Vacuum arc remelting (VAR) is an industrial metallurgical process widely used throughout the specialty metals industry to cast large alloy ingots. The VAR process is carried out in a vacuum with the aim of melting a large consumable electrode (.4 m in diameter and 3000 kg in mass and larger) in such a way that that the resulting ingot has improved homogeneity. The VAR control problem consists of adjusting arc current to control electrode melt rate, which also depends on the electrode temperature distribution and adjusting electrode ram speed to control the arc gap between the electrode and the ingot. The process is governed by a 1 dimensional heat conduction partial differential equation with a moving boundary, which leads to an infinite dimensional, nonlinear system. In addition to the process nonlinearity, the inputs and all of the available measurements are corrupted with noise. In order to design a controller and a Kalman based estimator for this process, integral methods are used to derive a set of two coupled nonlinear ordinary differential equations in time, which capture the steady state and transient characteristics of melting in a VAR furnace. The model with the experimentally measured noise is then used to construct an estimator and a controller. The system can be described by two state variables that change in time: thermal boundary layer and melted length or alternatively electrode gap. The reduced order model compares favorably to an accurate finite difference model as well as melting data acquired for Ti-6Al-4V. It will be shown how this model can be used to obtain dynamic closed loop melt rate control while simultaneously controlling electrode gap. This controller and estimator were tested on a laboratory furnace at Timet.

1.
Zanner
F. J.
, June
1979
, “
Metal transfer during vacuum consumable arc remelting
,”
Metallurgical Transactions B (Process Metallurgy)
, 1979,
10B
(
2
),
133
42
.
2.
Zanner
F. J.
, December
1981
, “
Vacuum consumable arc remelting electrode gap control strategies based on drop short propereties
,”
Metallurgical Transactions B (Process Metallurgy)
,
12B
(
4
)
721
8
.
3.
Williamson
R. L.
, October
1997
, “
Arc voltage distribution properties as a function of melting current, electrode gap, and CO pressure during vacuum arc remelting
,”
Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science
,
28
(
5
),
841
53
.
4.
Melgaard
D. K.
,
Williamson
R. L.
and
Beaman
J. J.
, March
1998
, “
Controlling remelting processes for superalloys and aerospace Ti alloys
,”
JOM
,
50
(
3
),
13
17
.
5.
Bertram, L.A., J. Brooks, D. G. Evans, A. Patel, J. A. Ven Den Navyle, and D. D. Wegman, 1999, “Transient Melt Rate Effects on the Solidification During VAR of 20 inch Alloy 718,” Proceedings of the 1999 International Symposium On Liquid Metal Processing and Casting, Alec Mitchell, Lisa Ridgeway, and Michael Baldwin, editors, Vacuum Metallurgy Division of American Vacuum Society, pp. 156–67.
6.
Carslaw, H. and J. Jaegar, 1959, Conduction of Heat in Solids, Chapter XI, Clarendon Press, Oxford.
7.
Ozisik, M., 1989, Boundary Value Problems of Heat Conduction, Dover, 332–338.
8.
Goodman
T.
,
1958
, “
The heat balance integral and its application to problems involving a change of phase
,”
ASME Trans.
80
(
2
),
335
342
.
9.
Zien
T.
,
1978
, “
Integral solution of ablation problems with time-dependent heat flux
,”
AIAA Journal
,
16
,
1287
1295
.
10.
Vujanovic
B.
, and
Jones
S.
,
1990
, “
Approximate solutions of canonical equations
,”
J. Heat Transfer, ASME
,
112
,
836
842
.
11.
Friedland, B., 1986, Control System Design: An Introduction to State-Space Methods, McGraw-Hill, Inc., New York, NY.
12.
Maybeck, P. S., 1979, Stochastic Models Estimation and Control, Vol 1, Academic Press.
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