Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup

Transcription

1 Journal of Engineering Technology and Education, Vol. 8, No.1 March 2011, pp Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup Thanh-Phong Dao, Shyh-Chour Huang* Department of Mechanical Engineering National Kaohsiung University of Applied Sciences Kaohsiung, Taiwan, R.O.C. Abstract Optimization the process parameters in hydromechanical deep drawing (HDD) of trapezoid cup is an important task for reducing production cost. To determine the optimum values of the process parameters, it is essential to determine their influence on the deformation behavior of the sheet metal. The most important process parameters for affecting thickness distribution of a trapezoid cup, namely punch speed, chamber pressure and friction coefficient, were determined. The Finite element method (FEM) combined with the Taguchi method served as a predictive tool to determine the influence parameters. FEM and the Taguchi method were used to identify the influence of each parameter considered in this study. The simulation was carried out with an orthogonal array (L9) of the Taguchi method. Based on analysis signal to noise and analysis of variance tests, it was found that optimal values of parameters are pressure at level 2 (8.5 MPa), friction coefficient at level 1 (0.005) and punch speed at level 2 (7500 m/s). Among these factors, friction efficiency has the greatest effect on thickness distribution in the HDD of the trapezoid cup. Keywords: Hydromechanical deep drawing; Optimization; Finite element method; Taguchi method. 1. Introduction One of the most important formative processes of sheet metal parts in manufacturing industries is hydromechanical deep drawing (HDD). The HDD process is a technique/tool which is often applied to fabricate hollow sheet metal parts with high drawing ratios or complicated shapes. The HDD is developed from conventional deep drawing. In HDD, the lower die set includes a drawing ring mounted on a pressure chamber in this process. The pressure chamber is filled with a hydraulic fluid. The punch acts as a mechanical press on the blank in terms of chamber pressure; therefore, the blank is deformed. The penetration of the punch into the hydraulic medium causes a pressure increase due to fluid compression that is controlled by the use of a pressure control valve. Friction between the punch and blank is raised because the blank is pressed firmly onto the punch due to pressure build up. As a result, higher forces, as compared to that in conventional deep drawing, can be transferred to the deformation zone. S.H. Zhang et al. [1] described when the HDD process is compared to the conventional deep drawing process, the limit drawing ratio (LDR) can be increased from 1.8 to 2.8, the tool costs can be decreased remarkably as only one tool half (the punch) is used; the female die is replaced with the chamber fluid, and only the punch needs to be varied when drawing parts with different shapes or dimensions. The formed parts have a more uniform thickness and better surface quality. L. Lang et al. [2] simulated and experimented for some different cups with uniform pressure onto the blank 2011 National Kaohsiung University of Applied Sciences, ISSN

2 54 Thanh-Phong Dao, Shyh-Chour Huang by using HDD process. Their results showed that with material AL Mg Si alloy, a cup with drawing ratio of 2.46 was reached and a cup with a drawing ratio of 2.54 was drawn, but there is a heavy body wrinkling appeared. They also found that the thickness distribution is significantly effected by the liquid pressure variation. Moreover, the results showed that some typical failure modes such as the V-type fracture, tears of the blank flange and heavy body wrinkling exist in this process. In other study, L. Lang et al. [3] discussed about the effect of the process parameters on forming of two parts in aircraft manufacturing with typical aluminum material (2B06). The results indicated that the forming process significantly is influenced by the blank shape and the pressure in the die cavity. And the optimization of both the blank shape and the pressure the part can be formed successfully. Usually, the optimized pressure in the die cavity should be within MPa for forming of typical aluminum material part (2B06). In this study, an approach based on the finite element method combined with the Taguchi method is used to determine the most important process parameters (punch speed, chamber pressure, and friction coefficient) for affecting thickness distribution of a trapezoid cup. In HDD system, the components include the blank, blank holder, chamber pressure (female die), and punch as shown in Fig. 1 [4]. The paper is organized in the following manner. The Taguchi method is introduced first. The simulation details of using finite element method to determine analyze the process parameters are described next. Then, the parameter design using Taguchi method is introduced. Finally, the paper concludes with a summary of this study. Fig. 1: Schematic illustration of the hydromechanical deep drawing system [4] 2. Taguchi method M. Nalbant et al. [5] described that Taguchi method is applied for designed experiment. This approach has applied firstly in design of experiment of the exclusive world of the statistician and then, it has used more widely into the field of manufacturing. Taguchi method suggested that engineering optimization of a process or product should be carried out in three step approaches, i.e., system design, parameter design, and tolerance design. First of all, in system design, by using a scientific and engineering knowledge to make a basis functional prototype design, this design includes the product design stage and the process design stage. In the product design stage, the selection of materials, components, experimental product parameter values, etc., are involved. As to the process design stage, the analysis of processing sequences, these selections of production equipment, tentative process parameter values, etc., are involved. Since system design is an initial functional design, it may be far from optimum in terms of quality and cost.

3 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup 55 The parameter design is used to optimize the settings of the process parameter values for improving performance characteristics and to identify the product parameter values under the optimal process parameter values. Moreover, it is expected that the optimal process parameter values obtained from the parameter design are insensitive to the variation of environmental condition and other noise factors. Therefore, the parameter design is the key step in the Taguchi method to achieving high quality without increasing cost. Developed by Fisher [6], the basic classical parameter design is complicated and difficult to use. In particular, when the number of process parameters increases, a large number of experiments are required; the Taguchi method uses a special design of orthogonal arrays to study the entire parameter space with only a small number of experiments required. A loss function is then defined to calculate the deviation between the experimental value and the desired value. Taguchi recommends the use of the loss function to measure the performance characteristic deviating from the desired value. The value of the loss function is further transformed into a signal to noise (S/N) ratio η. In the analysis of signal to noise, three categories of the performance characteristics are often used: the lower the better, the higher the better, and the nominal the better. The S/N ratio for each level of process parameters is computed based on the S/N analysis. Regardless of the category of the performance characteristic, the larger S/N ratio corresponds to the better performance characteristic. Therefore, the optimal level of the process parameters is the level with the highest S/N ratio η. Moreover, statistical analysis of variance (ANOVA) is applied to see which process parameters are statistically significant. With the S/N and ANOVA analyses, the optimal combination of the process parameters can be predicted. Finally, a confirmation experiment is conducted to verify the optimal process parameters obtained from the parameter design. Using parameter design of the Taguchi method to optimize a process with multiple performance characteristics includes the: select process parameters to be evaluated; determination the number of levels for the process parameters; selection orthogonal array; calculation the S/N ratio; using the S/N ratio and ANOVA to analyze the experimental results; verification the optimal process parameters by confirmation experiment. Then, three objectives can be achieved through the parameter design of the Taguchi method, i.e: determination of the optimal design parameters for a process or a product; estimation of each design parameter to the contribution of the quality characteristics; and prediction of the quality characteristics based on the optimal design parameters. In this study, Taguchi method of experimental design was used to plan the numerical simulations. 3. Simulation of Hydromechanical Deep Drawing of Trapezoid Cup The formability of blank sheet depends on the process parameters such as pressure, punch speed, friction coefficient, and blank holder force. Fracture and wrinkle are the major modes of failure in sheet metal parts. Hence, using proper process parameters are essential to restrict wrinkling tendency and avoid tearing. One of the quality criterions in sheet metal formed parts is thickness distribution. In this study, a trapezoid cup with mild steel (DQSK) and blank thick of 1 mm is simulated by using Dynafor-3D to study the effect of these parameters on failure modes and thickness distribution. The parameters for simulation are shown in Table 1. Locations of measurement the wall thickness distribution of trapezoid cup are shown as Fig. 2. The mean of thickness distribution can be calculated as following: 15 T M = t i i= 1 (1)

4 56 Thanh-Phong Dao, Shyh-Chour Huang Where t i is thickness of cup at point i, wall thickness distributions includes 15 points along with cup center line. Table 1: The values of initial process parameters The process parameters of HDD Pressure (MPa) 5.14 P 12 Punch speed (mm/s) 7000 Punch travel (mm) 60 Blank holder force (KN) 90 Friction coefficient ( blank and die) 0.01 Fiction coefficient ( blank and punch) 0.01 Fiction coefficient ( blank and binder) 0.01 Fiction coefficient ( blank edge and die) 0.01 Fig. 2: Thickness distribution along with trapezoid cup center (unit:mm) 3.1 Effect of the Pressure in the Die Cavity on Wall Thickness Distribution To study the influences of the pressure on wall thickness distribution, the simulation process was carried out with the four different variable pressure curves in the range from 5 to 12 MPa, one variable pressure curve in the range from 12 to 30 MPa and constant pressure values of 5MPa, and 12 MPa, as shown in Fig. 3, while other parameters have constant values, as shown in Table 1.

5 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup 57 Fig. 3: Pressure loading using for simulation HDD of trapezoid cup A comparison between wall thicknesses distributions of cup after analysis of simulation results, as shown in Fig. 4. When the pressure in the die cavity was 5 MPa, the thickness distribution along with cup center line was non-uniform. It can be found that when pressure in the die cavity is low, the wall thickness distribution is unevenly along with forming direction; the thinnest part is at the body of the cup. With high pressure of 12 MPa, thickness distribution was quite even along with forming direction; the thinnest regions were at the body of the cup. By using four variable pressure curves in the range value from 5 to 12 MPa, thickness distribution of cup in four of these cases had the same a value. The results showed that the wall thickness distribution by using constant pressure of 12 MPa is more even than using variable pressure in the range from 5 to 12MPa and variable pressure in the range from 12 to 30 MPa.

6 58 Thanh-Phong Dao, Shyh-Chour Huang Fig. 4: Thickness distribution of trapezoid cup along with its center Also, the results showed that wall thinning occurs at the bottom of the cup and thickening occurs near the top and at the flange. Near the top of the cup section and at the flange, blank thickening occurs due to the friction at the die and blank interface and the circumferential forces. 3.2 Effect of the Pressure on Wrinkling and Fracture of Formed Cup Fig. 5 illustrates four cases of forming limiting diagram of a trapezoid cup. When pressure in the die cavity was 5 MPa, wrinkling appeared close to the die entrance radius and fracture could occur. It shows that when the pressure is too low, there will be a risk of cracking at bottom the body of the cup. At the pressure of 12 MPa, fractures could appear; wrinkling occurred around the body of the cup below the die entrance corner radius; and the body of the cup was unevenly formed. Using variable pressure in the die cavity from 5 to 12 MPa, shape of the product was better and without failures. The cup was formed according to desired shape. Using variable pressure in the range from 12 to 30 MPa, fractures occurred at bottom of the body of product.

7 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup 59 a. Constant pressure 5 MPa b. Constant pressure 12 MPa c.variable pressure (5-12) MPa d. Variable pressure (12-30) MPa Fig. 5: Forming limitation diagram of trapezoid cup

8 60 Thanh-Phong Dao, Shyh-Chour Huang 3.3 Effect of Friction Coefficient on the Wrinkling and Fracture of Trapezoid Cup To analyze the effect of friction coefficient on the HDD process, the experiment simulated some friction coefficients, such as: 0.005, 0.01 and 0.02 while other parameters have constant values, as in Table 1 and loading path is a variable pressure in the range from 5 to 12 MPa, as shown in Fig. 6. Fig. 6: Variable pressure loading Fig. 7 illustrated the results of three cases of the friction coefficients. From Fig. 7, we can see when the friction coefficient was equal to 0.02, cracking occurred at bottom of the body of the cup. When the friction coefficient was and 0.01 there was no wrinkling and fracturing, the trapezoid cup would be formed successfully. It found that the friction coefficient is more than 0.01, fracturing and wrinkling will appear around body of cup. The friction coefficient is less than 0.005, lubrication will be more difficult, but there is no cracking and wrinkling, so the friction coefficient should be used in the range from to 0.01 in the HDD of trapezoid cup. The results show that friction is a key parameter in the HDD process of the trapezoid cup. To control friction coefficient between interfaces of parts, choosing a lubricant with consideration for temperature range of it, corrosion characteristics of material and the approaches of applying and removing the lubricant.

9 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup Effect of the Friction Coefficient on Wall Thickness Distribution Fig. 8 shows the wall thickness distribution along with cup center line by using friction coefficient is even more than using friction coefficient The results found that the friction coefficient is one of the important parameters effects on the thickness of the cup. a. Friction coefficient 0.02 b. Friction coefficient 0.01 c. Friction coefficient Fig. 7: Simulation process with friction coefficients: 0.02, 0.01, 0.005

10 62 Thanh-Phong Dao, Shyh-Chour Huang Fig. 8: Comparison thickness distribution between using friction coefficient and Effect of the Punch Speed on the Fracture of Cup The punch speed plays an important role in the deformation of cup. This simulation process was carried out with punch speed values such as 4 m/sec, 7 m/sec, 8 m/sec, 9 m/sec, 18 m/sec and 50 m/sec while other parameters have constant values, as in Table 1 and pressure loading as in Fig. 6. The results are shown in Fig. 9 and Fig.10 respectively. With 4 m/sec, 7 m/sec and 8 m/sec, the trapezoid cup was deformed successfully. When punch speed value was 9 m/sec, the fractures could occur at the bottom of the body of the cup. When punch speeds were 18 m/sec and 50 m/sec the fracture and wrinkling appeared. Comparison punch speed between 4 m/sec 7 m/sec, the results showed that in both cases, the trapezoid cup was formed successfully, but with value of 4 m/sec, time of simulation is greater than that with value of 7 m/sec. The analysis of simulated results showed that the punch speeds value are more than 8 m/sec, fractures occur at body of cup. Punch speed value is less than 7 m/sec, simulation process is very slowly. The results founded that punch speed increases, there will be more fractures and larger ones. Therefore, minimum punch speed value selected is 7 m/sec and maximum punch speed is 8 m/s. The most thinning wall of the cup is at the bottom of the body; when punch speed increases to the value of 50 m/s, the wall thickness at the bottom of cup will decrease, at the time, the pressure is always acting as a force around of the body of the cup. As a result, the necking occurs at the bottom of the cup.

11 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup 63 a. 4 m/s b. 7 m/s c. 8 m/s d. 9 m/s Fig. 9: Forming of trapezoid cup with punch speed: 4, 7, 8, and 9 m/s a. 18 m/s b. 50 m/s Fig. 10: Forming of trapezoid cup with punch speed: 18 m/s and 50 m/s

12 64 Thanh-Phong Dao, Shyh-Chour Huang. Fig. 11: Comparison wall thickness distribution between using punch speed 4 m/s and 8 m/s 3.6 Effect of Punch Speed on the Wall Thickness Distribution A comparison wall thickness distribution along with cup center line between by using the punch speed 4 m/s and 8 m/s, as in Fig. 11, the thickness distribution in case of 4 m/s is uniform more than in case of 8 m/s. It found that punch speed is an important parameter which affects the wall thickness distribution. 3.7 Effect of Blank Holder Force on the Wrinkling of Cup Flange To research the affecting of the blank holder force on wrinkling of cup flange, this study was carried out with some blank holder force values as 2, 5, and 90 KN while other parameters have constant values, as in Table 1 and pressure loading as Fig. 6. The results indicated that when blank holder force is very low, the wrinkling is possible to occur on the flange of cup, with 2 KN and 5 KN, the heavy wrinkling appears. But if blank holder force is equal to 90 KN, the wrinkling on flange of product does not occur, for example, as in Fig. 9. The results found that the blank holder force is chosen to be the upper limit press capability, 90 KN is selected as this process s blank holder force. Wrinkling on the flange of the cup occurs by using different values of blank holder force, as shown in Fig. 12, so the blank holder force plays an important role in cup hydromechanical deep drawing for affecting the wrinkling of flange of the cup, but it does not influent the thickness distribution of cup.

13 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup 65 a.2000n b N Fig. 12: The wrinkling of trapezoid cup flange holder force 3.8 The Values of Process Parameters After analysis results of this simulation process, there are only three main parameters which have a direct effect on the thickness distribution of the trapezoid cup, punch speed, chamber pressure, and friction coefficient. So the values of process parameters were determined. The friction coefficient between the surfaces of parts such as blank and blank holder, blank and die, blank and punch, blank edge and die assumed to be in the range of the same critical value. The results related to the HDD process parameter critical values are described in Table 2. Table 2: HDD process parameters values Symbol HDD parameters Range Unit A Variable Pressure 5-12 MPa B Friction C Punch speed 7-8 m/s 4. Determination of optimal hydromechanical deep drawing parameters After finding the main parameters by finite element analysis, in the next step, we need to determine which level of the parameters is better and specifically how much better it is. In this section, the Taguchi method of experimental design was used to plan the numerical simulations. The use of an orthogonal array to reduce the number of HDD experiments for design optimization of HDD parameters is presented. Based on the results of S/N ratio and ANOVA analyses, optimal settings of process parameters for wall thickness are obtained and verified.

14 66 Thanh-Phong Dao, Shyh-Chour Huang 4.1Orthogonal array experiment Among all of the process parameters, punch speed, chamber pressure and friction coefficient play an important role in affecting the thickness distribution of the cup along with the cup center; hence, the above parameters are considered in this study. The high order interactions among the above three factors are assumed to be negligible and the information on the main effects can be obtained by running 33 =27 experiments. However, the appropriate Taguchi orthogonal array for the above three parameters with three levels is L9 to conduct nine simulations. Every simulation repetition is three times. Table 3 shows levels of the parameters. Symbol HDD Parameters Table 3: HDD parameters and their levels Range Unit Level 1 Level 2 Level 3 A Pressure 5 12 MPa B Friction C Punch speed 7 8 m/s The quality of the formed part is dictated by the degree of influence of these process parameters used in the sheet metal-forming process. One of the quality criteria in sheet metal formed parts is thickness distribution. Failure in the deep drawn part usually occurs by thinning; therefore, it is important to determine the variation of strain in thickness direction during deformation. The experimental layout for the three HDD process parameters using the L9 orthogonal array is shown in Table 4. Nine trials with details values are given in Table 5. Table 4: Experimental layout using an L9 orthogonal array L 9 (3 4 ) Array Experimen t No. HDD parameters A B Pressure Friction C Punch speed

15 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup 67 Table 5: Nine trials with detail values Trial Pressure (Mpa) Friction Punch speed (m/s) Analysis S/N Ratio (db) Taguchi method uses the S/N ratio to measure the quality characteristic deviating from the desired value. The S/N ratio is defined as [7]: S/ N = 10log( MSD) Where MSD is mean squared deviation from the target value of the quality characteristic, and it can expressed as following MSD = [( y m) + ( y m) +...]/ n y Where 1, y2 are results of experiments, observation or quality characteristic such as length, weight, surface y finish, etc, m is target value of results, n is number of repetition ( i ). The results of mean of thickness distributions of trapezoid cup were calculated follow in Eq. 3, their results given in Table 6 and the results of S/N ratio, calculated in Eq. 2, are shown in Table 7. The results of mean S/N ratio at every level of parameters are illustrated in Table 8 below. (2) (3) Table 6: Mean of thickness of trapezoid cup The experiment Trial Mean of thickness T M (mm)

16 68 Thanh-Phong Dao, Shyh-Chour Huang Table 7: Experimental results for thickness and S/N ratio Trial Pressu re (Mpa) Frictio n Punch Speed (m/s) Mean of Thickne ss TM (mm) MSD (mm) S/N Ratio (db) After all of data are presented in Table 8, mean signal to noise (S/N) ratio graph for the thickness. Fig. 13 presents plots of the S/N ratio for the three control parameters A, B, and C studied at three levels for the thickness. Based on the data presented in Table 8 the optimal process parameters for thickness are pressure at level 2, friction at level 1, punch speed at level 2 in Fig. 13 is shown A2B1C2. Table 8: S/N response table for thickness symbol Process Mean S/N ratio (db) parameter Level 1 Level 2 Level 3 Max min A Pressure B Friction C Punch speed

17 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup 69 Fig. 13: Mean signal to noise (S/N) ratio graph for thickness 4.3 Analysis of Variance The purpose of the analysis of variance (ANOVA) is to investigate which process parameters significantly affect the quality characteristic. The ANOVA table for thickness of trapezoid cup is shown in Table 9. It can be found that the most significant HDD parameter is friction coefficient for affecting thickness distribution. It has a predominant effect with the highest percentage contribution. HDD parameters Table 9: Results of analysis of variance (ANOVA) for thickness Degrees of freedom Sum of squares (S) Mean square (V) F ratio Contribution P (%) Pressure Friction Punch speed Error Total Estimated Result at Optimum Condition The performance simulation process using significant parameters at optimal condition is to compare with using initial parameters A3B3C1 which influent the thickness distribution. Optimum conditions A2B1C2 are pressure at level 2 (8.5 Mpa), friction efficient at level 1 (0.005) and punch speed at level 2 (7500 N). The analysis of results using Dynaform-3D software, it confirmed that at optimum condition, thickness distribution is more uniform as Fig. 14 shown. Table 10 shows the results of confirmation test by FEM using the optimal HDD parameters for thickness of trapezoid cup. It is good agreement between predict performance and test by FEM. Based on the results of confirmation test, mean of thickness increased mm, and the S/N ratio from initial HDD parameters to optimal HDD parameters is db.

18 70 Thanh-Phong Dao, Shyh-Chour Huang Fig. 14: Thickness distribution of cup using initial parameters and optimal parameters Table 10: Results of confirmation test for thickness distribution Initial DD parameters Optimal HDD parameters Prediction Test by FEM Level A3B3C1 A2B1C2 A2B1C2 Mean of thickness (mm) S/N ratio (db) Improvement of S/N ratio = Conclusions This study investigated the effect of process parameters in hydromechanical deep drawing of a trapezoid cup and their optimization to affect thickness distribution. It illustrated the use of FEM with the Taguchi method to determine the proportion of contribution of three important process parameters in the HDD process: punch speed, pressure and friction coefficient which affect the thickness distribution of the cup along with the cup center. The results of this study can be summarized as follows: (1) Analysis signal to noise ratio results in Table 5.9 shows that the optimal values of process parameters are pressure at level 2 (8.5Mpa), friction at level 1(0.005) and punch speed at level 2 (7500 m/s); (2) Analysis of variance (ANOVA) was carried out and calculated percentage contribution of parameters calculated, as shown in Table Friction coefficient is the main factor with the greatest importance concerning in the thickness distribution of the trapezoid cup. In future works, some issues need to further research although trapezoid cup is formed and tested successfully within aim of this study. The future works will concentrate on following: (1) To research effects of other parameters on hydromechanical deep drawing process such as die radius and punch radius; (2) To research hydromechanical deep drawing of complicate shapes; (3) Confirmation test via real experiment after ANOVA is calculated; (4) A comparison with practical production.

19 Study on optimization of process parameters for hydromechanical deep drawing of trapezoid cup 71 References [1] Zhang S.H., Jensen M.R., Nielsen K.B., Danckert J., Lang b L.H., Kang D.C., Effect of anisotropy and prebulging on hydromechanical deep drawing of mild steel cups, Journal of Materials Processing Technology Volume 142, Issue 2, 25 November, Pages , [2] Lihui Lang, Joachim Danckert, Karl Brian Nielsen, Study on hydromechanical deep drawing with uniform pressure onto the blank, International Journal of Machine Tools and Manufacture Volume 44, Issue 5, April, Pages , [3] Lihui Lang, Tao Li, Dongyang Ana, Cailou Chi, Karl Brian Nielsen, Joachim Danckertb, Investigation into hydromechanical deep drawing of aluminum alloy complicated components in aircraft manufacturing, Materials Science and Engineering: A Volume 499, Issues 1-2, 15 January, Pages , [4] Zhang S.H., Nielsen K.B., Danckert J., Kang D.C., Lang L.H., Finite element analysis of the hydromechanical deep-drawing process of tapered rectangular boxes, Journal of Materials Processing Technology Volume 102, Issues 1-3, 15 May, Pages 1-8, [5] Nalbant M., Gokkaya H., Sur G., Application of Taguchi method in the optimization of cutting parameters for surface roughness in turning, Materials Volume 28, Issue 4, Pages , [6] Fisher R.A., Statistical methods for research worker, London: Oliver & Boyd, [7] Ranjit K. Roy, A Primer on the Taguchi method, Van Nostrand Reinhold New York, ISBN