Efficient warpage optimization of thin shell plastic parts using response surface methodology and genetic algorithm

During the production of thin shell plastic parts by injection molding, warpage depending on the process conditions is often encountered. In this study, efficient minimization of warpage on thin shell plastic parts by integrating finite element (FE) analysis, statistical design of experiment method, response surface methodology (RSM), and genetic algorithm (GA) is investigated. A bus ceiling lamp base is considered as a thin shell plastic part example. To achieve the minimum warpage, optimum process condition parameters are determined. Mold temperature, melt temperature, packing pressure, packing time, and cooling time are considered as process condition parameters. FE analyses are conducted for a combination of process parameters organized using statistical three-level full factorial experimental design. The most important process parameters influencing warpage are determined using FE analysis results based on analysis of variance (ANOVA) method. A predictive response surface model for warpage data is created using RSM. The response surface (RS) model is interfaced with an effective GA to find the optimum process parameter values.     

Analysis and modeling of effective parameters for dimension shrinkage variation of injection molded part with thin shell feature using response surface methodology

The injection molded housing part with thin shell feature could be produced to increase the internal space for packing more components. In this study, injection velocity, packing pressure, mold temperature, and melt temperature were selected as effective parameters for injection molding process. For the purpose of reducing dimension shrinkage variation of thin shell molded part, the response surface methodology was utilized to determine the relationship between input parameters and responses. Then the optimization condition was obtained according to the desirability function. Results show that melt temperature is the most significant factor on dimension shrinkage variation in transverse direction, followed by packing pressure, mold temperature, and injection velocity. However, in the longitudinal direction, packing pressure has the greatest influence on the dimension shrinkage variation, followed by injection velocity, melt temperature, and mold temperature. In accordance with verification experiments, the difference between the experimental data and predicted values ranges from ?9.8% to 1.8%. To obtain the optimal condition, the overall desirability must be larger than 0.9. Based on analysis of variance, the proposed models look reasonably accurate.     

Application of response surface methodology in controller fine-tuning

Despite the developments in advanced control techniques, the traditional PID controller is still being used in the majority of industrial processes. However, due to process non-linearities and modelling difficulties, common tuning techniques often yield tuning parameters that are not optimum. The subsequent fine-tuning stage is time-consuming because it is performed by trial and error. Several researchers have suggested that a statistically designed, experimental approach to controller tuning may be fruitful, e.g. Box and Kramer [1].

Using Response Surface Methodology (RSM), a model of the system performance as a function of the tuning parameters can be obtained. RSM can systematically lead the operator to improved tuning and provide a picture of the sensitivity of the process to the tuning parameters. The application of this technique in the fine-tuning of a simulated and real-time process is shown.     

响应面法优化火焰原子吸收仪检测Zn元素工作条件

采用响应面法优化火焰原子吸收仪检测Zn元素工作条件。通过在单因素基础上,用Design-Expert8.0软件中Box-Behnken Design试验设计研究灯电流、光谱通带、乙炔流量、燃烧器高度4个变量对Zn元素吸光度值的影响程度。用响应面法得出4个考察因素最优工作参数和吸光度预测值:灯电流1.0mA、光谱通带0.26nm、乙炔流量1302.01mL/min、燃烧器高度6.29mm,吸光度预测值0.356Abs。通过实验证实:吸光度真实值与预测值接近,对样品检测,样品平均回收率在93%~104%之间,RSD在0.18%~0.26%范围内。     

An investigation into the aspheric ultraprecision machining using the response surface methodology

Aspheric ultraprecision machining is increasingly important to the manufacturing industry. The performance of aspheric optical components manufactured by mass-production is largely dependent on the form error of molds and dies. It is believed that productivity of a machining process could be improved if the form error is predictable. In this study, the response surface methodology (RSM) was employed to derive predictive models of rough and compensation cuttings for an aspheric convex mold, with an outer aperture of ϕ12 mm and curve height of 0.6 mm. Two control factors, the depth of cut and spindle speed, were selected for study. The 2K factorial design with four center points was adopted. Two linear models for both rough and compensation cuttings were derived experimentally based on the form errors obtained. The models adequacy was examined through ANOVA (analysis of variance) results for the surface responses. It was found that the linear model of rough cutting is adequate, reflected by the significant regress coefficients and the high R² value. However, the model of compensation cutting was found to be inadequacy.     

Optimization of tool geometry parameters for turning operations based on the response surface methodology

This investigation focuses on the influence of tool geometry on the surface finish obtained in turning of AISI 1040 steel. In order to find out the effect of tool geometry parameters on the surface roughness during turning, response surface methodology (RSM) was used and a prediction model was developed related to average surface roughness (Ra) using experimental data. The results indicated that the tool nose radius was the dominant factor on the surface roughness. In addition, a good agreement between the predicted and measured surface roughness was observed. Therefore, the developed model can be effectively used to predict the surface roughness on the machining of AISI 1040 steel with in 95% confidence intervals ranges of parameters studied.     

System identification of a composite plate using hybrid response surface methodology and particle swarm optimization in time domain

Material properties of composites are identified using a novel hybrid RSM–PSO method in this paper. Different response surface methodology (RSM) methods and particle swarm optimization (PSO) methods are studied initially on a 4 degrees-of-freedom (4DOF) dynamic system on their performance in terms of speed and accuracy. The best combination is used as a hybrid RSM–PSO method to evaluate the performance on system identification of an orthotropic plate along with a 4DOF dynamic system and an isotropic plate. The novelty of the present paper is to identify the composite plate material properties using RSM methods based on time domain signals, which is not hitherto reported in the literature. Also, whereas previous papers have used full factorial design for system identification, here CCDI is used. The input factors (design variables) are the system parameters which are to be identified and the response (objective function) is error sum-of-square of acceleration response with respect to new test system. The performance of the proposed method is also evaluated with the addition of 5% Gaussian noise to simulate the experimental errors. The system parameters of the orthotropic plate were identified with 0% and 0.25% average prediction error with zero and 5% addition of noise respectively by the proposed hybrid RSM–PSO method. It is also showed a much better performance and robustness to noise addition when compared to the other RSM methods in the literature.     

产品稳健设计响应面模型法的试验设计

试验设计是产品稳健设计中的基础，对稳健设计中常用的响应面模型法的试验设计方法进行了研究。针对响应面法稳健设计中所采用的仿真试验与物理试验误差性质的不同，采取不同的试验设计方法，其中正交试验设计和拉丁方试验设计的应用克服了以往响应面法稳健设计中不能应用仿真试验的缺点。     

Optimization of drawbead design in sheet forming using one step finite element method coupled with response surface methodology

In a sheet forming process, drawbead plays an important role on the control of the material flow. In this paper, a numerical procedure for the design of forming processes is described. It is based on the coupling of an optimization technique and the simplified one step finite element method (also called inverse approach). The optimization technique allows adjustment of the process parameters so that specified criteria are fulfilled. Response surface methodology (RSM) is a global approximation method, which is ideally suited for solving highly nonlinear optimization problems. The finite element method, in addition to predicting the response of the process to certain parameters, allows assessment of the effect of a variation in these parameters on this response. The authors utilize the one step method at the preliminary design stage to supply stress or strain information for the following optimization using RSM. The procedure for this optimization process is fully described. The front fender for Numisheet 2002 is presented and the real defect free workpiece is produced to demonstrate the usefulness of the proposed optimization procedure. A comparison between the two forming limit curves (FLC) before and after optimization and results obtained using the precise incremental commercial software DYNAFORM based on the explicit dynamic approach verify that the optimization design method of drawbead could be successfully applied in designing actual tools of auto body cover panels.     

Application of response surface methodology on finding influencing parameters in servo pneumatic system

Servo pneumatic positioning system is a mechatronics approach that enables to use pneumatic cylinders as multi-position actuators. In the present study, an endeavor has been made to simulate the response of pneumatic cylinder parameters. Response surface methodology based analysis have been conducted to evaluate the influences of system parameters such as external load, supply pressure and cross sectional area of cylinder on the response characteristics such as settling time, maximum overshoot, integral time absolute error and maximum force generated using fuzzy rule base models. From the experimental results, it has been inferred that supply pressure has mostly influent nature on determining maximum overshoot and integral of time absolute error (ITAE). It has been observed that cross sectional area and external load has significantly affected the maximum generated force and settling time respectively.     

The response surface method and the analysis of mild oxidational wear

Instead of using the conventional oxidation theory to depict a disk’s wear rate as a function of contact temperature, the response surface method (RSM) is herein introduced to relieve the one-factor-at-a-time defect in portraying tribological characteristics. By means of a central composite design (CCD) technique, fewer operating conditions are needed to establish expressions for the wear rate parameter, the contact temperature and the friction coefficient as a function of sliding speed and applied load. A second degree polynomial was used to represent a curved surface which fits the experimental data. In addition to results for the designated operating conditions, wear rate parameters and contact temperatures obtained from the polynomials were compared with the experimental results. The activation energy in the wear rate expression can thus be derived as a function of sliding speed, applied load and contact temperature. The experimental data for the wear rate parameter can be expressed by smooth curves, instead of two different straight lines in two temperature subdivisions.     

Validation of a method using Taguchi,response surface,neural network,and genetic algorithm

Piston is one of the important parts for aircraft engine, and the quality of piston affects the efficiency and safety of the engine. This study applies Taguchi method, response surface methodology (RSM), and back-propagation neural networks (BPNN) combining with genetic algorithm (GA) on the quality improvement of piston manufacturing processes to enhance the process yield. The Taguchi parameter design concerns three nominal-the-best specifications, including ring groove diameter specification, inner groove diameter specification, and inner diameter of pistons. Together with five control factors consisting of (1) type of carbon steel, (2) type of cutting fluid, (3) cutting depth, (4) spindle speed, and (5) chuck pressure, the L₂₇(3¹³) orthogonal array was selected for this experiment. Three models: (1) Taguchi model, (2) Taguchi_RSM model, and (3) Taguchi_BPNN_GA model were constructed to find the parameter combinations of five control factors for each model. Confirmation experiments were done for each model and the performances of three models were also compared to indict the enhancement of manufacturing quality of piston.     

Sheet metal bending optimisation using response surface method, numerical simulation and design of experiments

Bending is one of the processes frequently applied during manufacturing of automotive safety parts that are obtained by successive sequences of blanking and bending. This paper describes a 3D finite element model used for the prediction of punch load and the stress distribution during the wiping-die bending process. The numerical simulation has been modelled by means of elastic plastic theory coupled with Lemaître's damage approach. Numerical simulations were carried out by using the ABAQUS/Standard FE code, for a sufficient number of process parameters combinations, particularly the die radius and the gap between the punch and die. An algorithmic loop, programmed in the Script Language of ABAQUS, was developed in order to investigate the mechanical response of parts bent on a mechanical press for each combination of process parameters. The punch load and stress distribution can be predicted in view of optimising the values of the main parameters involved in the process. Finally, a response surface methodology (RSM) based on design of experiments (DOE) was used in order to minimise the maximum punch load during the bending operation. Numerical results showed the suitability of the proposed model for analysing the bending process. Associated plots are shown to be very efficient for a quick choice of the optimum values of the bending process parameters.     

Application of response surface methodology for determining cutting force model in turning of LM6/SiCP metal matrix composite

In the present investigation an attempt is made to evaluate the effect of certain cutting variables on cutting forces in straight turning of aluminum metal matrix composites under dry cutting condition. Cutting speed, depth of cut and weight percentage of SiC_P are selected as the influencing parameters. The application of response surface methodology and face centered composite design for modeling, optimization, and an analysis of the influences of dominant cutting parameters on tangential cutting force, axial cutting force and radial cutting force of aluminum metal matrix composites produced through stir casting route. Experiments are carried out using aluminum (LM6) alloy reinforced with silicon carbide particles. The mathematical models are developed and tested for adequacy using analysis of variance and other adequacy measures using the developed models. The predicted values and measured values are fairly close, which indicate that the developed models can be effectively used to predict the responses in the turning of aluminum metal matrix composites. The contour plots of the process parameters revel that the low cutting forces are associated with the lowest level of depth of cut and the highest level of cutting speed and the sensitivity analysis revealed that cutting speed is most significant factor influencing the response variables investigated.     

基于响应面的伺服驱动单元散热器优化研究

针对某型号伺服驱动单元工作过程中IPM温升过高的问题,将数值仿真技术应用到伺服驱动单元散热器优化中。开展了散热器几何参数对IPM温升的影响分析,通过均匀设计和多项式拟合相结合的方法建立了关于散热器基板厚度、翅片数和翅片厚度的IPM温升二阶响应面模型,提出了一种基于响应面的散热器优化方法。利用方差分析和拟合优度检验对响应面模型的准确度进行了评价,并在CFD软件上对优化后的散热器方案进行了数值仿真试验。研究结果表明,二阶响应面模型的误差范围不超过2.88%,可以准确地拟合IPM温升与散热器几何参数之间的数学关系;在优化后的方案中IPM温升降低了5.48℃,有效地提高了设备的可靠性,为其他型号伺服驱动单元散热器及类似结构优化提供了参考。     

星点设计-效应面优化法在处方筛选和优化中的应用

介绍了星点设计-效应面优化法的基本原理和操作步骤,综述了该方法在处方筛选和优化中的实际应用,并分析了星点设计-效应面优化法与其他数据处理方法结合的设计试验,证明了其拥有很高的推广价值。     

星点设计—效应面优化法在中药提取中的应用

在科学实验中,星点设计—效应面优化法是同时考察多个因素对结果的影响时常用的实验设计和优化方法,具有预测性好、实验简单、高效等特点,可以很好地应用在中药有效成分提取的研究领域。现介绍了星点设计—效应面优化法的基本原理和操作步骤,综述了该方法在中药有效成分提取过程优化中的应用。     

Optimisation of springback in bending processes using FEM simulation and response surface method

The aim of this work includes the springback optimisation of bending processes using the concept of experimental design and response surface methodology (RSM). The optimisation method includes two phases. The first involves the objective function prediction using design of experiments and response surface method, while the second is an optimisation process using a FORTRAN gradient algorithm. Springback of sheet parts during bending processes is simulated using finite element model (FEM) including damage evolution effects within the sheet. The numerical simulation of the damage evolution has been modelled by means of continuum damage approach. The Lemaitre damage model, taking into account the influence of triaxiality, has been implemented into ABAQUS/Standard code in order to predict the external fibres rupture evolution during the process and the material characteristics changes after bending. The simulation included die corner radius and punch-die clearance as the main variables.     

Optimal design of a variable stiffness joint in a robot manipulator using the response surface method

The response surface method combined with the design of experiment-based design optimization of a variable stiffness joint (VSJ) is presented in this article. A VSJ used in a manipulator of a robot arm to support 1 kg payload at the end is designed by considering the minimization of the total weight as the objective function. Owing to the requirement of large rotational stiffness of the VSJ, over 10 N · m, ring-type permanent magnets are adopted. First, a model composed of two permanent magnets was initially manufactured and tested for comparison with the analysis results. Then, a three-ring-type permanent magnet-based model is suggested and optimized to increase the torque of VSJ. The finite element method is used as a magnetic field analysis method to substitute for the expensive experimental process. Optimization results decrease the weight from 0.899 kg to 0.538 kg, still satisfying the requirement for the rotational stiffness. This paper was recommended for publication in revised form by Associate Editor Tae Hee Lee Jeonghoon Yoo received his B.S. and M.S. degrees in Mechanical Design and Production Engineering from Seoul National University, in 1989 and 1991, respectively. He then received his Ph.D. degrees from the University of Michigan, Ann Arbor, in 1999. Dr. Yoo is currently a Professor at the School of Mechanical Engineering at Yonsei University in Seoul, Korea. Dr. Yoo’s research interests include analysis and design of electromagnetic field systems. Myung Wook Hyun received his B.S. and M.S. degrees in Mechanical Engineering from Yonsei University, Korea, in 1995 and 1997, respectively. While studying for his M.S. degree, Mr. Hyun also studied variable stiffness unit design. He is now working at Samsung Electronics, Co. Ltd.. Jun Ho Choi received his B.S. and M.S. degrees in Mechanical Design from Hanyang University, Korea and his Ph.D. degree from the University of Michigan, Ann Arbor. He is currently a senior research scientist in the Korea Institute of Science and Technology. His research interests include nonlinear control, manipulator control, and safe-joint design. Sungchul Kang received his B.S., M.S., and Ph.D. degrees in Mechanical Design and Production Engineering from Seoul National University, Korea, in 1989, 1991, and 1998 respectively. Dr. Kang is currently a Principal Research Scientist in the Center for Cognitive Robotics Research, Korea Institute of Science and Technology, in Seoul, Korea. Dr. Kang’s research interests include mobility and manipulation of field and service robots and haptics. Seung-Jong Kim received his B.S. degree in Mechanical Engineering from Seoul University, Korea, in 1989, and his M.S. and Ph.D. degrees from KAIST in 1991 and 1998, respectively. Dr. Kim is currently a Principal Research Scientist at the Korea Institute of Science and Technology in Seoul, Korea. Dr. Kim’s research interests include the design, control, and dynamic analysis of mechatronic systems.     

An investigative study of delamination in drilling of medium density fibreboard (MDF) using response surface models

The delamination in drilling of medium density fibreboard (MDF) materials significantly reduces the performance and aesthetical aspects of the final product. Therefore, understanding the delamination tendency and the parameters affecting the same is essential for controlling the delamination factor. The present study investigates the relationships and parametric interaction between two controllable variables, namely, feed rate and cutting speed on the delamination factor at entry and exit of the holes in drilling of MDF. The experiments have been planned as per Taguchi’s L ₁₈ mixed orthogonal array and the responses, namely, delamination factor at entry and exit of the holes have been modeled using response surface methodology (RSM). Two types of MDF panels, SUPERPAN DéCOR (melamine coating layer) and LAMIPAN PB (wood coating layer) were tested using cemented carbide (K20) drills. The analysis of variance (ANOVA) was performed to verify the adequacy of the mathematical models. The response surface analysis has been carried out to study the main and the interaction effects of the machining parameters.