- Email: [email protected]
Finite element analysis of sheet Hydromechanical forming of circular cup
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
journal homepage: www.elsevier.com/locate/jmatprotec
Finite element analysis of sheet Hydromechanical forming of circular cup Anup K. Sharma ∗ , Dinesh K. Rout Product Research Group, R & D, Tata Steel, Jamshedpur 831001, India
a r t i c l e
i n f o
a b s t r a c t
Article history:
Sheet hydroforming is a process of converting flat sheet into desired component geometry by
Received 13 February 2007
using water pressure in a controlled manner. This paper dealt with sheet Hydromechanical
Received in revised form
forming (SHMF) of circular cup. In this process, blank is first placed on the lower die (a fluid
6 March 2008
chamber combined with draw ring) and then after sealing the blank between blank holder
Accepted 28 March 2008
and draw ring, punch progresses to deform the blank. Pressure of the fluid chamber is also increased simultaneously with the punch progression. The present work endeavours to understand the effect of strain hardening exponent, anisotropy ratio and interfacial friction
Keywords:
between blank and tools surfaces for different modes of deformation––stretching to drawing
Sheet Hydromechanical forming
mode on sheet Hydromechanical forming of circular cups.
Finite element analysis
A finite element (FE) model was developed for simulating the SHMF process using dynamic
Taguchi robust design
explicit, commercial code, LsDyna. The model after experimental validation used for study-
Orthogonal array
ing the effect of above parameters on the process. The analysis reveals that higher cup depth with minimum thinning for forming dominated by stretching mode can be achieved with material of higher anisotropy ratio, strain hardening exponent by using a rough punch and effective lubrication at blank-die–blank holder interfaces. On the other hand in case of drawing as mode of deformation, thinning is influenced mainly by interfacial friction condition between blank and tool surfaces as compared to material properties. © 2008 Elsevier B.V. All rights reserved.
1.
Introduction
The automobile industry today is experiencing an increasing demand for producing vehicles with lower fuel consumption and reduced emission characteristics. In order to achieve these demands along with the stringent crash and safety requirements the vehicles having lower weight and higher structural stiffness need to be designed. The major strategies adopted by auto sector to address these challenges are by either replacing the existing component with thinner gauge higher strength steels or modification of the component design suiting new manufacturing technique or the combination of both. Sheet hydroforming is one of the advance
∗
Corresponding author. Tel.: +91 9234620840; fax: +91 657 2271748. E-mail address: [email protected] (A.K. Sharma). 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.03.070
technologies that enhance the manufacturability of complex profiles. Some of the potential candidates for sheet hydroforming are engine hood, roof panels, tail gate, fender, fuel tank, compressor housings, etc. Sheet hydroforming is a process of forming sheets into desired shapes inside the die cavity using hydraulic pressure. Sheet hydroforming offers various advantages over conventional stamping such as part consolidation, weight reduction, improved structural strength and stiffness, lower tooling costs, fewer secondary operations, tight dimensional tolerances, low springback, and reduced scrap. However, this new technology has certain disadvantages like slow cycle time, expensive equipment and lack of extensive knowledge base
1446
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
for process and tool design. In recent past lots of studies on the hydroforming technology were performed. But works from Wu and Yu (1996), Dohmann and Hartl (1997), Manabe and Nakamura (1999), Koc and Altan (2001) and Manabe and Amino (2002) have been mainly focused on tube hydroforming area. Automotive applications of sheet hydroforming and its development to some extent have been discussed by Lang et al. (2004), Zhang et al. (2004) and Oh et al. (2006) and emphasised on the usage of FEM for analysing the process and saving development cycle time. Hein and Vollertsen (1999) and Shin et al. (2002) studied welded blank hydroforming technology using exemplary geometries. Kandil’s (2003) work on Hydromechanical forming of copper and aluminium sheets showed higher LDR with uniform strain could be achieved as compared to conventional deep drawing. Multi stage sheet hydroforming is numerically modelled by Kim et al. (2003) and proposed a process sequence for forming of an oil pan and rectangular tube. Altan and co-workers (2004) carried out experiments of sheet hydroforming with viscous pressure medium to achieve better sealing and easier handling of fluid. Lang et al. (2005a) did experimental and numerical analysis for multi layer (two steel sheets with a thin layer of aluminium foil in between) sheet hydroforming. Lang et al. (2005b) also investigated defects occurring during of hydromechanical deep drawing of square bottom cup whereas Hama et al. (2007) studied elliptical cup deep drawing through finite element (FE) simulation. However, a detail understanding of sensitivity analysis of entire range of material properties of auto grade steels and process parameter on deformation behaviour during hydromechanical forming is required. This paper discusses the effect of formability properties (strain hardening exponent and plastic anisotropy ratio) and the interfacial friction condition on the sheet Hydromechanical (SHMF) forming of circular cup for the entire range of deformations modes (pure stretch and draw-in type of deformation). An experimentally validated finite element model simulating SHMF process is used for performing parametric study.
2. Procedure of sheet Hydromechanical forming process Step 1: Die cavity is filled with the fluid (water with rust inhibitor emulsion) through an opening at the bottom of the die. Step 2: Sheet is loaded, positioning is checked and lubrication applied. Step 3: Blank holder force is applied on the BH (draw) ring to hold the sheet. Step 4: The main ram attached to punch is moved down to form the cup. The internal fluid pressure is maintained inside the die cavity with help of an intensifier during the punch travel. Step 5: After the component is formed, the punch is taken back and the component is removed from the die.
Some of the unique features of sheet Hydromechanical forming process from conventional drawing process are:
- There is thick layer of pressurised fluid between the die cavity and the sheet throughout the drawing process. This provides a uniform pressure over the outer surface of the cup resulting in uniform thickness profile and better surface finish. - The punch has the exact representation of the component shape but the die cavity is sufficiently oversized to accommodate the pressurised fluid inside. Thus, similar die can be used for more than one component and saves tool cost.
3.
Methodology
In this work, SHMF process had been simulated numerically. The pre-processing of FE model had been done using Hypermesh and solutions were carried out in LsDyna 3D commercial software. In order to validate the model thickness profile of experimentally formed cup was compared with the predicted values. This validated model was then used to carry out simulation runs for each set of input parameters of Taguchi’s design of experiment. The sensitivity of input parameter on the SHMF process was then analysed using ANOVA technique.
3.1.
Taguchi robust design technique and ANOVA
Taguchi robust design of experiment is the statistical technique using systematic approach for setting up experimental investigation. It assumes the situation having linear cause–effect dependency, Eq. (1) and allows separation of the individual factor effect on performance. (Ai Bj Ck Dl ) = + ai + bj + ck + dl + e
(1)
where is the overall mean of (objective function) for all the experimental region; ai , bj , ck , dl the deviations from caused by setting factor A at level Ai , B at the level Bj , C at level Ck and D at level Dl , respectively, while e is the error of the additive approximation. The details of the technique are given by Phadke (1989). Taguchi’s DOE permits use of partial factorial design and simple arithmetic to reach optimum settings for each parameter. It yields maximum amount of information about the effect of variables and their interaction with minimum number of experiments. However, every case study needs to be verified for additivity by conducting experiments for optimum sets and confirm with the predicted results. Taguchi robust design methodology recommends experimental quality characteristic to transform to signal/noise (S/N) ratio. It aims at maximizing the S/N ratios which thus form the objective function, i.e. minimizing the sensitivity to the noise factor. The S/N ratios derived from quadratic loss function. The commonly used S/N ratios are: 1. Nominal the best: Objective function is targeted to have a non-zero finite value. 2. Smaller the better: Zero is the desired value. 3. Larger the better: Desired to have larger value. Although there are many factors that controls the SHMF like blank holding force (BHF), fluid pressure, sheet-tool inter-
1447
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Fig. 1 – Showing maximum cup height of the tube at the onset of cracking.
Table 2 – Degree of freedom calculation
Table 1 – Levels of various factors Factor
Level
Strain hardening exponent Anisotropy ratio Blank-punch interface friction coefficient Blank-die–blank holder friction coefficient
1
2
0.15 1.0 0.05 0.01
0.2 1.8 0.1 0.03
Factor 3 0.25 2.6 0.15 0.06
facial conditions, material properties, etc. this work studies the effect of material properties (strain hardening exponent and plastic anisotropy ratio) and the friction condition at the steel tool interface (blank-punch (friction A) and blank-die–blank holder (friction B)). The domain of strain hardening exponent and the anisotropy ratio covers entire range of drawing quality plain carbon steel, from drawing grade to interstitial free grade which are used extensively for automotive body panels. Coefficient of friction varies from well-lubricated to dry condition. Three levels (as shown in Table 1) were chosen for each parameter to capture the
Degree of freedom
Over all mean N-value, R-bar, blank-punch interface friction coefficient, blank-die–blank holder friction coefficient Total
1 4 × (3−1) = 8
9
curvature behaviour of the factor effects on the quality characteristics. The quality characteristics measured were the maximum cup depth just before tearing (shown in Fig. 1) and maximum thinning at that cup depth. Since higher cup depth and lower thinning values are desirable, larger the better with objective function = −10 log(1/cupdepth)2 and smaller the better with objective function = −10 log(maximum thinning)2 were used, respectively, for analysis (Phadke, 1989, Fratini et al., 1997). The total degree of freedom as calculated in Table 2 is nine and hence Taguchi’s standard orthogonal array L9 (as shown
Table 3 – L9 orthogonal array Exp. no. 1 2 3 4 5 6 7 8 9
N-value 0.15 0.15 0.15 0.2 0.2 0.2 0.25 0.25 0.25
R-bar 1 1.8 2.6 1 1.8 2.6 1 1.8 2.6
Blank-punch interface (friction A) 0.05 0.1 0.15 0.1 0.15 0.05 0.15 0.05 0.1
Blank-die–blank holder (friction B) 0.01 0.03 0.06 0.06 0.01 0.03 0.03 0.06 0.01
1448
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Table 4a – Material properties used for Experimental Sheet hydroforming Yield strength (MPa) 114.7
Tensile strength (MPa)
Density (kg/m3 )
Young’s modulus (GPa)
Possion’s ratio
R-bar
n-Value
278
7850
210
0.3
1.77
0.21
Table 4b – Material properties used for Numerical Simulation Yield strength (MPa) 114.7
Tensile strength (MPa)
Density (kg/m3 )
Young’s modulus (GPa)
Possion’s ratio
Strength coefficient (MPa)
278
7850
210
0.3
460
in Table 3), a set of experiments, is used as input design of experiments. Two sets of simulations were carried out for each stretching and drawing modes. Different mode of deformation was achieved by varying the blank holding pressure (BHP). Higher BHP was applied to restrict the metal flow from flange region into the die cavity for stretching mode and in case of drawing mode the applied BHP was just enough to suppress wrinkles formation. The objective function of each experiments were then analysed using Analysis of variance (ANOVA) technique. In this technique, sum of square of the objective function for each factor is calculated as the summation of square of the difference of overall mean of all the experimental function values to the average of individual factor level function values. The sum of square then divided with respective factor’s degree of freedom to calculate mean square of the factor. The variation ratio is calculated by dividing the mean square of the individual factors by the error mean square. As no degree of freedom (DOF of factors 8 + 1 = 9 = DOF of the L9 orthogonal array) is left to estimate the error variance, approximate estimation is obtained by pooling the sum of squares corresponding to the factors having the comparatively lower mean square (bottom half) The relative contribution of the each factor is given by the percentage of factor’s sum of squares to the total sum of square.
4. Finite element modelling of tube hydroforming
strain hardening exponent was calculated using the relationship given in Eq. (2): K = UTS
4.1.
Material and Material Model used
MAT TRANSVERSELY ANISOTROPIC ELASTIC PLASTIC option of LSDYNA was used to simulate the anisotropy behaviour of sheet metal. This material model is based on Hill’s 48 yield criteria. Holloman law was used to define the stress dependence on effective plastic strain. The material properties were generated from tensile test on 10 ton INSTRON tensile testing machine and are given in Table 4. The value of Strength coefficient required for carrying out the simulation for different
n
(2)
where K is the strength coefficient, e is the exponential coefficient, UTS is the ultimate tensile strength and n is the strain hardening exponent of the material (Leu, 1999).
4.2.
Steps in simulation
The solution of model was subdivided into precisely defined time periods. Time periods corresponds to the time to execute each unique boundary condition defining the motion of each die. SHMF process was executed in two steps. Both the steps involve explicit dynamic solution technique.
4.2.1.
Step 1
This is the clamping step in which linear motion is given to the blank holder which holds the sheet in between the die. This step lasts in 0.005 s.
4.2.2.
Step 2
In this step punch progresses and deforms the blank. Internal pressure is applied inside the die to support the blank. This step lasts in 0.026 s.
4.3. 3D model for toolings, i.e. die, punch, blank and blank holder, of SHMF process were developed using Unigraphics CAD software. The CAD surfaces were then imported in IGES format (Initial Graphics Exchange Specification is neutral exchange format for 3D CAD models) to Hypermesh for pre-processing (meshing, applying friction and boundary condition) of the model. Hypermesh also create FE input file which was then solved using explicit dynamic LsDyna solver.
e n
Contact condition
During the process of sheet Hydromechanical forming the tools––die, punch and blank holder comes in contact with the blank. CONTACT FORMING ONE WAY SURFACE TO SURFACE (penalty contact) was used to define contact between the blank and the tools along with various friction coefficients. In this slave part (deformable part) is checked for contact with master part (non-deformable). Penetration is prevented by applying penalty force. Classical isotropic Coulomb model was used for modelling interfacial friction (Hallquist, 1997).
4.4.
Meshing of the model
Quadrilateral Belytschko-Lin Tsay shell element with five integration points through the thickness and one in-plane integration point was used to mesh the model. Shell thickness is equal to the blank thickness. Tools were considered non-deformable and are modelled as rigid surface without any thickness (Hallquist, 1997).
1449
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Fig. 3 – Hydroformed cups drawn during the trials.
Fig. 2 – (a) Schematic sketch of sheet hydroforming set-up used for the trial and (b) process set-up in FE Model.
4.5.
Boundary conditions
Blank holder and punch were given linear velocity for clamping and deforming the blank in step 1. Die was kept fixed. In step 2, internal pressure was modelled by LOAD Shell option of LsDyna which apply distributed pressure load over all the shell elements (Hallquist, 1997). In all the cases maximum internal (forming) pressure is kept constant and is given by Eq. (3): Maximum forming pressure =
(UTS × T) D
(3)
where UTS is ultimate tensile strength, T is tube thickness and D is minimum die fillet radius. (Maximum forming pressure calculation is guided by the smallest radius to be formed on the component by stretching the material. The above equation is based on thin wall theory and yields a fairly conservative value of max forming pressure, Singh (2003)).
5.
Experiment
Experimental set-up has been designed and fabricated by Electropneumatics and Hydraulics Pvt Ltd., Pune. The set-up has a double action press, i.e. the blank holder movement is inde-
pendent of the punch movement. This helps in controlling the blank holding force irrespective of the punch position. Tool set-up shown in Fig. 2 was used for conducting the experiments. Dimensions of tools are tabulated in Table 5. The fluid line is connected to a fluid intensifier through a hydraulic regulator, which helps in accurate control of fluid pressure inside the die cavity/fluid chamber as the blank is deformed by the punch. If the pressure is too high, then pressure in the system is reduced to the appropriate level by a user defined program. If the pressure is too low, then the regulator puts additional pressurized fluid from a pressure vessel in the system. The pressure intensifier is used to supply necessary volume and pressure to the reservoir prior to start of hydroforming process. Running tap water mixed with a rust preventive chemical is used as the hydraulic medium. Hemispherical cups with inside diameter 80 mm have been drawn from circular blanks of 225 mm diameter shown in Fig. 3. The punch has the exact dimension, as the cup while die cavity is oversized to accommodate a layer of pressurised fluid. The trial has been conducted with different settings of internal pressure in the hydroforming press. Interstitial free steels of 1 mm thickness and properties described as in Table 4a was used for cup forming.
6.
Validation of the model
The circular cups of 100 mm depth were drawn. For validating the FE model predicted thickness was compared with the experimental values. The cup was cut from the centre and thickness at various locations was measured with micrometer with least count 0.001. Fig. 4 shows the comparison of thicknesses along the cup profile. X-axis shows the distance along the profile of the component. It can be observed that the FE model under predicts the thinning in the cup. However, over-
Table 5 – Die dimensions for sheet hydroforming Inside cup diameter (mm) 80
Initial blank diameter (mm)
Maximum cup height (mm)
Sheet thickness (mm)
Die fillet radius (mm)
Punch nose radius (mm)
225
100
1
10
10
1450
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Table 6 – Simulation results Exp. no.
Stretching mode Max. draw
1 2 3 4 5 6 7 8 9
Drawing mode
Min. thickness
45.67 38 34.6 38.71 77.32 49.98 38.6 49.66 77.34
Max. draw
0.59 0.6 0.664 0.57 0.85 0.5 0.58 0.48 0.84
Min. thickness
100 100 100 100 100 100 100 100 100
0.885 0.898 0.8988 0.886 0.914 0.883 0.9085 0.868 0.9045
Fig. 4 – Comparison of finite element simulation model.
all a good correlation was observed between simulation and experimental thicknesses and hence the model was further used for performing the sensitivity analysis values.
Fig. 5 – Plot of factor effect for maximum draw depth–stretching mode.
(4) was used:
7.
Results and discussion
Maximum cup depth and corresponding maximum thinning data of the simulation results performed for each orthogonal array input sets for stretching and deep drawing mode is given in Table 6. Table 7 shows the ANOVA table for the maximum cup depth formed with STRETCHING deformation mode. Since the higher the cup depth, better is the hydroformability, larger the better type approach with objective function in Eq.
= −10 log
1 cupdepth
2 (4)
ANOVA analysis reveals that the interfacial friction between die-blank–blank holder is the most influencing factor followed by strain hardening exponent and anisotropy ratio. Friction condition between punch and blank has the least effect on the draw depth.
Table 7 – ANOVA table for maximum draw depth–stretching mode S. no.
1 2 3 4 Error Total (Error) ∗
Factor
N-value R-bar Friction A Friction B
Average by factor level 1
2
3
31.85 32.22 33.69 36.24
34.49 34.42 33.7 32.43
34.47 34.17 33.42 32.15
Factors used for pooling.
DOF
2 2 2 2 0 8 4
Sum of square
Mean square
Variation ratio
13.83 8.7 0.15 31.30
6.91 4.35* 0.075* 15.65
1.562 0.982 0.017 3.536
53.98 8.85
2.21
Contribution ratios (%)
25.6 16.1 0.2 57.9
1451
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Table 8 – ANOVA table for maximum thinning–stretching mode S. no.
1 2 3 4 Error Total (Error) ∗
Average by factor level
Factor
N-value R-bar Friction A Friction B
1
2
3
4.19 4.7 5.65 2.5
4.1 4.07 3.61 5.06
4.2 3.69 3.23 4.94
DOF
2 2 2 2 0 8 4
Sum of square
Mean square
0.018 1.646 10.22 12.49
0.009* 0.82* 5.11 6.25
24.38 1.664
0.416
Variation ratio
Contribution ratios (%)
0.011 0.989 6.147 7.508
0.74 6.7 41.66 50.88
Factors used for pooling.
Fig. 5 shows the main effects, i.e. the effect of individual factor level, on the cup depth with stretching deformation mode. It can be observed that the cup depth increases with the decrease in interfacial friction between blank-die–blank holder. Cup depth also increases with increase strain hardening exponent, plastic anisotropy of the sheet. This effect is similar to conventional stamping process. As strain hardening is the ability of a metal to become stronger as it deforms. Material with higher strain hardening exponent, the flow stress increases rapidly with strain. This tends to distribute further strain to regions of lower strain and flow stress. Thus, a material with a high n-value has a better stretchability. Better lubrication between blank-die–blank holder reduces the blank holding effect thus increases the draw depth. This also allows draw-in of material in the initial stage causing plastic anisotropy one of the important process parameter. This is also confirmed by observing the strain history of the elements of the formed cup. Maximum thinning in the cup formed is also one of the quality characteristic which defines the cup quality. Hence, ANOVA for maximum thinning in the cup on above draw depths was observed and tabulated in Table 8. As lesser the thinning in the component better is the part quality, the objective function given in Eq. (5) was used: = −10 log (maximum thinning)2
(5)
Analysis shows that the maximum thinning is influenced by friction condition between blank-die–blank holder and blank-punch interface followed by anisotropy ratio. The ANOVA table reveals that the material properties are just over
Fig. 6 – Plot of factor effect for maximum thinning at max cup depth–stretching mode.
7% responsible for thinning in the component as compared to interfacial friction between the tools. Fig. 6 shows the effect of various levels of factors on thinning in the cup. Higher the anisotropy ratio lower will be thinning in the cup. It is evident with the fact that the anisotropy ratio is also defined as the resistance sheet metal to deform normal to the thickness direction. Higher punch blank interfacial friction reduces the thinning of the component. Higher friction at the blank-punch interface causes sticking of sheet at punch nose. The deformation is more in the wall region of cup thus avoid localized thinning. On the other hand friction at the blank-die–blank holder interface increases the thinning tendency by reducing the material flow into the die cavity.
Table 9 – ANOVA table for maximum thinning at 100 mm draw depth drawing mode S. no.
1 2 3 4 Error Total (Error) ∗
Factor
N-value R-bar Friction A Friction B
Average by factor level 1
2
3
0.894 0.893 0.878 0.901
0.894 0.893 0.896 0.896
0.893 0.895 0.907 0.884
Factors used for pooling.
DOF
2 2 2 2 0 8 4
Sum of square
Mean square
6.755E−07 9.575E−06 0.001234 0.000457
3.97E−05* 0.000487* 0.058522 0.021702
0.1615 0.00105
0.000263
Variation ratio
0.075 0.924 111.08 41.195
Contribution ratios (%) 0.048 0.6 72.5 26.8
1452
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
8.
Fig. 7 – Plot of factor effect for maximum thinning (100 mm depth) drawing mode.
Thus, in order to achieve higher cup depth with minimum thickness reduction in stretching dominated deformation, better lubrication at blank-die and blank holder interfaces, higher strain anisotropy ratio, strain hardening exponent and rough punch surface are required. ANOVA table for maximum thinning in the cup with DRAWING MODE of deformation is given in Table 9. Blank holding force is maintained just enough to avoid the formation of wrinkle. It was observed in all the simulation that whole blank flow into the die cavity and hence maximum thinning at 100 mm cup depth is taken as quality characteristics. Thickness reduction in case of deep drawn hydroformed cup is influenced primarily by blank-punch interfacial friction and blank-die–blank holder interfacial friction. In the present analysis thinning of the hydroformed cup with low blank holding force (prominent drawing mode of deformation) is least sensitive toward the material properties of the sheet. This could be possible because of large frictional values chosen in the analysis. Fig. 7 shows the factor effect thickness reduction in DRAWING MODE hydroformed cups. Its shows that drawn cup will experience lower thinning with higher friction between blankpunch interface and better lubrication between blank-die and blank holder. However, above analysis is based on the additive model and need to be verified with confirmatory test. Hence, the optimum thickness values at the 100 mm cup depth for drawing mode of deformation are predicted using the linear additive model and confirmed with simulation results for the same set of parameter. Optimum set of parameters considering the lesser the better criteria were observed as n-value at level 2, r-value at level 3, Interfacial friction blank-punch friction A at level 3 and interfacial friction blank-die, blank–blank holder friction B at level 1. Maximum thickness value for the drawing mode at 100 mm cup depth were predicted for the optimum set of parameter using additive model relationship as 0.916 mm (Eq. (1)). The maximum thickness value of confirmatory simulation with the parameters at above levels was observed 0.93 confirming the correctness of the usage of additive model assumption for the case.
Conclusions
1. Finite element model was developed using dynamic explicit code LsDyna to simulate SHMF process. 2. Experiments of SHMF showed higher draw depth with excellent surface finish as compared to conventional press forming. 3. Experimental thickness distribution along the profile was found in good agreement with the results predicted from FE model. 4. Taguchi’s design of experiment was conducted on validated FE model for sensitivity analysis of SHMF process for stretching and drawing deformation modes. 5. ANOVA analysis for maximum cup depth formed with STRETCHING deformation mode shows more sensitive towards interfacial friction between die-blank–blank holder followed by strain hardening exponent and anisotropy ratio. 6. ANOVA for maximum thinning in the cup for stretching mode is influenced by interfacial friction condition between blank-die–blank holder followed by blank and punch friction condition and anisotropy ratio. 7. With prominent stretching deformation mode, higher cup depth with minimum thinning could be achieved with the good lubrication at blank-die and blank holder interfaces, higher strain anisotropy ratio, strain hardening exponent and rough punch surface. 8. ANOVA analysis for maximum thinning in the cup with DRAWING MODE of deformation lower thinning is possible with higher friction between blank and punch and better lubrication between blank-die and blank holder. Thinning in this case is not affected by the material properties, i.e. strain hardening exponent and anisotropy ratio. 9. Confirmatory simulation results with optimum set of parameters showed that the additive model (Taguchi robust design of experiment) holds good for the study.
Acknowledgements We are thankful to Electropneumatics and Hydraulics Pvt Ltd., Chakan Works, PUNE for allowing us to use the hydroforming facilities at their press shop to carrying out the experiments and necessary support of their employees during the tests.
references
Ahmetoglu, M., Hua, J., Kulukuru, S., Altan, T., 2004. Hydroforming of sheet metal using viscous pressure medium. J. Mater. Process. Technol. 146, 97–107. Dohmann, F., Hartl, Ch., 1997. Tube hydroforming-research and practical application. J. Mater. Process. Technol. 71, 174– 186. Fratini, L., Plaia, A., Valenti, P., 1997. Optimizing a deep drawing operation by robust design technique. In: Singh, U.P., Geiger, M., Kals, H.J.J., Shirvani, B. (Eds.), Proceedings of the Fifth International Conference on Sheet Metal’97. University of Ulster, Belfast, pp. 275–284. Hallquist, J.O., 1997. LSDYNA3D User’s Manual, Version 940, Livermore Software Technology Corporation.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Hama, T., Hatakeyama, T., Asakawa, M., Amino, H., Makinouchi, A., Fujimoto, H., Takuda, H., 2007. Finite-element simulation of the elliptical cup deep drawing process by sheet hydroforming. Finite Elem. Anal. Des. 43, 234–246. Hein, P., Vollertsen, F., 1999. Hydroforming of sheet metal pair. J. Mater. Process. Technol. 87, 154–164. Kandil, A., 2003. An experimental study of hydroforming deep drawing. J. Mater. Process. Technol. 134, 70–80. Kim, T.J., Yang, D.Y., Han, S.S., 2003. Numerical modelling of the multi stage sheet pair hydroforming process. J. Mater. Process. Technol. 151, 48–53. Koc, M., Altan, T., 2001. An overall review of the tube hydroforming (THF) technology. J. Mater. Process. Technol. 108, 384–393. Lang, L., Wang, Z.R., Kang, D.C., Yuan, S.J., Zhang, S.H., Danckert, J., Nielsen, K.B., 2004. Hydroforming highlights: sheet hydroforming and tube hydroforming. J. Mater. Process. Technol. 151, 165–177. Lang, L., Danckert, J., Nielsen, K.B., 2005a. Multi-layer sheet hydroforming: experimental and numerical investigation into the very thin layer in the middle. J. Mater. Process. Technol. 170, 524–535. Lang, L., Danckert, J., Nielsen, K.B., Zhou, X., 2005b. Investigation into the forming of a complex cup locally constrained by a round die based on an innovative hydromechanical deep drawing method. J. Mater. Process. Technol. 167, 191–200. Leu, D.K., 1999. The limiting drawing ratio for plastic instability of the cup-drawing process. J. Mater. Process. Technol. 86, 168–176. Manabe, K., Amino, M., 2002. Effects of process parameters and material properties on deformation process in tube hydroforming. J. Mater. Process. Technol. 123, 285–291. Manabe, K., Nakamura, S., 1999. Finite element simulation of hydroforming process of prebent circular tubes. Numisheet’99, 503–508. Oh, S.I., Jeon, B.H., Kim, H.Y., Yang, J.B., 2006. Applications of hydroforming processes to automobile parts. J. Mater. Process. Technol. 174, 42–55. Phadke, M., 1989. Quality Engineering Using Robust Design. Prentice Hall International, New Jersey. Shin, Y.S., Kim, H.Y., Jeon, B.H., Oh, S.I., 2002. Prototype tryout and die design for automotive pats using welded blank
1453
hydroforming. J. Mater. Process. Technol. 130–131, 121–127. Singh, H., 2003. Fundamentals of Hydroforming. Society of Manufacturing Engineers. Wu, L., Yu, Y., 1996. Computer simulation of forming automotive structural parts by hydroforming process. Numisheet’96, 324–329. Zhang, S.H., Wang, Z.R., Xu, Y., Wang, Z.T., Zhou, L.X., 2004. Recent developments in sheet hydroforming technology. J. Mater. Process. Technol. 151, 237–241.
Glossary Glossary SHMF: Sheet Hydromechanical forming FE: Finite element model 3D: 3 dimension : Overall mean of objective function : Objective function for the experimental region ai , bj , ck , dl : Deviations from caused by setting factor A at level Ai , B at the level Bj , C at level Ck and D at level Dl , respectively e: Error of the additive approximation (S/N) ratio: Signal–noise ratio BHF: Blank holding force BHP: Blank holding pressure Friction A: Friction coefficient between blank-punch Friction B: Friction coefficient between blank-die–blank holder L9 : Standard orthogonal array DOE: Design of experiments UTS: Ultimate tensile strength T: Tube thickness D: Minimum die fillet radius. ANOVA: Analysis of variance CAD: Computer aided design IGES: Initial Graphics Exchange Specification K: Strength coefficient e: Exponential coefficient n: Strain hardening exponent DOF: Degree of freedom
journal homepage: www.elsevier.com/locate/jmatprotec
Finite element analysis of sheet Hydromechanical forming of circular cup Anup K. Sharma ∗ , Dinesh K. Rout Product Research Group, R & D, Tata Steel, Jamshedpur 831001, India
a r t i c l e
i n f o
a b s t r a c t
Article history:
Sheet hydroforming is a process of converting flat sheet into desired component geometry by
Received 13 February 2007
using water pressure in a controlled manner. This paper dealt with sheet Hydromechanical
Received in revised form
forming (SHMF) of circular cup. In this process, blank is first placed on the lower die (a fluid
6 March 2008
chamber combined with draw ring) and then after sealing the blank between blank holder
Accepted 28 March 2008
and draw ring, punch progresses to deform the blank. Pressure of the fluid chamber is also increased simultaneously with the punch progression. The present work endeavours to understand the effect of strain hardening exponent, anisotropy ratio and interfacial friction
Keywords:
between blank and tools surfaces for different modes of deformation––stretching to drawing
Sheet Hydromechanical forming
mode on sheet Hydromechanical forming of circular cups.
Finite element analysis
A finite element (FE) model was developed for simulating the SHMF process using dynamic
Taguchi robust design
explicit, commercial code, LsDyna. The model after experimental validation used for study-
Orthogonal array
ing the effect of above parameters on the process. The analysis reveals that higher cup depth with minimum thinning for forming dominated by stretching mode can be achieved with material of higher anisotropy ratio, strain hardening exponent by using a rough punch and effective lubrication at blank-die–blank holder interfaces. On the other hand in case of drawing as mode of deformation, thinning is influenced mainly by interfacial friction condition between blank and tool surfaces as compared to material properties. © 2008 Elsevier B.V. All rights reserved.
1.
Introduction
The automobile industry today is experiencing an increasing demand for producing vehicles with lower fuel consumption and reduced emission characteristics. In order to achieve these demands along with the stringent crash and safety requirements the vehicles having lower weight and higher structural stiffness need to be designed. The major strategies adopted by auto sector to address these challenges are by either replacing the existing component with thinner gauge higher strength steels or modification of the component design suiting new manufacturing technique or the combination of both. Sheet hydroforming is one of the advance
∗
Corresponding author. Tel.: +91 9234620840; fax: +91 657 2271748. E-mail address: [email protected] (A.K. Sharma). 0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.03.070
technologies that enhance the manufacturability of complex profiles. Some of the potential candidates for sheet hydroforming are engine hood, roof panels, tail gate, fender, fuel tank, compressor housings, etc. Sheet hydroforming is a process of forming sheets into desired shapes inside the die cavity using hydraulic pressure. Sheet hydroforming offers various advantages over conventional stamping such as part consolidation, weight reduction, improved structural strength and stiffness, lower tooling costs, fewer secondary operations, tight dimensional tolerances, low springback, and reduced scrap. However, this new technology has certain disadvantages like slow cycle time, expensive equipment and lack of extensive knowledge base
1446
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
for process and tool design. In recent past lots of studies on the hydroforming technology were performed. But works from Wu and Yu (1996), Dohmann and Hartl (1997), Manabe and Nakamura (1999), Koc and Altan (2001) and Manabe and Amino (2002) have been mainly focused on tube hydroforming area. Automotive applications of sheet hydroforming and its development to some extent have been discussed by Lang et al. (2004), Zhang et al. (2004) and Oh et al. (2006) and emphasised on the usage of FEM for analysing the process and saving development cycle time. Hein and Vollertsen (1999) and Shin et al. (2002) studied welded blank hydroforming technology using exemplary geometries. Kandil’s (2003) work on Hydromechanical forming of copper and aluminium sheets showed higher LDR with uniform strain could be achieved as compared to conventional deep drawing. Multi stage sheet hydroforming is numerically modelled by Kim et al. (2003) and proposed a process sequence for forming of an oil pan and rectangular tube. Altan and co-workers (2004) carried out experiments of sheet hydroforming with viscous pressure medium to achieve better sealing and easier handling of fluid. Lang et al. (2005a) did experimental and numerical analysis for multi layer (two steel sheets with a thin layer of aluminium foil in between) sheet hydroforming. Lang et al. (2005b) also investigated defects occurring during of hydromechanical deep drawing of square bottom cup whereas Hama et al. (2007) studied elliptical cup deep drawing through finite element (FE) simulation. However, a detail understanding of sensitivity analysis of entire range of material properties of auto grade steels and process parameter on deformation behaviour during hydromechanical forming is required. This paper discusses the effect of formability properties (strain hardening exponent and plastic anisotropy ratio) and the interfacial friction condition on the sheet Hydromechanical (SHMF) forming of circular cup for the entire range of deformations modes (pure stretch and draw-in type of deformation). An experimentally validated finite element model simulating SHMF process is used for performing parametric study.
2. Procedure of sheet Hydromechanical forming process Step 1: Die cavity is filled with the fluid (water with rust inhibitor emulsion) through an opening at the bottom of the die. Step 2: Sheet is loaded, positioning is checked and lubrication applied. Step 3: Blank holder force is applied on the BH (draw) ring to hold the sheet. Step 4: The main ram attached to punch is moved down to form the cup. The internal fluid pressure is maintained inside the die cavity with help of an intensifier during the punch travel. Step 5: After the component is formed, the punch is taken back and the component is removed from the die.
Some of the unique features of sheet Hydromechanical forming process from conventional drawing process are:
- There is thick layer of pressurised fluid between the die cavity and the sheet throughout the drawing process. This provides a uniform pressure over the outer surface of the cup resulting in uniform thickness profile and better surface finish. - The punch has the exact representation of the component shape but the die cavity is sufficiently oversized to accommodate the pressurised fluid inside. Thus, similar die can be used for more than one component and saves tool cost.
3.
Methodology
In this work, SHMF process had been simulated numerically. The pre-processing of FE model had been done using Hypermesh and solutions were carried out in LsDyna 3D commercial software. In order to validate the model thickness profile of experimentally formed cup was compared with the predicted values. This validated model was then used to carry out simulation runs for each set of input parameters of Taguchi’s design of experiment. The sensitivity of input parameter on the SHMF process was then analysed using ANOVA technique.
3.1.
Taguchi robust design technique and ANOVA
Taguchi robust design of experiment is the statistical technique using systematic approach for setting up experimental investigation. It assumes the situation having linear cause–effect dependency, Eq. (1) and allows separation of the individual factor effect on performance. (Ai Bj Ck Dl ) = + ai + bj + ck + dl + e
(1)
where is the overall mean of (objective function) for all the experimental region; ai , bj , ck , dl the deviations from caused by setting factor A at level Ai , B at the level Bj , C at level Ck and D at level Dl , respectively, while e is the error of the additive approximation. The details of the technique are given by Phadke (1989). Taguchi’s DOE permits use of partial factorial design and simple arithmetic to reach optimum settings for each parameter. It yields maximum amount of information about the effect of variables and their interaction with minimum number of experiments. However, every case study needs to be verified for additivity by conducting experiments for optimum sets and confirm with the predicted results. Taguchi robust design methodology recommends experimental quality characteristic to transform to signal/noise (S/N) ratio. It aims at maximizing the S/N ratios which thus form the objective function, i.e. minimizing the sensitivity to the noise factor. The S/N ratios derived from quadratic loss function. The commonly used S/N ratios are: 1. Nominal the best: Objective function is targeted to have a non-zero finite value. 2. Smaller the better: Zero is the desired value. 3. Larger the better: Desired to have larger value. Although there are many factors that controls the SHMF like blank holding force (BHF), fluid pressure, sheet-tool inter-
1447
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Fig. 1 – Showing maximum cup height of the tube at the onset of cracking.
Table 2 – Degree of freedom calculation
Table 1 – Levels of various factors Factor
Level
Strain hardening exponent Anisotropy ratio Blank-punch interface friction coefficient Blank-die–blank holder friction coefficient
1
2
0.15 1.0 0.05 0.01
0.2 1.8 0.1 0.03
Factor 3 0.25 2.6 0.15 0.06
facial conditions, material properties, etc. this work studies the effect of material properties (strain hardening exponent and plastic anisotropy ratio) and the friction condition at the steel tool interface (blank-punch (friction A) and blank-die–blank holder (friction B)). The domain of strain hardening exponent and the anisotropy ratio covers entire range of drawing quality plain carbon steel, from drawing grade to interstitial free grade which are used extensively for automotive body panels. Coefficient of friction varies from well-lubricated to dry condition. Three levels (as shown in Table 1) were chosen for each parameter to capture the
Degree of freedom
Over all mean N-value, R-bar, blank-punch interface friction coefficient, blank-die–blank holder friction coefficient Total
1 4 × (3−1) = 8
9
curvature behaviour of the factor effects on the quality characteristics. The quality characteristics measured were the maximum cup depth just before tearing (shown in Fig. 1) and maximum thinning at that cup depth. Since higher cup depth and lower thinning values are desirable, larger the better with objective function = −10 log(1/cupdepth)2 and smaller the better with objective function = −10 log(maximum thinning)2 were used, respectively, for analysis (Phadke, 1989, Fratini et al., 1997). The total degree of freedom as calculated in Table 2 is nine and hence Taguchi’s standard orthogonal array L9 (as shown
Table 3 – L9 orthogonal array Exp. no. 1 2 3 4 5 6 7 8 9
N-value 0.15 0.15 0.15 0.2 0.2 0.2 0.25 0.25 0.25
R-bar 1 1.8 2.6 1 1.8 2.6 1 1.8 2.6
Blank-punch interface (friction A) 0.05 0.1 0.15 0.1 0.15 0.05 0.15 0.05 0.1
Blank-die–blank holder (friction B) 0.01 0.03 0.06 0.06 0.01 0.03 0.03 0.06 0.01
1448
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Table 4a – Material properties used for Experimental Sheet hydroforming Yield strength (MPa) 114.7
Tensile strength (MPa)
Density (kg/m3 )
Young’s modulus (GPa)
Possion’s ratio
R-bar
n-Value
278
7850
210
0.3
1.77
0.21
Table 4b – Material properties used for Numerical Simulation Yield strength (MPa) 114.7
Tensile strength (MPa)
Density (kg/m3 )
Young’s modulus (GPa)
Possion’s ratio
Strength coefficient (MPa)
278
7850
210
0.3
460
in Table 3), a set of experiments, is used as input design of experiments. Two sets of simulations were carried out for each stretching and drawing modes. Different mode of deformation was achieved by varying the blank holding pressure (BHP). Higher BHP was applied to restrict the metal flow from flange region into the die cavity for stretching mode and in case of drawing mode the applied BHP was just enough to suppress wrinkles formation. The objective function of each experiments were then analysed using Analysis of variance (ANOVA) technique. In this technique, sum of square of the objective function for each factor is calculated as the summation of square of the difference of overall mean of all the experimental function values to the average of individual factor level function values. The sum of square then divided with respective factor’s degree of freedom to calculate mean square of the factor. The variation ratio is calculated by dividing the mean square of the individual factors by the error mean square. As no degree of freedom (DOF of factors 8 + 1 = 9 = DOF of the L9 orthogonal array) is left to estimate the error variance, approximate estimation is obtained by pooling the sum of squares corresponding to the factors having the comparatively lower mean square (bottom half) The relative contribution of the each factor is given by the percentage of factor’s sum of squares to the total sum of square.
4. Finite element modelling of tube hydroforming
strain hardening exponent was calculated using the relationship given in Eq. (2): K = UTS
4.1.
Material and Material Model used
MAT TRANSVERSELY ANISOTROPIC ELASTIC PLASTIC option of LSDYNA was used to simulate the anisotropy behaviour of sheet metal. This material model is based on Hill’s 48 yield criteria. Holloman law was used to define the stress dependence on effective plastic strain. The material properties were generated from tensile test on 10 ton INSTRON tensile testing machine and are given in Table 4. The value of Strength coefficient required for carrying out the simulation for different
n
(2)
where K is the strength coefficient, e is the exponential coefficient, UTS is the ultimate tensile strength and n is the strain hardening exponent of the material (Leu, 1999).
4.2.
Steps in simulation
The solution of model was subdivided into precisely defined time periods. Time periods corresponds to the time to execute each unique boundary condition defining the motion of each die. SHMF process was executed in two steps. Both the steps involve explicit dynamic solution technique.
4.2.1.
Step 1
This is the clamping step in which linear motion is given to the blank holder which holds the sheet in between the die. This step lasts in 0.005 s.
4.2.2.
Step 2
In this step punch progresses and deforms the blank. Internal pressure is applied inside the die to support the blank. This step lasts in 0.026 s.
4.3. 3D model for toolings, i.e. die, punch, blank and blank holder, of SHMF process were developed using Unigraphics CAD software. The CAD surfaces were then imported in IGES format (Initial Graphics Exchange Specification is neutral exchange format for 3D CAD models) to Hypermesh for pre-processing (meshing, applying friction and boundary condition) of the model. Hypermesh also create FE input file which was then solved using explicit dynamic LsDyna solver.
e n
Contact condition
During the process of sheet Hydromechanical forming the tools––die, punch and blank holder comes in contact with the blank. CONTACT FORMING ONE WAY SURFACE TO SURFACE (penalty contact) was used to define contact between the blank and the tools along with various friction coefficients. In this slave part (deformable part) is checked for contact with master part (non-deformable). Penetration is prevented by applying penalty force. Classical isotropic Coulomb model was used for modelling interfacial friction (Hallquist, 1997).
4.4.
Meshing of the model
Quadrilateral Belytschko-Lin Tsay shell element with five integration points through the thickness and one in-plane integration point was used to mesh the model. Shell thickness is equal to the blank thickness. Tools were considered non-deformable and are modelled as rigid surface without any thickness (Hallquist, 1997).
1449
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Fig. 3 – Hydroformed cups drawn during the trials.
Fig. 2 – (a) Schematic sketch of sheet hydroforming set-up used for the trial and (b) process set-up in FE Model.
4.5.
Boundary conditions
Blank holder and punch were given linear velocity for clamping and deforming the blank in step 1. Die was kept fixed. In step 2, internal pressure was modelled by LOAD Shell option of LsDyna which apply distributed pressure load over all the shell elements (Hallquist, 1997). In all the cases maximum internal (forming) pressure is kept constant and is given by Eq. (3): Maximum forming pressure =
(UTS × T) D
(3)
where UTS is ultimate tensile strength, T is tube thickness and D is minimum die fillet radius. (Maximum forming pressure calculation is guided by the smallest radius to be formed on the component by stretching the material. The above equation is based on thin wall theory and yields a fairly conservative value of max forming pressure, Singh (2003)).
5.
Experiment
Experimental set-up has been designed and fabricated by Electropneumatics and Hydraulics Pvt Ltd., Pune. The set-up has a double action press, i.e. the blank holder movement is inde-
pendent of the punch movement. This helps in controlling the blank holding force irrespective of the punch position. Tool set-up shown in Fig. 2 was used for conducting the experiments. Dimensions of tools are tabulated in Table 5. The fluid line is connected to a fluid intensifier through a hydraulic regulator, which helps in accurate control of fluid pressure inside the die cavity/fluid chamber as the blank is deformed by the punch. If the pressure is too high, then pressure in the system is reduced to the appropriate level by a user defined program. If the pressure is too low, then the regulator puts additional pressurized fluid from a pressure vessel in the system. The pressure intensifier is used to supply necessary volume and pressure to the reservoir prior to start of hydroforming process. Running tap water mixed with a rust preventive chemical is used as the hydraulic medium. Hemispherical cups with inside diameter 80 mm have been drawn from circular blanks of 225 mm diameter shown in Fig. 3. The punch has the exact dimension, as the cup while die cavity is oversized to accommodate a layer of pressurised fluid. The trial has been conducted with different settings of internal pressure in the hydroforming press. Interstitial free steels of 1 mm thickness and properties described as in Table 4a was used for cup forming.
6.
Validation of the model
The circular cups of 100 mm depth were drawn. For validating the FE model predicted thickness was compared with the experimental values. The cup was cut from the centre and thickness at various locations was measured with micrometer with least count 0.001. Fig. 4 shows the comparison of thicknesses along the cup profile. X-axis shows the distance along the profile of the component. It can be observed that the FE model under predicts the thinning in the cup. However, over-
Table 5 – Die dimensions for sheet hydroforming Inside cup diameter (mm) 80
Initial blank diameter (mm)
Maximum cup height (mm)
Sheet thickness (mm)
Die fillet radius (mm)
Punch nose radius (mm)
225
100
1
10
10
1450
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Table 6 – Simulation results Exp. no.
Stretching mode Max. draw
1 2 3 4 5 6 7 8 9
Drawing mode
Min. thickness
45.67 38 34.6 38.71 77.32 49.98 38.6 49.66 77.34
Max. draw
0.59 0.6 0.664 0.57 0.85 0.5 0.58 0.48 0.84
Min. thickness
100 100 100 100 100 100 100 100 100
0.885 0.898 0.8988 0.886 0.914 0.883 0.9085 0.868 0.9045
Fig. 4 – Comparison of finite element simulation model.
all a good correlation was observed between simulation and experimental thicknesses and hence the model was further used for performing the sensitivity analysis values.
Fig. 5 – Plot of factor effect for maximum draw depth–stretching mode.
(4) was used:
7.
Results and discussion
Maximum cup depth and corresponding maximum thinning data of the simulation results performed for each orthogonal array input sets for stretching and deep drawing mode is given in Table 6. Table 7 shows the ANOVA table for the maximum cup depth formed with STRETCHING deformation mode. Since the higher the cup depth, better is the hydroformability, larger the better type approach with objective function in Eq.
= −10 log
1 cupdepth
2 (4)
ANOVA analysis reveals that the interfacial friction between die-blank–blank holder is the most influencing factor followed by strain hardening exponent and anisotropy ratio. Friction condition between punch and blank has the least effect on the draw depth.
Table 7 – ANOVA table for maximum draw depth–stretching mode S. no.
1 2 3 4 Error Total (Error) ∗
Factor
N-value R-bar Friction A Friction B
Average by factor level 1
2
3
31.85 32.22 33.69 36.24
34.49 34.42 33.7 32.43
34.47 34.17 33.42 32.15
Factors used for pooling.
DOF
2 2 2 2 0 8 4
Sum of square
Mean square
Variation ratio
13.83 8.7 0.15 31.30
6.91 4.35* 0.075* 15.65
1.562 0.982 0.017 3.536
53.98 8.85
2.21
Contribution ratios (%)
25.6 16.1 0.2 57.9
1451
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Table 8 – ANOVA table for maximum thinning–stretching mode S. no.
1 2 3 4 Error Total (Error) ∗
Average by factor level
Factor
N-value R-bar Friction A Friction B
1
2
3
4.19 4.7 5.65 2.5
4.1 4.07 3.61 5.06
4.2 3.69 3.23 4.94
DOF
2 2 2 2 0 8 4
Sum of square
Mean square
0.018 1.646 10.22 12.49
0.009* 0.82* 5.11 6.25
24.38 1.664
0.416
Variation ratio
Contribution ratios (%)
0.011 0.989 6.147 7.508
0.74 6.7 41.66 50.88
Factors used for pooling.
Fig. 5 shows the main effects, i.e. the effect of individual factor level, on the cup depth with stretching deformation mode. It can be observed that the cup depth increases with the decrease in interfacial friction between blank-die–blank holder. Cup depth also increases with increase strain hardening exponent, plastic anisotropy of the sheet. This effect is similar to conventional stamping process. As strain hardening is the ability of a metal to become stronger as it deforms. Material with higher strain hardening exponent, the flow stress increases rapidly with strain. This tends to distribute further strain to regions of lower strain and flow stress. Thus, a material with a high n-value has a better stretchability. Better lubrication between blank-die–blank holder reduces the blank holding effect thus increases the draw depth. This also allows draw-in of material in the initial stage causing plastic anisotropy one of the important process parameter. This is also confirmed by observing the strain history of the elements of the formed cup. Maximum thinning in the cup formed is also one of the quality characteristic which defines the cup quality. Hence, ANOVA for maximum thinning in the cup on above draw depths was observed and tabulated in Table 8. As lesser the thinning in the component better is the part quality, the objective function given in Eq. (5) was used: = −10 log (maximum thinning)2
(5)
Analysis shows that the maximum thinning is influenced by friction condition between blank-die–blank holder and blank-punch interface followed by anisotropy ratio. The ANOVA table reveals that the material properties are just over
Fig. 6 – Plot of factor effect for maximum thinning at max cup depth–stretching mode.
7% responsible for thinning in the component as compared to interfacial friction between the tools. Fig. 6 shows the effect of various levels of factors on thinning in the cup. Higher the anisotropy ratio lower will be thinning in the cup. It is evident with the fact that the anisotropy ratio is also defined as the resistance sheet metal to deform normal to the thickness direction. Higher punch blank interfacial friction reduces the thinning of the component. Higher friction at the blank-punch interface causes sticking of sheet at punch nose. The deformation is more in the wall region of cup thus avoid localized thinning. On the other hand friction at the blank-die–blank holder interface increases the thinning tendency by reducing the material flow into the die cavity.
Table 9 – ANOVA table for maximum thinning at 100 mm draw depth drawing mode S. no.
1 2 3 4 Error Total (Error) ∗
Factor
N-value R-bar Friction A Friction B
Average by factor level 1
2
3
0.894 0.893 0.878 0.901
0.894 0.893 0.896 0.896
0.893 0.895 0.907 0.884
Factors used for pooling.
DOF
2 2 2 2 0 8 4
Sum of square
Mean square
6.755E−07 9.575E−06 0.001234 0.000457
3.97E−05* 0.000487* 0.058522 0.021702
0.1615 0.00105
0.000263
Variation ratio
0.075 0.924 111.08 41.195
Contribution ratios (%) 0.048 0.6 72.5 26.8
1452
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
8.
Fig. 7 – Plot of factor effect for maximum thinning (100 mm depth) drawing mode.
Thus, in order to achieve higher cup depth with minimum thickness reduction in stretching dominated deformation, better lubrication at blank-die and blank holder interfaces, higher strain anisotropy ratio, strain hardening exponent and rough punch surface are required. ANOVA table for maximum thinning in the cup with DRAWING MODE of deformation is given in Table 9. Blank holding force is maintained just enough to avoid the formation of wrinkle. It was observed in all the simulation that whole blank flow into the die cavity and hence maximum thinning at 100 mm cup depth is taken as quality characteristics. Thickness reduction in case of deep drawn hydroformed cup is influenced primarily by blank-punch interfacial friction and blank-die–blank holder interfacial friction. In the present analysis thinning of the hydroformed cup with low blank holding force (prominent drawing mode of deformation) is least sensitive toward the material properties of the sheet. This could be possible because of large frictional values chosen in the analysis. Fig. 7 shows the factor effect thickness reduction in DRAWING MODE hydroformed cups. Its shows that drawn cup will experience lower thinning with higher friction between blankpunch interface and better lubrication between blank-die and blank holder. However, above analysis is based on the additive model and need to be verified with confirmatory test. Hence, the optimum thickness values at the 100 mm cup depth for drawing mode of deformation are predicted using the linear additive model and confirmed with simulation results for the same set of parameter. Optimum set of parameters considering the lesser the better criteria were observed as n-value at level 2, r-value at level 3, Interfacial friction blank-punch friction A at level 3 and interfacial friction blank-die, blank–blank holder friction B at level 1. Maximum thickness value for the drawing mode at 100 mm cup depth were predicted for the optimum set of parameter using additive model relationship as 0.916 mm (Eq. (1)). The maximum thickness value of confirmatory simulation with the parameters at above levels was observed 0.93 confirming the correctness of the usage of additive model assumption for the case.
Conclusions
1. Finite element model was developed using dynamic explicit code LsDyna to simulate SHMF process. 2. Experiments of SHMF showed higher draw depth with excellent surface finish as compared to conventional press forming. 3. Experimental thickness distribution along the profile was found in good agreement with the results predicted from FE model. 4. Taguchi’s design of experiment was conducted on validated FE model for sensitivity analysis of SHMF process for stretching and drawing deformation modes. 5. ANOVA analysis for maximum cup depth formed with STRETCHING deformation mode shows more sensitive towards interfacial friction between die-blank–blank holder followed by strain hardening exponent and anisotropy ratio. 6. ANOVA for maximum thinning in the cup for stretching mode is influenced by interfacial friction condition between blank-die–blank holder followed by blank and punch friction condition and anisotropy ratio. 7. With prominent stretching deformation mode, higher cup depth with minimum thinning could be achieved with the good lubrication at blank-die and blank holder interfaces, higher strain anisotropy ratio, strain hardening exponent and rough punch surface. 8. ANOVA analysis for maximum thinning in the cup with DRAWING MODE of deformation lower thinning is possible with higher friction between blank and punch and better lubrication between blank-die and blank holder. Thinning in this case is not affected by the material properties, i.e. strain hardening exponent and anisotropy ratio. 9. Confirmatory simulation results with optimum set of parameters showed that the additive model (Taguchi robust design of experiment) holds good for the study.
Acknowledgements We are thankful to Electropneumatics and Hydraulics Pvt Ltd., Chakan Works, PUNE for allowing us to use the hydroforming facilities at their press shop to carrying out the experiments and necessary support of their employees during the tests.
references
Ahmetoglu, M., Hua, J., Kulukuru, S., Altan, T., 2004. Hydroforming of sheet metal using viscous pressure medium. J. Mater. Process. Technol. 146, 97–107. Dohmann, F., Hartl, Ch., 1997. Tube hydroforming-research and practical application. J. Mater. Process. Technol. 71, 174– 186. Fratini, L., Plaia, A., Valenti, P., 1997. Optimizing a deep drawing operation by robust design technique. In: Singh, U.P., Geiger, M., Kals, H.J.J., Shirvani, B. (Eds.), Proceedings of the Fifth International Conference on Sheet Metal’97. University of Ulster, Belfast, pp. 275–284. Hallquist, J.O., 1997. LSDYNA3D User’s Manual, Version 940, Livermore Software Technology Corporation.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1445–1453
Hama, T., Hatakeyama, T., Asakawa, M., Amino, H., Makinouchi, A., Fujimoto, H., Takuda, H., 2007. Finite-element simulation of the elliptical cup deep drawing process by sheet hydroforming. Finite Elem. Anal. Des. 43, 234–246. Hein, P., Vollertsen, F., 1999. Hydroforming of sheet metal pair. J. Mater. Process. Technol. 87, 154–164. Kandil, A., 2003. An experimental study of hydroforming deep drawing. J. Mater. Process. Technol. 134, 70–80. Kim, T.J., Yang, D.Y., Han, S.S., 2003. Numerical modelling of the multi stage sheet pair hydroforming process. J. Mater. Process. Technol. 151, 48–53. Koc, M., Altan, T., 2001. An overall review of the tube hydroforming (THF) technology. J. Mater. Process. Technol. 108, 384–393. Lang, L., Wang, Z.R., Kang, D.C., Yuan, S.J., Zhang, S.H., Danckert, J., Nielsen, K.B., 2004. Hydroforming highlights: sheet hydroforming and tube hydroforming. J. Mater. Process. Technol. 151, 165–177. Lang, L., Danckert, J., Nielsen, K.B., 2005a. Multi-layer sheet hydroforming: experimental and numerical investigation into the very thin layer in the middle. J. Mater. Process. Technol. 170, 524–535. Lang, L., Danckert, J., Nielsen, K.B., Zhou, X., 2005b. Investigation into the forming of a complex cup locally constrained by a round die based on an innovative hydromechanical deep drawing method. J. Mater. Process. Technol. 167, 191–200. Leu, D.K., 1999. The limiting drawing ratio for plastic instability of the cup-drawing process. J. Mater. Process. Technol. 86, 168–176. Manabe, K., Amino, M., 2002. Effects of process parameters and material properties on deformation process in tube hydroforming. J. Mater. Process. Technol. 123, 285–291. Manabe, K., Nakamura, S., 1999. Finite element simulation of hydroforming process of prebent circular tubes. Numisheet’99, 503–508. Oh, S.I., Jeon, B.H., Kim, H.Y., Yang, J.B., 2006. Applications of hydroforming processes to automobile parts. J. Mater. Process. Technol. 174, 42–55. Phadke, M., 1989. Quality Engineering Using Robust Design. Prentice Hall International, New Jersey. Shin, Y.S., Kim, H.Y., Jeon, B.H., Oh, S.I., 2002. Prototype tryout and die design for automotive pats using welded blank
1453
hydroforming. J. Mater. Process. Technol. 130–131, 121–127. Singh, H., 2003. Fundamentals of Hydroforming. Society of Manufacturing Engineers. Wu, L., Yu, Y., 1996. Computer simulation of forming automotive structural parts by hydroforming process. Numisheet’96, 324–329. Zhang, S.H., Wang, Z.R., Xu, Y., Wang, Z.T., Zhou, L.X., 2004. Recent developments in sheet hydroforming technology. J. Mater. Process. Technol. 151, 237–241.
Glossary Glossary SHMF: Sheet Hydromechanical forming FE: Finite element model 3D: 3 dimension : Overall mean of objective function : Objective function for the experimental region ai , bj , ck , dl : Deviations from caused by setting factor A at level Ai , B at the level Bj , C at level Ck and D at level Dl , respectively e: Error of the additive approximation (S/N) ratio: Signal–noise ratio BHF: Blank holding force BHP: Blank holding pressure Friction A: Friction coefficient between blank-punch Friction B: Friction coefficient between blank-die–blank holder L9 : Standard orthogonal array DOE: Design of experiments UTS: Ultimate tensile strength T: Tube thickness D: Minimum die fillet radius. ANOVA: Analysis of variance CAD: Computer aided design IGES: Initial Graphics Exchange Specification K: Strength coefficient e: Exponential coefficient n: Strain hardening exponent DOF: Degree of freedom