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.     

Statistical investigation of die wear in metal extrusion processes

The aim of this paper is the statistical process control analysis of the tool wear evolution during metal extrusion process for better understanding the principal causes that generate the variability of such a complex phenomenon. The wear prediction is carried out using finite element simulation including the Archard wear model. The tool wear modeling is presented briefly as well as the response surface methodology. The study is based on the application of the central composites designs and allows for the analysis of the response (wear) sensitivity of the tool. The statistical investigation of the process makes it possible to study the influence of each process parameter on the response sensitivity.     

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。     

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.     

Damage identification by response surface based model updating using D-optimal design

Statistical tools, as well as mathematical ones, have been widely adopted and their performance has been shown in different engineering problems where randomicity usually exists. In the realm of engineering, merging statistical analysis into structural evaluation and assessment will be a tendency in the future. As a combination of mathematical and statistical techniques, response surface methodology has been successfully applied to design optimization, response prediction and model validation. This methodology provides explicit functions to represent the relationships between the inputs and outputs of a physical system, which is also a desirable advantage in damage identification. However, so far little research has been carried out in applying the response surface methodology to structural damage identification. This paper presents a damage identification method achieved by response surface based model updating using D-optimal designs. Compared with some common designs constructing response surfaces, D-optimal designs generally require a minimum number of numerical samples and this merit is quite desirable when analysts cannot obtain enough samples. In this study, firstly D-optimal designs are used to establish response surface models for screening out non-significant updating parameters and then first-order response surface models are constructed to substitute for finite element models in predicting the dynamic responses of an intact or damaged physical system. Three case studies of a numerical beam, a tested reinforced concrete frame and a tested full-scale bridge have been used to verify the proposed method. Physical properties such as Young’s modulus and section inertias were chosen as the input features and modal frequency was the only response feature. It has been observed that the proposed method gives enough accuracy in damage prediction of not only the numerical but also the real-world structures with single and multiple damage scenarios, and the first-order response surface models based on the D-optimal criterion are adequate for such damage identification purposes.     

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.     

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.     

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.     

Optimization of contact forces in tailor-welded blanks forming process

To attain the objective of minimizing the harmful movement of the weld joint in tailor-welded blanks (TWBs) forming, a novel optimization methodology based on dynamic explicit finite element simulation is presented to determine optimum contact forces. In this methodology, forming limit diagram (FLD) models developed for different types of TWBs are treated as a criterion of constraint in optimizations. Due to the highly nonlinear nature of the forming process, response surface methodology (RSM) is utilized to construct sequential response surfaces to approximately describe the objective the constraint functions and the optimum contact forces of TWBs stamping are obtained with some successive iterations. However, a large number of numerical simulation runs are needed for optimization with higher-order approximate models or many design variables. To improve the efficiency of optimization, the space mapping (SM) technique utilizing surrogate models is integrated with RSM. Two examples are used to validate this algorithm: one optimization for TWBs stamping with the same thickness but different materials, and the other optimization for TWBs stamping with the same material but different thicknesses. The results demonstrate that the method is efficient and effective in solving contact forces optimization problems.     

Optimisation of machining parameters for turning operations based on response surface methodology

Design of experiments has been used to study the effect of the main turning parameters such as feed rate, tool nose radius, cutting speed and depth of cut on the surface roughness of AISI 410 steel. A mathematical prediction model of the surface roughness has been developed in terms of above parameters. The effect of these parameters on the surface roughness has been investigated by using Response Surface Methodology (RSM). Response surface contours were constructed for determining the optimum conditions for a required surface roughness. The developed prediction equation shows that the feed rate is the main factor followed by tool nose radius influences the surface roughness. The surface roughness was found to increase with the increase in the feed and it decreased with increase in the tool nose radius. The verification experiment is carried out to check the validity of the developed model that predicted surface roughness within 6% error.     

Development of friction force model for mineral oil basestock containing palm olein and antiwear additive

Palm oil is also another choice of vegetable that is being eyed as a potential vegetable oil in the lubricating area. This paper presents a study of the development of a fiction force model for mineral oil basestock containing palm olein, and antiwear amine phosphate as additive, tested on a four-ball tribotester. The model is developed using terms of wear load, speed and operating time. These variables were investigated using the design of experiments and utilization of the response surface methodology (RSM). Moreover, the effect of palm oil on wear scars of material tested was also discussed. This paper shows palm olein itself indeed is a good antiwear lubricant compared to mineral oil basestock (SN500), but the use of additives shows an increase in better lubrication as smaller wear scars are found out from using palm olein in the test runs.     

Determining the optimum variable blank-holder forces using adaptive response surface methodology (ARSM)

Wrinkling and fracture are main defects in sheet-metal forming. They can be reduced or eliminated by manipulating a suitable blank-holder force (BHF). But it is difficult to attain the optimum BHF during sheet-metal forming. In this article, a new optimization algorithm integrating the finite element method (FEM) and adaptive response surface methodology $(r)ARSM$(c) is presented to determinate the optimum BHF. To assure convergence, the trust region modes management strategies are used to adjust the move limit of design spaces. Finally, the optimum results of rectangular box deep drawing are given. Experiments are performed to verify the optimal result.     

Analysis and optimization of micro-geometry of miniature spur gears manufactured by wire electric discharge machining

This paper reports about the analysis and optimization of micro-geometry parameters (i.e. total profile deviation ‘F_a’ and accumulated pitch deviation ‘F_p’) of the wire electric discharge machined (WEDMed) fine-pitch miniature spur gears made of brass. Effects of four WEDM process parameters namely voltage, pulse-on time, pulse-off time and wire feed rate on the micro-geometry of the miniature gears were analyzed by conducting the experiments designed using Box–Behnken approach of response surface methodology (RSM). Analysis of variance study found all four input parameters significant. Larger deviations in profile and pitch were observed with higher values of the voltage and pulse-on time, and with lower values of wire feed rate and pulse-off time. Multi-performance optimization of WEDM parameters was done using the desirability analysis to minimize profile deviation and pitch deviation simultaneously. The values of F_a and F_p of the gear obtained by the confirmation experiment conducted at the optimized WEDM parameters were as 11.5 μm and 9.1 μm respectively. These values categorize the WEDMed gear having DIN quality number as 7 and 5 respectively for profile and pitch which are better than those obtained by the conventional miniature gear manufacturing processes.     

The use of mixture experiments in tolerance allocation problems

The response surface methodology (RSM) approach can be used to determine the optimal component tolerances in an assembly. Frequently, response surface designs such as Box-Behnken design and central composite design are used in tolerance allocation problems. In this article, mixture experiments, which are essentially constructed for designing a blend composition, are proposed instead of response surface designs in order to observe the cost values. Also some advantages and disadvantages of mixture designs are discussed.     

基于响应面法的麦弗逊悬架优化设计

用响应面法对麦弗逊悬架结构参数进行优化设计。基于多刚体动力学软件ADAMS构建麦弗逊悬架模型;在ADAMS/Insight模块中用析出法得到影响各定位参数的主要因子;接着,采用响应面法建模的中心组合设计法仿真得到响应面模型方程。并依据结果进行悬架系统的优化研究。     

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.     

Statistical analysis of repeatability in laser percussion drilling

This study investigates the effect of six parameters in the repeatability of drilled holes in laser percussion drilling process by means of statistical techniques. Peak power, pulse width, pulse frequency, number of pulses, gas pressure and focal plane position were considered as independent process parameters. Experiments were designed with the aim of reducing the number of required experiments. The response surface method was used to develop the models for required responses. The significant factors in the process were selected based on the analysis of the variance (ANOVA). The experiments were conducted in mild steel sheet with a thickness of 2 mm. Each experiment was repeated 35 times in order to investigate the repeatability of the process. The equivalent entrance diameter, percentage of standard deviation of entrance diameter (%STD Eq Dia), circularity (ratio of minimum to maximum Feret’s diameter) and its standard deviation (STD circularity) were selected as process characteristics. The %STD Eq Dia and STD circularity, respectively, show the repeatability of equivalent diameter and circularity in the process. The results show that the process of drilling smaller hole diameters is more repeatable than drilling larger holes. Pulse width, gas pressure, focal plane position, peak power and number of pulses, respectively, have significant effect on the repeatability of hole diameter and circularity. Pulse frequency has no significant effect on the repeatability of the process.     

Dry sliding wear of epoxy/cenosphere syntactic foams

Dry sliding wear behavior of epoxy matrix syntactic foams filled with 20, 40 and 60 wt% fly ash cenosphere is reported based on response surface methodology. Empirical models are constructed and validated based on analysis of variance. Results show that syntactic foams have higher wear resistance than the matrix resin. Among the parameters studied, the applied normal load (F) had a prominent effect on wear rate, specific wear rate (w_s) and coefficient of friction (μ). With increasing F, the wear rate increased, whereas w_s and μ decreased. With increase in filler content, the wear rate and w_s decreased, while the μ increased. With increase in sliding velocity as well as sliding distance, the wear rate and w_s show decreasing trends. Microscopy revealed broken cenospheres forming debris and extensive deformation marks on the wear surface.     

Surface roughness prediction for the milling of Ti–6Al–4V ELI alloy with the use of statistical and soft computing techniques

This study focuses on Ti–6Al–4V ELI titanium alloy machining by means of plain peripheral down milling process and subsequent modeling of this process, in order to predict surface quality of the workpiece and identify optimal cutting parameters, that lead to minimum surface roughness. For the purpose of accomplishing this task a set of experiments were performed on a CNC milling centre and design of experiments based on Box Behnken Design (BBD) for a three factor and three level central composite design concept was conducted. Depth of cut, cutting speed and feed rate were selected as input parameters and surface roughness was measured after each experiment performed. At first, Response Surface Methodology (RSM) was employed for establishing a quadratic relationship between input and output parameters. Analysis of variance (ANOVA) was then conducted for the evaluation of the proposed formula. RSM was also used for the optimization analysis that followed for the determination of milling cutting parameters for minimum surface roughness. The analysis indicates that the use of BBD can reduce the number of experiments needed for modeling and optimizing the milling operation of Titanium alloys. Furthermore, this method is able to provide models that can reliably be used for any cutting conditions within the limits of the input data. Finally, Artificial Neural Networks (ANN) models were developed to allow for a more robust simulation model to be built and comparison between ANN and RSM models to be performed. From the presented results, for RSM, the mean square error and the correlation coefficient were determined to be 8.633 × 10⁻³ and 0.9713, respectively; for ANN models, the corresponding values were 2 × 10⁻³ and 0.9824, for the test group of the optimum model. Simulations indicated that, although input data were too few, a considerably reliable ANN model was able to be built and despite of its complexity compared to RSM model, it was proven to be superior in terms of prediction accuracy.     

Response surface analysis of electro jet drilled holes

Modern trend towards miniaturization has given a new impetus to the development of nontraditional small hole drilling techniques. Electro jet drilling (EJD) is one such promising technique which is finding ever increasing applications in several industries including aerospace, space, medical, automobile and microfabrication (electronic and computers). The present study investigates the relationships and parametric interactions between three controllable variables on the material removal, radial overcut and hole taper in the EJD process. Experiments have been conducted on SUPERNI 263A workpieces. Applied voltage, electrolyte concentration and feed rate were selected as independent process variables. The responses have been modelled using a response surface model based on a central composite rotatable experimental design. The significant coefficients were obtained by performing analysis of variance (ANOVA) at 1% and 5% level of significance. It was found that applied voltage, electrolyte concentration and feed rate have significant effect on the material removal, radial overcut and hole taper.