Relationship between Furnace Voltage Signatures and the

Operational Parameters Arc Power, Arc Current, CO Pressure,

and Electrode Gap during Vacuum Arc Melting INCONEL 718
F.J. ZANNER, L.A. BERTRAM, R. HARRISON, and H. D. FLANDERS

Transfer of metal during vacuum arc remelting creates a signature on the voltage waveform called a
drop short, and subsequent arc reignition sometimes creates a signature called an anode spike. The
frequency of these events is used for in situ control of electrode gap and, at the present time, their use
is limited to melting at conditions of constant current and CO pressure. Statistically designed experi-
ments were conducted in a production melt shop to evaluate the influence of the independent variables
arc power or current, CO pressure, and electrode gap on the frequency of these events. Approximately
5000 kg of INCONEL* 718 alloy 0.406 m diameter electrodes were vacuum arc remelted into
0.457 m diameter ingots. The experimental results produced regression models which show a three
way interaction of the independent variables to be the dominant term with increases in each indepen-
dent variable producing a power-law reduction in frequency. The inverse nature of these relationships
is created by the behavior of the cathode spots, system geometry, and unresolved physics. The models
perform accurately at gaps <25 mm and exhibit considerable error at gaps >25 mm. Implications of
the results are discussed from the standpoint of arc furnace control.

I. INTRODUCTION value are usually controlled by one of (1) drop short fre-
quency, (2) anode spike frequency (commonly called hash),
OPTIMIZATION of vacuum arc remelt ingot quality oc- (3) furnace voltage, or (4) operator intervention.
curs when steady melting and solidification conditions are The basic geometry of the vacuum arc remelt process
maintained. Melting and solidification are coupled to the dictates that control will be difficult in part because of strong
metal vapor arc which supplies the energy for melting and sensitivity of electrode gap ge (mm) to electrode uniformity.
generates the Lorentz and buoyancy forces which drive the
For example, suppose a uniform electrode of cross sectional
liquid metal in the pool ahead of the dendritic solidification area Ae (mm 2) and density, p (g/mm 3) is being melted at a
front. The maintenance of optimal steady melting conditions constant mass melt rate M (g/s) into an ingot of area A,
is accomplished by stabilizing the arc in a diffuse state so it (mm2). Then constant electrode gap will result when
behaves as a macro-uniform source of heat (on a macro time
scale appropriate to the thermal diffusion speed) across the
electrode face and generates a diffuse steady distribution of ve = -1 ) Ill
current on the anode surfaces including the pool.
During melting the furnace operator can control, with holds. This means that changes in electrode uniformity AAe
good accuracy and resolution, the melting current and the cause fractional velocity changes hVe/Ve which are propor-
electrode velocity. He strives to maintain steady conditions, tional to the ratio A A e / ( A , / A e - 1). For large melts
usually by holding the melting current constant and match- (A,/Ae - 1) is a small quantity, and as a result electrode
ing the electrode velocity to the melt rate and thereby main- nonuniformity due to solidification pipe, porosity, and sur-
taining a constant electrode gap.* Because it is not possible face conditioning can require large changes of Ve in order to
maintain constant gap.
*Electrode gap is arbitrarily defined as the average spacing between the In the velocity Eq. [ 1], melt rate ~/appears as a factor.
electrodes and is determined by measuring the distance required to drive the
electrode down to sustain a short of 0.1 second.t
Thus, anything which alters melt rate requires velocity
changes to maintain gap. It has been shown in previous
to obtain a direct measurement of electrode gap during pro- work that melt rate depends on an interaction of electrode
duction melting, algorithms based on drop short and anode gap and arc power. For instance, increasing the gap from
spike frequency or period ~ are sometimes utilized to esti- 5 mm to 50 mm creates a 25 pct reduction in melt rate
mate gap. during vacuum arc remelting of INCONEL 718 alloy. 2 This
Present gap control practice, then, consists of varying the power-gap interaction suggests a connection between gap
electrode velocity or feed rate V~ (mm/s) around a nominal and arc configuration. Such a connection was supported by
value which is selected based on previous experience. Ad- the observation of changing ingot surface conditions as a
justments to the feed rate AVe (mm/s) around the nominal function of electrode gap and power] When operating at
intermediate and long electrode gaps (25 to 50 mm), these
*INCONEL is a trademark of the INCO family of companies.
melt rate and surface condition changes implied a con-
stricted arc which can create an unsteady nonuniform cur-
E J. ZANNER and L. A. BERTRAM are with Sandia National Labora- rent distribution on the anode or pool surface and in turn
tories, Albuquerque, NM 87185; R. HARRISON is with Cameron Iron
Works, Houston, TX; and H. D. FLANDERS is with Special Metals Cor-
influence the ingot fluid flow. Similar observations were
poration, New Hartford, NY 13413. also made when CO pressure in the furnace was increased
Manuscript submitted May 6, 1985. from 1.33 Pa (10/xm Hg) to 13.3 Pa (100/zm). 2

METALLURGICAL TRANSACTIONS B VOLUME 17B, JUNE 1986--357

 Another implication of electrode gap interaction with arc center point of the cube, two trials were made at a point
power to change the arc configuration is that the electrode within the factor space, and selected trials were made at the
shape can change. This results from the nonuniform heat vertices of the cube (see Figure 1) to improve prediction
distribution on the molten face of the electrode. It is clear efficiency. Only data from Experiment II in Reference 2 are
that the changing shape requires changing V~ to hold con- used in this paper, and observation 35 was dropped because
stant effective gap. it was discovered that a lateral translation of the electrode
This paper addresses the physics questions which control was performed shortly before observation 35 was made.
the frequency of the drop short and anode spike events as a This translation precluded an assumption of quasi-steady
function of the independent variables arc power, CO pres- conditions at the electrode (cathode) face. Data from
sure or arc current, and electrode gap. The goal of this work Experiment I in Reference 2 were not used because of mar-
is to develop and evaluate algorithms which incorporate ginal steadiness in some of the low melt rate trials as dis-
these independent variables and can be used to predict the cussed in that work. It should be pointed out that a load cell,
electrode gap in a production environment. Experiments which provided continuous measurement of the electrode
were conducted during vacuum arc remelting of a 0.406 m mass, was used in Experiment II to determine, in situ, the
diameter INCONEL 718 alloy electrode into a 0.457 m attainment of quasi-steady conditions on the electrode face.
diameter ingot. Responses of the dependent variables drop Electrode travel rate (ram velocity) was selected by trial and
short frequency and anode spike frequency were evaluated error to provide a constant electrode gap over each experi-
as a function of the independent variables utilizing a modi- mental interval.
fied Box-Behnken experimental design. 3 Independent variables for these experiments are arc
The paper starts with a section on experimental details. power Pro, arC current 1~, CO pressure Pco, and electrode
Experimental apparatus, data acquisition, experimental de- gap ge. The experimental ranges for these variables are as
sign, and statistical techniques are discussed in this section. follows:
Next the experimental results are presented. Regression
models are presented for drop short frequency and anode 95kW-<Pm < 257kW
spike frequency as a function of the independent variables.
An error analysis is also included in this section. Lastly, the 5 k A - < l m - < 10kA
results are enumerated in a discussion section followed by 1.46 Pa (11 p,m) < Pco -< 14.63 Pa (110/zm)
conclusions.
5 m m - < g e -< 5 4 m m .

II. EXPERIMENTAL DETAILS The dependent variables are drop short frequency fos (Hz)
and anode spike frequency fAs (Hz).
General details concerning the experiments and data ac- Magnetic tapes containing a continuous analog record for
quisition were published in Reference 2. The experimental each trial were used to archive the data with at least l0 kHz
factor space was arranged according to a modified Box- resolution. The independent variable records on the mag-
Behnken design where values of the independent variables netic tape were digitized at 10 points per second and aver-
lie on the center points of the cube edges as shown in aged over the trial interval with a DEC 11/34 computer.
Figure I. This design was chosen to minimize the number Drop shorts and anode spikes were detected on the voltage
of trials required and to improve prediction accuracy of waveform with a digital differentiating technique. This tech-
nonlinear effects. In addition, four trials were made at the nique was selected because the rise and fall slopes associ-
ated with the leading and trailing edges of drop shorts and
anode spikes are of the order of l05 v/s. 4 These voltage
gradients are much larger than any other gradients on the
voltage waveforrn. Thus, the gradients can provide a posi-
tive identification scheme which is not dependent on voltage
threshold settings. Differentiation was accomplished by
q digitizing the voltage waveform from the magnetic tape at
l0 kHz and subtracting adjacent points. The voltage level of
the digitized signal was also used to test the differentiation
9 9 scheme. A plot of dv/dt as a function of time yields the

9; J typical signatures illustrated in Figures 2 and 3. Pattern

recognition software was used to distinguish anode spikes
and drop shorts and each event was added to a totaling
register in the computer. Average frequencies were obtained
u
from these totals. A complete tabulation of the data and
averages is contained in Table I.
1.33 4 Multiple linear regression 5 and nonlinear estimating 6'7
CO Pressure (Pa) techniques were used to construct models which describe the
Fig. 1 --Experimental design: dots represent approximate location of rep- response of the dependent variable as a function of the
licate trials. magnitude of the independent variables.

358--VOLUME 17B, JUNE 1986 METALLURGICAL TRANSACTIONS B

 -50 I I I

-40-
a)
3~l
-25

0
"0 " 2o
-30-
Q
01
Q 9O~ - 1 5 -
-20- 4,P
0 m
O
> -lO-

-10-
--5"

O" I I 10 s 0 - ---------;~
b)
10 s b)

0O I
v
to
v
0

-10 s

-10 S
- I I i i'
0 0.005 0.010 0.015 0.020
0 0.005 0.010 0.015 0.020
Time (seconds)
Fig. 2--Voltage waveform (a) and its derivative (b) for a drop short with Time (seconds)
an anode spike. Fig. 3 - - V o l t a g e waveform (a) and its derivative (b) for a drop short
without an anode spike,

llI. RESULTS which demonstrate the response of these models to changes

All of the models are of the form in P~ and ge and I~ and ge at a constant CO pressure of
1.33 Pa (10/xm) are presented in Figures 4 through 7. In
-{XI \ c l [ X 2 \ c2 [ X 3 \ e3
addition, the effect of pressure is demonstrated with plots of
drop short frequency as a function of ge and I, at CO
pressures of 6.65 Pa (50/zm) and 13.3 Pa (100 ~m) in
where f is the estimated value of frequency (Hz), B0 is a Figures 8 and 9, respectively.
constant; X] is melting power, Pm (kW), or melting current, A residual vs time plot for the drop short frequency model
Im (kA); X2 is CO pressure, Pco (/xm Hg); X3 is electrode (Ira, Pco, ge) is illustrated in Figure 10. This plot is typical
gap, ge (mm), e is the standard error of the residuals, and for all frequency models.
f is the measured value of frequency. A bar over a variable Two sigma error intervals for each trial based on ge were
indicates the average value of the variable for all of the computed utilizing a calibration interval estimation proce-
experimental trials. dure based on the Z prime - Z inverse (D) matrix5 and
It should be pointed out that models of this form are not natural log linearization of each model. A detailed descrip-
unique but they were selected based on surveys of linear tion of this procedure is included in the Appendix. The
models with all cross products and quadratic terms and performance of each model in predicting ge is demonstrated
nonlinear models of the form in plots of ge, +- 2~ vs ge, in Figures 11 through 14. A line
= (X2) Cl + having a slope of one is drawn from the origin in these plots
to demonstrate the response for a perfect fit.
Trials 7, 8, 27, and 28 in Table I were made in the center
In every instance, models described by Eq. [2] produced an region of the factor space. Drop short frequencies of 3.06,
error that was less than all other models surveyed. 2.28, 0.44, and 0.50 Hz, respectively, and anode spike
Constants, exponents, and error terms for drop short and frequencies of 1.07, 0.87, 0.17, and 0.20 Hz, respectively,
anode spike frequency models as a function of Pro, Pco, and were observed for these trials. Trials 7 and 8 produced
g, and Ira, Pco, and g~ are listed in Table II. Contour plots If - f l / f ratios of 0.10 to 0.11 for the drop short frequency

METALLURGICAL TRANSACTIONS B VOLUME 17B, JUNE 1986--359

 Table I. Data for Experiment II, INCO 718 Alloy
Melting Melting CO Electrode Drop Short Anode Spike
Current Voltage Pressure Gap Frequency Frequency
Trial # kA V /x mm Hz Hz
1 9.91 25.8 17 15.9 0.83 0.49
2 9.92 25.9 17 17.0 1.38 0.57
3 7.47 22.6 16 5.1 11.08 5.57
4 7.49 22.7 16 6.5 9.82 4.76
5 7.43 24.4 12 52.1 0.38 0.83
6 7.39 24.4 11 52.8 0.27 0.64
7 7.49 21.4 59 15.5 3.06 1.07
8 7.50 21.4 59 20.0 2.28 0.87
9 7.49 23.3 19 20.6 2.74 1.79
10 7.52 24.1 106 44.3 0.19 0.12
11 7.51 23.4 105 44.1 0.21 0.20
12 5.03 19.1 58 6.2 13.93 6.03
13 5.03 19.6 58 7.0 14.84 6.77
14 5.04 22.2 17 20.6 4.18 3.75
15 5.03 21.8 18 6.2 22.54 15.33
16 5.04 21.0 18 5.2 30.65 21.59
17 5.05 22.7 17 20.8 3.42 2.04
18 5.03 22.9 17 19.8 4.06 2.56
19 5.09 19.3 106 20.1 2.98 2.01
20 5.09 19.8 104 21.2 2.44 1.46
21 5.00 22.3 50 50.8 0.55 0.79
22 5.00 22.4 50 46.6 0.43 0.68
23 5.05 21.3 1 I0 46.3 0.08 O. 13
24 5.04 21.2 109 53.9 0.06 0.05
25 6.60 22.2 23 9.6 5.75 2.71
26 6.60 22.1 23 9.9 4.71 2.22
27 7.52 23.3 50 16.7 0.44 0.17
28 7.52 23.5 5! 19.1 0.50 0.20
29 7.53 20.8 106 5.5 3.83 1.27
30 7.51 20.9 105 7.4 4.38 1.52
31 9.88 22.7 16 6.0 4.80 1.82
32 9.89 22.6 17 6.9 5.15 2.02
33 9.92 22.0 55 6.5 3.14 1.15
34 9.91 21.8 55 7.8 2.18 0.76
Average 6.93 22.2 49.12 20.9 4.92 2.76
0.406 m diameter electrode
0.457 m diameter crucible

Table II. Model Coefficients and Errors

Model Bo S.E. Bo C1 S.E. CI C2 S.E. C2 C3 S.E. C3 e
los = F(P,,,Pco, ge) 0.25 0.02 -2.16 0.10 -0.54 0.04 -1.32 0.07 0.18
fos = F(]m, Pco, ge) 0.26 0.02 -2.54 0.12 -0.36 0.04 -1.44 0.07 0.19
fAS = F(Pm, Pco, ge) 0.16 0.02 -2.98 0.15 -0.97 0.06 -1.28 0.08 0.21
fAS = F(l,,,Pco, ge) 0.17 0.02 -3.34 0.17 -0.70 0.06 -I.46 0.08 0.22

models and 0.20 to 0.22 for the anode spike frequency I. The additive error term in the nonlinear models.
models. Trial 27 produced ratios of 0.39 and 0.45 for the 2. Nonrandomization o f the trial sequence.
drop short frequency models with Pm and Ira, respectively, 3. The difference in response between replicate data sets at
and 0.48 and 0.67 for the anode spike frequency models the center point of the factor space.
with P,, and lm, respectively. Trial 28 produced ratios o f Nonlinear frequency models with additive error were cho-
0.22 and 0.29 for the drop short frequency models with P,, sen instead o f linearized logarithmic models with multi-
and Im, respectively, and 0.21 and 0.25 for anode spike plicative error to model the data. With the nonlinear model,
models with Pm and I,,, respectively. the errors at low frequencies are deliberately understated
because the r e s i d u a l s are small in m a g n i t u d e but the
IV. DISCUSSION
If - f l / f ratio is large. However, this model provides accu-
rate estimation of error at higher frequencies because of the
Three statistical issues need to be addressed concerning larger residuals with small I f - f l / f ratios, and it is in this
this work: region (gaps < 2 5 mm) that the model has intended applica-

360--VOLUME 17B,JUNE 1986 METALLURGICALTRANSACTIONSB

 30 30

25 25

~, 20 20
c
o g
e
o
'- 15 u. 1,5

r
o ]46 kW
W

~ 10
o g
<C

5 10 15 20 25 5 10 15 20 25

E l e c t r o d e Gap (mm) E l e c t r o d e Gap (mm)

Fig. 4--Predicted drop short frequency as a function of electrode gap at Fig. 6 - - Predicted anode spike frequency as a function of electrode gap at
a constant CO pressure of 1.33 Pa ( 10 p,m Hg). Contour lines represent the a constant CO pressure of 1.33 Pa (10/zm Hg). Contour lines represent the
function at constant arc power levels. function at constant arc power levels.

tion. The results clearly show that the range of gap selected Due to the expense created from the difficulty of achiev-
for this experiment was too large in that the response of ing quasi-steady heat transfer conditions at the electrode tip,
frequency is minimal at gaps larger than - 2 5 mm (trials 5, it was not possible to randomize the sequence of trials.
6, 10, 11, 23, and 24 in Table I and Figures 4 through 9). Instead, the run sequence was designed to minimize the
This lack of response and large If - f l / f ratio at larger gaps equilibration time between trials (even with this sequence
is also reflected in the electrode gap predictive plots (see holding times as long as three hours were required2). This
Figures 11 through 14) where the above-mentioned trials bias of run sequence with time could introduce time de-
result in large predictive errors and even larger calibration pendent errors into the experiment. We believe it is unlikely,
intervals. If a model with multiplicative error were chosen, if these errors exist, that they make a major contribution
then errors at low frequencies would be weighted to produce because of the typical randomness found in the plots of
an undesirable adjustment in fit at the higher frequencies. residuals as a function of time as shown typically in
Figure 10.

~
30 30

25
25
kA 5 . 0 kA

20 ~, 20
r
G
6 . 5 kA o
g
0 e
,- 15
o
0
c/)
r 10
.o o
Q c

J
5 1'O 15 20 25 10 15 20 25

E l e c t r o d e Gap (mm) E l e c t r o d e Gap (ram)

Fig. 5--Predicted drop short frequency as a function of electrode gap at Fig. 7 - - Predicted anode spike frequency as a function of electrode gap at
a constant CO pressure of 1.33 Pa (10/zm Hg). Contour lines represent the a constant CO pressure of 1.33 Pa (10/zm Hg). Contour lines represent the
function at constant arc current levels. function at constant arc current levels.

METALLURGICAL TRANSACTIONS B VOLUME 17B, JUNE 1986--361

 20 .50

15 .25 a . ~ ,h

9 9
c
o
g e, 9 at.
q) g
u. 10 O.O ~, 9
o 9 IO 9
J= 9 9 9
G)
9 O 9
o
~O
I 9
-.25

-.50
,'o ,'5 ,o - O 5 10 15 20 25 30 35

Electrode Gap (ram) Time

Fig. 8 - - Predncted drop short frequency as a function of electrode gap at Fig. 1 0 - - Resxduals as a functton of expenmental sequence in time for the
a constant CO pressure of 6.65 Pa (50/zm Hg). Contour hnes represent the drop short frequency model with independent variables (I,, Pco, g,).
function at constant arc current levels.

ics) to create and stabilize each mode are dominant and

The difference in response between replicated data sets in reproducible at the outer regions of the factor space as evi-
the center of the factor space (trials 7, 8 and 27, 28) suggest denced by the systematic behavior of the models. However,
that an important unconsidered independent variable was in the central region of the factor space, we believe that
out of control. We believe this difference in response is the forces which create these behavioral changes are in
caused by changes in arc behavior. Specifically, short gaps fine balance. As a result, subtle changes in experimental
and low pressures stabilize the arc in a diffuse mode, cre- conditions could cause either mode to exist or perhaps a
ating macro-uniform heating of the electrode face, and long time-variant oscillation between modes. The electrode gap
gaps and high pressures stabilize the arc in a constricted predictive plots demonstrate this in that the models treat
mode, creating nonuniform heating in the central region of trials 27 and 28 (trials with low frequency) as outliers.
the electrode.2 The forces (determined by complicated phys-
100

20

75
E
,t
15 e
o
e
5.0 kA o
cr 50
h, e
Ik w
10 27
e
k~
U) 28
'o
ob.
a
i 25

0
0 is ~o A ' loo
r
5 10 15 2'0 25 Observed Electrode Gap (mm)

Fig. 11 - - Predicted electrode gap as a function of measured electrode gap

Electrode Gap (ram)
for the drop short frequency model with independent variables (Pro, Pco,
Fig. 9 - - Predicted drop short frequency as a function of electrode gap at g,). Error bands are 95 pct confidence level calibration intervals for each
a constant CO pressure of 13.3 Pa (100/zm Hg). Contour lines represent trial. Trial numbers next to points designate specific trials. The line drawn
the function at constant arc current levels. through the origin represents a perfect fit.

362-- VOLUME 17B, JUNE 1986 METALLURGICAL TRANSACTIONS B

 100 100
24

75 75
E E
23--~
e e
o o
O 0
"o "o
0L. 0

u 50
e e
ui m
"o
o 27\\. b
/
u
"o
e 28 f
~. 25 e

/
25 i

0
0 25 5'0 7'5 ' 1 O0 o 2,5 ' 5'0 75 100

Observed Electrode Gel) (ram) Observed E l e c t r o d e Gap (mm)

Fig. 12--Predicted electrode gap as a function of measured electrode gap Fig. 14 - - Predicted electrode gap as a function of measured electrode gap
for the drop short frequency model with independent variables (lm,/)co, g,). for the anode spike frequency model with independent variables (Ira, Pco,
Error bands are 95 pct confidence level calibration intervals for each trial. g,). Error bands are 95 pct confidence level calibration intervals for each
Trial numbers next to points designate specific trials. The line drawn tnal. Trial numbers next to points designate specific trials. The line drawn
through the origin represents a perfect fit. through the origin represents a perfect fit.

A basic question left unresolved by the data in Table II is and the direct relationship between voltage and gap mea-
the issue of whether arc power or current ought to be chosen sured in earlier work. 2 As a result, the overall fit to the
as an independent variable. When power is used instead of frequency data is nearly identical for models utilizing either
current, the CO pressure exponent increases and the gap arc power or arc current. This is demonstrated in the contour
exponent decreases. These changes could be anticipated plots (for example, comparing Figures 4 and 5). Because
from the inverse relationship between voltage and pressure there is so little difference between two choices, we include
both models based on current and on arc power.
The largest exponent in the power-law models, Eq. [2],
100 appears on melt current in both drop short and anode spike
frequency models (Table II). This could be explained by
noting that drop short formation can be suppressed by in-
creasing current because more cathode spots are available to
accumulate at the bottom of protuberances. 4 As a result, the
75 impulse from this cathode spot accumulation prevents the
protuberance from shorting and simultaneously provides
t~ more current to magnetically pinch the protuberance. Under
these conditions, the metal is transferred to the anode with-
out the occurrence of a short. A further support for this
5o
explanation is found by noting that very high currents (25 to
35 kA) are utilized when vacuum arc remelting Ti elec-
2T,....
trodes of similar size, and drop shorts are seldom observed
during these melts. 8 As electrode gap increases, drop
~. 25 short formation is also suppressed. At longer gaps there is
a greater tendency for necking down of the upper end of the
protuberance and subsequent separation near cathode by
magnetic pinching before the lower end can touch the
anode. This phenomenon has been visually observed during
vacuum arc melting of WASPALLOY* and a U-6 wt pct Nb
' 2; s'* r,5 loo
*WASPALLOY is a trademark of United Technologies Corporation.
Observed Electrode Gap (mm)
Fig. 1 3 - Pre&cted electrode gap as a function of measured electrode gap alloy at electrode gaps exceeding 15 mm. 9
for the anode spike frequency model with independent variables (Pro, ,~ Increases in CO pressure also suppress drop short and
gel Error bands are 95 pct confidence level calibration intervals for each
trial. Trial numbers next to points designate specific trials. The line drawn anode spike formation. It should be emphasized that the CO
through the origin represents a perfect fit. pressure within the gap is not known and could be consid-

METALLURGICAL TRANSACTIONS B VOLUME 17B, JUNE 1986--363

erably higher than the ambient furnace pressure. This could is sensed by the arc. At this instant, a highly constricted
be very important in melting situations where a localized arc will accumulate under the protuberance. In both cases,
carbon boil is occurring. Evidence in Reference 2 suggests the anode spike over voltage is presumably supplied by
that increases in both CO pressure and electrode gap within the energy in the inductive magnetic field surrounding
the experimental range tend to constrict the arc as noted in the column.
the Introduction. Such constriction could tend to suppress The larger melting current exponent in the anode spike
drop short formation if the electrode becomes tunneled or model (3.34 as compared to 2.54 for the drop short model)
concave at the axis. However, little is known about the means that measured frequency will fall off much faster as
physics involving this type of arc. current is increased. This implies that frequency sensitivity
Overall, then, it can be said that some qualitative under- to changes of gap will be correspondingly less. For exam-
standing of the dominant effects of melt current and gap ple, in the gap range of 10 to 15 mm at 6.5 kA the average
on frequency is available, but the secondary effects due slope for the drop short model is 0.35 H z / m m as compared
to gas pressure involve much more complicated physical to 0.25 for the anode spike model (see Figures 5 and 7).
processes. The predictive capability plots also show that the drop
Evaluation of JBK alloy data from Reference 2 in the short models consistently predict a longer gap than is ob-
drop short frequency domain yields a model served at gaps in the 40 to 50 mm range whereas the anode
- [ g e ~c3
spike models generally predict a frequency which changes
to, = + to: little or none with increases of gap. This difference is very
significant when applied to control of a vacuum arc furnace.
where B0 = 0.48 +- 0.05, C3 = - 1 . 8 1 +-- 0.11, fos = For example, if the gap is long and undergoes an increase
3.59 Hz, ge = 20.72 mm, and e = 0.16. The melting while under drop short frequency control, the model will
parameters used to obtain these data were considerably dif- always respond with a correction that increases electrode
ferent from those utilized for the INCONEL 718 in this velocity downward bringing the system toward the desired
work; namely, Im= 2.2 kA, vm = 24 volts, furnace pres- shorter gap. Under identical conditions the anode spike
sure = 0.54 Pa (4 Ixm), electrode diameter = 0.105 m, model would generally not detect the gap change and would
and ingot diameter = 0.154 m. That is, current and pres- make no change or a small change to the electrode velocity
sure were held constant in melting much smaller electrodes downward. This situation could actually cause the gap to
of a much different (Fe-base) alloy. It is interesting to note increase further and result in unstable and unsafe operation
that the same form of model fits gap frequency data from of the arc furnace.
different materials and different electrode ingot diameters The importance of achieving the same thermal conditions
with only modestly different exponent C3 values. at the electrode face before frequency data are compared
Comparing the drop short and anode spike models reveals between investigators cannot be overemphasized. For ex-
that, though they share the same power-law form, either ample, previous work t~ has shown that "hash" frequency is
may be more numerous (Tables I and II). In fact, Table I related to electrode gap as illustrated in Figure 15. In this
indicates that drop shorts outnumber anode spikes under all figure frequency falls as gap increases until a certain level
conditions except when both frequencies are very small; of gap is reached. At this point the frequency starts to
i.e., long gaps at low to intermediate current and any pres- increase, passing through a maximum, and then decreasing
sure from low to high. In particular, trials 5, 6, 21, 22, and again as gap is increased. Gap in this case was determined
23 are the only trials with anode spike/drop short frequency by a linear interpolation between two measurements. The
ratios greater than unity, values being, respectively, 2.2, first measurement was made by driving the electrode to a
2.4, 1.5, 1.6, and 1.6. Electrode gaps for these trials were short and then raising it a fixed distance. Next, the electrode
all greater than 46 mm. At shorter electrode gaps, anode was held fixed while melting was allowed to continue for a
spikes occur at arc reignition approximately 50 to 70 pct prescribed time interval. After completion of the time inter-
of the time; i . e . , anode spike/drop short ratio is less val, the gap was measured a second time by again driving
than unity. the electrode to a short. N We postulate that the hump in
Both of these behaviors are consistent with the following
hypothesis involving arc reignition and concentration: anode
10-
spikes are created as a result of arc concentration on the tip
of the molten metal column when (1) the arc reignites after
8-
the column shorts, and (2) the protuberance or molten col-
umn stretches to within a short distance of the anode at large
6-
electrode gaps. At short gaps, the localized geometry at arc
reignition controls the degree of arc concentration. If the
protuberance tip has a small radius of curvature (i.e., a 4-
.. , ' " \,
small aspherity at the arc reignition site, then the arc will be
2-
highly concentrated and an anode spike will be created. If,
however, reignition occurs over a larger area, the severe
constriction does not occur and an anode spike will not be 0 I I I I I
0 5 10 15 20 25 30
created. At long electrode gaps anode spikes will be created Electrode Gap {ram)
if the arc reignites after shorting because the protuberance Fig 1 5 - - H a s h frequency as a function of electrode gap at a melting
tip has a small radius of curvature or if the protuberance current of 6 kA. This plot has redrawn units of Hz and mm from the work
stretches to within very near the anode surface before it of Pridgeon, et al. io

364--VOLUME 17B, JUNE 1986 METALLURGICAL TRANSACTIONS B

Figure 15 was caused when the arc constricted as gap in- Replace
creased and metal drained from the central region of the
electrode to the mid radius. As a result, the "local gap" , D(1,J)]
D(1,J) o y ~ ]
at the electrode midradius decreased and anode spike
frequency increased until this metal was melted away. A
similar phenomenon was observed in this work during the LD(I,1) ' D(I, 1) |
DY B o J
thermal stabilization period after the gap was increased
to 50 mm. Measurements made under quasi-steady condi- Z l = (1, In Xl, In )(2)
tions would have only produced the power-law portion of
3 3
this curve.
It can be observed from the above comments that control- U = E • Z(1)Z(JJ)D(I,J)
1=1 J=l
ling the gap during vacuum arc melting is not an "exact" art.
However, the ranges of the independent variables chosen for [RMS ( 1 ) ^ ]v2
this work are very broad when compared to the situation that S = L C3 2 \ f 2 + U + (In X 3 ) 2 D ( 4 , 4 ) ]
actually exists during production melting. In most control
situations, the melter would strive to operate the furnace at then the calibration interval is:
^
gaps less than 20 mm. As long as the gap is short, both exp(ln X3 +- ts)
pressure and current can increase while still maintaining
good predictive capabilities.
ACKNOWLEDGMENTS

V. CONCLUSIONS Because of the scope of the experimental effort, a large

number of people deserve to be recognized for contribu-
1. Drop short and anode spike frequency are influenced by tions to this work. Richard Schwoebel, John Pridgeon, and
a three way interaction involving lm, Pco, and g3. All of Norman Wilkinson from Sandia National Laboratories,
these independent variables influence frequency by an Special Metals Corp., and Cameron Iron Works, respec-
inverse power-law relationship. tively, deserve thanks for allocating the resources neces-
2. Frequency models accurately predict electrode gap at sary to conduct and analyze these experiments. Edward
gaps less than 20 mm provided that the CO pressure is Raymond, Will Sutton, Roy Matway, Charlie Adasczik,
low (<2.66 Pa or 20/zm Hg). Tim O'Brien, Oded Naftali, and Ken Vincent all made
3. At gaps greater than 20 mm, the models exhibit large important contributions to the experimental effort. Robert
errors in predicting gap. In the center region of the factor Easterling assisted with the statistics and David Melgaard
space, the error is created by uncontrolled arc behavior. developed all of the software used in the data analysis.
At large gaps, the error is created by lack of frequency Lastly, James Maroone made important contributions in
response. both the experimental and data reduction effort.

APPENDIX REFERENCES
Procedure for prediction of calibration intervals for 1. EJ. Zanner: Metall. Trans. B. 1981, vol. 12B, p. 21
electrode gap based on the frequency models 2. E J. Zanner, C. Adasczik, T. O'Bnen, and L.A. Bertram: Metall.
Trans. B, 1984, vol. 15B, p. 117.
Inputs are: 3. G. E. P. Box and D.W. Behnken: Technometrics. 1960, vol. 2,
p. 455.
D is a 4 • 4 matrix from the nonlinear estimation 4. F.J. Zanner: Metall. Trans. B, 1979, vol. 10B, p. 133.
program 5. N.R. Draper and H. Smith: Apphed Regression Analysis, John Wiley,
B0, C1, C2, C3 1966, p. 171.
XI, X2, f 6. D.W. Marquard: J. Soc. Ind. Appl. Math., 1963, vol. 2, p. 431.
7. D.A. Meeter: "Program GAUSHAUS," Numerical Analysis Labora-
tory, Univ. of Wisconsin, Madison, WI, 1964 (Ref. 1966)
RMS or ~(?~__________~)2 8. G. Dooley: U.S. Bureau of Mines, Albany, OR, personal commu-
n=l nication, 1985.
9. E J. Zanner and L. A. Bertram: Sandia National Laboratories, Albu-
t from student t table at 95 pct confidence - 2 querque, NM, unpublished reserach, 1982.
Calculate for each trial: 10. J.W. Pridgeon, F.N. Darmara, J. S. Huntington, and W. H. Sutton:
^ Conf. Proceedings USA-China, AIME Bilateral Conf., J. K. Tlen and
lnX3 = ( l n f - In Bo - C1 In X1 - C2 In X2)/C3 J. F Elliott, eds , Beijing, China, Nov. 13-22, 1981, pp. 261-76.
11. H. Flanders: Special Metals Corp., New Hartford, NY, personal com-
munication, 1985.

METALLURGICALTRANSACTIONS B VOLUME 17B, JUNE 1986--365