A theory employing the concept of potential flow and an easily implemented numerical method are developed. It can offer a preliminary prediction of the optimum blank shape with a little computational effort. The effects of the material anisotropy and the interfacial friction between the workpiece and blank holder on the material flow can be modeled by superimposing a “sink” or “source” term in the potential field. Variations in the cup wall thickness are considered. Both convex and non-convex punch profiles are studied. Generally speaking, the contours of the present theory are smoother than the solutions from the slip-line method. The discrepancy of the optimum blank contours between the plane strain and anisotropic cases is more significant for polygon and irregular cup drawing. The influence of friction on the optimum blank contour is not negligible.
Issue Section:
Research Papers
1.
Almetoglu
M.
Broek
T. R.
Kinzel
G.
Altan
T.
1995
, “Control of Blank Holder Force to Eliminate Wrinkling and Fracture in Deep-Drawing Rectangular Parts
,” Annals of the CIRP
, Vol. 44
, pp. 247
–250
.2.
Banerjee, P. K., and Butterfield, R., 1981, Boundary Element Methods in Engineering Science, McGraw-Hill, London, UK.
3.
Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C., 1984, Boundary Element Techniques, Springer Verlag, Berlin and New York.
4.
Chen, J. T., and Hong, H. K., 1992, Boundary Element Method, 2nd Edt., Taipei Publ., Taipei, Taiwan.
5.
Doege, E., 1985, “Prediction of Failure in Deep Drawing,” Computer Modelling of Sheet Metal Forming Process; Theory, Verification and Application, 12th Automotive Material Symposium, TMS-AIME, Wang, N. M., and Tang, S. C., eds., University of Michigan, Ann Arbor, Michigan, pp. 209–224.
6.
Duncan
J. L.
Sowerby
R.
1981
, “Computer Aids in Sheet Metal Forming
,” Annals of the CIRP
, Vol. 30
, No. 2
, pp. 541
–546
.7.
Hill
R.
The Mathematical Theory of Plasticity
, Oxford University Press, (also Proc. Roy. Soc.
, Vol. 198A
, p. 281
281
, 1948
)8.
Hasek, V. V., and Lange, K., 1979, “Use of Slip Line Field Method in Deep Drawing of Large Irregular Shaped Components,” Proc. of 7th NAMRC, Ann Arbor, Michigan, pp. 65–71.
9.
Hosford, W. F., and Caddell, R. M., 1993, Metal Forming, Mechanics and Metallurgy, 2nd Int. Ed., Prentice Hall.
10.
Iseki, H., and Murota, T., 1984, “Analysis of Deep Drawing of Non-Axisymmetric Cups by the Finite Element Method,” Proc. 1st ICTP, pp. 678–684, Tokyo.
11.
Jimma
T.
1970
, “Deep Drawing of Convex Polygon-Shells—Researches on the Deep Drawing of Sheet Metal by the Slip Line Theory, 1st Report
,” J. Japan Soc. Technology for Plasticity
, Vol. 11
, No. 116
, pp. 653
–670
.12.
Jimma
T.
Kuwabara
T.
Choi
S. C.
1984
, “Researches on the Deep Drawing of Reentrant Contour Shell
,” Advanced Tech. of Plasticity
, Vol. 2
, pp. 1091
–1096
.13.
Johnson, W., Sowerby, R., and Venter, R. D., 1982, Plane Strain Slip Line Fields for Metal Deformation Processes, Pergamon Press, Oxford, U.K.
14.
Karima
M.
1989
, “Blank Development and Tooling Design for Drawn Parts Using a Modified Slip Line Field Based on Approach
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 111
, No. 4
, pp. 345
–350
.15.
Kawai
N.
Mori
T.
Hayashi
H.
Kondoh
F.
1987
, “Effects of Punch Cross-Section on deep Drawability of Square Shell of Aluminum Sheet
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 109
, pp. 355
–361
.16.
Liu
F.
Sowerby
R.
1991
, “The Determination of Optimum Blank Shapes When Deep Drawing Prismatic Cups
,” J. Mater. Shaping Technol.
, Vol. 9
, No. 3
, pp. 153
–159
.17.
Mielnik, E. M., 1993, Metalworking Science and Engineering, McGraw-Hill.
18.
Osakada
K.
Wang
C. C.
Mori
K.
1995
, “Controlled FEM Simulation for Determining history of Blank Holding Force in Deep Drawing
,” Annals of the CIRP
, Vol. 44
, pp. 243
–246
.19.
Rubenkova, L. A., 1969, “Determination of the Stress Field in the Flange of a Blank at the Start of Drawing,” Kuznechno-Shtampovochnoe Proizvodstvo, No. 3, pp. 27–33.
20.
Rubenkova, L. A., and Kazakov, Y. P., 1969, “Plastic Flow in a Complex Shaped Flange during Drawing,” Plastic Flow of Metals, Tomlenov, A. D., ed., Vol. 2, No. 3, pp. 28–33.
21.
Saha, P. K., 1993, “Boundary Friction Measurements in Sheet Metal Forming,” PhD dissertation, Northwestern University, Evanston, IL.
22.
Siegert
K.
1993
, “CNC Hydraulic Multipoint Blank Holder System for Sheet Metal Forming Processes
,” Annals of the CIRP
, Vol. 42
, No. 1
, pp. 319
–322
.23.
Siegert
K.
Dannenmann
E.
Wagner
S.
Galaiko
A.
1995
, “Closed-Loop Control System for Blank Holder Forces in Deep Drawing
,” Annals of the CIRP
, Vol. 44
, No. 1
, pp. 251
–254
.24.
Toh
C. H.
Kobayashi
S.
1985
, “Deformation Analysis and Blank Design in Square Cup Drawing
,” Int. J. Machine Tool Design and Res.
, Vol. 25
, pp. 15
–32
.25.
Wilson
D. V.
Butler
R. D.
1961
–2
, “The Role of Cup-Drawing Tests in Measuring Drawability
,” J. Inst. Met.
, Vol. 90
, pp. 473
–483
.26.
Wood, R. D., Mattiasson, K., Honnor, M. E., and Zienkowicz, O. C, 1986, “Viscous Flow and Solid Mechanics Approaches to the Analysis of Thin Sheet Forming,” Computer Modeling of Sheet Metal Forming Processes, Wang, N. M. and Tang, S. C., eds., pp. 121–130.
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