A process analysis model to determine the limiting drawing ratio for the first draw as well as for redraws is presented considering the effects of normal anisotropy, co-efficient of friction, strain hardening and die arc radius. Predictions of the model presented are in good agreement with the available experimental results. The model can be used by the process planners to determine the minimum number of passes required to achieve the final component geometry. Using the present model, feasible operation sequences which have the minimum number of stages through which the desired cup specification can be achieved is presented for two different cup geometries.

1.
Atkinson
,
M.
,
1967
,
Sheet Metal Industries
,
44
, p.
167
167
.
2.
Chiang
,
D. C.
, and
Kobayashi
,
S.
,
1966
, “
The Effect of Anisotropy and Workhardening Characteristics on Stress and Strain Distribution in Deep Drawing
,”
ASME J. Eng. Ind.
,
88
, p.
443
443
.
3.
El-Sebaie
,
M. G.
, and
Mellor
,
P. B.
,
1972
, “
Plastic Instability Conditions in the Deep Drawing of a Circular Blank of Sheet Metal
,”
Int. J. Mech. Sci.
,
14
, p.
535
535
.
4.
Leu
,
D. K.
,
1997
, “
Prediction of the Limiting Drawing Ratio and the Maximum Drawing Load in Cup Drawing
,”
Int. J. Mach. Tools Manuf.
,
37
, p.
201
201
.
5.
Leu
,
D. K.
,
1999
, “
The Limiting Drawing Ratio for Plastic Instability of the Cup Drawing Process
,”
J. Mater. Process. Technol.
,
86
, p.
168
168
.
6.
Whitely
,
R. L.
,
1960
,
Trans. ASM
,
52
, p.
154
154
.
7.
Woo
,
D. M.
,
1968
, “
On The Complete Solution The Deep Drawing Problem
,”
Int. J. Mech. Sci.
,
10
, p.
83
83
.
8.
Wright
,
J. C.
,
1962
, “
Relationship Between Mechanical Properties, Deep Drawablity and Stretch-Formability for Some Non-ferrous Sheet Materials
,”
Sheet Metal Industries
,
39
, p.
887
887
.
9.
Hill, R., 1950, The Mathematical Theory of Plasticity, Clarendon Press, Oxford, U.K.
10.
Korhonen
,
A. S.
,
1982
, “
Drawing Force in Deep Drawing of Cylindrical Cup with Flat Nosed Punch
,”
ASME J. Eng. Ind.
,
104
, p.
29
29
.
11.
Reissner
,
J.
, and
Ehrismann
,
R.
,
1987
, “
Computer-Aided Deep Drawing of Two Part Cans
,”
CIRP Ann.
,
36
, p.
199
199
.
12.
Oskada
,
K.
,
Wang
,
C. C.
, and
Mori
,
K.
,
1995
, “
Controlled FEM Simulation for Determining History of Blank Holding Force in Deep Drawing
,”
CIRP Ann.
,
44
, p.
243
243
.
13.
Ahmetoglu
,
M.
,
Broek
,
T. R.
,
Kinzel
,
G.
, and
Altan
,
T.
,
1995
, “
Control of Blank Holder Force to Eliminate Wrinkling and Fracture in Deep Drawing Rectangular Parts
,”
CIRP Ann.
,
44
, p.
247
247
.
14.
Siegert
,
K.
,
Dannenmann
,
E.
,
Wagner
,
S.
, and
Galaiko
,
A.
,
1995
, “
Closed Loop Conrol System For Blank Holder Forces in Deep Drawing
,”
CIRP Ann.
,
44
, p.
251
251
.
15.
Esche
,
S. K.
,
Khamitkar
,
S.
,
Kinzel
,
G. L.
, and
Altan
,
T.
,
1996
, “
Process and Die Design for Multi-step Forming of Round Parts from Sheet Metal
,”
J. Mater. Process. Technol.
,
59
, p.
24
24
.
16.
Fogg
,
B.
,
1968
, “
Theoretical Analysis for the Redrawing of the Cylindrical Cups Through Conical Dies Without Pressure Sleeves
,”
J. Mech. Eng. Sci.
,
10
, p.
141
141
.
17.
Parsa
,
M. H.
,
Yamaguchi
,
K.
,
Takakura
,
N.
, and
Imatani
,
S.
,
1994
, “
Consideration of the Redrawing of Sheet Metals Based on Finite Element Simulation
,”
J. Mater. Process. Technol.
,
47
, p.
87
87
.
18.
Min
,
D. K.
,
Jeon
,
B. H.
,
Kim
,
H. J.
, and
Kim
,
N.
,
1995
, “
A Study on Process Improvements of Multi-Stage Deep Drawing by The Finite Element Method
,”
J. Mater. Process. Technol.
,
54
, p.
230
230
.
19.
Esche
,
S. K.
,
Ahmetoglu
,
M.
,
Kinzel
,
G. L.
, and
Altan
,
T.
,
2000
, “
Numerical and Experimental Investigation of Redrawing of Sheet Metals
,”
J. Mater. Process. Technol.
,
98
, p.
17
17
.
20.
Eshel
,
G.
,
Barash
,
M.
, and
Johnson
,
W.
,
1986
, “
Rule Based Modeling for Planning Axisymmetrical Deep Drawing
,”
J. Mech. Work. Technol.
,
14
, p.
1
1
.
21.
Sitaram
,
S. K.
,
Kinzel
,
G. L.
, and
Altan
,
T.
,
1991
, “
A Knowledge Based System for Process Sequence Design in Axisymmetric Sheet Metal Forming
,”
J. Mater. Process. Technol.
,
25
, p.
247
247
.
22.
Doege
,
E.
, and
Schulte
,
S.
,
1992
, “
Design of Deep Drawn Components with Elementary Calculation Methods
,”
J. Mater. Process. Technol.
,
34
, p.
439
439
.
23.
Tisza
,
M.
,
1995
, “
Expert Systems for Metal Forming
,”
J. Mater. Process. Technol.
,
53
, p.
423
423
.
24.
Ghosh, A., and Mallik, A. K., 1985, Manufacturing Science, Affiliated Ease-West Press Publishers Ltd., India.
25.
Lange, K., 1985, HandBook of Metal Forming, McGraw-Hill.
26.
Hosford, W. F., and Caddell, R. M., 1983, Metal Forming—Mechanics and Metallurgy, Prentice Hall.
27.
Rogers, R. W., and Anderson, W. A., 1971, Metal Forming—Interrelation between Theory and Practice, A. L. Hoffmanner, ed., Plenium Press.
28.
Schuler, 1988, Metal Forming HandBook, Springer.
29.
Thorp
,
J. M.
,
1973
,
Sheet Met. Ind.
,
50
, p.
99
99
.
30.
Eary, D. F., and Reed, E. A., 1974, Techniques of Pressworking Sheet Metal, Prentice Hall.
31.
Miller, F. H., 1949, Analytical Geometry and Calculus, Chapman and Hall.
You do not currently have access to this content.