In a material hot forging process, rational preform design not only ensures that metal flows properly in die cavity and that final products have excellent quality, but also reduces tooling cost. In the present work, it is proved in theory that the differential equation of electric potential $(∇2ϕ=0)$ in the electrostatic field is similar to the differential equations of velocity potential function $(∇2φ=0)$ and velocity stream function $(∇2ψ=0)$ in velocity field during the material forming process, with all three represented in the form of the Laplace equation. Moreover, the material flow in the plastic stage and the energy in electrostatic field all meet the least-energy principle. Therefore, according to the similarity criteria, an equi-potential line (EPL) method is proposed for the design of the preform shape in material hot forging. Different voltages are applied to the billet shape and the final product shape to generate a proper electrostatic field. One optimal equi-potential line is selected among the innumerable equi-potential lines as the basic shape of the preform shape and is processed into the preform shape following a three-step procedure. The preform design by the EPL method is compared with that by the traditional industrial method. The results show that the proposed method for preform design is feasible and reliable for practical applications.

1.
Johnson
,
W.
,
Sowerby
,
R.
, and
,
J. B.
, 1970,
Plane Strain Slip Line Field: Theory and Bibliography
,
Elsevier
,
New York
.
2.
Kobayashi
,
S.
,
Oh
,
S.
, and
Alatan
,
T.
, 1989,
Metal Forming and the Finite Element Method
,
Oxford University Press
,
Oxford, UK
.
3.
,
S.
, and
Zabaras
,
N.
, 1996, “
A Sensitivity Analysis for the Design of Metal Forming Processes
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
129
, pp.
319
348
.
4.
Colla
,
D.
,
Peterwen
,
S. B.
,
Balendra
,
R.
et al.
, 1997, “
Injection Forging of Industrial Components From Thick-walled Tubes
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
119
(
4A
), pp.
537
541
.
5.
Chou
,
I. N.
, and
Hung
,
C.
, 1997, “
Three—Dimensional Finite Element Analysis of Sheet-Metal Bending With Complex Die Geometry
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
119
(
3
), pp.
324
331
.
6.
Zhao
,
G.
,
Wright
,
E.
, and
Grandhi
,
R.
, 1997, “
,”
Int. J. Numer. Methods Eng.
0029-5981,
40
, pp.
1213
1230
.
7.
Almohaileb
,
M.
,
Gunasekera
,
J. S.
,
Mehta
,
B. V.
, and
Oyekarmi
,
B.
, 2004, “
Modified Upper Bound Elemental Technique (MUBET) for Preform Design in Closed Die Forging
,”
AIP Conference Proceedings
, No. 712, Part 2,
S.
Ghosh
,
J. C.
Castro
, and
J. K.
Lee
, eds., pp.
2062
2067
.
8.
Dessenberger
,
R. B.
, and
Tucker
,
C. L.
, 2003, “
Ideal Forming Analysis for Random Fiber Preforms
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
125
(
1
), pp.
146
153
.
9.
Oh
,
S. I.
, and
Yoon
,
S. M.
, 1994, “
A New Method to Design Blocker
,”
CIRP Ann.
0007-8506,
43
, pp.
245
248
.
10.
Lee
,
S. R.
,
Lee
,
Y. K.
,
Park
,
C. H.
, and
Yang
,
D. Y.
, 2002, “
A New Method of Preform Design in Hot Forging by Using Electric Field Theory
,”
Int. J. Mech. Sci.
0020-7403,
44
(
4
), pp.
773
792
.
11.
Wang
,
J.
, 1991,
Modern Mechanical Principles of Metal Forming
,
Metallurgical Industry Press
,
Beijing
[in Chinese].
12.
Drucker
,
D. C.
,
Prager
,
W.
, and
Greenberg
,
H. J.
, 1952, “
Extended Limit Design Theorems for Continuous Media
,”
Q. J. Mech. Appl. Math.
0033-5614,
9
, pp.
381
389
.
13.
Feynman
,
R. P.
,
Leighton
,
R. B.
, and
Sands
,
M.
, 1981,
The Feynman Lectures on Physics
,
Shanghai Scientific and Technical Publishers
,
Shanghai
, Vol.
2
, pp.
221
235
[in Chinese].
14.
Liu
,
Y.
, 2004, “
Simulation and Control for Isothermal Forging Process of PM Superalloy
.” Ph.D. dissertation, Northwestern Polytechnical University, China.
15.
Liu
,
Y.
,
Li
,
F.
, and
Wu
,
S.
, 2003, “
Flow Behavior Study on Fine Grain FGH96 P/M Superalloy During Hot Deformation
,”
ACTA Aeronaut. Astronaut. Sinica
1000-6893,
24
(
3
), pp.
278
281
(in Chinese).