A Finite Element Based Die Design Algorithm for Sheet-Metal Forming on Reconfigurable Tools

[+] Author and Article Information
Simona Socrate, Mary C. Boyce

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

J. Eng. Mater. Technol 123(4), 489-495 (Jul 24, 2000) (7 pages) doi:10.1115/1.1395576 History: Received July 24, 2000
Copyright © 2001 by ASME
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Hardt, D. E., Boyce, M. C., Ousterhout, K. B., Karafillis, A., and Eigen, G. M., 1993, “A CAD Driven Flexible Forming System for Three-Dimensional Sheet Metal Parts,” Sheet Metal and Stamping Symposium, Int. Cong. and Exp., Detroit, MI, SAE Technical Paper Series 930282, pp. 69–76.
Valjavec, M. 1999, “A Closed-loop Shape Control Methodology for Flexible Stretch Forming over a Reconfigurable Tool,” Ph.D. thesis, MIT.
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.
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.
Cao,  J., and Boyce,  M. C., 1997, “A Predictive Tool for Delaying Wrinkling and Tearing Failures in Sheet Metal Forming,” ASME J. Eng. Mater. Technol., 119, pp. 354–365.
Grodzinsky M. S., 1996, ‘Testing a Closed-loop Forming Algorithm on a Part Created by Discrete Die Stretch Forming,’ MEEE thesis, MIT.
Webb,  R. D. and Hardt,  D. E., 1991, “A Transfer Function Description of Sheet Metal Forming for Process Control.” ASME J. Eng. Ind., 113, pp. 44–54.


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(a) The full scale tool measures 4ft×6 ft in plan area with 2688 1.25 in square pins. (b) Sheet metal part formed on reconfigurable die. Note the interpolating polymer layer (white) inserted between the workpiece and the die to prevent dimpling of the part.
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Models of individual pins with different choices for the smoothing parameter
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Stretch forming on discrete die without an interpolating layer. (a) Pressure on the workpiece (1/4 symmetry). Note that the individual pins are not part of the model, and are only shown to help visualize the die geometry. (b) Pattern of residual plastic strain in the workpiece (dimpling). (c) Deformed configuration of the workpiece at the end of the wrapping stage (1/4 symmetry). The deformation is magnified by a factor of 30.
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(a) Finite element model for stretch forming over a discrete die with an interpolator. (b) Distribution of pressure in the interpolator at the end of the wrapping stage.
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Geometry of the die used in the validation of the detailed numerical model
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Detailed model representing conditions in the central region of the die
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Comparison between predictions of unloaded sheet configurations obtained by the detailed model for two different levels of friction, and experimental measurements 6
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Geometry of the simplified equivalent die model in relation to pin positions. The offset between the pin surface and the equivalent die surface is equal to the interpolator thickness.
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Compression stress in the interpolator for a 3×3 pin array indentation test (double symmetry conditions are used to reduce the model to 1/4 of the actual geometry)
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Equivalent die model for an asymmetric die. The corresponding discrete die comprises 23×24 1/2 in. pins with a 1/2 in. interpolator. The finite element mesh for the blank is also shown.
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Comparison between equivalent model predictions and experimental part shape
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Double curvature die. Surface through the centers of the pin caps.
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Double curvature die. (a) Finite element mesh (1/4 symmetry). (b) Contact pressure between the sheet and the equivalent die at the end of the wrapping stage.
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Springback deflection of the workpiece upon unloading [in]. Numerical predictions of the equivalent die model. (a) view from (−1 −1 1); (b) view from (001); (c) view from (−1, 0, 0). Stretching direction is (1,0,0).
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Springback deflection of the workpiece upon unloading [in]. Experimental measurements. (a) view from (−1 −1 1); (b) view from (001); (c) view from (−1, 0, 0). Stretching direction is (1,0,0).
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A schematic representation of the spring-forward algorithm. (a) unloading from reference die. (b) Unloading from spring-forward die. (c) load reference shape to obtain spring-forward die shape. The loading conditions, M′ , are not known a priori and must be determined iteratively.
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Comparison of experimental part shapes formed on the “reference die” and on the “spring-forward die.” The solid line indicates the reference/desired part shape.



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