of dressing, the feed rate of dressing, the diameter of the grinding wheel, and the speed of the regulating wheel. The responses were the surface roughness, the roundness error, and the dressing force. The results show that the dressing time was reduced, generating an increase in machine productivity, the surface roughness of the work pieces was reduced with an improvement in quality, and the dressing force was proportional to the depth of dressing.     

Constrained grinding optimization for time,cost, and surface roughness using NSGA-II

Selection of parameters in machining process significantly affects quality, productivity, and cost of a component. This paper presents an optimization procedure to determine the optimal values of wheel speed, workpiece speed, and depth of cut in a grinding process considering certain grinding conditions. Experimental studies have been carried out to obtain optimum conditions. Mathematical models have also been developed for estimating the surface roughness based on experimental investigations. A non-dominated sorting genetic algorithm (NSGA II) is then used to solve this multi-objective optimization problem. The objectives under investigation in this study are surface finish, total grinding time, and production cost subjected to the constraints of production rate and wheel wear parameters. The Pareto-optimal fronts provide a wide range of trade-off operating conditions which an appropriate operating point can be selected by a decision maker. The results show the proposed algorithm demonstrates applicability of machining optimization considering conflicting objectives.     

Methodology of Taguchi optimization for multi-objective drilling problem to minimize burr size

Formation of exit burr on part edges during drilling has several undesirable features with regard to product quality and functionality. Hence it is essential to select optimum drilling process parameters to minimize burr size at the production stage. This paper presents the application of the Taguchi optimization method for simultaneous minimization of burr height and burr thickness influenced by cutting conditions and drill geometry. The Taguchi design approach to the multi-objective optimization problem is based on the introduction of a new concept of fitness function for each trial of orthogonal array. The fitness function is derived through mapping the objective functions of the drill optimization problem. In the present work, optimal values of cutting speed, feed, point angle and lip clearance angle are determined for selected drill diameter values to minimize burr height and burr thickness during drilling of AISI 316L stainless steel workpieces. The details of experimentation, analysis of means and analysis of variance are presented in the paper.     

Simultaneous optimization of multiple performance characteristics of carbonitrided pellets: a case study

The performance of a product is generally characterized by more than one response variable. Hence, the management often faces the problem of simultaneous optimization of many response variables. In recent years, a lot of literature has been published on various methodologies for tackling the multi-response optimization problems. Among them, the approach based on Taguchi’s quality loss function is very popular. This paper discusses a case study on multiple response optimization in carbonitriding process. The surface hardness, case depth, and dimensional variation of carbonitrided pellets were simultaneously optimized using quality loss function methodology. The optimum obtained through loss function approach was found to be superior to the ones obtained through optimizing the response variables separately. The result obtained through the implementation of the solution is also presented in the study.     

A study of Taguchi optimization method for identifying optimum surface roughness in CNC face milling of cobalt-based alloy (stellite 6)

The aim of this work is to develop a study of Taguchi optimization method for low surface roughness value in terms of cutting parameters when face milling of the cobalt-based alloy (stellite 6) material. The milling parameters evaluated are feed rate, cutting speed and depth of cut, a series of milling experiments are performed to measure the surface roughness data. The settings of face milling parameters were determined by using Taguchi experimental design method. Orthogonal arrays of Taguchi, the signal-to-noise (S/N) ratio, the analysis of variance (ANOVA) are employed to find the optimal levels and to analyze the effect of the milling parameters on surface roughness. Confirmation tests with the optimal levels of cutting parameters are carried out in order to illustrate the effectiveness of Taguchi optimization method. It is thus shown that the Taguchi method is very suitable to solve the surface quality problem occurring the face milling of stellite 6 material.     

Multi-objective optimization of forming parameters for tube hydroforming process based on the Taguchi method

Tube hydroforming is an attractive manufacturing technology which is now widely used in many industries, especially the automobile industry. The purpose of this study is to develop a method to analyze the effects of the forming parameters on the quality of part formability and determine the optimal combination of the forming parameters for the process. The effects of the forming parameters on the tube hydroforming process are studied by finite element analysis and the Taguchi method. The Taguchi method is applied to design an orthogonal experimental array, and the virtual experiments are analyzed by the use of the finite element method (FEM). The predicted results are then analyzed by the use of the Taguchi method from which the effect of each parameter on the hydroformed tube is given. In this work, a free bulging tube hydroforming process is employed to find the optimal forming parameters combination for the highest bulge ratio and the lowest thinning ratio. A multi-objective optimization approach is proposed by simultaneously maximizing the bulge ratio and minimizing the thinning ratio. The optimization problem is solved by using a goal attainment method. An example is given to illustrate the practicality of this approach and ease of use by the designers and process engineers.     

A study of the Taguchi optimization method for surface roughness in finish milling of mold surfaces

The objective of this paper is to develop a Taguchi optimization method for low surface roughness in terms of process parameters when milling the mold surfaces of 7075-T6 aluminum material. Considering the process parameters of feed, cutting speed, axial-radial depth of cut, and machining tolerance, a series of milling experiments were performed to measure the roughness data. A regression analysis was applied to determine the fitness of data used in the Taguchi optimization method using milling experiments based on a full factorial design. Taguchi orthogonal arrays, signal-to-noise (S/N) ratio, and analysis of variance (ANOVA) are used to find the optimal levels and the effect of the process parameters on surface roughness. A confirmation experiment with the optimal levels of process parameters was carried out in order to demonstrate the effectiveness of the Taguchi method. It can be concluded that Taguchi method is very suitable in solving the surface quality problem of mold surfaces.     

蜗杆砂轮磨齿加工参数优化

以蜗杆砂轮磨削加工20CrMnTi齿轮为研究对象,选择均匀设计试验法,研究磨削参数（砂轮线速度vs、砂轮沿齿轮轴向进给速度vw、磨削厚度ap）对齿面粗糙度的影响。采用二级逐步回归方法建立磨削参数与齿面粗糙度的回归模型,构建了以加工效率、齿面粗糙度为多目标的优化模型,采用粒子群优化算法对磨削参数进行了优化。试验结果表明,使用优化后的磨削参数加工可以提高加工效率、减小齿面粗糙度。     

Hole characteristics optimization in Nd:YAG laser micro-drilling of zirconium oxide by grey relation analysis

The use of the Taguchi method with grey relational analysis, to determine the laser micro-drilling parameters with consideration of multiple quality characteristics, is studied in this paper. The effort has been made to minimize the micro-drilling defects, such as hole taper and heat-affected zone width, to produce high-quality micro-drills. The Taguchi method coupled with grey relational analysis is therefore used as statistical design of experiment tools for optimization of both the quality characteristics, simultaneously. The optimal result obtained has been verified with the help of an additional confirmatory experiment. This indicates the application feasibility of the grey–Taguchi technique for continuous improvement in product quality in the manufacturing industry.     

二级圆柱齿轮减速器优化的数学模型

对二级圆柱齿轮减速器进行多目标优化。建立了以二级圆柱齿轮减速器结构参数的多目标优化数学模型。该问题是一个具有四个设计变量、八个不等式约束、三个分目标函数的多目标函数的优化设计问题。采用复合形法对实例进行了结构参数的优化计算,结果表明优化计算是可行的,效果是显著的。     

A sequentially integrated multi-criteria optimization approach applied to laser transmission weld quality enhancement—a case study

In the present research, a sequentially integrated optimization approach, based on Taguchi method, response surface methodology, and desirability function analysis, is proposed for evaluating the optimal set of laser transmission welding parameters. Two quality characteristics namely, weld strength and weld width, and three welding parameters namely laser power, welding speed, and focal position are selected for experimental work. Taguchi quality loss function is first used to find the optimum level of control factors. The outputs of Taguchi analysis is further used in central composite design for developing response surface models. Desirability function analysis is performed next using the developed response surface models, to evaluate the optimal parameters setting by considering multiple objectives. The weld quality is improved markedly at the optimal process condition, as verified by additional confirmation tests. The performance of the proposed optimization approach is also compared with the Taguchi method and grey–Taguchi method and found that the proposed optimization approach gives better results than the other two techniques.     

面向绿色高效制造的铣削工艺参数多目标优化

为了实现数控机床的绿色高效制造,考虑加工过程中刀具寿命和零件表面质量的实际约束条件,建立了以能量效率最高、碳排放最低和材料去除率最高为目标的多目标优化模型。通过设计面中心复合试验获取试验数据,采用信噪比方法将不同要求的优化目标转换成同要求的信噪比,使用基于组合权重的灰色关联分析法将多目标优化转化为单目标优化问题,基于响应曲面法建立关联度与工艺参数的二阶关系模型,应用量子遗传算法对优化模型进行求解。最后通过试验验证了该多目标优化模型的有效性。