046 Blank Design for a Sheet Product Based on Direct Design Method and FEM Analysis

7/27/2019 046 Blank Design for a Sheet Product Based on Direct Design Method and FEM Analysis

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Blank Design for A Sheet Metal Product Based on Direct Design Method and FEM Analysis

J.W. Yoona

, S.K. Kima

, K. Chungb

J.R Younb

and E.J. Yeonc

aLG Production Engineering Research Center, 19-1 Cheongho-Ri, Jinwuy-Myun,

PyungtaekCity, Kyungki-Do, 451-713, Korea.bSchool of Material Science and Engineering, Seoul National University, 56-1 Shinlim-Dong,

Kwanak-Gu, Seoul, 151-742, Korea.cVCR OBU, LG Electronics, 19-1 Cheongho-Ri, Jinwuy-Myun,

PyungtaekCity, Kyungki-Do, 451-713, Korea.

Abstract

The ideal forming theory was previously developed as a direct design method to guide iterative

design practices by optimizing initial blank shapes in the sheet metal forming process. In this work,

the sequential design method based on the ideal forming theory and FEM analysis was applied to

optimize a practical die design procedure for sheet metal forming. In particular, the design method

was applied to optimize the forming process of complicated sheet metal part (VCR deck chassis)

which is difficult to fabricate without good lubricant. In this sequential method, the ideal forming

theory was used to obtain an initial optimum blank shape which complies with the minimum plastic

work path condition. Based on the solution of the ideal forming theory, the FEM analysis was

iteratively utilized to further optimize the blank shape by taking account the realistic process

condition under the non-lubrication state. The experiment showed that the optimum banks obtained

from the sequential design method can form the final parts without lubrication, confirming that the

proposed sequential design procedure based on the direct design method and FEM analysis can be

successfully applied to optimize the practical die design procedure of sheet metal forming processes.

Keywords: Direct design method, Ideal forming, Optimum blank design, FEM analysis

1.IntroductionIn order to improve conventional trial-and-error based practices for optimizing forming processes,

a direct design method, called the ideal forming theory, has been previously developed [1 - 4]. In

this theory, materials are prescribed to deform following the proportional true strain path (or the

minimum plastic work path for isotropic materials) and the initial blank shape is obtained from a


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one-step backward calculation in which the final sheet product shape is specified. The theory can

be used to determine the ideal initial blank shape needed to best achieve a specified final shape

while resulting in optimum strain distributions. Because of its assumed deformation path, the

result of the theory does not completely comply with real forming so that it is used to guide the

iterative design procedure based on analytic methods.

The blank design procedure based on the ideal forming theory and the iterative applications of the

FEM analysis was shown to be effective [5, 6]. In this sequential design method, as shown in

Fig.1, the optimum blank shape obtained from the direct design method can be effectively used as

good initial guess for incremental analysis codes in order to significantly save computational and

experimental trials in the die design stage. In order to demonstrate the practical used of the

sequential method, the method was applied to design an optimum blank of a complicated VCR

deck chassis in this work. Experiments were also carried out using the optimum blank shape

developed from the sequential method to confirm the validity of the method. The automatic strain

measurement system (ASAME)[7] was also used to measure the formability of the formed part.

Fig.1 Sequential procedure utilizing Fig. 2 Target final shape(VCR deck

the direct design method chassis) to be formed

2.TheoryWhen materials are discretized with meshes and the surface traction is approximated by point

forces, the plastic work is a function of the initial position vectors X and the final position vectors

x:

Direct Design FEM Code

Incremental Analysis Code

Experimental Trials


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)X,x(WW 2,1i3,2,1ie === . (1)

In Equation 1, the value of the effective strain e is dependent on the deformation paths of

material elements and so is the plastic work. In the ideal forming theory, the minimum plastic

work path is imposed for each material. The minimum plastic work path is equivalent to the

proportional true strain path, whose principal directions are restricted to be aligned with specific

material directions for anisotropic materials. However, in the design code, the principal directions

are allowed to be arbitrary. When the proportional true strain path is imposed, the effective strain

in Equation 1, obtained from the effective strain-rate by substituting the rate of deformation

tensor & with the true strain tensor , becomes a function of x and X. In fact, the effective

strain is obtained from the flow theory by applying the deformation theory based on the minimum

plastic work path[8, 9]. When the final sheet product shape is prescribed, the final configuration

is specified so that the plastic work in Equation 1 is a function of X only. Furthermore, the initial

sheet surface on which the initial blank resides is specified in advance. The blank shape is

obtained by optimizing the plastic work [3];i.e.,

2and1ibdVX

)( ioi

eee ==

(2)

where e is the effective stress, Vo is the material volume and bi is the component of a kind of

force vector related to the external force vector. After the initial blank cutout is obtained from

Equation 2, the optimum strain distribution and intermediate shapes of a sheet during forming as

well as nodal force history are obtained under the minimum plastic work path assumption.

3.Results and DiscussionsFig.2 shows the VCR deck chassis on which a VCR head drum is located. The product requires

precise dimensional accuracy for height and slope in order to prevent the distortion of the headdrum when it is placed on the chassis. The process to fabricate this product was newly changed

from die-casting to press forming because of productivity and cost competitiveness. But, when

press forming is employed to make the product, tearing problem is the most difficult obstacle to

overcome because of the severe stretching of this product during the forming process. Fig.3

shows a schematic diagram to design the optimum blank shape using the direct design method

and incremental FEM analysis code. In the figure, the optimum blank shape is predicted by the

direct design method, when the final target shape and initial thickness are specified. Then, FEM

analysis was performed based on the optimum blank to account for the detailed process


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Fig. 3 Sequential design procedure using the direct design method and FEM analysis

Fig.4 Initial blank shapes before and after modifications

conditions, including non-proportional true strain paths, during sheet forming. Fig. 4 shows two

initial blank shapes: a blank previously obtained from 14 times experimental trials and a blank

obtained from seqiential design method. The differences were marked in the figure. In the

present work, the ABAQUS Explicit code [10] was used for the process analysis. In order to

describe no lubricant condition in this process, 0.2 was used for the Coulomb friction coefficient.

In Fig.4, the ideal blank shape obtained from the sequential design method is supposed to best

achieve a specified final shape while resulting in optimum strain distributions. In order to verify

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((OOppttiimmuumm bbllaannkkddeessiiggnn))

AAnnaallyyssiiss CCooddee

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< Blank shape obtained by

experimentally before modification >

< Blank shape optimized by

the sequential design method >


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Fig.5 Comparison of forming limit diagrams between before and after modifications

Fig.6 FLD measured by ASAME for the part formed from the modified blank

the optimum blank, incremental analysis code was introduced to perform forming analysis. Fig.5

shows FEM analysis results obtained for the blank experimentally optimized and the blank

optimized, respectively. As shown in the figure, the result obtained from the blank modified using

0

0.2

0.4

0.6

0.8

1

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

FLD(instability)FLD(fracture)Final modification

Ma

jorstrain

Minor strain

0

0.2

0.4

0.6

0.8

1

1.2

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

FLD (fracture)FLD (instability)Original (without lubrication)

Ma

jorstrain

Minor strain

Maximum thickness strain : 0.39

< Blank optimized experimentally > < Blank optimized by sequential design method>



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the sequential design method is in the safe region of FLD and the minimum thickness strain is

improved about 50 % compared to that obtained from the blank experimentally optimized. Finally,

real forming was performed using the optimum blank shape obtained from the sequential design

method to verify the better performance. Fig. 6 shows FLD measured by the automatic strain

measurement system (ASAME). It is shown that the simulation and experimental results are

compatible in Fig.5 and Fig.6, confirming the significantly improved performance of the new blank.

The optimum blank shape has been successfully feed-backed to the mass production line. LG

Electronics produces 5 million pieces of deck chassises per year using the optimum blank shape.

4.ConclusionsPractical application of the sequential design method involving the direct design method was

introduced to design the optimum blank shape of VCR deck chassis when the final target shape,

initial thickness and martial properties are specified. Experimental verification showed that the

new blank optimized using the direct design method and the sequential use of the FEM analysis

significantly better preformed than that previously optimized only experimentally. Therefore, it

was confirmed that the new design method based on the direct design method and FEM analysis

can be useful for the practical blank design procedure.

References

[1] K. Chung & O. Richmond, Int. J. Mech. Sci. 34 (1992) 575-591.

[2] K. Chung & O. Richmond, Int. J. Mech. Sci. 34 (1992) 617-633.

[3] K. Chung, J.W. Yoon and O. Richmond, Int. J. of Plasticity 16 (2000) 595-610.

[4] J.W. Yoon, K. Chung, O. Richmond and F. Barlat, Proceedings of Plasticity2000 (Eds. A.S.

Khan et al.), Neat Press, 2000, p.267.

[5] K. Chung, F. Barlat, J.C. Brem, D.J. Lege & O. Richmond, Int. J. Mech. Sci. 39 (1997) 105-

120.

[6] S.H. Park, J.W. Yoon, D.Y. Yang and Y.H. Kim, Int. J. of Mech. Sci. 41, (1999) 1217-1232.

[7] CamSys Inc., ASAME reference manual, Ver. 3.8, 1995.

[8] K. Chung & O. Richmond, Int. J. of Plasticity 9 (1993) 907-920.

[9] J.W.Yoon, D.Y. Yang and K. Chung, Comp. Methods in Appl. Mech. & Eng. 174 (1999) 23-56.

[10] HKS Inc., ABAQUS/ Exaplicit manual, Ver. 5.8, 1998.


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Figure List

Fig.1 Sequential procedure utilizing the direct design method

Fig.2 Target final shape(VCR deck chassis) to be formed

Fig.3 Sequential design procedure using the direct design method and FEM analysis





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Fig.1 Sequential procedure utilizing the direct design method

Direct Design FEM Code

Incremental Analysis Code

Experimental Trials


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Fig. 2 Target final shape(VCR deck chassis) to be formed


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Fig. 3 Sequential design procedure using the direct design method and FEM analysis

FFiinnaall TTaarrggeett SShhaappee

DDiirreecctt DDeessiiggnn MMeetthhoodd

((OOppttiimmuumm bbllaannkkddeessiiggnn))

AAnnaallyyssiiss CCooddee

((FFoorrmmiinngg AAnnaallyyssiiss))


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< Blank shape obtained by

experimentally before modification >

< Blank shape optimized by

the sequential design method >


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0

0.2

0.4

0.6

0.8

1

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

FLD(instability)FLD(fracture)Final modification

Majorstrain

Minor strain

0

0.2

0.4

0.6

0.8

1

1.2

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

FLD (fracture)FLD (instability)Original (without lubrication)

Majorstrain

Minor strain


< Blank optimized experimentally > < Blank optimized by sequential design method>



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046 Blank Design for a Sheet Product Based on Direct Design Method and FEM Analysis

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