In this paper, an optimum design is carried out with finite element analysis to determine process parameters which reduce the amount of springback and improve shape accuracy of a deep drawn product with the channel shape. Without springback simulation usually performed with an implicit solving scheme, the study uses the amount of stress deviation through the sheet thickness direction in the deep drawn product as an indicator of springback. The simulation incorporates the explicit elasto-plastic finite element method for calculation of the final shape and the stress deviation of the final product. The optimization method adopts the response surface methodology in order to seek the optimum condition of process parameters such as the blank holding force and the draw-bead force. The present optimization scheme is applied to the design of the variable blank holding force in the U-draw bending process and the application is further extended to the design of draw-bead force in a front side member formed with advanced high-strength steel (AHSS) sheets made of DP600. Results demonstrate that the optimum design of process parameters decreases the stress deviation throughout the thickness of the sheet and reduces the amount of springback of the channel shaped part. The present analysis provides a guideline in the tool design stage for controlling the evolution of springback based on the finite element simulation of complicated parts.

1.
Luo
,
L.
, and
Ghosh
,
A. K.
, 2003, “
Elastic and Inelastic Recovery after Plastic Deformation of DQSK Steel Sheet
,”
J. Eng. Mater. Technol.
0094-4289,
125
, pp.
237
246
.
2.
Chun
,
B. K.
,
Kim
,
H. Y.
, and
Lee
,
J. K.
, 2002, “
Modeling the Baushinger Effect for Sheet Metals, Part II: applications
,”
Int. J. Plast.
0749-6419,
18
, pp.
597
616
.
3.
Gau
,
J. T.
, and
Kinzel
,
G. L.
, 2001, “
A New Model for Springback Prediction in which the Bauschinger Effect is Considered
,”
Int. J. Mech. Sci.
0020-7403,
43
, pp.
1813
1832
.
4.
Huang
,
H. M.
,
Liu
,
S. D.
, and
Jiang
,
S.
, 2001, “
Stress and Strain Histories of Multiple Bending-Unbending Springback Process
,”
J. Eng. Mater. Technol.
0094-4289,
123
, pp.
384
390
.
5.
Karafillis
,
A. P.
, and
Boyce
,
M. C.
, 1996, “
Tooling and Binder Design for Sheet Metal Forming Compensating Springback Error
,”
Int. J. Mach. Tools Manuf.
0890-6955,
36
, pp.
503
526
.
6.
Song
,
N.
,
Qian
,
D.
,
Cao
,
J.
, and
Liu
,
W. K.
, 2001, “
Effective Models for Prediction of Springback In Flanging
,”
J. Eng. Mater. Technol.
0094-4289,
123
, pp.
456
461
.
7.
Gan
,
W.
,
Wagoner
,
R. H.
,
Mao
,
K.
,
Price
,
S.
, and
Rasouli
,
F.
, 2004, “
Practical Methods for the Design of Sheet Formed Components
,”
J. Eng. Mater. Technol.
0094-4289,
126
, pp.
360
367
.
8.
Gan
,
W.
, and
Wagoner
,
R. H.
, 2004, “
Die Design Method for Sheet Springback
,”
Int. J. Mech. Sci.
0020-7403,
46
, pp.
1097
1113
.
9.
Chou
,
C. H.
, and
Hung
,
I. N.
, 1999, “
Finite Element Analysis and Optimization on Springback Reduction
,”
Int. J. Mach. Tools Manuf.
0890-6955,
39
, pp.
517
536
.
10.
Liu
,
G.
,
Lin
,
Z.
,
Xu
,
W.
, and
Bao
,
Y.
, 2002, “
Variable Blankholder Force in U-shaped Part Forming for Eliminating Springback Error
,”
J. Mater. Process. Technol.
0924-0136,
120
, pp.
259
264
.
11.
Kim
,
S. H.
, and
Huh
,
H.
, 2002, “
Design Sensitivity Analysis of Sheet Metal Forming Processes with a Direct Differentiation Method
,”
J. Mater. Process. Technol.
0924-0136,
130–131
, pp.
504
510
.
12.
Palaniswamy
,
H.
,
Ngaile
,
G.
, and
Altan
,
T.
, 2004, “
Optimization of Blank Dimensions to Reduce Springback in the Flexforming Process
,”
J. Mater. Process. Technol.
0924-0136,
146
, pp.
28
34
.
13.
Viswanathan
,
V.
,
Kinsey
,
B.
, and
Cao
,
J.
, 2003, “
Experimental Implementation of Neural Network Springback Control for Sheet Metal Forming
,”
J. Eng. Mater. Technol.
0094-4289,
125
, pp.
141
147
.
14.
Cao
,
J.
,
Kinsey
,
B.
, and
Solla
,
S. A.
, 2000, “
Consistent and Minimal Springback Using a Stepped Binder Force Trajectory and Neural Network Control
,”
J. Eng. Mater. Technol.
0094-4289,
122
, pp.
113
118
.
15.
Sunseri
,
M.
,
Cao
,
J.
, and
Karafillis
,
A. P.
, 1996, “
Accommodation of Springback Error in Channel Forming using Active Binder Force Control: Numerical Simulations and Experiments
,”
J. Eng. Mater. Technol.
0094-4289,
118
, pp.
426
435
.
16.
Han
,
S. S.
, and
Park
,
K. C.
1999, “
An Investigation of the Factors Influencing Springback by Empirical and Simulative Techniques
,”
Proceeding of the 4th International Conference NUMISHEET’99
,
J. C.
Gelin
and
P.
Picart
, eds., Besançon, France, September 13–17, pp.
53
57
.
17.
Lee
,
S. W.
, and
Yang
,
D. Y.
, 1998, “
An Assessment of Numerical Parameters Influencing Springback in Explicit Finite Element Analysis of Sheet Metal Forming Process
,”
J. Mater. Process. Technol.
0924-0136,
80–81
, pp.
60
67
.
18.
Samuel
,
M.
, 2000, “
Experimental and Numerical Prediction of Springback and Side Wall Curl in U-Bending of Anisotropic Sheet Metals
,”
J. Mater. Process. Technol.
0924-0136,
105
, pp.
382
393
.
19.
Xu
,
W. L.
,
Ma
,
C. H.
,
Li
,
C. H.
, and
Feng
,
W. J.
, 2004, “
Sensitive Factors in Springback Simulation for Sheet Metal Forming
,”
J. Mater. Process. Technol.
0924-0136,
151
, pp.
217
222
.
20.
Wagoner
,
R. H.
, and
Li
,
M.
, 2005, “
Advances in Springback
,”
Proceeding of the 6th International Conference NUMISHEET 2005
,
L. M.
Smith
,
F.
Pourboghrat
,
J.-W.
Yoon
, and
T. B.
Stoughton
, eds., Detroit, MI, pp.
209
214
.
21.
Huh
,
H.
, and
Kim
,
S. H.
, 2001, “
Optimum Process Design in Sheet-Metal Forming with Finite Element Analysis
,”
J. Eng. Mater. Technol.
0094-4289,
123
, pp.
476
481
.
22.
Myers
,
R. H.
, and
Montgomery
,
D. C.
, 1995,
Response Surface Methodology: Process and Product Optimization using Design Experiments
,
Wiley
, New York.
23.
LS-DYNA3D, 2003, Keyword User’s Manual, Version 9.7, Livermore Software Technology Cooperation, Livermore, CA.
24.
HyperStudy, 2004, User’s Manual, Version 7.0, Altair Engineering, Troy, MI.
25.
Makinouchi
,
A.
,
Nakamachi
,
E.
,
Onãte
,
E.
, and
Wagoner
,
R. H.
, 1993,
Proceedings of the 2nd International Conference NUMISHEET’93
, Ishihara, Japan, August 31–September 2.
26.
Choi
,
T. H.
,
Huh
,
H.
,
Chun
,
B. K.
, and
Lee
,
J. H.
, 1997, “
Draw-Bead Simulation by an Elasto-plastic Finite Element Method with Directional Reduced Integration
,”
J. Mater. Process. Technol.
0924-0136,
63
, pp.
666
671
.
27.
Liu
,
G.
,
Lin
,
Z.
, and
Bao
,
Y.
, 2002, “
Optimization Design of Drawbead in Drawing Tools of Autobody Cover Panel
,”
J. Eng. Mater. Technol.
0094-4289,
124
, pp.
278
285
.
28.
Huh
,
H.
,
Song
,
J. H.
,
Kim
,
S. H.
, and
Kim
,
S. H.
, 2004, “
Effect of Draw-bead and Blank Holding Force on Sheet Metal Forming Process
,”
Proceeding of the 8th International Conference NUMIFORM 2004
,
S.
Ghosh
,
J. M.
Castro
, and
J. K.
Lee
, eds., Columbus, OH, pp.
766
771
.
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