U.S. patent application number 13/374170 was filed with the patent office on 2012-05-03 for pool power-based apparatus to control vacuum arc remelting processes.
Invention is credited to Joseph J. Beaman, David K. Melgaard, Rodney L. Williamson.
Application Number | 20120106588 13/374170 |
Document ID | / |
Family ID | 45092724 |
Filed Date | 2012-05-03 |
United States Patent
Application |
20120106588 |
Kind Code |
A1 |
Williamson; Rodney L. ; et
al. |
May 3, 2012 |
Pool power-based apparatus to control vacuum arc remelting
processes
Abstract
An apparatus for controlling a vacuum remelting furnace
comprising a controller capable of adjusting electrical current to
an electrode and a controller capable of adjusting the electrode's
drive speed. The controllers adjust the current and drive speed
based on a predetermined pool power reference value. The apparatus
may also comprise a third controller that receives the adjusted
current and drive speed as inputs and sends estimated electrode
drive speed bias as output to the drive speed controller and
estimated current bias as output to the current controller.
Inventors: |
Williamson; Rodney L.;
(Albuquerque, NM) ; Melgaard; David K.;
(Albuquerque, NM) ; Beaman; Joseph J.; (Austin,
TX) |
Family ID: |
45092724 |
Appl. No.: |
13/374170 |
Filed: |
December 13, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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11501198 |
Aug 8, 2006 |
8077754 |
|
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13374170 |
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Current U.S.
Class: |
373/88 |
Current CPC
Class: |
F27B 3/085 20130101;
F27D 21/00 20130101; Y02P 10/256 20151101; Y02P 10/259 20151101;
F27D 11/08 20130101; Y02P 10/25 20151101; H05B 7/144 20130101; F27D
19/00 20130101 |
Class at
Publication: |
373/88 |
International
Class: |
H05B 7/06 20060101
H05B007/06 |
Goverment Interests
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND
DEVELOPMENT:
[0002] The United States Government has rights to this invention
pursuant to Contract No. DE-AC04-94AL85000 awarded by the U.S.
Department of Energy.
Claims
1. An apparatus for controlling a remelting furnace, said apparatus
comprising: a. an electrode located in a remelting furnace; b. an
electrical current supply capable of supplying current to the
electrode; c. a first controller capable of adjusting the current
supplied to the electrode based upon a predetermined pool power
reference value; and d. a second controller capable of adjusting
electrode drive speed based upon a predetermined pool power
reference value.
2. The apparatus of claim 1 additionally comprising a third
controller capable of receiving adjusted current and adjusted
electrode drive speed as inputs.
3. The apparatus of claim 1 additionally comprising a non-linear
third controller capable of receiving adjusted current and adjusted
electrode drive speed as inputs.
4. The apparatus of claim 1 additionally comprising a third
controller capable of receiving adjusted current and adjusted
electrode drive speed as inputs, wherein the first and second
controllers are capable of adjusting current and drive speed based
upon output from the third controller.
5. The apparatus of claim 4 wherein the third controller outputs an
estimated current bias to adjust current supplied to the
electrode.
6. The apparatus of claim 4 wherein the third controller outputs an
estimated electrode drive speed bias to adjust the electrode drive
speed.
7. The apparatus of claim 2 wherein said third controller employs
the following equation in its operation: I = - V CF 2 ( R I + R G G
) + ( V CF 2 ( R I + R G G ) ) 2 + P pool + .alpha. r C S .DELTA. A
e h sup .DELTA. ( .mu. C Sp h sup h m + ) ( R I + R G G ) ,
##EQU00005## wherein P.sub.pool is a pool power reference setpoint,
.sub.sup is a volume specific enthalpy at superheat temperature, c
is an arc power fraction to the pool surface, V.sub.CF is a cathode
fall voltage, R.sub.I is a VAR circuit resistance less an electrode
gap resistance, R.sub.G is an experimentally determined electrode
gap resistance parameter, G is an electrode gap, A.sub.e is an
electrode cross-sectional area, .alpha..sub.rr is a room
temperature thermal diffusivity, C.sub.S.DELTA. and C.sub.Sp are
material dependent constants, .mu. is a process efficiency, .DELTA.
is an electrode thermal boundary layer, and h.sub.m, is a volume
specific enthalpy at melt temperature.
8. The apparatus of claim 1 wherein said first controller employs
the following equation in its operation: f I = - ( V CF + V ^ b ) 2
( R I + R G G ^ ) + ( ( V CF + V ^ b ) 2 ( R I + R G G ^ ) ) 2 + P
pool , ref + .alpha. r C S .DELTA. A e h sup .DELTA. ^ ( .mu. ^ C
Sp h sup h m + ) ( R I + R G G ^ ) , ##EQU00006## wherein
P.sub.pool is a pool power reference setpoint, h.sub.sup is a
volume specific enthalpy at superheat temperature, c is an arc
power fraction to the pool surface, V.sub.CF is a cathode fall
voltage, R.sub.I is a VAR circuit resistance less an electrode gap
resistance, R.sub.G is an experimentally determined electrode gap
resistance parameter, G is an electrode gap, A.sub.e is an
electrode cross-sectional area, .alpha..sub.rr is a room
temperature thermal diffusivity, C.sub.S.DELTA. and C.sub.Sp are
material dependent constants, .mu. is a process efficiency, .DELTA.
is an electrode thermal boundary layer, and h.sub.m is a volume
specific enthalpy at melt temperature, V.sub.b is a voltage bias, a
circumflex over a variable indicates that it is an estimated value
supplied by a nonlinear remelting estimator, and the angular
brackets indicate variables supplied to the equation as opposed to
constants.
9. The apparatus of claim 1 wherein said second controller employs
the following equation in its operation: f G = .alpha. ^ h sup A e
{ P pool , ref - [ ( V CF + V ^ b ) I c + ( R I + R G G ^ ) I c 2 ]
} , ##EQU00007## wherein P.sub.pool is a pool power reference
setpoint, h.sub.sup is a volume specific enthalpy at superheat
temperature, c is an arc power fraction to the pool surface,
V.sub.CF is a cathode fall voltage, R.sub.I is a VAR circuit
resistance less an electrode gap resistance, R.sub.G is an
experimentally determined electrode gap resistance parameter, G is
an electrode gap, A.sub.e is an electrode cross-sectional area,
I.sub.c is a commanded current, a circumflex over a variable
indicates that it is an estimated value supplied by a nonlinear
remelting estimator, and angular brackets indicate variables
supplied to the equation as opposed to constants.
10. The apparatus of claim 1. wherein the second controller adjusts
drive speed based upon a predetermined gap distance of the
electrode from a surface of a pool of molten metal or a
predetermined depth of the electrode in slag.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a divisional patent application from
U.S. patent application Ser. No. 11/501,198 filed Aug. 8, 2006
titled "Pool Power Control in Remelting Systems" by the same
inventors and claims priority therefrom (the "Parent Application").
This divisional application is being filed in response to a
restriction requirement contained in an office action dated Apr.
13, 2009, and contains the apparatus disclosed and claimed in the
Parent Application, as officially filed, but not elected in
applicant's response to the restriction requirement. The Parent
Application is fully incorporated herein by means of this
reference.
THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT:
Non-applicable
INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC:
Non-applicable
BACKGROUND OF THE INVENTION
[0003] 1. Field of the Invention
[0004] The invention relates generally to apparatuses for
controlling remelting processes, namely vacuum arc remelting (VAR)
and electro-slag remelting (ESR) processes.
Description of the Related Art Including Information Disclosed
Under 37 CFR 1.97 and 37 CFR 1.98
[0005] In the VAR process, a cylindrically shaped, alloy electrode
is loaded into the water-cooled, copper crucible of a VAR furnace,
the furnace is evacuated, and a direct current (dc) arc is struck
between the electrode (cathode) and some start material (e.g.,
metal chips) at the bottom of the crucible (anode). The arc heats
both the start material and the electrode tip, eventually melting
both. As the electrode tip is melted away, molten metal drips off
and an ingot forms in the copper crucible. Because the crucible
diameter is larger than the electrode diameter, the electrode must
be translated downward toward the anode pool to keep the mean
distance between the electrode tip and pool surface constant. The
speed at which the electrode is driven down is called the electrode
feed rate or drive speed. The mean distance between the electrode
tip and the ingot pool surface is called the electrode gap.
[0006] Pool power control involves simultaneously controlling the
electrode feed rate and melting current to regulate the energy flux
to the ingot pool surface. The fraction of total power consumed by
melting is given by p. Under the assumption of steady-state thermal
conditions in the electrode, conduction losses along the electrode
may be neglected because the electrode burn-off rate matches the
rate at which the thermal boundary layer front propagates up the
electrode. Neglecting radiation, the melting power is equal to the
total power absorbed from the arc plasma by the electrode tip due
to electron and ion impacts. This power is input to the ingot pool
as heat contained in the dripping metal. The pool also receives
power from the arc plasma. Thus, under nominal, steady-state
conditions, total power to the ingot surface is approximated by
P.sub.pool.apprxeq.{dot over (M)}h.sub.M,sup+f(1-.mu.)IV
where f is the fraction of the arc plasma power collected by the
ingot surface, I is current, V is voltage, {dot over (M)} is
electrode melt rate and h.sub.M,sup is the mass specific enthalpy
at superheat temperature contained in the metal dripping from the
electrode tip. Under nominal processing conditions for Alloy 718,
.about.85% of the total power available is collected by the pool as
arc power and melt power, the rest being collected as arc power by
the crucible wall above the ingot surface.
[0007] The present invention provides a method and apparatus to
control a VAR (or ESR) process by controlling P.sub.pool during it.
Current state-of-the-art VAR controllers seek to control electrode
gap and melt rate. However, melt rate control during transient
melting conditions allows for large excursions in melt power and,
therefore, power delivered to the ingot pool surface. This, in
turn, causes variations in the solidification rate of the electrode
which may lead to the formation of solidification defects in the
ingot.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0008] The accompanying drawings, which are incorporated into and
form a part of the specification, illustrate one or more
embodiments of the present invention and, together with the
description, serve to explain the principles of the invention. The
drawings are only for the purpose of illustrating one or more
preferred embodiments of the invention and are not to be construed
as limiting the invention. In the drawings:
[0009] FIG. 1 is a schematic diagram of the preferred pool power
controller of the invention, with reference inputs G.sub.ref and
P.sub.pool,ref and process input commands I.sub.c and U.sub.ram,c
(commanded electrode velocity) or X.sub.ram,c (commanded electrode
position)--the VAR estimator for this controller contains a model
of the VAR melting dynamics and provides the estimated outputs
shown given the measured furnace variables and process inputs;
[0010] FIG. 2 is a diagram of the target factor space used for Test
2 of the example;
[0011] FIG. 3 is a graph of voltage and current traces for the
factor space experiment of the example--the letters GC mark gap
checks;
[0012] FIG. 4 is a plot of the gap check data against the estimated
gap from the controller;
[0013] FIG. 5 is a plot of estimated pool power, electrode gap, and
gap reference;
[0014] FIG. 6 is plot of the estimated pool power fraction for the
three powers used in the factor space experiment;
[0015] FIG. 7 is a depiction of the Test 3 electrode of the example
showing the locations of the three welds--the electrode segments
were gas tungsten arc (TIG) welded around the electrode
circumference;
[0016] FIG. 8 is a plot showing voltage and current histories for
Test 3;
[0017] FIG. 9 is a plot showing estimated pool power and melt rate
for Test 3; and
[0018] FIG. 10 is a plot showing load cell data and estimated
efficiency for Test 3.
DETAILED DESCRIPTION OF THE INVENTION
[0019] The present invention is of a VAR apparatus and method
wherein process control is accomplished primarily through control
of pool power.
[0020] To reiterate, the most common form of modern VAR process
control seeks to control process current and electrode gap.
Typically, process current is controlled to a reference setpoint
using a proportional-integral (PI) or
proportional-integral-derivative (PID) control feedback loop.
Electrode gap is usually controlled open loop by controlling the
process either to a reference voltage or a reference drip-short
frequency. Either method is based on the assumption that the
electrode gap will be controlled to a constant value if the process
is forced to faithfully track the voltage or drip-short frequency
reference. Other important open loop variables are electrode
melting rate, electrode tip shape, crown and shelf formation, power
input to the ingot top surface (pool power), the ingot-crucible
contact boundary, ingot surface morphology, and ingot pool shape
(i.e., liquidus and solidus isotherms positions). Some of these
variables are, of course, related. There are two commanded inputs
to the system for VAR of nickel-base alloys: current (I.sub.c) and
electrode ram velocity (U.sub.ram,c) or position (X.sub.ram,c).
There are two additional command inputs for titanium alloy melting:
stirring coil current and reversal time.
[0021] A different means of control involves controlling electrode
gap and electrode melting rate instead of electrode gap and process
current. In this system, process current replaces electrode melting
rate in the list of open loop variables. In other words, the
current is made to be whatever it needs to be in order to meet the
melting rate reference. A major difficulty with this method has to
do with the fact that the relationship between electrode melting
rate and melting power is both nonlinear and history dependent.
This difficulty was addressed through the development of a
nine-state advanced VAR (AVARC-I) control technology, as disclosed
in U.S. Pat. No. 6,115,404 and in Williamson et al, "Model-Based
Melt Rate Control during Vacuum Arc Remelting of Alloy 718,"
Metallurgical and Materials Transactions B, Volume 35B, February
2004, pp.101-113.
[0022] The pool power controller of the present invention
preferably employs the following assumptions: 1) a uniform, diffuse
arc exists throughout the inter-electrode region; 2) contributions
to pool power due to radiation may be neglected; 3) steady-state
melt power all returns to the pool as enthalpy contained in the
molten metal dripping from the electrode; and 4) arc plasma power
is distributed between the pool and ingot wall above the pool
according to simple geometry. Given these assumptions, the
following equation may be derived describing the pool power:
P pool = M . h sup .rho. + [ V CF I + ( R I + R G G ) I 2 ] where (
1 ) M . = - .rho. A e .alpha. r C S .DELTA. .DELTA. + .rho. C Sp
.mu. [ V CF I + ( R I + R G G ) I 2 ] h m . ( 2 ) ##EQU00001##
[0023] In these equations, {dot over (M)} is melt rate, .rho. is
density at superheat temperature, h.sub.sup is volume specific
enthalpy at superheat temperature, .epsilon. is arc power fraction
to the pool surface, V.sub.CF is the cathode fall voltage, I is the
process current, R.sub.1 is the VAR circuit resistance less the
electrode gap resistance, R.sub.G is the experimentally determined
electrode gap resistance parameter, G is electrode gap, A.sub.e is
electrode cross-sectional area, .alpha..sub.r is room temperature
thermal diffusivity, C.sub.S.DELTA. and C.sub.Sp are material
dependent constants, .mu. is process efficiency, A is electrode
thermal boundary layer, and h.sub.m is volume specific enthalpy at
melt temperature. Note that the quantity enclosed in square
brackets in these expressions defines the process electrical power
function. This quantity multiplied by e gives the fraction of the
total power collected at the pool surface from the arc plasma.
Thus, Equation (1) states that the pool power is equal to the total
enthalpy input due to the melting electrode plus the total arc
plasma power collected by the pool surface. If Equation (2) is
substituted into Equation (1) and the result is solved for current,
the pool power control equation of the invention is obtained:
I = - V CF 2 ( R I + R G G ) + ( V CF 2 ( R I + R G G ) ) 2 + P
pool + .alpha. r C S .DELTA. A e h sup .DELTA. ( .mu. C Sp h sup h
m + ) ( R I + R G G ) . ( 3 ) ##EQU00002##
[0024] This equation is preferred in order to find the current
required to give pool power P.sub.pool. A nonlinear controller is
then used that employs Equation (3). The result is similar to the
AVARC-I controller, but reference inputs are G.sub.ref and
P.sub.pool,ref instead of G.sub.ref and {dot over (M)}.sub.ref .
The process input commands are still I.sub.c and U.sub.ram,c or
X.sub.ram,c. A schematic diagram of the controller is shown in FIG.
1. The VAR estimator for this controller is preferably identical to
that of AVARC-I and so the Kalman gains are the same.
[0025] The function boxes (controllers, which can be software or
hardware components of a monolithic controller or implemened
separately in hardware/software) in FIG. 1 have the following
preferred definitions, in which a variable in angular brackets
indicates a variable that is fed into the function box and a hat
over a variable indicates an estimated quantity:
f I = - ( V CF + V ^ b ) 2 ( R I + R G G ^ ) + ( ( V CF + V ^ b ) 2
( R I + R G G ^ ) ) 2 + P pool , ref + .alpha. r C S .DELTA. A e h
sup .DELTA. ^ ( .mu. ^ C Sp h sup h m + ) ( R I + R G G ^ ) ( 4 ) f
G = a ^ h sup A e { P pool , ref - [ ( V CF + V ^ b ) I c + ( R I +
R G G ^ ) I c 2 ] } ( 5 ) ##EQU00003##
{circumflex over (V)}.sub.b in these equations is the estimated
voltage bias. Likewise, I.sub.b and .sub.ram,b in FIG. 1 are
estimated current bias and ram velocity bias, respectively.
INDUSTRIAL APPLICABILITY
[0026] The invention is further illustrated by the following
non-limiting example, which shows the efficacy of the method and
apparatus of the invention in controlling the VAR process to create
high quality metal ingots.
Example 1:
[0027] The pool power controller (method and apparatus) of the
invention was tested on an existing VAR furnace. Three tests were
performed, all melting 0.15 m (6 inch) diameter 304SS electrode
into 0.22 m (8.5 inch) diameter ingot. Test 1 was used to work out
hardware and software issues and will not be discussed. Test 2
(heat 03V-53) used a full 9-state controller to perform a factor
space experiment to confirm control under different melting
conditions. Test 3 (heat 03V-54) involved using the controller to
melt through welds. For these tests, the arc power fraction was
estimated to be 0.3.
Test 2:
[0028] A 158 kg electrode was melted at several different electrode
gap and pool power settings. The various target conditions are
shown in FIG. 2. FIG. 3 shows the voltage and current traces
associated with this test. Seven gap checks were performed by
driving the electrode down until a dead short occurred. Gap check 5
did not yield good data and the other measurements were somewhat
noisy as can be seen in FIG. 4.
[0029] FIG. 5 shows plots of estimated pool power, gap, and gap
reference. The figure shows that the estimator "believes" it is
controlling the melt correctly. It is also seen that the gap checks
constitute relatively severe perturbations to the estimated
electrode gap. This coupled with the frequent changes in electrode
gap reference probably accounts for much of the scatter in the plot
shown in FIG. 4.
[0030] The controller of the invention can be tested for internal
consistency by determining if the estimated pool powers used for
the factor space all give a value of 0.3 for .epsilon.. .epsilon.
can be calculated from the estimated pool power using the following
equation:
^ = P ^ pool - M . ^ h sup .rho. V CF + ( R I + R G G meas ) I meas
. ( 6 ) ##EQU00004##
[0031] The estimated power fraction obtained from Equation (6) and
the estimated pool power data are plotted in FIG. 6. It is evident
from this figure that the controller is functioning correctly
though there is no direct evidence that the pool power estimates
are correct in an absolute sense.
[0032] Test 3:
[0033] A 158.5 kg electrode was melted using a full 9-state
controller. The electrode consisted of four pieces butt-welded
together as depicted in FIG. 7. Each weld extended around the
electrode circumference and was performed without filler metal.
[0034] FIG. 8 shows plots of the voltage and current histories for
Test 3. The positions of the welds are marked in the figure with
the exception of Weld 3, which occurred at the very end of melting.
That is, the melt was shut off as soon as the weld was encountered.
A gap check is also marked in the figure.
[0035] FIG. 9 shows plots of estimated pool power and melt rate.
Note the relatively flat power profile and the fluctuations in melt
rate in response to the welds. It is seen that the controller is
controlling pool power while letting the melt rate float open
loop.
[0036] FIG. 10 shows load cell and estimated efficiency data for
this test. Note the efficiency spikes associated with the "flat"
spots in the load cell history. These regions correspond to pieces
of electrode falling into the pool as the melt zone encounters the
welds. Analysis shows that 0.710 kg of material fell in during the
first, 2.410 kg during the second, and 2.160 kg during the third
weld event. The sudden loss in weight causes the efficiency to
spike: the controller "thinks" that this material has melted
instantaneously. It responds by dropping the current (FIG. 8).
However, the controller soon recovers and raises the current once
it detects that the melt rate has actually slowed due to the melt
zone encountering the "cold" material above the weld.
[0037] The ingot was sliced lengthwise, polished, and macro-etched.
The melt pool profile was visible in the two places where electrode
sections fell in when the welds were melted through. The columnar
grain structure was maintained through the regions marking the weld
effects. Thus, it appears that the electrode fall-in material
melted after initially chilling the melt pool. Also visible was the
porosity and rough ingot top due to the fact that the melt was
terminated at full power when the third weld was melted though.
[0038] The tests described above demonstrate pool power control
under the assumptions used to derive Equation (3). The controller
held estimated pool power at its reference setpoint by manipulating
melt rate. Gap control during the factor space experiment was
characterized by a significant amount of noise, much of which was
probably due to the frequent gap checks and setpoint changes.
[0039] The preceding example can be repeated with similar success
by substituting the generically or specifically described reactants
and/or operating conditions of this invention for those used in the
preceding example.
[0040] Although the invention has been described in detail with
particular reference to these preferred embodiments, other
embodiments can achieve the same results. Variations and
modifications of the present invention will be obvious to those
skilled in the art and it is intended to cover in the appended
claims all such modifications and equivalents. The entire
disclosures of all references, applications, patents, and
publications cited above are hereby incorporated by reference.
* * * * *