# 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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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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