This paper considers the problem of selecting the ram velocity profile in an isothermal forging, to best obtain a desired material microstructure. This is to be accomplished by tracking a prescribed strain rate profile. A weighting function, reflecting the rate at which the microstructure is transforming, describes the relative importance of different parts of the billet. Finding the optimal solution generally requires a search over an infinite-dimensional function space. However, for a certain class of forgings the task reduces to solving a single ordinary differential equation. The result is a globally optimal and unique ram velocity profile. The method is demonstrated for the simulated forging of a TiAl turbine disk.

1.
Berg
J.
,
Adams
R. J.
,
Malas
J. C.
, and
Banda
S. S.
,
1995
a, “
Nonlinear Optimization-Based Design of Ram Velocity Profiles for Isothermal Forging
,”
IEEE Transactions on Control Systems Technology
, Vol.
3
, No.
3
, pp.
269
278
.
2.
Berg, J., Chaudhary, A., and Malas, J., 1995b, “Open-Loop Control of a Hot Forming Process,” Simulation of Materials Processing: Theory, Methods, and Applications, A. A. Balkema, Rotterdam, pp. 539–544, S.-F. Shen and P. R. Dawson, eds.
3.
Chen, C.-C., 1978, “Finite Element Analysis of Plastic Deformation in Metal Forming Processes,” Ph.D. Thesis, University of California, Berkeley.
4.
Grandhi
R.
,
Kumar
A.
,
Chaudhary
A.
, and
Malas
J.
,
1993
, “
State-Space Representation and Optimal Control of Non-Linear Material Deformation Using the Finite Element Method
,”
International Journal for Numerical Methods in Engineering
, Vol.
36
, pp.
1967
1986
.
5.
Guillard, S., 1994, “High Temperature Micro-Morphological Stability of the (α2 + γ) Lamellar Structure in Titanium Aluminides,” Ph.D. Thesis, Clemson University.
6.
Hill, R., 1950, Mathematical Theory of Plasticity, Oxford University Press, London.
7.
Lange, K., 1975, Handbook of Metal Forming, McGraw-Hill, New York.
8.
Lee
C. H.
, and
Kobayashi
S.
,
1973
, “
New Solutions to Rigid-Plastic Deformation Problems Using a Matrix Method
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
95
, pp.
865
873
.
9.
Malas, J. C., Chaudhary, A., Mullins, W. M., Medina, E. A., Venugopal, S., Medeiros, S., Irwin, R. D., Frazier, W. G., and Srinivasan, R., 1996, Optimization of Microstructure Development: Application to Hot Metal Extrusion, ASME Conference on Engineering Systems Design and Analysis, Montpellier, France.
10.
Malas
J. C.
,
Irwin
R. D.
, and
Grandhi
R. V.
,
1993
, “
An Innovative Strategy for Open Loop Control of Hot Deformation Processes
,”
Journal of Materials Engineering and Performance
, Vol.
2
, No.
5
, pp.
703
714
.
11.
Malas
J. C.
, and
Seetharaman
V.
,
1992
, “
Using Material Behavior Models to Develop Process Control Strategies
,”
JOM
, Vol.
44
, No.
6
, pp.
8
13
.
12.
Maniatty, A., and Chen, M.-F., 1995, “Shape Sensitivity Analysis for Steady Metal Forming Processes,” Simulation of Materials Processing: Theory, Methods, and Applications, pp. 545–550, A. A. Balkema, Rotterdam, S.-F. Shen and P. R. Dawson, eds.
13.
Meyer
D.
, and
Wadley
H. N. G.
,
1993
, “
Model-Based Feedback Control of Deformation Processing with Microstructure Goals
,”
Metallurgical Transactions B
, Vol.
24B
, pp.
289
300
.
14.
Mullins, W. M., Medeiros, S. C., Frazier, W. G., and DuBrosky, B. M., 1995, Self-Improving Methods for Materials and Process Design: Sub-Scale IBR Forging from α γ-TiAl Alloy, USAF Wright Laboratory WL/MLIM Report, unpublished.
15.
Oh
S. I.
,
1982
, “
Finite Element Analysis of Metal Forming Processes with Arbitrarily Shaped Dies
,”
International Journal of Mechanical Science
, Vol.
24
, No.
8
, pp.
479
493
.
16.
Oh, S. I., Lahoti, G. D., and Aitan, T., 1981, ALPID—A General Purpose FEM Program for Metal Forming, Proceedings of NAMRC IX, State College, PA, pp. 83–92.
17.
Pietrzyk, M., Roucoules, C., and Hodgson, P. D., 1995, “Dislocation Model for Work Hardening and Recrystallization Applied to the Finite-Element Simulation of Hot Forming,” Simulation of Materials Processing: Theory, Methods, and Applications, A. A. Balkema, Rotterdam, pp. 315–320, S.-F. Shen and P. R. Dawson, eds.
18.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1986, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge. R@Rack, H. J., 1994, Private Communication, Department of Materials Science and Engineering, Clemson University, Clemson, SC.
19.
Roberts, W., Bode´n, H., and Ahlblom, B., 1979, “Dynamic Recrystallization Kinetics,” Metal Science, March-April, pp. 195–205.
20.
Schwartz, C. A., Berg, J., Mears, M., and Chang, R., 1995, “Neural Network Identification and Control in Metal Forging,” Proceedings of the American Control Conference, Seattle, WA, pp. 1782–1786.
21.
Senuma, T., and Yada, H., 1986, “Microstructural Evolution of Plain Carbon Steels in Multiple Hot Working,” Annealing Processes—Recovery, Recrystallization, and Grain Growth, Proceedings of the 7th Riso International Symposium on Metallurgy and Materials, Riso National Laboratory, Roshilde, Denmark, pp. 547–552, S. S. Hansen et al., eds.
22.
Vancheeswaran, R., Meyer, D. G., and Wadley, H. N. G., 1996, “Path Planning the Processing of Titanium Matrix Composites,” Proceedings of the IEEE International Conference on Control Applications, Dearborn, MI, pp. 834–839.
23.
Xu
S.-G.
,
Weinmann
K. J.
,
Majlessi
S. A.
, and
Cao
Q.-X.
,
1995
, “
Computer Modeling of Microstructural Evolution in the Block Upsetting of Hot Steel
,”
Transactions of NAMRI/SME
, Vol.
XXIII
, pp.
91
96
.
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