A trajectory optimization approach is applied to the design of a sequence of open-die forging operations in order to control the transient thermal response of a large titanium alloy billet. The amount of time the billet is soaked in furnace prior to each successive forging operation is optimized to minimize the total process time while simultaneously satisfying constraints on the maximum and minimum values of the billet’s temperature distribution to avoid microstructural defects during forging. The results indicate that a “differential” heating profile is the most effective at meeting these design goals.

Issue Section:
Technical Papers
Keywords:
forging, forming processes, optimisation, temperature distribution, transient response, control systems
Topics:
Design, Forging, Furnaces, Optimization, Temperature, Temperature distribution, Trajectories (Physics), Transients (Dynamics), Heating, Deformation
1.
Seagle
,
S. R.
,
Yu
,
K. O.
, and
Giangiordano
,
S.
,
1999
, “
Considerations in Processing Titanium
,”
Mater. Sci. Eng., A
,
263
, pp.
237
–
242
.
2.
Seshacharyulu
,
T.
,
Medeiros
,
S. C.
,
Morgan
,
J. T.
,
Malas
,
J. C.
,
Frazier
,
W. G.
, and
Prasad
,
Y. V. R. K.
,
2000
, “
Hot Deformation and Microstructural Damage Mechanisms in Extra-Low Interstitial (ELI) Grade Ti-6Al-4V
,”
Mater. Sci. Eng., A
,
279
, pp.
289
–
299
.
3.
Stengel, R. F., 1994, Optimal Control and Estimation, Dover, New York.
4.
Kirk, D. E., 1970, Optimal Control Theory: An Introduction, Prentice-Hall, Englewood Cliffs.
5.
Seshacharyulu
,
T.
,
Medeiros
,
S. C.
,
Frazier
,
W. G.
, and
Prasad
,
Y. V. R. K.
,
2001
, “
Strain-Induced Porosity During Cogging of Extra-Low Interstitial Grade Ti-6Al-4V
,”
J. Mater. Eng. Perform.
,
10
(
2
), pp.
125
–
130
.
6.
Frazier
,
W. G.
,
Malas
,
J. C.
,
Medina
,
E. A.
,
Medeiros
,
S.
,
Venugopal
,
S.
,
Mullins
,
W. M.
,
Chaudhary
,
A.
, and
Irwin
,
R. D.
,
1998
, “
Application of Control Theory Principles to Optimization of Grain Size During Hot Extrusion
,”
Mater. Sci. Technol.
,
14
, pp.
25
–
31
.
7.
Berg
,
J. M.
,
Frazier
,
W. G.
,
Chaudhary
,
A.
, and
Banda
,
S. S.
,
1998
, “
Optimal Open-Loop Ram Velocity Profiles for Isothermal Forging: A Variational Approach
,”
ASME J. Manuf. Sci. Eng.
,
120
(
4
), pp.
774
–
780
.
8.
Fedorov
,
A. G.
,
Lee
,
K. H.
, and
Viskanta
,
R.
,
1998
, “
Inverse Optimal Design of the Radiant Heating in Materials Processing and Manufacturing
,”
J. Mater. Eng. Perform.
,
7
(
6
), pp.
719
–
726
.
9.
Zabaras
,
N.
, and
Yang
,
G.
,
1997
, “
A Functional Optimization and Implementation for an Inverse Natural Convection Problem
,”
Comput. Methods Appl. Mech. Eng.
,
144
, pp.
245
–
274
.
10.
Zabaras
,
N.
,
Bao
,
Y.
,
Srikanth
,
A.
, and
Frazier
,
W. G.
,
2000
, “
A Continuum Sensitivity Analysis for Large Deformation Processes with Application to Die Design Problems
,”
Int. J. Numer. Methods Eng.
,
48
, pp.
679
–
720
.
11.
Zhao
,
G.
,
Wright
,
E.
, and
Grandhi
,
R. V.
,
1997
, “
Preform Shape Design in Metal Forming Using an Optimization Method
,”
Int. J. Numer. Methods Eng.
,
40
, pp.
1213
–
1230
.
12.
Fourment
,
L.
, and
Chenot
,
J. L.
,
1996
, “
Optimal Design for Non-Steady State Metal Forming Processes-I. Shape Optimization Method
,”
Int. J. Numer. Methods Eng.
,
39
, pp.
33
–
50
.
13.
Chung
,
S. H.
, and
Hwang
,
S. M.
,
1998
, “
Optimal Process Design in Non-Isothermal Non-Steady Metal Forming by the Finite Element Method
,”
Int. J. Numer. Methods Eng.
,
42
, pp.
1343
–
1390
.
14.
Holman, J. P., 1997, Heat Transfer, 8th ed., Mc-Graw Hill, New York.
15.
Gill, P. E., Murray, W., and Wright, M. H., 1981, Practical Optimization, Academic Press, New York.
16.
Boyer, R. R., Welsch, G. E., and Collings, E. W., Eds., 1994, Materials Properties Handbook: Titanium Alloys, ASM International, Materials Park, OH.
Copyright © 2002
 by ASME
You do not currently have access to this content.