Commercial methods for the mechanical design of part and die shapes often rely on trial-and-error methods applied to either experiments or simulation, as guided by intuition. Academic alternatives based on optimization techniques have had slow acceptance because they require programming access to finite element analysis programs. Two practical design methods were developed for use in conjunction with standard finite element software. The first of these produces a part shape that will exhibit a specified contact area and pressure when in contact with a deformable body. The second procedure produces die shape compensated for springback, to form a specified target part shape. The simplicity and effectiveness of these techniques were illustrated by a case study for the design of a contact heating device. The methods were shown to be robust and efficient, and an automated procedure was implemented to illustrate their practicality for a production environment. Use of these techniques can substantially reduce the cost and lead time required to produce optimal sheet-formed parts while improving performance. Extensions to other design criteria and situations can be envisioned.

1.
FE-Simulation of 3-D Sheet Metal Forming Processes in Automotive Industry, 1991, Proceedings of the International Conference With Workshop Held in Zurich, Switzerland in 1991, T. Altan et al., eds., VDI Berichte, Netherlands.
2.
NUMISHEET ’93: Proceedings of the 2nd International Conference on Numerical Simulation of 3-D Sheet Metal Forming Processes, 1993, A. Makinouchi, E. Nakamachi, E. Onate, and R. H. Wagoner, eds., The Institute of Physical and Chemical Research.
3.
NUMISHEET ’96: Proceedings of the 3rd International Conference on Numerical Simulation of 3-D Sheet Forming Processes, 1996, J. K. Lee, G. L. Kinzel, and R. H. Wagoner, eds., The Ohio State University.
4.
NUMISHEET ’99: Proceedings of the 4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, 1999, J. C. Gelin and P. Picart, eds., Besanscon, France.
5.
NUMISHEET ’02: Proceedings of the 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, 2002, D. Y. Yang, S. I. Oh, H. Huh, and Y. H. Kim, eds., Jeju Island, Korea.
6.
Eary, D. F. and Reed, E. A., 1974, Techniques of Pressworking Sheet Metal, 2nd ed., Prentice-Hall Inc.
7.
Kang
,
C. G.
,
Son
,
Y. I.
, and
Youn
,
S. W.
,
2001
, “
Experimental Investigation of Semi-Solid Casting and Die Design by Thermal Fluid-solidification Analysis
,”
J. Mater. Process. Technol.
,
113
(
1–3
), pp.
251
256
.
8.
Pilani
,
R.
,
Narasimhan
,
K.
,
Maiti
,
S. K.
et al.
,
2000
, “
A Hybrid Intelligent Systems Approach for Die Design in Sheet Metal Forming
,”
Int. J. Adv. Manuf. Tech.
,
16
(
5
), pp.
370
375
.
9.
Santos
,
A. D.
,
Duarte
,
J. F.
,
Reis
,
A.
et al.
,
2001
, “
The Use of Finite Element Simulation for Optimization of Metal Forming and Tool Design
,”
J. Mater. Process. Technol.
,
119
(
1–3
), pp.
152
157
.
10.
Esche
,
S. K.
,
Khamitkar
,
S.
,
Kinzel
,
G. L.
et al.
,
1996
, “
Process and Die Design for Multi-step Forming of Round Parts from Sheet Metal
,”
J. Mater. Process. Technol.
,
59
(
1–2
), pp.
24
33
.
11.
Makinouchi
,
A.
, and
Kawka
,
M.
,
1994
, “
Process Simulation in Sheet Metal Forming
,”
J. Mater. Process. Technol.
,
46
(
3–4
), pp.
291
307
.
12.
Givoli
,
D.
, and
Demchenko
,
T.
,
2000
, “
A Boundary-Perturbation Finite Element Approach for Shape Optimization
,”
Int. J. Numer. Methods Eng.
,
47
(
4
), pp.
801
819
.
13.
Bendsoe M. P., 1995, Optimization of Structural Topology; Shape and Material, Springer, Berlin.
14.
Newman
,
J. C.
,
Taylor
,
A. C.
,
Barnwell
,
R. W.
et al.
,
1999
, “
Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations
,”
J. Aircr.
,
36
(
1
), pp.
87
96
.
15.
Ding
,
Y. L.
,
1986
, “
Shape Optimization of Structures—A Literature Survey
,”
Comput. Struct.
,
24
(
6
), pp.
985
1004
.
16.
Hsu
,
Y. L.
,
1994
, “
A Review of Structural Shape Optimization
,”
Comput Ind.
,
25
(
1
), pp.
3
13
.
17.
Phan
,
A. V.
,
Mukherjee
,
S.
, and
Mayer
,
J. R. R.
,
1998
, “
Stresses, Stress Sensitivities and Shape Optimization in Two-Dimensional Linear Elasticity by the Boundary Contour Method
,”
Int. J. Numer. Methods Eng.
,
42
, pp.
1391
1407
.
18.
Yamazaki
,
K.
, and
Shibuya
,
K.
,
1998
, “
Sensitivity Analysis of Nonlinear Material and Its Application to Shape Optimization
,”
AIAA J.
,
36
, pp.
1113
1115
.
19.
Le Riche
,
R.
, and
Cailletaud
,
G.
,
1998
, “
A Mixed Evolutionary/Heuristic Approach to Shape Optimization
,”
Int. J. Numer. Methods Eng.
,
41
, pp.
1463
1484
.
20.
Oral
,
S.
, and
Darendeliler
,
H.
,
1997
, “
The Optimum Die Profile for the Cylindrical Bending of Plates
,”
J. Mater. Process. Technol.
,
70
(
1–3
), pp.
151
155
.
21.
Kim
,
N. H.
,
Choi
,
K. K.
, and
Chen
,
J. S.
,
2001
, “
Die Shape Design Optimization of Sheet Metal Stamping Process Using Meshfree Method
,”
Int. J. Numer. Methods Eng.
,
51
(
12
), pp.
1385
1405
.
22.
Ghouati, O., Joannic, D., and Gelin, J. C., 1998, “Optimization of Process Parameters for the Control of Springback in Deep Drawing,” Numiform ’98, Netherlands, pp. 819–824.
23.
Chou
,
I.
, and
Hung
,
C.
,
1999
, “
Finite Element Analysis and Optimization on Springback Reduction
,”
Int. J. Mach. Tools Manuf.
,
39
, pp.
517
536
.
24.
Li
,
G. Y.
,
Tan
,
M. J.
, and
Liew
,
K. M.
,
1999
, “
Springback Analysis for Sheet Forming Processes by Explicit Finite Element Method in Conjunction With the Orthogonal Regression Analysis
,”
Int. J. Solids Struct.
,
36
(
30
), pp.
4653
4668
.
25.
ABAQUS Standard 5.8, 2004, Hibbitt, Karlsson & Sorensen, Inc., 1080 Main Street, Pawtucket, RI.
26.
Haug
,
E. J.
, and
Kwak
,
B. M.
,
1978
, “
Contact Stress Minimization by Contour Design
,”
Int. J. Numer. Methods Eng.
,
12
, pp.
917
930
.
27.
Li
,
W.
,
Li
,
Q.
,
Steven
,
G. P.
, and
Xie
,
Y. M.
,
2003
, “
An Evolutionary Shape Optimization Procedure for Contact Problems in Mechanical Designs
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
217
, pp.
435
446
.
28.
Hilding
,
D.
,
Torstenfelt
,
B.
, and
Klarbring
,
A.
,
2001
, “
A Computational Methodology for Shape Optimization of Structures in Frictionless Contact
,”
Comput. Methods Appl. Mech. Eng.
,
190
, pp.
4043
4060
.
29.
Karafillis
,
A. P.
, and
Boyce
,
M. C.
,
1992
, “
Tooling Design in Sheet Metal Forming Using Springback Calculations
,”
Int. J. Mech. Sci.
,
34
, pp.
113
131
.
30.
Karafillis
,
A. P.
, and
Boyce
,
M. C.
,
1992
, “
Tooling Design Accommodating Springback Errors
,”
J. Mater. Process. Technol.
,
32
, pp.
499
508
.
31.
Karafillis
,
A. P.
, and
Boyce
,
M. C.
,
1996
, “
Tooling and Binder Design for Sheet Metal Forming Processes Compensating Springback Error
,”
Int. J. Mach. Tools Manuf.
,
36
, pp.
503
526
.
32.
Gan, W., and Wagoner, R. H., 2004, “Die Design Method for Springback,” Int. J. Mech. Sci., accepted for publication.
33.
Karafillis, A. P., 1994, “Tooling Design for Three-Dimensional Sheet Metal Forming Using Finite Element Analysis,” Ph.D. thesis, MIT.
34.
Hajaligol
,
M. R.
,
Deevi
,
S. C.
,
Sikka
,
V. K.
et al.
,
1998
, “
A Thermomechanical Process to Make Iron Aluminide (FeAl) Sheet
,”
Mater. Sci. Eng., A
,
258
(
1–2
), pp.
249
257
.
35.
Deevi
,
S. C.
, and
Swindeman
,
R. W.
,
1998
, “
Yielding, Hardening and Creep Behavior of Iron Aluminides
,”
Mater. Sci. Eng., A
,
258
(
1–2
),
203
210
.
36.
Deevi
,
S. C.
,
2000
, “
Powder Processing of FeAl Sheets by Roll Compaction
,”
Intermetallics
,
8
(
5–6
),
679
685
.
37.
Stoloff
,
N. S.
,
Liu
,
C. T.
, and
Deevi
,
S. C.
,
2000
, “
Emerging Applications of Intermetallics
,”
Intermetallics
,
8
(
9–11
),
1313
1320
.
38.
Stoloff
,
N. S.
,
1998
, “
Iron Aluminides: Present Status and Future Prospects
,”
Mater. Sci. Eng., A
,
258
(
1–2
),
1
14
.
39.
ABAQUS Standard 5.8 Manual, 1998, Element B21, ABAQUS, Inc. Pawtucket, RI. pp. 15.8.3-1.
40.
Li
,
K. P.
,
Carden
,
W. P.
, and
Wagoner
,
R. H.
,
2002
, “
Simulation of Springback
,”
Int. J. Mech. Sci.
,
44
, pp.
103
122
.
41.
Wagoner, R. H., “Sheet Springback,” chpt. in Continuum Scale Simulation of Engineering Materials, D. Raabe et al., eds., Wiley.
42.
Geng
,
L. M.
, and
Wagoner
,
R. H.
,
2002
, “
Role of Plastic Anisotropy and Its Evolution on Springback
,”
Int. J. Mech. Sci.
,
44
, pp.
123
148
.
43.
Carden
,
W. D.
,
Geng
,
L. M.
,
Matlock
,
D. K.
, and
Wagoner
,
R. H.
,
2002
, “
Measurement of Springback
,”
Int. J. Mech. Sci.
,
44
, pp.
79
101
.
44.
Wagoner, R. H., Carden, W. D., Carden, W. P., and Matlock, D. K., 1997, “Springback after Drawing and Bending of Metal Sheets,” Proc. IPMM ’97-Intelligent Processing and Manufacturing of Materials, T. Chandra, S. R. Leclair, J. A. Meech, B. Verma, M. Smith, and B. Balachandran, eds., University of Wollongong, 1, pp. 1–10.
45.
Sachs, G., 1951, Principles and Methods of Sheet Metal Fabricating, Reinhold Publishing Corp., New York.
46.
Wilson, F. W., 1955, Die Design Handbook, First Edition, McGraw-Hill, New York.
47.
Gardiner
,
F. J.
,
1957
, “
The Springback of Metals
,”
Trans. ASME
,
79
, pp.
1
9
.
48.
Schroeder
,
W.
,
1943
, “
Mechanics of Sheet-Metal Bending
,”
Trans. ASME
,
65
, pp.
817
827
.
49.
Smith D. A., 1990, Die Design Handbook, Third Edition, Society of Manufacturing Engineers.
50.
Suchy, I., 1997, Handbook of Die Design, McGraw-Hill, New York.
51.
Sanchez, L., Robertson, R. D., and Gerdeen, J. C., 1996, “Springback of Sheet Metal Bent to Small Radius/Thickness Ratios,” SAE Paper 960595, Warrendale, PA, Society of Automotive Engineers.
52.
Model FX10K, Wire EDM, Mitsubishi, MC Machinery Systems, Inc., Wood Dale, Illinois, USA.
53.
Model QC-10SA, Laser Profiler, Quest Integrated, Inc., Kent, Washington, USA.
You do not currently have access to this content.