Using the Taguchi Method for Experimental and Numerical Investigations on the Square-Cup Deep-Drawing Process for Aluminum/Steel Laminated Sheets

Using the Taguchi Method for Experimental and Numerical Investigations on the Square-Cup Deep-Drawing Process for Aluminum/Steel Laminated Sheets

M. Mahmoodi ^*, H. Sohrabi

School of Mechanical Engineering, Semnan University, Semnan, Iran

1. Introduction   

        Deep drawing is a process for the formation of sheet metals, in which a blank is drawn radially by the mechanical action of a punch into a die or forming cavity. This process involves several input parameters, including the die shoulder radius (DR), punch nose radius (PR), blank holder force (BHF), and the clearance between a punch and die (CPD).

        Because of the combination of special characteristics in multilayer sheets, such as corrosion resistance and electrical resistance, these materials have been extensively used in modern industries, including automobile and aerospace manufacturing [1]. Investigating the behavior of multilayer and, more specifically, double-layer sheet metals is essential to the deep-drawing process. By means of stretching and deep-drawing processes, Harhash et al. [2] studied the mechanical properties and formation behaviors of laminated steel/polymer sandwich panels.

        Wrinkling and tearing are two common defects encountered in the deep-drawing process. Preventing these defects necessitates the use of an appropriate BHF value. Previous research confirmed the key role of BHF in the creation or prevention of the aforementioned problems [3, 4]. Kitayama et al. [5] used a system of adjustable BHFs and closed-loop algorithms to achieve an optimal BHF in square-section deep drawing. Savas et al. [6] examined the effects of die and blank holder shapes on the quality of deep drawing. In their experimental investigations, the authors demonstrated that the angle between a die surface and blank affects the distribution of BHF and forming force. Asadian et al. [7] probed into the deep drawing of tailor-welded interstitial free steel blanks with non-uniform BHF.

Aside from BHF, PR and DR are two other effective parameters in sheet metal formation via deep drawing; the optimum values of these parameters figure importantly in the quality of produced parts. Behrens [8] analyzed the effects of different tool geometries on the limiting drawing ratio in micro deep drawing.

        Many researchers have used the finite element method to obtain appropriate parameters [9–12]. Sezek et al. [13], for example, used finite element simulation and experimental tests to investigate the deep drawing of blank sheets with circular sections. Their objective was to explore effective parameters and thereby improve the drawing ratio of workpieces and reduce BHF. Watiti et al. [14] applied experimental and finite element analyses to develop a methodology for determining the forming limits of AZ31 magnesium alloy and optimal forming parameters, such as PR, temperature, profile radius, and forming depth. Ghaffari et al. [15] developed a finite element model as a coupled thermomechanical model for the deep drawing of AZ31 alloy sheet. Castillo et al. [16] applied theoretical, numerical, and experimental techniques to obtain the allowable height for the deep drawing of single-layer steel sheets with square sections. Hashemi et al. [17] studied the probability of failure in hydrodynamic deep drawing. Neto et al. [18] conducted a finite element analysis of the reverse deep drawing of a cylindrical cup, for which the authors modeled forming tools as either rigid or deformable bodies to evaluate the elastic deformation of the tools.

        Padmanabhan et al. [19] used the Taguchi technique to explore the effects of DR, BHF, and friction coefficient on the thickness variations of single-layer blanks. Using the same technique, Reddy et al. [20] studied the influence of DR, BHF, and a parameter disregarded by Padmanabhan et al., namely, PR [19].

        Of the few studies directed toward multilayer sheet metal forming, that of Morovvati et al. [1] involved the use of numerical and experimental techniques to investigate the wrinkling and tearing defects that occur in double-layer metal sheets during the deep drawing of circular sections. Atrian and Fereshteh-Sanaiee [21] carried out finite element analysis and experimental tests to study the deep drawing of double-layer aluminum/brass sheets with circular sections. The authors determined the location of tearing that occurred in the experiments.

        The purpose of the present work was to investigate the wrinkling and tearing defects that occur in a double-layer metal sheet during square-section deep drawing. This research also examined the effects of PR, DR, BHF, CPD, and layer arrangement (LA) on the aforementioned defects. To these ends, Taguchi’s design of experiments was used and a finite element simulation was carried out. The simulation results were then validated by experimental tests.

1. Materials and methods

        A double-layer blank sheet made of St14 steel and 1200 aluminum was used in the experiments. Each layer of the material was 0.7 mm thick, and the initial blank was square with a dimension of 80 mm. The aluminum/steel laminated sheet was produced by explosive forming [22, 23]. The mechanical properties of the layers are listed in Table 1.

        A schematic of the die fabricated for the experiments is shown in Figure 1, and the experimental die setup is depicted in Figure 2. This assembly includes the die, punch, blank holder, and guide bars. The die is made of CK45 steel. Its surface was hardened through carburization at 900°C for 9 hours, after which it was polished to prevent wear and corrosion.

        The coefficients of friction between different contact surfaces are presented in Table 2. The blank holder system of the die was designed in such a way that a variable BHF of 2000 to 10000 N can be achieved. The tests were performed using a 200-ton hydraulic press with a speed of 0.17 mm/s.

        ABAQUS software and explicit analysis were adopted to simulate the deep-drawing process for the selected material. Figure 3 illustrates the geometrical model of the die used in the square-section deep-drawing process. Given geometrical symmetry, only one-quarter of the entire model was analyzed.

        In the simulation, fixed boundary conditions (zero displacement) were applied to the die. The blank holder and punch were assigned one degree of freedom in the vertical direction (punch axis). The two-layer sheet was modeled in the shell plane using four-node shell elements (S4R), and the “tie” constraint was defined. The die, punch, and blank holder were modeled using rigid surface elements (R3D4). The size of the elements used to model the sheets was 1 mm. As indicated in Figure 4, mesh size was obtained by using a mesh sensitivity diagram in accordance with changes in sheet thickness at a specific point for different element sizes.

Table 1. Mechanical properties of steel and aluminum sheets

Table 2. Coefficients of friction between contact surfaces [1]

        When difficulty is encountered in expressing the relationship between the input and output parameters of a process as a clear mathematical model, optimization techniques and design of experiments must be used to address the difficulty. Design of experiments is a scientific approach in which targeted changes in input factors affect a process or product. The resultant changes in the output are then examined, and extensive information is gained about the process or product.

        This research employed Taguchi’s design of experiments to explore the effects of several input parameters on the quality of double-layer samples produced via square-section deep drawing. Signal-to-noise (S/N) ratio analysis was then carried out, and the variations in output functions with respect to the input parameters were determined. ANOVA was then performed to identify the percentage of contribution of each parameter [24].

        As previously stated, the input parameters considered in this work were PR, DR, BHF, CPD, and LA. Different values for these parameters are listed in Table 3. On the basis of preliminary tests conducted in a laboratory, the appropriate parameters and corresponding input values were chosen.

        The number of tests proposed in the Taguchi method for examining the effects of input parameters on the quality of final samples produced by deep drawing is 16. These tests are listed in Table 4. Wrinkling and thinning defects were selected as the outputs of the Taguchi experiments for each sample. The maximum wrinkling wave height was regarded as the wrinkling defect index. In investigating thinning defects, the maximum thickness reduction in each layer was chosen as the thinning defect index. In the Taguchi analysis, the maximum thickness reduction in each layer served as the index for obtaining the optimal values of input parameters that minimize thinning. In other words, two outputs were used in each test with regard to thinning. The first output was the extent of thinning in the aluminum layer, and the second was the extent of thinning in the steel layer.

1. Results and discussion

        As indicated in the results of the experiments and finite element analysis, specimen thickness increased or decreased at different regions. To investigate thinning in the deformed pieces, the maximum thickness reduction produced in each sample was chosen as the critical thinning index and regarded as the basis of the analysis. Figure 5 illustrates the results of Test #1 for the experiments indicated in Table 4. The initial thickness of the steel layer was 0.7 mm. Contours were plotted on the basis of the thickness values obtained following the deformation of the sample. As shown in Figure 5, after the sheet’s deformation, its thickness underwent variations, which included an increase in thickness in some areas (e.g., wrinkle waves) and a reduction in thickness in other regions.

The maximum thickness increase and decrease in the steel layer were 13% and 16.7%, respectively. These values were obtained from equation 1.

Table 3. Input parameters for the process and levels allocated to them (t = initial thickness)

Table 4. L16 vertical arrays of the Taguchi method

        The maximum wrinkling wave height obtained from the simulation for the first test was 5.91 mm. To validate the simulation results, the wrinkle height of the sample obtained from the simulation was compared with that of the sample obtained from the experimental test (experimental wrinkle height = 6.1 mm). Figure 6 indicates good agreement between the finite element analysis and experimental results.

        For the Taguchi analysis, the maximum percentage of thickness reduction was considered the criterion of thinning in the examined sample. The values of thinning for each test were recorded, and the results are presented in Figure 7. The graphs in the figure indicate the S/N ratios related to the values of each parameter. The S/N ratio was a statistical index obtained from equations 2 and 3.

        A high ratio indicates good quality of a final product with respect to a specified quality index. The abscissa of each diagram in Figure 7 shows the value of each parameter, and the ordinate of a diagram represents the S/N ratio at a given parameter value.

        In equations 2–4, MSD denotes the mean square deviation, n represents the test number, and y is the smallest thickness measured in each test. The selection of the constraints “larger is better” and “smaller is better” depended on output index. In the analysis of thinning defects, the “larger is better” logic was adopted because the closer the maximum extent of thinning to the initial thickness of the sheet, the higher the quality of the produced sample. Figure 7 shows the diagrams pertaining to the effects of the input parameters on thickness deviation. As is indicated in the S/N ratio graph related to various values of the DR parameter, the optimum DR that minimizes the percentage of thinning in the double-layer sample was 5.35 mm. The S/N ratio at different values of the PR parameter was highest at the 4^th-level radius (i.e., 8.35 mm). The S/N ratio diagram for PR demonstrates that with increasing PR, the occurrence of thinning and, thus, tearing in the sheets became less likely; choosing an appropriate PR enabled a greater drawing depth for the blank.

        As shown in Figure 7, a BHF of 2000 N for the double-layer sheet led to the highest S/N ratio. This optimal BHF was the lowest among the four values allocated to this parameter.

        The effects of BHF were compared with the results of Kitayama et al. [5] for the square-section deep drawing of single-layer sheets. The comparison indicated that with the application of a small BHF in the forming of single- and double-layer sheets, small thickness variations will occur in a deformed specimen. In previous works on the deep-drawing process [21, 25], different values were considered for CPD.

A necessary requirement in the current work, therefore, was to explore the optimal value of CPD. The S/N ratio diagrams for the effects of CPD on the maximum thickness deviation of the aluminum/steel sheet indicate that a CPD of 1.1 t was the optimal value for the prevention of sheet thinning.

        Investigation was also directed toward the effects of LA on maximum thinning. The Taguchi analysis results indicated that if the steel layer is in contact with the die surface and the aluminum layer is in contact with the blank holder, the deformed piece will undergo less thinning than when the order of sheets is reversed.

        By using the information in Table 5 and equations 5–8, the contribution of each parameter to thinning and wrinkling defects are obtained as follows:

        The overall mean S/N ratio and the sum of squares due to variations around the overall mean are expressed as equations 5 and 6. For the i_th process parameter, the sum of squares due to variations about the mean is expressed as equation 7. This summation is over the two levels of study for LA and four levels of study for the other process parameters.

        The contributions of the input parameters to the thickness deviation of the sheet are listed in Table 6.

        According to the results, PR exerted the strongest effect on thinning in the aluminum/steel double-layer sheet. In investigating the effects of input parameters on the thickness deviation of single-layer stainless steel sheets during the deep-drawing of circular blanks and without consideration for PR as an input parameter, Padmanabhan et al. [19] determined the contribution of DR to thinning defects as close to 90%. This percentage leaves a very small proportion of contribution for other parameters, such as friction and BHF.

Table 6. Contributions of input parameters to thinning

Table 7. Contributions of input parameters to wrinkling

        The contributions of the input parameters to the maximum wrinkle height were obtained. The results are presented in Table 7, which shows that BHF was the most effective parameter, as evidenced by its contribution of 49.8%. The optimum values of the input parameters differed depending on the selected quality indices (maximum thickness reduction and maximum wrinkling wave height). With regard to the wrinkle height index, for instance, the optimum value of BHF was 8000 N, but with respect to the thinning index, this value was 2000 N.

        To select an appropriate BHF value in a way that minimizes both wrinkling and thinning defects, the contribution of this parameter to the defects should be evaluated. BHF contributed 5.2% and 49.8% to thickness variations and wrinkling defects, respectively. Given that this parameter had a much stronger effect on wrinkling defects than thinning defects, the magnitude of this force must be close to its optimal value on the basis of the wrinkle height index. Thus, the 3^rd-level value of the BHF parameter (i.e., 6000 N) was the most suitable for the formation of the aluminum/steel double-layer sheet.

        Because DR contributed 17.3% to wrinkling and 9.2% to thinning, its 3^rd-level value (i.e., 5.35 mm) was considered the optimum value of the parameter. From the perspective of both indices, the 4^th-level value of PR (i.e., 8.35 mm) was the optimal value for this parameter. CPD affected wrinkling to an extent of 14% and thinning to a degree of 1.3%. Given that its contribution to wrinkling is much greater than its contribution to thinning, the 3^rd-level value of CPD (i.e., 1.3 t) was the optimum value of this parameter.

        LA affected thinning and wrinkle height to an extent of 11.4% and 0.5%, respectively, indicating the significance of this parameter in the thinning and eventual tearing of the double-layer sheet used in the square-section deep drawing. In view of this significance, the 1^st-level arrangement of this parameter (i.e., Steel is in contact with the die surface.) was considered the optimal arrangement for this input parameter.

        The optimum values of the input parameters are given in Table 8.

Table 8. Optimum values of input parameters in the square-section deep drawing of aluminum/steel double-layer sheet

        The experimental and simulated samples obtained from this process through the optimum values of input parameters are presented in Figure 9. The figure indicates that the samples obtained from the experimental tests and the finite element simulation showed good agreement.

1. Conclusion

        The square-section deep-drawing process for blanks is highly sensitive to the values of input parameters. Preventing thinning necessitates the appropriate selection of optimal PR and LA in double-layer sheets. To prevent wrinkling, an essential requirement is to choose an optimal BHF. As indicated in the results, BHF must also have an intermediate value between the optimum values associated with wrinkling and thinning indices because although a large BHF prevents wrinkling, it contributes to tearing. Additionally, even though a small BHF reduces the extent of thinning in sheets, it causes wrinkling.

        The design of experiments based on the Taguchi method of vertical arrays can be used to determine the effects of parameters in the deep-drawing process. The optimum values obtained through this method for the input parameters of the deep drawing of an aluminum/steel double-layer sheet were 5.35 mm for DR, 8.35 mm for PR, 6000 N for BHF, and 1.3 t for CPD. LA was associated with the level 1 arrangement (i.e., The aluminum layer is in contact with the blank holder, and the steel layer is in contact with the die surface.).

        The ANOVA of the input parameters indicated that BHF (with a contribution of 49.8%) exerted the strongest influence on the occurrence of wrinkling and that PR (with a contribution of 72.9%) posed the greatest effect on the occurrence of thinning. These parameters were therefore the most significant among the examined input parameters.

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