Американский Научный Журнал FLAT TWO-PHASE LINEAR INDUCTION MHD MACHINE FOR METALLURGICAL PURPOSES

Abstract. Linear induction MHD machines with a low-frequency power inverter form a complex of electromagnetic stirring of liquid aluminum in smelting furnaces. The article discusses the classification features and characteristics of four-zone inductors of a longitudinal magnetic field with two-phase power. To calculate the operating parameters of a linear induction MHD machine, a nonlinear multiphase model of a magnetic circuit was used. As a result of an iterative calculation, the distribution of the integral magnetic fluxes in the tooth zone of a flat inductor is obtained, and vector diagrams of electromagnetic regime parameters are constructed. According to the results of the analysis, the main tasks and the sequence of stages of their solution were formulated when developing energy-efficient induction MHD machines of a longitudinal magnetic field. In the course of the study, directions for optimizing the mode of a low-pole induction machine are shown in order to obtain the best distribution of currents in the windings. Скачать в формате PDF
American Scientific Journal № (27 ) / 201 9 61
ЭНЕРГЕТИКА

FLAT TWO -PHASE LINEAR INDUCTION MHD MACHINE FOR METALLURGICAL PURPOSES

Tyapin A.A.
Postgraduate student,
Siberi an Federal University,
Svobodny prospect, 79, Krasnoyarsk, Russia, 660041
Kinev E.S.
Сandidate of technical science s,
Director Thermal Electric Systems LLC,
Chernyshevsky St., 104, off. 85, Krasnoyarsk, Russia, 660043

ПЛОСКАЯ ДВУХФАЗНАЯ ЛИНЕЙНАЯ ИНДУКЦИОН НАЯ МГД -МАШИНА
МЕТАЛЛУРГИЧЕСКОГО НАЗНАЧЕНИЯ

Тяпин Aлексей Андреевич
Аспирант, ФГАОУ ВО Сибирский Федеральный Униве рситет,
Свободный проспект, 79, Красноярск, Россия, 660041
Кинев Евгений Сергеевич
К.т.н., директор ООО Тепловые электрические системы
Спанда ряна, 12, офис 5, Красноярск, Россия, 660020

Abstract . Linear induction MHD machines with a low -frequency power inverter form a complex of
electromagnetic stirring of liquid aluminum in smelting furnaces. The article discusses the classification features
and characteristics of four -zone inductors of a longitudinal magnetic field with two -phase power. To calculate the
operating parameters of a linear induction MHD machine, a nonlinear multiphase model of a magnetic circuit was
used. As a result of an iterat ive calculation, the distribution of the integral magnetic fluxes in the tooth zone of a
flat inductor is obtained, and vector diagrams of electromagnetic regime parameters are constructed. According to
the results of the analysis, the main tasks and the sequence of stages of their solution were formulated when
developing energy -efficient induction MHD machines of a longitudinal magnetic fiel d. In the course of the study,
directions for optimizing the mode of a low -pole induction machine are shown in order to obtain the best
distribution of currents in the windings.
Keywords . Induction MHD machine, inductor of longitudi nal magnetic field, electromagnetic stirrer, running
magnetic field, multiphase magnetic circuit model, vector magnetic flux diagram, two -pha se power supply system,
frequency inverter.

Introduction . For stirring metal melts in furnaces,
linear induction machines of transverse and
longitudinal magnetic fields are used. The cost of each
technical solution, along with the technological and
energ y efficiency of induction machines, is a decisive
factor in the decision to modernize production or to
develop of new construction of smelting furnaces. As
induction machines for stirring aluminum alloys in
mixers and furnaces, in addition to the transvers e field
inductors, high -tech shortened inductors of the
longitudinal field are used. Among the simplest flat
induct ion MHD machines, two constructive solutions
can be distinguished that determine the type of machine
by the number of windings inducing the force
(induction zones).
These design features appropriately characterize
the polarity of the inductor and the magni tude of the
synchronous velocity of the traveling magnetic field in
the melt. The following designations are used as
constructive and operati onal parameters in the
description:
2p is the number of poles of the inductor;
Z is the number of teeth of the core ;
q is the number of grooves of the core per pole and
phase;
α is the phase zone of the inductor;
m is the number of phases of a multiphase winding
inductor;
 is the working gap.
The classical induction MHD machine of a
longitudinal magnetic field can hav e four or three
windings (a four -zone or three -zone inductor). In
addition, the power supply of induction machines can
be provided in a two -phase or three -phase version.
Thus, when developing inductors and evaluating their
effectiveness, four main options should be considered
for constructing shortened low -pole induction
machines of a longitudinal magnetic field.
1. Four -zone inductor with two -phase power
supply.
2p = 2, Z = 5, q = 1, m = 2, α = 90 .
2. Four -zone inductor with a three -phase power
supply.
2p = 4/3, Z = 5, q = 1, m = 3, α = 60 .
3. Three -zone inductor with a two -phase power
supply.
2p = 3/2, Z = 4, q = 1, m = 2, α = 90 .
4. Three -zone inductor with a three -phase power
supply.
2p = 1, Z = 4, q = 1, m = 3, α = 60 .

62 American Scientific Journal № ( 27 ) / 20 19
This article discusses some of the classification
characteristics and features of four -zone inductors of a
longitudinal magnetic field with two -phase power. A
sketch of the construction of a shortened induction
MHD machine is shown in Fig. 1. The inductor has four
windings 1, designate d w1, w2, w3, w4. They are made
in the form of two -way disk sections, which are
grouped in series or parallel connection. The windings
are placed on a steel laminated magnetic core 2.
Between the windings 1 are placed steel teeth 3, which
serve as magnetic field concentrators. In the windings
connected to the inverter, alternating currents with a
frequency of about 1 Hz arise, which create a traveling
magnetic field in the surrounding space and
capacitance 4 with aluminum melt 5.
For such an inductor design , a two -phase power
supply from a transistor inverter of a modified voltage
can be applied, and the inductor itself becomes a four -
pole, with a corresponding change in the traction
characteristics. By inversely turning on the phases, a
pair of windings cha nge the polarity of the induction
machine (IM). The presence of four windings allows to
increase the raster of the coating of the molten meta l,
located in the region of the dentate zone, by magnetic
fluxes.


Figure 1

For presented on fig. 1 AxBy XaYb winding
designations receive a system of balanced voltages in
the two -phase variant with a phase shift of voltages of
about /2. There is an effect of the mutual influence of
currents and distortion of the field pattern due to edge
effects and the ope n-ended configuration of the
magnetic circuit, as well as the transfer of power
between the windings due to mutual inductance. Due to
the pro ximity of the windings on the common magnetic
core, the phase shifts of the currents differ from  = /2,
therefore the refined distribution of magnetic fluxes is
estimated by calculation and experiment. To control the
amplitude -phase ratios of magnetic fluxes include
measures of regime regulation, special circuit solutions
and algorithmic control of the state of the transistor
inverter.
An example of a spatial phas e representation of
the characteristics for the steady state of an idealized
two -phase induct or with a power source is shown in
Fig. 2. The use of phase coordinates allows to show
vector diagrams of currents, voltages and magnetic
fluxes more clearly.


a b
Figure 2

American Scientific Journal № (27 ) / 201 9 63
The nature of the multi -phase power supply
system is largely determine d by the wiring pattern of
the inducing windings. It should be noted that in the
considered two -phase configuration of the MHD
inductor, the power supply system, in contrast to the
three -phase one, is balanced, therefore the side effects
caused by the puls ating component of the magnetic
field are substantially weakened. In addition, the power
and vibration loads on the metal structures of the
inductor and the frequency converter, as well as
additional losses, are significantly less. A distinctive
feature of the power mode of the windings of a two -
phase machine can be considered as a separate pair
connection of sections to half -bridges of a transistor
source. The phasing of the half bridges of the power
link of the inverter is performed in such a way as to
ensure a phase shift of about π/2 between the currents
of adjacent windings. An example of the connection
scheme of the windings of a two -phase induction
machine is shown in fig. 3


In addition to the four -pole variant of the inclusion
of the windings of the four -zone inductor, for the
presented design of IM, a bipolar inclusion is possible.
Changing the number of poles is performed by
switching the windings and changing the power supply
circuit. The change of polarity necessarily leads to a
change in traction characteristics, therefore, for each
configuration of a longitudinal magnetic field inductor,
the effective ness of the effect on the melt is estimated
in advance and recommendations are made for the
application of each type of induction machine.
Judging by the scheme of fig. 3 each pair of
windings of one phase is connected in series with each
other. Such a con nection provides the specified
character of the distribution of magnetomotive forces
(MMF), according to the initial vector diagram, in fig.
2. It should be noted that the presence of edge effects
leads to a distortion of the field pattern; therefore, the
initial distribution should be considered idealized. If
there is a need for advanced regulation of the linear
current load of the inductor, the connection diagram of
the windings of fig. 3 can be modified and transferred
to the mode of separate connection of the phases to the
inverter with an increased number of half -bridges, or
similar to the parallel connection of the windings.
A sketch of the four -zone inductor model,
designed for research in the Maxwell software
environment, is shown in fig. 4. When for ming the
model, the geometry was saved and the main operating
parameters of the linear induction machine 2p = 2 were
set, for a pair connecti on of the windings in the ABXY
scheme. The spatial description of the model is made in
the Cartesian coordinate sys tem.


Figure 4

For the two -phase power supply of the field
model, a simulated idealized chain model of a transistor
inverter is used. The initial configuration of the power
source is built using ideal EMF sources, without taking
into account the mutual influence of the phases,
assuming that the errors from the modified voltage of
the PWM inverter are irrelevant. The value of
asymmetr y of the winding currents is limited to 15%.
The resulting picture of the intensity distribution of the
magnetic field vector H in the longitudinal section of
the two -phase magnetic circuit is shown in Fig. 5.
Judging by the color selection, on a scale (A / m), one
can estimate the field intensity in the center of the core
and take control measures to change the field
redistribution with a decrease in saturation and
overload.

64 American Scientific Journal № ( 27 ) / 20 19

Figure 5

Taking into account the characteristics of the steel,
the fie ld is corrected in such a way as to limit the
magnitude of the losses in the yoke of the magnetic
circuit for the steady state at induction values B <1.9 T
and maintaining an acceptable traction force in the
tooth zone outside the magnetic circuit. The
dis tribution pattern of the x-components of the
magnetic field vector outside the core in the axial
section of the ind uction machine magnetic circuit is
shown in Fig. 6


Figure 6

By the nature of the color selection, using the scale
it is easy to judge the intensity of the components, the
force vectors of the field. By the numerical values in
the tables of calc ulated results, it is easy to get an idea
of the differential parameters of the mode. At the same
time, the possibility of representing integ ral mode
parameters in many cases in such modeling systems is
limited. Therefore, it is convenient to apply circuit
simulation of the magnetic system of an induction
machine, presented in a chain configuration, for
evaluating integral tooth magnetic fluxes .
An example of the distribution model of the
integral working flows of the dentate zone in a
longitudinal axial section of the inductor is shown in
Fig. 7, a. The distribution diagram for the teeth of the
MMF vectors of the balanced system in the reverse
order of the phase rotation is shown in Fig. 7, b.



a b
Figure 7

The flow distribution down is not considered,
since it does not affect the molten metal in the bath. The
calculated values of the flows down are less than the
useful tooth flows directed into the melt (Fig. 1), due to
the presence of ferromagnetic teeth on top of the core,
which serve as mag netic field concentrators.
The calculation of the electromagnetic modes of
the induction machine of the longitudinal magnetic

American Scientific Journal № (27 ) / 201 9 65
field is conven iently carried out using the multiphase
model of the magnetic circuit [12]. The structure and
parameters of the mod el are determined by the actual
geometry of the inductor and the winding mode. The
indicated magnetizing forces take the values of
equivalent sinusoidal currents taking into account
saturation for a fixed inductor mode. Increased values
of MMF of the side windings are applied according to
the results of the parametric optimization of the
distribution of integral gear waves [11] under the
condit ion of the greatest achievable homogeneity in a
circular raster.
A fragment of the spatial circuit model of a two -
phase nonlinear magnetic circuit is shown in Fig. 8. The
construction and determination of parameters of a
detailed magnetic circuit model are considered in [8, 9].
A feature of the presented model can be considered the
use as magnetizing sources, controlle d sources. The
matrix description of the controlled source of magnetic
voltage corresponds to the traditional four -pole element
of the theory of circuits, referred to as a voltage source
controlled by current. Here the principle of analogy of
electric and magnetic circuits is used. The
magnetization control mode allows changing the
coefficients k1, k2, k3, k4 to take into account the
changing harmonic composition when magnetizing the
steel magnetic circuit. It should be understood that, by
the principle of analogy of electric and magnetic
circuits, we are talking about sources of magnetic
voltage (MMF) controlled by magnetic flux or
magnetic vol tage.


Figure 8

Practical iterative calculations showed that in the
steady state in the center of the ma gnetic circuit, the
relative magnetic permeability can be reduced to 20 –30
units with a corresponding increase in the magnetic
resistance (H – 1) of the circuit. The order of
complexity of the model can be very significant,
however, the study showed that an increase in the
number of nodes, for example from 200 to 1000, with
correct determination of the integral parameters of the
model, does not lead to a significant increase in the
accura cy of the calculation. The description of the
mathematical model is formed manually, in the ASCII
code, similar to some versions of the Ansys software.
The results of the iterative calculation of
electromagnetic mode of IM are presented in the form
of a vector diagram. The distribution diagram of the
amplitude vectors of wor king magnetic fluxes is shown
in Fig. 9. The diagram shows an expanded raster of the
magnetic field above 7/6, as the sum of the phase
angle s (φ1-2, φ2-3, φ3-4, φ4-5). The equivalent raster
of magnetic fluxes can be estimated by the arrangement
of the vec tors of the fluxes Ф1, Ф2, Ф3, Ф4, Ф5 with a
circular movement counterclockwise from the vector
Ф1 to the Ф5 vector. This indicates the magne tic poles
raster expansion for four -zone inductor with a two -
phase supply beyond 2p = 2 when moving
counterclockwis e along a spiral path between points n
and m.
Regulation of the magnetizing forces of the
windings F1 and F3 on the value of F1 and F3
redi stribute the tooth flows Ф1, Ф2, Ф3, Ф4, Ф5,
changing their intensity and phase shifts. Naturally,
with a pair -wise counter -switching windings of
different phases, the possibilities of regulation are
limited, even if there is the possibility of program -
alg orithmic control of the inverter mode.

Figure 9

66 American Scientific Journal № ( 27 ) / 20 19
Somewhat better regulation results can be
obtained for powerful electromagnetic melt -mixing
complexes using separate control of the windings of the
induction machine. For such a solution, it is poss ible to
obtain a different coordinated mode of separate power
supply in phases, varying the voltage and current of the
power transistor link in accordance with the complex
requirements for power supply. You need to understand
that this option is somewhat more expensive, so it is
accepted after the feasibility study. An example of the
scheme of a separate connection of the windings of the
inductor 1 to a two -phase transistor inverter 2 is shown
in Fig. 10.


Figure 10

With this approach, there is another consequence
of the new circuit design. Compared to the three -phase
connection of the inductor windings, 4 copper
connection cables (195 mm 2 each) must be used for
separate control. This is greater than in the original
three -wire circuit. Given the large currents, and
sometimes the considerable length of the cable line,
they receive a slight increase in voltage losses, which
can reduce the efficiency of the complex as a whole.
A way out of the situation can be considered a
constructive solution with the combination of an
induction machine and a power source in a single
structure, when placing such a complex under the
furnace. Thus, the wires can be shortened, and to
maintain the thermal conditions in harsh temperature
conditions under the furnace, in the IGBT inverter, you
should use the air conditioning system with air
conditioning and air cleaning.
It should be noted that a detailed study of the
possibility of controlling the shifts of magnetic fluxes
is the subject of parametric optimization. In this case,
the optimization criteria can be set substantially
different, both for uniform distribution of the prong
flo ws, and for extremely non -uniform. The main
parameter in the design of the optimization objective
function should be the amount of traction in the melt
developed by these flows. It is noteworthy that it is in
the two -phase power supply system that there are
expanded possibilities for separate control of the
windings of the induction machine, while the three -
phase system is limited in control capabilities, since it
is coherent.
It should be noted that the results presented here
should be considered as a stat ement of the problem and
the first approximation to the calculation of the
electromagnetic mode in the development format of the
induction MH D machine of the above configuration.
Conclusion . When building energy -efficient two -
phase induction MHD machines, several interrelated
problems should be solved. Evaluation of the
effectiveness of the effect of inductors on the molten
metal when changing the operating characteristics is
the essence of the magnetohydrodynamic problem. The
study of the characteristics and features of the
electromagnetic field of an induction machine, as well
as the methods of controlling the redistribution of
magnetic flux, relates to the field of mathematical
modeling and optimization of the inductor magnetic
system. Creating an effecti ve winding scheme,
controlling the number of poles and the speed of a
traveling magnetic field should also be considered as a
task in the fie ld of research of the field of flat induction
machines of a longitudinal magnetic field. In addition,
it should be understood that the standard three -phase
inverters rotating asynchronous electric drive are not
suitable for powering two -phase machines. The refore,
when building complexes of different dimensions,
intended for electromagnetic mixing of the melt, it is
nec essary to create a series of economical and reliable
power sources for induction machines, with a different
number of phases and various circ uitry of winding
activation. For each of the designated tasks and the
whole variety of designs of induction machine s it is
necessary to devote a separate study.

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