optimization of influential process parameters on the deep drawing

OPTIMIZATION OF INFLUENTIAL PROCESS PARAMETERS ON THE DEEP DRAWING OFALUMINIUM 6061 SHEET USING TAGUCHI AND FINITE ELEMENT METHOD

Van Quang Nguyen, Balamurugan Ramamurthy and Jau-Wen LinDepartment of Mechanical Engineering, National Kaohsiung University of Applied Sciences,

Kaohsiung, Taiwan, R.O.C.E-mail: [email protected]

ICETI-2014 X1038_SCINo. 15-CSME-37, E.I.C. Accession Number 3812

ABSTRACTThe plastic deformation behavior of axis symmetric aluminium 6061 cups was determined by analyzing thefour important deep drawing process parameters, namely blank temperature, die edge radius, blank holderforce and friction coefficient. Taguchi techniques along with finite element method (FEM) were used todetermine the importance of process parameters. The Taguchi method was used to analyze the influence ofeach process parameter. From the deformation result and analysis of variance (ANOVA), it was determinedthat the temperature of the blank has a major influence on the deformation characteristic of aluminium 6061sheets followed by die edge radius, coefficient of friction, and blank holder force. The optimum levels ofthe four factors in determining the deformed cup heights are found to be blank temperature of 450◦C, dieedge radius of 14 mm, coefficient of friction of 0.60 and blank holder force of 9 KN.

Keywords: deep drawing; FEM; Taguchi; ANOVA.

OPTIMISATION DE L’INFLUENCE DES PARAMÈTRES DE PROCÉDÉS SURL’EMBOUTISSAGE PROFOND DE FEUILLES D’ALUMINIUM 6061 UTILISANT LES

MÉTHODES TAGUCHI ET DES ÉLÉMENTS FINIS

RÉSUMÉLe comportement de la déformation plastique de l’axe de symétrie de cuvettes en AL-6061 a été déterminépar l’analyse des quatre paramètres de conception des procédés d’emboutissage profond, à savoir la tempé-rature de l’ébauche, le rayon de l’arête de la matrice, la force du serre-flan de l’ébauche et le coefficient defrottement. La technique Taguchi avec la méthode des éléments finis ont été utilisées pour déterminer l’im-portance des paramètres de procédé. La méthode Taguchi a été utilisée pour analyser l’influence de chaqueparamètre de procédé. Le résultat de la déformation et de l’analyse de la variance ont démontré que la tempé-rature de l’ébauche a une influence majeure sur les caractéristiques de déformation des feuilles d’aluminium6061, suivi du rayon d’arête de la matrice, le coefficient de frottement, et le serre-flan de l’ébauche. Leniveau optimal des quatre facteurs de déformation des cuvettes ont été déterminés comme étant la tempéra-ture de 450◦C de l’ébauche, le bord de l’arête de 14 mm, le coefficient de frottement de 0,60 et la force duserre-flan de 9 KN.

Mots-clés : profondeur de l’emboutissage; Taguchi; ANOVA.

Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015 605

1. INTRODUCTION

Sheet metal forming is the most extensively used manufacturing process to produce a large variety of auto-mobile and aeronautical parts. In sheet metal forming, a thin blank sheet is subjected to plastic deformationusing forming tools to get the desired shape. All processes of sheet-metal forming can be divided into twotypes: cutting processes-shearing, blanking, punching, notching, piercing, and so on; and plastic deforma-tion processes – bending, stretch form, deep drawing, and various other forming processes. The first typeof processes involves cutting material by subjecting it to shear stresses usually between punch and die orbetween the blades of a shear. The second type of processes involves partial or complete plastic deformationof the work material. Especially, deep drawing is the process where a punch is used to force sheet metal toflow between the surfaces of punch and die, forming a flat sheet of metal blank into a cylindrical, conic, orbox-shape part. The process parameters that influence the success and failure of the deep drawing processare the temperature of blank, die edge radius, Punch edge radius, punch and die clearance, punch velocity,blank holder force, coefficient of friction etc. Among these, the blank temperature [1], die edge radius [2],blank holder force [3–6] and coefficient of friction [7, 8] are considered to be significant parameters in deepdrawing process. Process parameters in addition to mechanical properties and the geometry of the part,determine the formability of a blank sheet. Tetsuo and Yoshida [9] described the effect and significanceof temperature in the deep drawing of AL-Mg alloy sheet. Ayres and Wenner [1] described the changes inAl-Mg alloys material properties with increasing temperature during warm forming. They investigated thatflow stress is significantly reduced and stated that the improvement in formability is due to increased strainrate hardening and increased limit strains. The ductility of common aluminium alloys increases with tem-perature. Thus forming at elevated temperatures close to the recrystallization temperature of about 300◦C,also called warm forming, is another promising method to improve formability.

Toros et al. [10] figured that warm forming is favorable for formability and the alloys of Al-Mg showgood formability at 200 to 300◦C. They created an empirical model to measure the deep drawing processat elevated temperatures and under different blank holder force and identified that blank temperature, punchspeed, blank holder force, and friction are the main factors that influence formability. Failure in sheetmetal parts is mainly due to fracture and wrinkle. The flange region (sheet metal in the die shoulder area)experiences a radial drawing stress and a tangential compressive stress due to the material retention property.These compressive stresses (hoop stresses) result in flange wrinkles (wrinkles of the first order). Wrinklescan be prevented by using a blank holder which assists controlled material flow into the die radius. Yoshiharaet al. [11] emphasize the role of blank holder force in forming and suggested different blank holder forceapplication schemes to eliminate the failure modes. Proper punch velocity and lubrication conditions furtherenhance the flow of material in to die cavity.

The lightweight aluminium alloy is used in a wide range of applications like aircraft fittings, gears andshafts, fuse parts, meter shafts due to its attractive properties such as low density, height, strength, ductility,toughness and resistance to fatigue. The objective of this study is to seek a way to improve the formabilityby investigating the effects of four parameters, namely coefficient of friction, blank temperature, die edgeradius and blank holder force on the deformed cup height of aluminium alloy 6061.

A statistical approach based on Taguchi’s design of the experiment and Anova technique was also adoptedto determine the degree of importance of each of the process parameters. A three-dimensional Finite ele-ment model for numerical simulation was carried out using ANSYS-AUTODYN to examine the (height)deformation behavior of deep drawn circular cup and to determine the optimum combination of these fourprocess parameters. Finally from the optimized process parameters, an optimal deep drawn Al 6065 cupwas simulated and verified.

606 Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015

Fig. 1. The geometry of the tools used in the deep drawing simulations (radii and dimensions are in mm).

2. METHODOLOGY

2.1. 3-D Explicit Dynamics-Finite Element Simulation of Aluminium 6061 CupDeep drawing simulations were carried out using the ANSYS AUTODYN software. Explicit dynamicsmodule in ANSYS was used to simulate the sheet metal forming process. Figure 1 illustrates the dimensionand geometry of the model used in FE simulation. 3D 8-node structural solid element of SOLID 45 wasused for the workpiece. The tool set (punch and die) was modeled as rigid bodies. Automatic contactprocedure in Ansys 13.0 was used to model the complex interaction between the blank and tooling. Forrigid (tool set)-flexible (blank) contact 3D 8-node quadrilateral target element of TARGE170 was used torepresent 3D target (toolset) surface which was associated with the deformable body (blank) represented by3D 8-node contact element of CONTA174 (ANSYS 2010). The contact and target surfaces constituted a“contact pair”, which was used to represent contact between the surface of the tool set and the workpiece(blank). The movement of the punch was defined using a pilot node. The coefficient of friction between thedeforming blank sheet and forming tools (die, punch and blank) was assumed to be same and maintainedat three levels (Table 2). The material of blank is 6000 series aluminium alloy type AA 6061 of diameter130 mm, with 2.75 mm thickness.

The properties of the blank material are: density is 2704 kg/m3, Young’s modulus is 70.000 GPa, Pois-son’s ratio is 0.33. The work hardening behavior and visco-plastic anisotropy are described by JohnsonCook flow stress model:

σy(εp, ε̇p,T ) = [A+B(εp)n] · [1+C ln(ε̇∗

p)] · [1− (T ∗)m], (1)

where εp is the equivalent plastic strain, ε∗p is the plastic strain-rate, and A,B,C,n,m are material constants,

time rates strain and stress are written as ε̇ and σ̇ , respectively. The normalized strain-rate and temperaturein Eq. (1) are defined as

ε∗p = ε̇p/ε̇p0

andT ∗ = (T −T0)/(Tm −T0),

where ε̇p0 is the effective plastic strain-rate of the quasi-static test used to determine the yield and hardeningparameters A,B and n. This is not as it is often thought just a parameter to make ε̇∗

p non-dimensional. T0 isa reference temperature, and Tm is a reference melt temperature. For conditions where T ∗ < 0, we assume


Table 1. Johnson Cook Strength for aluminium alloy AA6061.Initial Yield Hardening Hardening Strain Rate Thermal Softtening Melting Reference StrainStress (MPa) Constant (Pa) Exponent Constant Exponent Temperature ◦C Rate (/Sec)

420 827 0.11 1 1.9×10−2 946.85 1

Fig. 2. Illustrate the meshing of the deep drawing model used in FEM simulation.

that m = 1. Johnson Cook strength for the blank material, aluminium alloy AA 6061 is shown in Table 1and it is inputted to ANSYS for simulation.

The whole model mainly uses the explicit mesh solver with hourglass control. The meshes of the blankconsist of tetrahedral (Tet) elements which have the capability of modeling the plastic behavior. The meshused to model the aluminium 6061 sheet consists of 36369 nodes and 29506 elements as shown in Fig. 2.

2.2. Taguchi MethodIn the present study, the Taguchi method [13, 14] of experimental design involving the orthogonal array wasused to execute the numerical simulations. The process parameters studied were, the punch edge radius,the die edge radius, the blank temperature, blank holder force, coefficient of friction, the punch velocity,clearance between punch and the draw depth. The levels used for process parameters were in the orderof low, medium and high workable values. Other process parameters such as punch edge radius, drawdepth, punch velocity, clearance between punch and die etc. were fixed to the recommended values in thesimulations. Table 2 shows the chosen process parameters and their levels used in the FE simulations.

The appropriate Taguchi orthogonal array for the above four parameters with three levels is L9 to conductnine simulations as shown in Table 3. After designing the experiments with various combinations of processparameter levels, finite element simulations were carried out using ANSYS-AUTODYN software to predictthe deformation behavior of the aluminium sheet.

3. RESULTS AND DISCUSSION

3.1. Punch Force EvolutionFigure 3 shows punch force versus punch displacement plot of the Al 6061 axi-symmetric deep-drawingcup. Marginal differences in the punch forces are observed between the experiments. In the first threeexperiments, when the blank temperature was at the lowest level, higher punch is required as compared tothe remaining six cases, due to higher flow stresses. The punch force drops rapidly after about 12 mm ofpunch displacement indicating the onset of plastic instability in the part. In experiment 1 (most unfavorablecombination of choosing process parameters), the cup fails at the punch displacement at about 17 mmwhich is observed from the distinct drop in the punch force. Whereas in other cases (experiments 4–9), thepunch force continues to increase until the end of deep-drawing process (20 mm). It is apparent that the


Table 2. Process parameters and their levels for Al 6061 sheets.Factors Process parameter description Level 1 Level 2 Level 3T Blank temperature (T, ◦C) 200 350 450R Die edge radius (R, mm) 9 12 14B Blank holder force (B, kN) 6 9 12µ Coefficient of friction (µ) 0.25 0.40 0.60

Table 3. Orthogonal array (L9) of Taguchi method.Parameters

T R B µ

1 250 9 6 0.252 250 12 9 0.403 250 14 12 0.604 350 9 9 0.605 350 12 12 0.256 350 14 6 0.407 450 9 12 0.408 450 12 6 0.609 450 14 9 0.25

Fig. 3. Punch force evolution.

blank temperature has a very important role in deep-drawing process. For experiments 7–9 (450◦C blanktemperature), the minimum punch force required when comparing remaining experiments, indicating thereduction in the flow stress by heating blank to higher temperature. The lowest punch force was observedin experiment 9 which has excellent formability. The friction coefficient, die edge radius and blank holderforce have moderate influence of the deep drawing process. In the case of aluminium 6061 alloy whenheated to high temperature, it reaches nearer to solutionizing temperature as it is a natural age hardeningalloy, so the disadvantage of high temperature forming is denied in this alloy.


Fig. 4. Equivalent tensile stress-strain curve.

3.2. Influence of Process Parameter on Stress-StrainFigure 4 shows the stress-strain curves in the simulations. For aluminium alloys, most of the viscous-plasticity mechanisms are thermally driven resulting in softening of the material and may eventually befollowed by lowering of stresses at high temperatures. In the first three experiments (1, 2, 3), higher yieldstresses are observed. In experiment 3, high coefficient of friction (0.25) and large die edge radius allowthe free flow of material into the die cavity which reduced the yield stress and subsequently increased thecup height. In the second set of experiments, experiment numbers 4, 5 and 6, the yield stress drops as thecoefficient of friction decreases and die edge arc radius increases. In the third set of experiments, experimentnumbers 7, 8 and 9, the yield stress drops as the blank temperature (450◦C) increases. It is clearly seen thatexperiment 9 has resulted in lower yield stress, which exhibits excellent formability as compared to theremaining set of experiments. All the curves exhibit a peak stress at a certain strain, followed by a dynamicflow softening regime up to the end of straining. The flow stress levels are increased with increasing strain.

It is observed that the stress decreases steadily with increasing temperature, as friction coefficient de-creases with increasing temperature. This is consistent with the observations made during the simulationprocess. It is commonly understood that the friction force at elevated temperatures stems from the deforma-tion of surface material and the bonding of the contact pairs. As temperature increases, the friction force dueto the deformation of the asperities decreases significantly because of the softening of the surface material.It indicates blank temperature and coefficient of friction has significant influence on the yield stress. Die arcradius and blank holder force has moderate influence on the yield stress.

3.3. Influence of Process Parameter on DeformationDeformation (cup height) is one of the major quality characteristics in sheet metal formed parts. The re-sults of the finite element simulation of all the nine experiments are shown in Table 4. The behavior ofdeformation (cup height) of various process parameters is listed in Table 2. Figure 5a indicates the resultof experiment number 1 of first set experiment, in which the blank was deep drawn at 250◦C, and very lowdeformations were observed. Figure 5b indicates the experiment number 5 of the second set experiments, inwhich the blank was deep drawn at 350◦C, causing marginal increase in deformation comparing with firstset of experiments. But in experiment 5, we can observe a slight increase in the deformation (cup height)due to large die edge radius, which allows smooth metal flow into the die cavity. Fig 5c indicates the results


Table 4. S/N ratio for deep drawn aluminium 6061 cups.Experiment Blank temperature Die edge Blank holder Coefficient of Deformed cup S/N ratio

number T (◦)C radius R (mm) force B (kN) friction µ height (mm)1 250 9 6 0.25 11.72 21.38082 250 12 9 0.40 12.55 21.97293 250 14 12 0.60 12.80 22.14624 350 9 9 0.60 15.66 23.89925 350 12 12 0.25 14.98 23.51026 350 14 6 0.40 15.55 23.83747 450 9 12 0.40 17.08 24.64988 450 12 6 0.60 18.10 25.15369 450 14 9 0.25 18.54 25.3622

Fig. 5. (a–c). Deformed deep drawn cup of 6061 aluminium alloy under different conditions for experiments 1, 5, 9as shown in Table 3.

of the experiment number 9 of the third set experiments, in which the blank was deep drawn at 450◦C. Theyield stress drops as the blank temperature increases, large deformation was observed when compared withtwo remaining sets of experimental results in the increase of cup height. It is clearly seen that the exper-iment number 9 involving process parameters blank temperature of 450◦C, coefficient of friction of 0.6,die arc radius of 14 mm and the blank holder force of 9 kN has highest cup height, which exhibits excel-lent formability as compared to the remaining set of experiments. The precipitation hardening is the mainstrengthening mechanism in these alloys. Increasing the amount of Zn, Mg and Cu, as the major elements ofthe precipitations strengthening, enhances the strength of these alloys but at the same time may deterioratetheir formability. One of the main advantages of Al-Zn-Mg-Cu alloys in comparison with other aluminum-


base alloys is their high strength combined with high ductility. This alloy contains typically 1.2% Mg,0.25% Zn and 0.15% Cu. The high strength of these alloys makes them very suitable for aeronautical andautomobile applications where there are strong demands for high strength combined with minimum weight.One disadvantage of these alloys is that their high room-temperature strength is accompanied with a highdeformation resistance at hot working temperatures. The high deformation resistance is mainly attributedto the presence of magnesium, copper, chromium, and zirconium. It is observed that blank temperature hasa vital role in the deep drawing of aluminium 6061 sheets. The coefficient of friction, die edge radius andblank holder force also have mitigated importance on the formability of aluminium.

3.4. Analysis of Variance (ANOVA)The results obtained from the FE simulations were treated using statistical approach, namely the analysisof variance ANOVA. A better way to compare the sheet metal behavior to deep drawing is to use the meansquared deviation, which combines the effects of both average and standard deviation of the results. Inorder to increase the robustness of design against noises and to accommodate wide ranging data, a logarith-mic transformation of MSD for analysis of results was used. By using S/N ratio, the optimum conditionidentified from such analysis is more likely to produce consistent performance. With the S/N and ANOVAanalyses, the optimal combination of the process parameters can be predicted.

The S/N ratio is used to measure the deformation deviation. In determination of S/N ratio, the larger isbetter quality characteristic has been selected for this study. The S/N ratio is explained as S/N =−10log10(MSD), where MSD is mean square deviation expressed as

MSD =1n

n

∑i=1

(1

Y 2

).

For the output characteristics; n is the number of experiments (for one set of parameters, n = 1) and Y isthe evaluated value of the deformed cup height of the simulation experiments.

The overall mean S/N is expressed as (SN

)=

19

9

∑1

(SN

)i. (2)

The calculated value of this expression is 23.51. Based on the data presented in Table 4, the correspondingS/N response table and S/N response graph can be derived, as presented in Table 5 and Fig. 6 for thedeformed cup height of Al6061 sheet, respectively.

In accordance with the principles of the Taguchi method, the present study assumes that the highestproduct quality is indicated by the maximum S/N ratio. Analyzing the response for signal to noise ratiosfrom Table 5 the degree of importance of each parameter can be found. It shows the blank temperaturehas high effect value of 3.22, it has the primary effect with rank 1, followed by die edge radius with effect

Table 5. Factor response table for aluminium 6061 deep drawn cup.Control Factor

Blank temperature, T Die edge radius, R Blank holder force, B Coefficient of friction, µ

Level 1 21.83 23.31 23.46 23.42Level 2 23.75 23.55 23.74 23.49Level 3 25.06 23.78 23.44 23.73Effects 3.22 0.47 0.31 0.32Rank 1 2 4 3


Fig. 6. S/N response graph for aluminium 6061 deep drawn cup.

Fig. 7. Deep drawn aluminium 6061 cups using optimal process parameters.

0.47, coefficient of friction with effect 0.32, and blank holder force with effect 0.31. Figure 6 and Table 5reveal the optimal design parameter combination and the corresponding value of each factor (Table 2) forthe deformed cup height of 6061 sheet, i.e. T3: the blank temperature 450◦C, R3: die edge radius 14 mm,B2: blank holder force 9 kN and µ3: coefficient of friction 0.60.

3.5. Confirmation of ExperimentTo determine the optimal conditions, and to compare the result with the expected performance, it is necessaryto perform a confirmatory experiment. If the generated design fails to meet the specified requirement, theprocess must be reiterated using a new system unit in which the required criteria are satisfied. In the presentstudy, the confirmation experiment was performed by setting the design parameter combination for Al 6061sheets as: T3R3B2 µ3 (Table 2). The results indicated that the new deformed cup height was 28.32 mm,with an S/N value of 29.0431. These values represent an improvement over the original results, and hencethis verification exercise enhances confidence in the technique.

4. CONCLUSIONS

This study demonstrates the use of 3D, explicit dynamics-finite element method with Taguchi techniqueto determine the impact of four important process parameters in the deep-drawing process, namely blanktemperature, die edge radius, blank holder force and friction coefficient. The combination of FEM withTaguchi technique forms a productive tool to predict the influence of process parameters. The analysis ofvariance (ANOVA) was carried out to examine the influence of process parameters on the quality charac-teristics (deformed cup height) of the circular cup. The results obtained from ANOVA indicated that blank


temperature has a major influence on the deep-drawing process, followed by die edge radius, coefficient offriction and blank holder force. The optimal parameter combination includes blank temperature 450◦C, dieedge radius 14 mm, blank holder force 9 KN and coefficient of friction 0.60. A confirmation experimentwas performed by setting the optimal design parameter combination for Al 6061 and the results indicatedthat significant increase in the deformed cup height can be achieved. Further optimization of these processparameters value can be facilitated based on the degree of influence of the factors on the deep-drawing be-havior of the circular cup in order to improve the quality of the part. The study provided an insight intothe deep drawing of aluminium 6061 blank sheets. The quality of the drawn part depends on the drawingconditions and the suitable combination of optimal process parameters which are essential for deep-drawingprocess. At elevated temperature in the deep drawing process, heat transfer takes place between die-punchand blank which has not been considered in the present case and it is suggested to carry out further studiesin this field. In the future study, the current author intends to verify the model presented in this paper bycomparing the analytic and simulated results with experimental measurements.

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optimization of influential process parameters on the deep drawing

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