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The Estimation and Control of the Electroslag Remelting Melt

Rate by Mechanism-Based Modeling

WANZHOU LI, WEIYU WANG, YUECHEN HU, and YIXING CHEN

The process control of industrial electroslag remelting production is addressed in this work. This

article proposes a mechanism-based model using electrode displacement to estimate the melt

rate, designs the remelting process control system, and uses practical application data to verify

the validity of the model. The soft measurement of the melt rate based on mechanism modelin g

is proved to be an economical and reliable solution to the online melt rate estimation and

control for large industrial electroslag remelting furnaces.

DOI: 10.1007/s11663-011-9606-2

Ó The Minerals, Metals & Materials Society and ASM International 2011

I. INTRODUCTION

THIS article is organized as follows. Section I

introduces related research and the proposed approach.

Section II discusses the modeling procedures and the

coeﬃcient modiﬁcation method. The model validity is

evaluated using practical application data in Section III.

Section IV serves as a con clusion. The deduction of the

melt rate equation is presented in Appendix A. The

symbols and explanations are listed in the Nomenclature

table.

A. Electroslag Remelting

Electroslag remelting (ESR) technology has been

employed eﬀectively in the metallurgy of special steel

and alloy steel. The ﬁne-grained, high-purity ingot

products are used widely in the production of turbine

disks for aircraft engines, aeronautical bearings, sub-

marine shells, gun steels, titanium alloys for astro nau-

tics, crank axles for ships, cold rollers, and high-speed

tool steels.

In the ESR process, a high current passes through the

consumable electrode and the molten slag. Then, the

electrode melts in the superheated slag pool and

resolidiﬁes in the molten, water-co oled mold. High-

quality solidiﬁcation processes require that the melt rate

of the electrode be stable. Thus, the melted metal per

minute is rather small compared with the ingot mass. As

a result, the nonmetal impurities in the molten pool are

more likely to conglomerate and ﬂoat, and the molten

metal droplet detached from the electrode tip will be

ﬁltered fully in the slag pool. The ESR mechanism is

illustrated in Figure 1(a), and its equivalent circuit is

shown in Figure 1(b). The slag resistance is a time-

varying parameter in the ESR process.

Major technol ogical parameters aﬀecting the ESR

process include the following:

(a) Electric current density, i.e., the current per unit

cross-sectional area of the electrode (A/cm

). The

ratio of the current density to the electrode diameter

is restricted to a range so that the ESR process is

stable. A ratio exceeding either the upper or the

lower limit will result in an unstable remelting or an

arc process. As the electrode diameter increases, the

current density for stable remelting decreases. Spe-

ciﬁc data depend on the ﬁll ratio.

(b) Fill ratio, i.e., the ratio of the electrode diameter to

the inner diameter of the crucible. This parameter

aﬀects heavily the stability, quality, and power

consumption of remelting. When the ﬁll ratio is

large, an increase in power and the skin eﬀect will

lead to a ﬂat end-proﬁle of the electrode, a shallow

electrode immersion, sparsely distributed molten

droplets, a homogenized slag–metal interface tem-

perature, and an inverse-trapezoidal shape of the

molten pool bottom. Under this condition, if a lar-

ger power is used, then solidiﬁcation tends to be

upright while the pool bottom is still relatively ﬂat.

Therefore, increasing the power can reduce the time

cost without compromising the remelting quality.

depth of the molten pool for a given input power.

A thick slag layer results in a low slag temperature,

a shallow molten pool, and good electroslag stability;

a thin slag layer results in a high slag temperature, a

deep molt en pool, and poor electroslag stability.

(d) Furnace voltage. For a given input power and slag

layer thickness, an excessively high furnace voltage

will cause a large electric current ﬂuctuation, an

unstable electroslag process, a high slag-layer tem-

perature, a shallow molten pool, and a high melt

rate. In the case of a low voltage, the slag layer will

have a lower temperature, the molten pool will

deepen, and the melt rate will slow down. A voltage-

swing control system can control the furnace voltage

by means of an integrated circuit. As the current

decreases, the furnace voltage falls; for instance, the

WANZHOU LI, Professor, and WEIYU WANG, YUECHEN

HU, and YIXING CHEN, Students, are with the Department of

Automation, Tsinghua University, Beijing 100084, P.R. China.

Contact e-mail: lwz@mail.tsinghua.edu.cn

Manuscript submitted August 6, 2011.

Article published online December 6, 2011.

276—VOLUME 43B, APRIL 2012 METALLURGICAL AND MATERIALS TRANSACTIONS B

fall may be from more than 50 V in the beginning to

approximately 40 V in the end. The furnace voltage

also inﬂuences the melt rate and power consumption

signiﬁcantly.

(e) Melt rate. Increasing the melt rate can reduce the

power cost greatly. As the melt rate increases, the

power imparted to the slag pool increases. Conse-

quently, the crystallographic axial angle decreases

quickly, and the ingot tends to crystallize radially

rather than along the desired axial direction.

Moreover, a deeper molten pool increases the time

for solidiﬁcation, which means a higher possibility of

defects, such as segregation and inclusion; the sur-

face quality of the ingot worsens accordingly. It is

generally accepted that a reasonable melt rate results

in the optimum molten pool shape, a solidiﬁcation

corner between 70 deg and 110 deg, and a good-

quality ingot surface.

(f) Slag system, which aﬀects directly the stability of

the ESR process and the quality of the solid iﬁed

ingot. The slag system must satisfy the following

conditions: (1) appropriate electrical conductivity to

ensure adequate supply of energy and stable

remelting process; (2) relatively low melting point

and viscosity to assure the surfa ce quality of the

solidiﬁed ingot; (3) relatively large density, which

helps increase the slag-metal contact time and

makes the reaction to proceed in full swing; and (4)

relatively small surface tension. Besides all these

requirements, the slag system must meet the rele-

vant requirements for permea bility and vapor

pressure.

B. Mechanism Analysis of the ESR Mechanism

1. Model for the ESR mechanism

Researchers have long been engaged in the study of

ESR mechan ism and its mathematical model. Dilawari

and Szekely

[1]

ﬁrst developed a mathematical represen-

tation of the velocity ﬁeld distribution of the ﬂuid ﬂow

in the slag pool and the molt en pool. They assumed a

known size and shape of the molten pool, an isothermal

condition for the slag pool and the molten pool,

cylindrical symmetry, negligible eﬀects of molten droplet

on the motion of molten pool, and a negligible damping

eﬀect of the turbulent ﬂows caused by the electromag-

netic ﬁeld. Dilawari and Szekely

[2]

extended the model

by relaxing the assumptions of isothermality and the

molten-droplet eﬀect.

Choudhary and Szekely

[3–5]

proposed an improved

model of pool proﬁle, velocity ﬁeld, and temperature

proﬁle. They claimed that the movements of slag pool

were aﬀected mainly by the buoyant and electromag-

netic forces and that electrode immersion had a consid-

erable impact on the melt rate but little inﬂuence on

other process variables such as temperature ﬁeld and

velocity ﬁeld.

Ferng et al.

[6]

developed an integrated numerical model

of ﬂow ﬁeld and temperatur e distribution while simulta-

neously solving the molten pool proﬁle. They discussed

also the direct current/alternating current power supply

mode, the electric current amplitude, and the impact of

electrode feed rate on the ESR process. They concluded

that the melt rate and the electric current magnitude

played a major role in the shaping of the molten pool and

Fig. 1—(a) The ESR mechanism and (b) the equivalent circuit.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, APRIL 2012—277

that the outside disturbances exerted a heavy inﬂuence on

the temperature ﬁeld distribution.

Hernandez-Moorales and Mitchell

[7]

reviewed the

previous work on mathematical models of transport

phenomena in the ESR process and concluded that

whereas the models for ﬂuid ﬂow and heat transfer had

been well developed, mass transfer phenomena needed

additional study in the future. Cefalu et al.

[8]

discussed

the ESR process for a certain type of ingots.

2. The theory of ESR melt rate estimation

Melt rate has long been regarded as the most

important factor aﬀecting the depth and shape of the

molten pool. This view has been veriﬁed by theoretical

model calculation that assumes calculation.

[9]

Because the depth and the shape of the molten pool are

the main determinants of the solidiﬁcation direction and

segregation, these parameters need to be maintained at a

constant level to ensure that high-quality ingots with a

homogeneous composition and consistent properties are

produced. Because online detection of depth and shape of

the molten pool is rather diﬃcult, a stable melt rate is

often used as the alternative control objective.

The melt rate is given by Dilawari and Szekely.

[2]

¼ k

 k



DHðÞ ½1

The melt rate can be obtained based on the temper-

ature ﬁeld distribution given by the heat-ﬂo w equation

and the liquid-ﬂow equation. However, this approach

leads to a theoretical a chievement rather than a practical

solution. First, too many physical parameters are

needed, and these parameters depend on the particular

electrode, slag composition, and slag amount. Second,

the procedure for obtaining the temperature ﬁeld

distribution by (simultaneously) solving several partial

diﬀerential equations using the ﬁnite-element method is

too complicated for real-time computation.

Yet, theoretical derivations and experimental data

reveal an approximately linear relationship between the

stable de pth of the molten pool and the melt rate of the

electrode.

[10,11]

The formula relating the molten pool

depth, the current, and the ingot height is given by

[12]

hO; YðÞ¼Ae



½2

As a result, there is

¼ AI

ESR

ðÞe



BðI

ESR

 C

½3

The current work uses the experimental data collected

from tests on a 20 – t ESR furnace equipped with

electronic scale weighing system. A, B,andC

are

obtained by least-squares ﬁtting. The melt rate

computed with Eq. [3] and the actual melt rate measured

with the electronic scale are compared.

The melt rate estimated by Eq. [3] is, on the whole,

consistent with the actual rate, except for in the

unsteady shrinkage compensation stage. But the esti-

mation of the Eq. [3] coeﬃcients is diﬃcult in the ﬁeld

(see the average electrode density and average ingot

density modiﬁcation in Section II–B).

In summary, a mechanism-based, practically feasible

online melt rate estimation for indu strial ESR produc-

tion remains unavailable in the published literature.

C. The ESR Process Control System

A coupled-control approach based on a reduced-

order linear ESR model and a typical process measure-

ment has been developed.

[13,14]

In this approach, a

Kalman ﬁlter is used to estimate the states in eight

process models and to control the melt rate and the

immersion depth simultaneously. An intelligent control

based on neural network has also been studied by Wang

and Tu.

[15]

The authors of this article developed a

constant-melt-rate control system based on time-varying

parameters and used it for a 15 – t coaxial furnace in an

ESR workshop at Xing Tai, China.

[16]

As for the process control method, Kim and Kwon

[17]

presented a minimum-maximum, generalized predictive

control of the burn-through point in the sintering

process using an event-based mo del. The controller

design must meet certain constraints on its output. Silva

et al.

[18]

proposed a predictive adaptive controller for

the regulation of superheated steam temperature in

commercial boilers and made a comparison with

an optimized cascade control system. Wang et al.

[19]

developed a hybrid supervisor control system for a

reheat furnace and conducted simulation and industrial

experiments.

The proposed ESR process control system is illustrated

in Figure 2. Figure 2(a) presents the current cascade

control system. Under the condition of constant distance

between the electrode and the molten pool, the proposed

melt rate estimation model, which uses the electrode

displacement and technical parameter as inputs, can

provide precise online estimation of the melt rate.

A ﬁeld measurement of electrodes of diﬀerent mate-

rials, diameters, and lengths shows that the voltage drop

on the electrode amounts to virtually nil; the measure-

ment of the solidiﬁed ingot impedance also reveals a

virtually nil value. For this reason, only the bus-bar

impedance and the slag resistance are considered in the

equivalent circuit shown in Figure 2(a).

Figure 2(b) shows the control system for the distance

between the electrode and the molten pool. Through the

voltage swing amplitude control, the electrode immer-

sion depth can be co ntrolled precisely to keep the

distance between the electrode and the molten pool

constant in the remelting process.

D. The Current Work

The proposed mechanism-based model is an online

melt rate estimation method that applies to the ESR

*The symbols used in the article are listed and explained in the

Nomenclature table.

278—VOLUME 43B, APRIL 2012 METALLURGICAL AND MATERIALS TRANSACTIONS B

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