Vacuum arc remelting (VAR) is an industrial metallurgical process widely used throughout the specialty metals industry to cast large alloy ingots. The final ingot grain structure is strongly influenced by the molten metal pool profile, which in turn depends on the temperature distribution in the ingot. A reduced-order model of the solidifying ingot was developed specifically for dynamic control and estimation of the depth of molten liquid pool atop the ingot in a VAR process. This model accounts only for the thermal aspects of the system ignoring other physical domains such as fluid flow and electromagnetic effects. Spectral methods were used to obtain a set of nonlinear dynamic equations which capture the transient characteristics of liquid pool profile variations around a quasi-steady operating condition. These nonlinear equations are then linearized and further simplified by suppressing fast modes. The resulting system was used to construct a linear-quadratic-gaussian (LQG) controller which was tested in a laboratory-scale furnace showing a good performance. A high-fidelity physics-based model is used in real-time to provide information about the solidifying ingot and potential solidification defects.

References

References
1.
Choudhury
,
A.
,
1990
,
Vacuum Metallurgy
,
ASM International
,
Materials Park, OH
.
2.
Winkler
,
O.
, and
Bakish
,
R.
, eds.,
1971
,
Vacuum Metallurgy
,
Elsevier Publishing Company
, New York.
3.
Yu
,
K.-O.
,
Domingue
,
J. A.
, and
Maurer
,
G.
,
1986
, “
Macrosegregation in ESR and VAR Processes
,”
JOM
,
38
(
1
), pp.
46
50
.10.1007/BF03257955
4.
Kou
,
S.
,
1978
, “
Macrosegregation in Electroslag Remelted Ingots
,” Ph.D. thesis, Department of Materials Science and Engineering, MIT, Cambridge, MA.
5.
Yuan
,
L.
,
Djambazov
,
G.
,
Lee
,
P. D.
, and
Pericleous
,
K.
,
2009
, “
Multiscale Modeling of the Vacuum Arc Remelting Process for Prediction on Microstructure Formation
,”
Int. J. Mod. Phys. B
,
23
, pp.
1584
1590
.10.1142/S0217979209061305
6.
Bertram
,
L.
,
Schunk
,
P.
,
Kempka
,
S.
,
Spadafora
,
F.
, and
Minisandram
,
R.
,
1998
, “
The Macroscale Simulation of Remelting Processes
,”
JOM
,
50
(
3
), pp.
18
21
.10.1007/s11837-998-0373-8
7.
Kelkar
,
K. M.
,
Patankar
,
S. V.
,
Mitchell
,
A.
,
Kanou
,
O.
,
Fukada
,
N.
, and
Suzuki
,
K.
,
2007
, “
Computational Modeling of the Vacuum Arc Remelting (VAR) Process Used for the Production of Ingots of Titanium Alloys
,” 11th World Conference on Titanium (Ti-2007), Kyoto, Japan, June 3–7.
8.
Adasczik
,
C.
,
Bertram
,
L.
,
Evans
,
D.
,
Minisandram
,
R.
,
Sackinger
,
P.
,
Wegman
,
D.
, and
Williamson
,
R. L.
,
1997
, “
Quantitative Simulation of a Superalloy VAR Ingot at the Macroscale
,”
Proceedings of the AVS Vacuum Metallurgy Conference
, Santa Fe, NM, February 16–19.
9.
Yu
,
K.-O.
, ed.,
2002
,
Modeling for Casting and Solidification Processing
,
CRC Press
, New York.
10.
Kondrashov
,
E. N.
,
Musatov
,
M. I.
,
Maksimov
,
A. Y.
,
Goncharov
,
A. E.
, and
Konovalov
,
L. V.
,
2007
, “
Calculation of the Molten Pool Depth in Vacuum Arc Remelting of Alloy Vt3-1
,”
J. Eng. Thermophys.
,
16
(
1
), pp.
19
25
.10.1134/S1810232807010031
11.
Minisandram
,
R. S.
,
Arnold
,
M.
, and
Williamson
,
R. L.
,
2005
, “
VAR Pool Depth Measurement and Simulation for a Large Diameter Ti-6Al-4V Ingot
,”
Proceedings of the 2005 International Symposium on Liquid Metal Processing and Casting (LMPC 2005), Santa Fe, NM, September 18-21
,
ASM International
,
Materials Park
, OH, Santa Fe, NM, February 21–24, pp.
1
6
.
12.
Bertram
,
L.
,
1999
, “
Transient Melt Rate Effects on Solidification During VAR of 20 Inch Alloy 718
,”
Proceedings of the 1999 International Symposium on Liquid Metal Processing and Casting
, Santa Fe, NM, February 21–24, pp.
156
167
.
13.
Yu
,
K.-O.
,
1986
, “
Comparison of ESR-VAR Processes. Part I: Heat Transfer Characteristics of Crucibles
,”
Proceedings AVS Vacuum Metallurgy Conference
on Speciality Metals Melting and Processing, Pittsburgh, PA, June 9–11, pp.
83
92
.
14.
Duda
,
J. L.
,
Malone
,
M. F.
,
Notter
,
R. H.
, and
Vrentas
,
J. S.
,
1975
, “
Analysis of Two Dimensional Diffusion Controlled Moving Boundary Problems
,”
Int. J. Heat Mass Transfer
,
18
, pp.
901
910
.10.1016/0017-9310(75)90182-9
15.
Boyd
,
J. P.
,
2001
,
Chebyshev and Fourier Spectral Methods
,
Dove
,
New York
.
16.
Beaman
,
J. J.
,
Williamson
,
R. L.
,
Melgaard
,
D. K.
, and
Hamel
,
J.
,
2005
, “
A Nonlinear Reduced Order Model for Estimation and Control of Vacuum Arc Remelting of Metal Alloys
,”
2005 ASME International Mechanical Engineering Congress and Exposition
, Orlando, FL, November 5–11,
ASME
Paper No. IMECE2005-79239, pp. 1059–1067.10.1115/IMECE2005-79239
17.
Hysinger
,
C. L.
,
Beaman
,
J. J.
,
Williamson
,
R. L.
, and
Melgaard
,
D. K.
,
1999
, “
Multiple Input Electrode Gap Control During Vacuum Arc Remelting
,”
International Symposium on Liquid Metal Processing and Casting
(LMPC 1999). Santa Fe, NM, February 21–24.
18.
Athans
,
M.
,
1971
, “
The Role and Use of the Stochastic Linear-Quadratic-Gaussian Problem in Control System Design
,”
IEEE Trans. Autom. Control
,
AC-16
, pp.
529
552
.10.1109/TAC.1971.1099818
19.
Maybeck
,
P. S.
,
1979
,
Stochastic Models, Estimation and Control, Vol. 1
,
Academic Press Inc.
, New York.
20.
Ingle
,
V. K.
, and
Proakis
,
J. G.
,
2007
,
Digital Signal Processing Using MATLAB
,
Cengage Learning
, New York.
21.
Watt
,
T. J.
,
Taleff
,
E. M.
,
Beaman
,
J. J.
,
Lopez
,
L. F.
,
Moser
,
R.
,
Bauman
,
P.
, and
Williamson
,
R. L.
,
2013
, “
Solidification Mapping of a Nickel 718 Laboratory VAR Ingot
,”
Proceedings of the International Symposium on Liquid Metal Processing and Casting
(LMPC 2013), Austin, TX, September 22–25.
22.
Van Den Avyle
,
J. A.
,
Brooks
,
J. A.
, and
Powell
,
A. C.
,
1998
, “
Reducing Defects in Remelting Processes for High-Performance Alloys
,”
J. Mater.
,
50
(
3
), pp.
22
26
.10.1007/s11837-998-0374-7
You do not currently have access to this content.