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The purpose of this paper is to develop a mathematical model for surface roughness and delamination through response surface methodology (RSM) and analyse the influences of the entire individual input machining parameters (cutting speed, fibre orientation angle, depth of cut and feed rate) on the responses in milling of glass fibre reinforced plastics (GFRP) composites with solid carbide end mill cutter coated with PCD.

Four factors, five level central composites and a rotatable design matrix in response surface methodology were employed to carry out the experimental investigation. “Design Expert 8.0” software was used for regression and graphical analysis of the data were collected. The optimum values of the selected variables were obtained by solving the regression equation and by analyzing the response surface contour plots. Analysis of variance (ANOVA) was applied to check the validity of the model and for finding the significant parameters.

The developed second order response surface model was used to calculate the surface roughness and delamination of the machined surfaces at different cutting conditions with the chosen range with 95 per cent confidence intervals. Using such a model, remarkable savings in time and cost can be obtained.

The effect of fibre orientation during milling of GFRP laminates using RSM has not been previously attempted for analysis.

Determining whether a set of tolerances on a part can be met by a rapid prototyping (RP) machine is often difficult. To achieve a set of tolerances as closely as possible, relationships between part geometry, tolerances, and process variables must be understood quantitatively. This paper presents an empirical model for stereolithography apparatus (SLA) accuracy, as specified by geometric tolerances, and a process planning method based on response surface methodology and multiobjective optimization. Response surfaces are used to capture the relationships among part surfaces, tolerances, and process variables. These response surfaces were generated by extensive design‐of‐experiment studies for a variety of geometries. An annotated STL data format is also presented that enables the inclusion of tolerance and surface information in faceted representations. Application of the accuracy models and process planning method is illustrated on one part.

In a structural optimization design-based single-level response surface, the number of optimal variables is too much, which not only increases the number of experiment times, but also reduces the fitting accuracy of the response surface. In addition, the uncertainty of the optimal variables and their boundary conditions makes the optimal solution difficult to obtain. The purpose of this paper is to propose a method of fuzzy optimization design-based multi-level response surface to deal with the problem.

The main optimal variables are determined by Monte Carlo simulation, and are classified into four levels according to their sensitivity. The linear membership function and the optimal level cut set method are applied to deal with the uncertainties of optimal variables and their boundary conditions, as well as the non-fuzzy processing is carried out. Based on this, the response surface function of the first-level design variables is established based on the design of experiments. A combinatorial optimization algorithm is developed to compute the optimal solution of the response surface function and bring the optimal solution into the calculation of the next level response surface, and so on. The objective value of the fourth-level response surface is an optimal solution under the optimal design variables combination.

The results show that the proposed method is superior to the traditional method in computational efficiency and accuracy, and improves 50.7 and 5.3 percent, respectively.

Most of the previous work on optimization was based on single-level response surface and single optimization algorithm, without considering the uncertainty of design variables. There are very few studies which discuss the optimization efficiency and accuracy of multiple design variables. This research illustrates the importance of uncertainty factors and hierarchical surrogate models for multi-variable optimization design.

Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).

In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.

The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.

This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

The purpose of this paper is to develop a mathematical model for the surface delamination through response surface methodology (RSM) and analyse the influences of the entire individual input machining parameters (cutting speed, feed rate and depth of cut) on the responses in milling of carbon fibre reinforced polymer (CFRP) composites with solid carbide end mill cutter coated with polycrystalline diamond.

Three factors, three level face-centered central composite design in RSM was employed to carry out the experimental investigation. The “Design Expert 8.0” software was used for regression and graphical analysis of the data collected. The optimum values of the selected variables were obtained by solving the regression equation and by analyzing the response surface contour plots. Analysis of variance was used to check the validity of the model and for finding the significant parameters.

The developed second-order response surface model is used to calculate the delamination of the machined surfaces at different cutting conditions with the chosen range with 95 per cent confidence intervals. Using such model, one can obtain remarkable savings in time and cost.

The effect of machining parameters on surface delamination during milling of CFRP composites using RSM has not been previously analysed.

In a multistage process, the final quality in the last stage not only depends on the quality of the task performed in that stage but is also dependent on the quality of the products and services in intermediate stages as well as the design parameters in each stage. One of the most efficient statistical approaches used to model the multistage problems is the response surface method (RSM). However, it is necessary to optimize each response in all stages so to achieve the best solution for the whole problem. Robust optimization can produce very accurate solutions in this case.

In order to model a multistage problem, the RSM is often used by the researchers. A classical approach to estimate response surfaces is the ordinary least squares (OLS) method. However, this method is very sensitive to outliers. To overcome this drawback, some robust estimation methods have been presented in the literature. In optimization phase, the global criterion (GC) method is used to optimize the response surfaces estimated by the robust approach in a multistage problem.

The results of a numerical study show that our proposed robust optimization approach, considering both the sum of square error (SSE) index in model estimation and also GC index in optimization phase, will perform better than the classical full information maximum likelihood (FIML) estimation method.

To the best of the authors’ knowledge, there are few papers focusing on quality-oriented designs in the multistage problem by means of RSM. Development of robust approaches for the response surface estimation and also optimization of the estimated response surfaces are the main novelties in this study. The proposed approach will produce more robust and accurate solutions for multistage problems rather than classical approaches.

There is growing evidence of a knowledge gap in the association of maintenance with production activities in bottling plants. Indeed, insights into how to jointly optimise these activities are not clear. In this paper, two optimisation models, Taguchi schemes and response surface methodology are proposed.

Borrowing from the “hard” total quality management elements in optimisation and prioritisation literature, two new models were developed based on factor, level and orthogonal array selection, signal-to-noise ratio, analysis of variance and optimal parametric settings as Taguchi–ABC and Taguchi–Pareto. An additional model of response surface methodology was created with analysis on regression, main effects, residual plots and surface plots.

The Taguchi S/N ratio table ranked planned maintenance as the highest. The Taguchi–Pareto shows the optimal parametric setting as A4B4C1 (28 h of production, 30.56 shifts and 37 h of planned maintenance). Taguchi ABC reveals that the planned maintenance and number of shifts will influence the outcome of production greatly. The surface regression table reveals that the production hours worked decrease at a value of planned maintenance with a decrease in the number of shifts.

This is the first time that joint optimisation for bottling plant will be approached using Taguchi–ABC and Taguchi–Pareto. It is also the first time that response surface will be applied to optimise a unique platform of the bottling process plant.

The paper aims to develop a mathematical model for delamination and surface roughness during end milling by using response surface methodology (RSM) and to determine how the input parameters (cutting speed, depth of cut, helix angle and feed rate) influence the output response (delamination and surface roughness) in machining of hybrid glass fibre reinforced plastic (GFRP; Abaca and Glass) composite using solid carbide end mill cutter.

Four-factor, three-level Taguchi orthogonal array design in RSM is used to carry out the experimental investigation. The “Design Expert 8.0” is used to analyse the data collected graphically. Analysis of variance is carried out to validate the model and for determining the most significant parameter.

The feed rate is the cutting parameter which has greater influence on delamination (88.39 per cent), and cutting speed is the cutting parameter which has greater influence on surface roughness (53.42 per cent) for hybrid GFRP composite materials. Both surface roughness and delamination increase as feed rate increases, which means that the composite damage is larger for higher feed rates.

Effect of milling of hybrid GFRP composite on delamination and surface roughness with various helix angles of solid carbide end mill has not been analysed yet using RSM.

This paper aims to focus on an experimental study of surface roughness, dimensional accuracy and time of fabrication of parts produced by fused deposition modelling (FDM) technique of additive manufacturing. The fabricated parts of acrylonitrile butadiene styrene (ABS) material have pyramidal and conical features. Influence of five process parameters of FDM, namely, layer thickness, wall print speed, build orientation, wall thickness and extrusion temperature is studied on response characteristics. Furthermore, regression models for responses are developed and significant process parameters are optimized.

Comprehensive experimental study is performed using response surface methodology. Analysis of variance is used to investigate the influence of process parameters on surface roughness, dimensional accuracy and time of fabrication in both outer pyramidal and inner conical regions of part. Furthermore, a multi-response optimization using desirability function is performed to minimize surface roughness, improve dimensional accuracy and minimize time of fabrication of parts.

It is found that layer thickness and build orientation are significant process parameters for surface roughness of parts. Surface roughness increases with increase in layer thickness, while it decreases initially and then increases with increase in build orientation. Layer thickness, wall print speed and build orientation are significant process parameters for dimensional accuracy of FDM parts. For the time of fabrication, layer thickness and build orientation are found as significant process parameters. Based on the analysis, statistical non-linear quadratic models are developed to predict surface roughness, dimensional accuracy and time of fabrication. Optimization of process parameters is also performed using desirability function.

The present study is restricted to the parts of ABS material with pyramidal and conical features only fabricated on FDM machine with delta configuration.

From the critical review of literature it is found that some researchers have made to study the influence of few process parameters on surface roughness, dimensional accuracy and time of fabrication of simple geometrical parts. Also, regression models and optimization of process parameters has been performed for simple parts. The present work is focussed on studying all these aspects in complicated geometrical parts with pyramidal and conical features.

The advancement of additive manufacturing technologies has resulted in producing parts of high quality and reduced manufacturing time. This paper aims to achieve a simultaneous optimal solution for build time and surface roughness as the output data and also to find the best values for the input data consisting of build orientation, extrusion width, layer thickness, infill percentage and raster angle.

For this purpose, the effects of process parameters on the response variables were investigated by the design of experiments approach to develop empirical models using response surface methodology. The experimental parts of this research were conducted using an inexpensive and locally assembled fused filament fabrication (FFF) machine. A total of 50 runs for 4 different geometries, namely, cylinder, prism, 3DBenchy and twist gear vase, were performed using the rotatable central composite design, and each process parameters were investigated in two levels to develop empirical models. Also, a novel optimization method, namely, the posterior-based method, was accomplished to find the best values for the response variables.

The results demonstrated that not only the build orientation and layer thickness have notable effects on both response variables but also build time is dependent on extrusion width and infill percentage. Low infill percentage and high extrusion width resulted in increasing build time. By reducing layer thickness and infill percentage while increasing extrusion width, parts of high-quality surface finish and reduced built time were produced. Optimum process parameters were found to be of build direction of 0°, extrusion width of 0.61 mm, layer thickness of 0.22 mm, infill percentage of 20% and raster angle of 0°.

Through the developed empirical models and by minimizing build orientation and layer thickness, and also considerations for process parameters, parts of high-quality surface finish and reduced built time could be produced on FFF machines. To compensate for increased build time because of reduction in layer thickness, extrusion width and infill percentage must have their maximum and minimum value, respectively.