Issue 
Manufacturing Rev.
Volume 8, 2021



Article Number  7  
Number of page(s)  10  
DOI  https://doi.org/10.1051/mfreview/2021005  
Published online  02 March 2021 
Research Article
Optimisation of micro Wbending process parameters using Ioptimal designbased response surface methodology
^{1}
School of Mechanical Engineering, Sichuan University, Chengdu, PR China
^{2}
Centre for Precision Manufacturing, Department of Design, Manufacturing and Engineering Management, The University of Strathclyde, Glasgow, UK
^{3}
Malaysian Institute of Aviation Technology, Universiti Kuala Lumpur, Dengkil, Malaysia
^{*} email: yangtze86@163.com
Received:
29
January
2021
Accepted:
3
February
2021
There is an increasingly recognised requirement for high dimensional accuracy in microbent parts. Springback has an important influence on dimensional accuracy and it is significantly influenced by various process parameters. In order to optimise process parameters and improve dimensional accuracy, an approach to quantify the influence of these parameters is proposed in this study. Experiments were conducted on a micro Wbending process by using an Ioptimal design method, breaking through the limitations of the traditional methods of design of experiment (DOE). The mathematical model was established by response surface methodology (RSM). Statistical analysis indicated that the developed model was adequate to describe the relationship between process parameters and springback. It was also revealed that the foil thickness was the most significant parameter affecting the springback. Moreover, the foil thickness and grain size not only affected the dimensional accuracy, but also had noteworthy influence on the springback behaviour in the micro Wbending process. By applying the proposed model, the optimum process parameters to minimize springback and improve the dimensional accuracy were obtained. It is evident from this study that the Ioptimal designbased RSM is a promising method for parameter optimisation and dimensional accuracy improvement in the microbending process.
Key words: Microforming / microbending / springback / response surface methodology / Ioptimal design / optimisation
© X. Liu et al., Published by EDP Sciences 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
The rapid development of microforming processes, including the microbending process, has focused attention on the requirements for fabricating micro parts with high dimensional accuracy and good forming quality [1,2]. With respect to the microbending process, springback, caused by the elastic recovery after releasing the load, is usually adopted to evaluate the dimensional accuracy and forming quality of microbent parts. In general, the springback of microbent parts is closely associated with the process parameters selected [3,4]. Therefore, establishing a mathematical model to investigate the relationship between process parameters and springback and to explore the optimum parameter combination, is of utmost importance to improve the dimensional accuracy and maintain good forming quality of microbent parts.
In recent years, a number of studies have attempted to explore the influences of various parameters on springback. Chikalthankar et al. presented a review on the influences of several parameters, such as punch angle, punch radius, material thickness and rolling direction on the springback of microbent parts [5]. Le et al. conducted experiments in a Ubending process to study the influences of different punch radii and the gap between punch and die on springback [6]. Micro Ubending experiments were also carried out by Wang et al. to examine the influence of size effects on the springback behavior [7]. It was found that the springback angle increased with a decrease of sheet thickness. Xu et al. studied the influences of punch angle, material thickness and grain size on springback in the micro Vbending process. Experimental results showed that the amount of springback decreased with decreasing grain size and punch angle [8]. Choudhury et al. employed the orthogonal experimental method to investigate the influences of 11 parameters in the micro Vbending process. It was suggested that the punch holding time, material type and lubrication condition were the three key factors affecting springback [9]. Gau et al. carried out threepoint bending experiments to assess the effects of grain size and brasssheet thickness on springback [10].
Considering that the relationship between the process parameters and springback is nonlinear, some researchers have committed to conducting research by using statistical methods [11–13]. Liu et al. utilized the artificial neural network (ANN) method combined with a genetic algorithm to establish a springback model to study the relationship between material thickness, bending radius and springback [14]. In addition, other ANN methods, such as backpropagation neural network (BPNN) and counter propagation neural network (CPNN), were used by Teimouri et al. to develop models to investigate the influences of punch tip radius, material thickness and rolling direction on springback of CK67 steel sheet in the Vbending process [15]. Dib et al. selected and compared several methods including multilayer perceptron (MLP), decision tree (DT), random forest (RF), support vector machine (SVM) and Knearest neighbours (KNN) to explore the influences of sheet thickness, material properties and blank holder force on springback in the Ubending process [16]. Khamneh et al. established a mathematical model using Doptimal designbased response surface methodology (RSM) to optimise the parameters of springback in a creep age forming process, providing a novel approach to solve the parameter optimisation problem [17].
To date, most of these studies have predominantly concentrated on the qualitative analysis of the influence of process parameters on springback. Few studies however have provided a quantitative analysis of process parameters. Although ANN has become the most popular method to analyse the influence of process parameters, the equation of a mathematical model could not be obtained. Moreover, previous studies have mainly dealt with conventional bending processes, such as Vbending, Ubending and threepoint bending, complex bending processes have received little attention. This study therefore set out to develop a method to achieve the parameter optimisation and improve the dimensional accuracy in a micro Wbending process. In this study, a computergenerated design of experiment (DOE), an Ioptimal DOE, was employed to solve the problem of an irregular experiment matrix during the design of experiment. Subsequently, a mathematical model based on the Ioptimal designbased RSM was established, and its adequacy was evaluated and validated. The parameter optimisation was further performed and the optimum combination of parameters in the micro Wbending process was obtained.
2 Experimentation
2.1 Material preparation
Brass is widely used in microforming due to its good mechanical properties and excellent forming performance. In this study CuZn37 brass foils from cold rolling were adopted as the experimental material, with the thickness ranging from 25 to 100 μm. With a view to eliminating the effects of rolling texture and obtaining various grain sizes annealing treatments were conducted under temperatures ranging from 450 to 650 °C with 1–3 h' holding time. All the annealing treatment were carried out in the protection condition to prevent the formation of the oxidation layer on the material. The average grain sizes under corresponding thicknesses and annealing conditions are listed in Table 1.
Grain sizes under corresponding thicknesses and annealing conditions (μm).
2.2 Micro Wbending process
The Wshaped microbent parts have been employed in the fields of fiberoptic communication, fiberoptic sensing systems and some electronics products. To fabricate this kind of microbent part, a micro Wbending process was proposed. The micro Wbending experiments were carried out on a benchtop microforming machine, equipped with the Wshaped punch and die, as shown in Figure 1. It is shown that a bending angle of 80° was to be achieved for this micro part. The punch stroke is measured by a positional encoder with the verticalpositionresolution of 0.1 µm.
Fig. 1 (a) Microforming machine; (b) schematic illustrations of bending punch and die; (c) Wshaped microbent part. 
2.3 Response surface methodology
Response surface methodology is a comprehensive analysis method integrating modelling, optimisation and prediction, which is developed on the basis of mathematical statistics theory [18–21]. It is well suited when a response is influenced by several variables. The objective of applying RSM is to simultaneously optimise the levels of these variables to obtain the best response. To achieve this objective a linear or quadratic polynomial function is usually employed to establish the mathematical models between the response and the variables.(1) (2)where y is the estimated response, x _{ i } is the variable, k represents the number of variables, β _{0} is the constant, β _{ i }, β _{ ii } and β _{ ij } represent the coefficients of the linear, quadratic and the interaction parameters, respectively. ϵ describes the residual related to the experiments.
2.4 Ioptimal design of experiments
Before applying the response surface methodology, it is first necessary to select the process parameters and their corresponding levels in the micro Wbending process. According to our preliminary pilot investigations, foil thickness, punch stroke, punching frequency and grain size do have significant influences on the springback of the Wshaped micro parts [22,23]. Regarding this there should be at least three levels for each parameter when applying RSM, 3–4 levels were selected for each parameter, as listed in Table 2.
With the consideration that the selected parameters had different levels of contributions to an irregular experimental matrix, and the grain sizes of different foil thicknesses varied considerably under the same conditions, the Ioptimal design of experiment was adopted in this study with only 56 runs at 3–4 factor levels. It is also known as IVoptimal DOE, which is a novel computergenerated optimal design method recommended to accomplish response surface designs with the aim to optimising the factor settings and achieving a better accuracy in the estimation of the response [24–26]. Compared to the Taguchi method and full factorial method which may be used for regular designs (e.g. each factor may have a same number of the level), the Ioptimal DOE is more appropriate for the irregular experimental matrix. By applying the Ioptimal DOE, 44 runs of four process parameters at different levels were designed. Replicates and extra model points were additionally added to reduce the standard error and estimate lack of fit, thus, improving the accuracy of the mathematical model established. The Ioptimal designed matrix is presented in Table 3.
Process parameters and their corresponding levels.
Ioptimal DOE and corresponding response.
3 Results, analysis and discussion
According to the Ioptimal DOE, 56 tests were carried out to investigate the influence of the parameters on springback. The experimental results are shown in Table 3. It was demonstrated that both positive and negative springback behaviour occurred in the experiments. A visionmeasuring microscope, Mitutoyo Quick Scope, was used to measure the final bent angle. Thus, the springback was calculated based on the measured final bent angle minus 80°. With a view to ensuring the accuracy of measurement each Wshaped micro part was measured three times and the results were then averaged.
3.1 Establishment of the mathematical model
In this study, DesignExpert 8 (StatEase Inc.) software was employed to perform the regression and graphical analysis, and the analysis of variance (ANOVA). In order to choose the best model which could fit the experimental data well, linear, twofactor interaction (2FI), quadratic and cubic models were analysed and compared. The statistical analysis results of the models are listed in Table 4.
In Table 4, there are six indices to evaluate the adequacy of the abovelisted four models. If the Pvalue is smaller than 0.05, it indicates the factors or their interaction effects significantly influence the response. The second index is R^{2}, which interprets how well the model fits. The closer the R^{2} to one, the better the model fits the data. The adjusted R^{2} () is the third index used to calculate the amount of variation around the mean of the model. The predicted R^{2} is then adopted to estimate how accurately the model predicts a response value. PRESS is the predicted residual error sum of squares. The smaller the PRESS is, the more accurate the model will be. Moreover, it is expected to be a good fit, if the lackoffit Pvalue is not significant.
It is evident from the results obtain that R^{2} of the quadratic model is higher than that of the linear and 2FI models. is also in good agreement with . Furthermore, in the quadratic model, the Pvalue is significant and the PRESS is the smallest with an insignificant lackoffit compared to the other models. Consequently, the quadratic model was selected since it could shed light on the relationship between several process parameters and the response more accurately. Although R^{2} and of the cubic model were higher than those of the quadratic model, it was still not chosen to develop the mathematical model since it was aliased.
After selecting the quadratic model as the regression method, the mathematical relationship was established between the process parameters and springback, which could be expressed in equation (3). The established mathematical model is subject to some constraints: 25 µm ≤ A (foil thickness) ≤ 100 µm, 9.582 mm ≤ B (punch stroke) ≤ 9.688 mm, 0.15 Hz ≤ C (punching frequency) ≤ 0.25 Hz, 26 µm ≤ D (grain size) ≤ 105.7 µm.(3)
Comparisons of several RSM models for springback.
3.2 Adequacy evaluation of the mathematical model
The adequacy of the established quadratic model was evaluated by employing the ANOVA and the results are presented in Table 5.
It is shown in the table that Pvalue of the developed model for springback is smaller than 0.05, suggesting the model is significant at a 95% confidence interval. Meanwhile, the ANOVA results reveal that the foil thickness, punch stroke, punching frequency and grain size have significant influence on the response. In addition, the lackoffit Pvalue 0.1449 is more than 0.05, which is not significant compared with pure error, demonstrating that the experimental error is mainly caused by random error. This model could be further used to analyse and predict the response quantitatively. Furthermore, there are other indices used to evaluate the adequacy of the developed model. R^{2} of the model is 0.9406, which is very close to one, indicating the model has a good fit performance between the parameters and the response. Adj R^{2} (0.9204) is in good agreement with Pred R^{2} (0.8921), implying the model has a high prediction accuracy and a good consistency between the predicted values and the experimental values. The adequacy precision ratio of the model is 29.0290 (Adeq Precision > 4), which indicates the model has excellent discrimination. The reliability of the developed model is additionally checked by drawing the normal probability plot of residuals. As illustrated in Figure 2, the experimental errors distribute normally, indicating a high degree of fit between the model and the experimental results.
ANOVA results of RSM model for springback.
Fig. 2 Normal probability plot of residuals for percentage change in springback. 
3.3 Response surface analysis
It is suggested from the evaluation of the adequacy of the established model that the quadratic model of springback has good fitting performance, small experimental error and high prediction accuracy. Accordingly, it could be used to investigate the influence of the main effects and the interaction effects of the process parameters on springback of the Wshaped microbent parts.
3.3.1 Influence of the main effects of parameters on springback
The main effects of parameters on springback were plotted by Minitab17 software. As shown in Figure 3, when the foil thickness increases from 25 to 50 µm, the amount of springback decreases sharply, denoting the dimensional accuracy increases. When the thickness increases from 50 to 75 µm, the springback behaviour of the micro parts changes from positive springback to negative springback with the amount of negative springback increasing significantly. As the thickness continues to increase to 100 µm, the amount of negative springback only shows a small increase, indicating that the dimensional accuracy of the microbent parts has a slight decline. In addition, punch stroke also presents a similar influence to that from the foil thickness on springback. With the increase of punch stroke, the dimensional accuracy of microbent parts increases first and then decreases. However, punching frequency displays an opposite influence trend compared to the above two parameters. As the frequency increases, the amount of negative springback decreases gradually. When the frequency is equal to 0.2 Hz, the springback of the micro part is close to zero, exhibiting high dimensional accuracy. Then as the punching frequency continues to increase, the amount of positive springback increases, demonstrating that the dimensional accuracy decreases gradually. It can also be seen from Figure 3 that the grain size of the material also has a significant effect on the dimensional accuracy. The amount of positive springback decreases with the increase of grain size. When the grain size increases to Level 3, a slight negative springback behaviour is observed. The amount of negative springback then increases significantly with the increase of grain size. Consequently, it could be noticed in Figure 3 that the foil thickness is the most critical parameter affecting the springback behaviour and the dimensional accuracy of microbent parts.
Fig. 3 Main effects plot for springback. 
3.3.2 Influence of the interaction effects of parameters on springback
It can be observed in Table 5 that the interactions between foil thickness and punch stroke, foil thickness and punching frequency, foil thickness and grain size, punch stroke and grain size, punching frequency and grain size, do have significant influences on the response. Meanwhile, it also can be seen in the main effects plot for springback that the foil thickness influences the springback most. Therefore, the 3D response surface graphs between foil thickness and the other three parameters were plotted in Figure 4, and these are utilized to explore the influence of interaction effects of parameters on springback.
Figure 4a shows the 3D response surface plot of the interaction effect of foil thickness and punch stroke when the punching frequency is 0.2 Hz and grain size remains constant at Level 3. It can be observed that if the punch stroke remains at 9.582 mm, the springback amount varies by 13.339° (from 9.592° to −3.747°) when the foil thickness increases from 25 to 100 µm. If the foil thickness remains at 25 µm, the springback amount varies by 5.351° (from 9.592° to 4.241°) when the punch stroke increases from 9.582 to 9.688 mm. Hence, it can be noted that the influence of the punch stroke is less than that of the foil thickness.
The surface plot of the interaction effect between the foil thickness and punching frequency is illustrated in Figure 4b. It reveals that when the foil thickness is constant at 25 µm, the amount of positive springback increases significantly (from 0.039° to 9.748°) with the increase of punching frequency, whereas the amount of negative springback decreases slightly (from −6.225° to −4.655°) with an increasing punching frequency when the foil thickness is constant at 100 µm. Additionally, when the foil thickness is 25 µm and the punching frequency is 0.15 Hz, the springback is 0.039°, presenting good dimensional accuracy of the microbent parts.
Figure 4c depicts the interaction plot of thickness and grain size on springback. When the punch stroke and punching frequency are kept at their intermediate levels, the parts with a thickness of 25 µm present positive springback behaviour at all the levels of grain size, and the springback amount decreases with increasing grain size, indicating increasing dimensional accuracy. Conversely, the negative springback behaviour is exhibited when the foil thickness is 100 µm, and the springback amount increases with the increase of grain size. From this figure, it can be noticed that the springback behavior with different thicknesses is not consistent, suggesting that the springback behavior and dimensional accuracy are more sensitive to the foil thickness than the grain size.
Fig. 4 Interaction effects of parameters on springback. (a) response surface plot of interactions between thickness and stroke on springback; (b) response surface plot of interactions between thickness and frequency on springback; (c) interaction plot of thickness and grain size on springback. 
3.4 Optimisation of response
The objective of conducting this parametric investigation into the springback in the micro Wbending process is to achieve desired dimensional accuracy with optimised process parameters. Therefore, the response surface optimisation was performed to obtain the optimum combination of the process parameters, minimise the springback amount and improve the dimensional accuracy of microbent parts. RSM optimisation results for springback are shown in Table 6. The goal of the optimisation is to achieve the minimisation of the springback amount. The optimum process parameters are found to be a foil thickness of 75 µm, punch stroke of 9.635 mm, punching frequency of 0.2 Hz and Level 1 of the grain size. The corresponding springback after optimisation is −0.047°, as presented in Figure 5.
RSM optimisation result for springbak.
Fig. 5 Contour plot of the optimised springback. 
4 Conclusions
An Ioptimal DOEbased response surface methodology was developed in this study to optimise the parameters of a micro Wbending process. This proposed method offers an efficient approach to achieve the optimisation of various process parameters at different levels, which could not be solved by traditional DOE. By applying this method, a mathematical model was established to describe the relationship between the process parameters and the springback, which was used to represent the dimensional accuracy of microbent parts. Afterwards, the adequacy of the developed model was evaluated and validated. The influence of the main and interaction effects of the parameters on springback were subsequently analysed. Optimisation was also performed to determine the optimum combination of process parameters. Based on the results obtained, the following conclusions can be drawn:

The statistical analysis and comparison results of several RSM models have suggested that the quadratic model is most applicable to describe the relationship between process parameters and the response.

A mathematical model was established based on the quadratic polynomial regression method. Statistical analysis has proved that the developed model is evidently significant at a 95% confidence interval with good fitting performance (R^{2} is 0.9406), small experimental errors (PRESS is 217.3, Std. Dev. is 1.71) and high prediction accuracy (Pred R^{2} is 0.8921).

It can be drawn from the analysis of the main parameter effects of the foil thickness, punch stroke and grain size that they have demonstrated similar influences on the springback. That is the amount of positive springback decreases and the amount of negative springback increases with the increase of the corresponding parameter level, whereas the punching frequency exhibits an opposite tendency. In addition, foil thickness is the most significant parameter affecting springback in the micro Wbending process.

Analysis of the interactions between the foil thickness and punch stroke, foil thickness and punching frequency, foil thickness and grain size, have revealed their statistically significant influences on springback. It can also be noticed that the foil thickness and grain size not only affect the dimensional accuracy, but also have an influence on the springback behaviour in the micro Wbending process.

RSM optimisation shows that the optimum process parameters to minimise the springback amount and achieve a better dimensional accuracy of microbent parts are 75 µm, 9.635 mm, 0.2 Hz and Level 1 for foil thickness, punch stroke, punching frequency and grain size, respectively.
Taken together, the research that was demonstrated experimentally and statistically in this study has verified that the Ioptimal DOEbased response surface methodology is an effective and adequate method for the optimisation of micro Wbending process parameters. More broadly, the present investigation is important for conducting further indepth research on the dimensional accuracy evaluation and quality control of the micro parts fabricated by various forming processes. In particular, further studies regarding the influences of the grain size on the dimensional accuracy of the micro parts formed by microforming would be worthwhile.
Acknowledgments
The authors would like to thank the financial support from Sichuan Science and Technology Program (Grant No. 2018JY0573). The authors also would like to express their sincere appreciation to The University of Strathclyde for providing the facility and support to the experiment.
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Cite this article as: Xiaoyu Liu, Xiao Han, Shiping Zhao, Yi Qin, WanAdlan WanNawang, Tianen Yang, Optimisation of micro Wbending process parameters using Ioptimal designbased response surface methodology, Manufacturing Rev. 8, 7 (2021)
All Tables
All Figures
Fig. 1 (a) Microforming machine; (b) schematic illustrations of bending punch and die; (c) Wshaped microbent part. 

In the text 
Fig. 2 Normal probability plot of residuals for percentage change in springback. 

In the text 
Fig. 3 Main effects plot for springback. 

In the text 
Fig. 4 Interaction effects of parameters on springback. (a) response surface plot of interactions between thickness and stroke on springback; (b) response surface plot of interactions between thickness and frequency on springback; (c) interaction plot of thickness and grain size on springback. 

In the text 
Fig. 5 Contour plot of the optimised springback. 

In the text 
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