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8БЕЗЗУБЦОВЫЙ ИНДУКТОР ДЛЯ ТЕХНОЛОГИИ МГД-ПЕРЕМЕШИВАНИЯ РАСПЛАВА
АЛЮМИНИЯ В ПЕЧАХ
Тяпин А.А.
аспирант,
ФГОУ ВО Сибирский федеральный университет, г. Красноярск, Россия
Кинев Е.С. к.т.н., директор,
ООО Тепловые электрические системы, г. Красноярск, Россия
A TOOTHLESS INDUCTOR FOR THE TECHNOLOGY OF MHD STIRRING OF ALUMINUM
MELT IN FURNACES
Tyapin A.
Postgraduate student, Siberian Federal University
Kinev E.
Ph.D., director of Thermal Electrical Systems LLC
Аннотация
В статье представлен МГД-индуктор, отличающийся повышенной тяговой эффективностью. Предлагаемое техническое решение заключается в выгодном перераспределении нормальной и тангенциальной составляющих электромагнитного усилия в жидком металле. Предварительный анализ распределения электромагнитных сил показал, что формованная ступенчатая конструкция обмоток и наклонное их рас-положенияе позволяет увеличить тяговое усилие в расплаве. Особенностью беззубцовой конструкции маг-нитопровода можно считать повышение КПД за счет снижения потерь в стали индуктора. Изменение конструкции плоской индукционной машины приводит к улучшению электромагнитной обстановки за счет уменьшения потоков рассеяния во внешней среде. Предлагаемое техническое решение может применяться к двухфазным, трехфазным и многофазным индукторам, которые становятся значительно короче. Для питания обмоток МГД-машины можно использовать стандартный транзисторный преобразователь частоты. Уменьшение влияния нелинейностей улучшает симметрию электромагнитного режима системы электроснабжения. Принятые решения позволяют рассчитывать на повышение электромагнитной совместимости оборудования, в технологии электромагнитного перемешивания жидкого алюминия, при приготовлении сплавов в миксерах и печах.
Abstract
The article presents the design of the MHD inductor, which is characterized by increased traction efficiency. The proposed technical solution consists in an advantageous redistribution of the normal and tangential components of the electromagnetic force in the liquid metal. A preliminary analysis of the electromagnetic forces showed that the molded stepped design of the windings and the change in their placement, allows increasing the traction force in the aluminum melt. The features of the toothless design of the magnetic circuit increase the efficiency by reducing losses in the steel of the inductor. A change in the design of a flat induction machine leads to an improvement in the electromagnetic environment due to a decrease in scattering fluxes in the external environment. The proposed technical solution can be applied to two-phase, three-phase and multi-phase inductors, which become significantly shorter. A standard transistor frequency converter can be used to power the windings of a flat MHD machine. Reducing the influence of nonlinearities improves the symmetry of the electromagnetic regime of the power supply system. The decisions taken make it possible to count on improving the electromagnetic compatibility of equipment, in the technology of electromagnetic stirring of liquid aluminum, in the preparation of alloys in mixers and furnaces.
Ключевые слова: линейная индукционная машина, МГД-перемешиватель, бегущее магнитное поле, электромагнитные силы, расплав алюминия, математическое моделирование.
Keywords: Linear induction machine, MHD stirrer, running magnetic field, electromagnetic forces, aluminum melt, mathematical modeling.
Introduction. For stirring the aluminum melt in furnaces, MHD induction machines with copper windings placed on a steel magnetic circuit are used [1]. The magnetic field of low-frequency currents in the windings serves as a source of traction in the melt. To weaken the shielding resistance of the steel frame of the furnace, a window is cut out in the bottom and a sheet of non-magnetic stainless steel is welded in. Thus, the magnetic field of each coil penetrates the refractory lining and penetrates into the melt [2]. To create a traction force, phase alternation of currents in the inductor coils or the movement of permanent magnets is provided,
thus obtaining the effect of a traveling magnetic field
[3]. To overcome non-magnetic gaps of more than half a meter, shortened transverse field inductors are used
[4]. Less commonly, one-sided longitudinal field inductors are used, which have a number of disadvantages.
The arrangement of the annular windings of the longitudinal field inductors is such that they cover the yoke and the magnetic field is directed along the bottom, closing by scattering in the melt. Therefore, the mixing intensity is somewhat less than that of trans-
verse field inductors. At the same time, the large radiation of the inductor windings into the external environment creates an extremely unfavorable electromagnetic environment. Even with a colossal linear current load of the inductor, and with a high use of the normal component of the electromagnetic force, significant stray fields in the melt are often insufficient [5].
The arrangement of concentric windings in the transverse field inductors is such that they cover the tooth, and the field of each coil is directed into the melt. Under heavy loads, the inductor causes perceptible vibrations of the melt surface, destroying the oxide film and increasing the waste of liquid metal. In this case, the filling factor of the groove is in any case less than 0.5. It should be noted that the traction force of such inductors, as a rule, is sufficient for mixing the melt in furnaces with a capacity of up to 50 tons. When the thickness of the lining in the furnace bottom is more than 0.5-0.6 meters, the majority of induction MHD machines may have a problem of reducing the efficiency of mixing the melt [6]. This applies to both three-phase and two-phase inductors. To improve the
traction force, one has to follow the path of increasing the current in the windings. This leads to an increase in the size of the inductors, increased losses and increased equipment costs. Therefore, the resulting efficiency of solutions remains at a low level [7].
Based on the results of studying flat induction MHD machines of longitudinal and transverse fields, it is necessary to propose and develop a new design solution for an MHD inductor, which allows increasing the traction force in the melt. To power the windings, it is necessary to use typical three-phase or multiphase inverters at a low current frequency. At the same time, it is necessary to avoid a significant increase in the operating characteristics of the power supply and a significant increase in power consumption. In the course of the study, it is necessary to first assess the possibilities of optimizing the device.
A sketch of the phase winding configuration in the form of an assembly of two-layer concentric sections is shown in Fig. 1, a, b. The diagram of the traction components of the electromagnetic force is shown in Fig. 1, c.
a b
Fig. 1. Sketch of the arrangement of the
To study the features of the distribution of the normal and tangential components of the electromagnetic force, it is necessary to perform geometric constructions and change the technological approach to the manufacture of windings of induction machines of translational motion [8].
The technical method, changing the horizontal position of the windings to an inclined one, makes it possible to obtain a redistribution of forces in the melt. However, such a constructive solution is suitable only for the ratio of the repulsive and traction components of the electromagnetic force adopted here [9]. The required ratio of the components of the force largely depends on the design of the windings of the MHD inductors with increased traction efficiency. In the accepted notation, the value of 9 means the angle of attack for the inclined placement of the inductive windings. However, the calculated ratios are based on the values of other angles, measured from the normal to the plane of the winding. Mathematical modeling of electromagnetic modes and magnetohydrodynamic flows in a melt
c
winding turns of the induction machine
is performed using the Ansys Multiphysics environment program [10]. In the analysis of the electromagnetic field and circuitry of power circuits of induction machines, the recommendations set forth in the literature are used [11].
The magnitude of the thrust vectors Fmi, Fm2 is determined from the geometric relationships fixed in Fig. 1, c.
Fm2 = Fml + AFm2 , Fm2 = F2 cos 9 + Ft1,
Fm\ = Fx\ . (1)
a = arctg(Fni /FxX), 9 = ^/2-y, y = P + a = arcsin( F2/ Fm2), (2)
where: a is the operating angle, p is the control angle, y is the equivalent angle, 9 is the angle of attack, F„1, Fti - are the projections of the thrust vector, F1 is the equivalent of the horizontal winding thrust, F2 is the equivalent of the inclined winding thrust.
Others, necessary in calculating the ratio of vectors, for different projections of the force, are also determined from the sketch shown in Fig. 1, c.
Examples of a molded two-layer winding section and a single-phase winding assembly are shown in Fig.
2, a. A sketch of the design of an induction MHD machine with molded stepped concentric phase windings is shown in Fig. 2, b.
H3 E53
■ fl
a b
Fig. 2. Sketch of a winding section (a) and an example of inductor design (b)
It can be assumed that an additional improvement in the characteristics of MHD inductors can be achieved by using molded stepped winding sections. This measure allows you to reduce the distance between the centers of adjacent windings, without a significant increase in cross-magnetic connections of adjacent phases. Considering that usually the place in the center of the winding is usually occupied by the steel of the prong, the resulting effect can be considered to be somewhat similar to the reduction in the width of the prong.
Preliminary studies have shown that the presence of a tooth in the structure is not necessary at all. The point is that a decrease in the distance between the active conductors of a section serves to decrease the longitudinal dimensions of the MHD inductor itself. This increases the density of the turns and improves the equivalent copper fill factor of the conditional slot. The absence of teeth makes it possible to place the means for fastening the windings in the center, and the additional free space, to a certain extent, improves the conditions for connecting and cooling the windings. With proper design, the proposed measures can improve the installation technology and increase the reliability of the device.
Numerical modeling and physical experiments have shown that with a significant linear current load of the inductor, a high magnetic field strength leads to saturation of the ferromagnetic cores, so the field concentration in the steel is low [12]. The increase in traction efficiency due to the teeth does not exceed 5-7 %. But in the teeth of the cores, significant heat power is released, measured in kilowatts and reducing the energy efficiency of the induction machine. Therefore, teeth are not needed in the proposed design.
To solve the problem of determining the best traction efficiency of an MHD machine, it is necessary to carry out an optimization study using several vectors of
independent optimization variables. The simplest step is to optimize the design parameters of the inductor itself. By introducing the coefficients of the geometry of the winding in width and height ( K , ^ ) and relative units, it is possible to show the control characteristics of the parameters that affect the magnitude of the thrust.
K = k-[b/2c], « = k2-[h/2c],
9* = (*-29)/*, F* = Fml! Fm
ml ■
(3)
where ki, k2 are geometry scaling factors, 9* is the relative value of the angle of attack, Fm1 is the traction force of the horizontal winding, Fm2 is the traction force of the inclined winding, F* is the multiplicity of the traction force.
For the optimization search, it is convenient to use software for the genetic algorithm [13]. Taking into account the truncated purpose of the study, the search conditions are limited to the use of the shorthand expression of the objective function.
F (K, 9) = "n^i Fo - F (K) / F0 F0 - F (*) / F0 \ +
Fo - F(9*)
/ F0^ min. (4)
In the accepted notation, the characteristics F( K ), F( ^ ), F(9*) correspond to the functions of the relative value of the tractive effort, qk are the weight coefficients.
An example of a family of dependencies, the magnitude of the winding thrust, proposed by the MHD inductor, on the value of the angle of attack is shown in Fig. 3. As a reference characteristic, highlighted by spe-
cial symbols, some quasi-optimal distribution of traction forces obtained from the simulation results is taken. When adjusting the value of the coefficient
X = k • \b / 2c] in one direction with a step of 5 %, a family of curves is obtained
XI = {I, 2, 3, 4, 5, 6, 7, 8, 9}, shown in Fig. 3.
When adjusting in the opposite direction, other curves are obtained. According to characteristics 1 - 9, it can be seen that the greatest tractive effort is developed by different windings at different angles of attack, the values of which are easy to obtain from the trajectories of the dotted arrows.
Fig. 3. Graphs of thrust ratio versus angle of attack for coefficient X
You can do the same with another geometry factor « = k2 • \h/2c] . When adjusting its value in the direction of increase in 5 % steps, the family of curves ^ = {1, 2, 3, 4, 5, 6, 7, 8, 9}, shown in Fig. 4. Regulation in the other direction gives a different family of characteristics. However, manual manipulations in this algorithm are ineffective and only allow us to
determine an approximate result suitable for an indirect assessment. To obtain comparatively accurate results for the most efficient winding design, automatic multipurpose optimization must be used.
1,30
1,35
1,50
1,55
1,60
1,65
1,70
1,75
1,80
Fig. 4. Graphs of the thrust ratio on the angle of attack for the coefficient ^
It should be understood that the improvement of the traction properties for a given configuration of the inductor depends on many factors [14]. These are the design characteristics and geometrical parameters of the windings, the polarity and the number of working zones of the MHD machine, the linear current load, the operating characteristics of the power supply system, etc. As a result, the most important should be considered the ratio of the normal and tangential components of the electromagnetic force developed by the windings [15].
It is convenient to perform the task of informal multicriteria optimization of the induction system of the stirrer at the stage of experimental design study of the MHD device. Taking into account many factors, the optimization algorithm turns out to be very difficult, so the optimization study should be singled out as a separate project. Some disadvantages of the proposed design of the induction machine can be noted, for example, the use of stepped molded sections for the windings. However, for the traditional standard sizes of the
used copper winding PSDKT wires (tires) in size, for example, 3 x 11 mm, the procedure for winding and forming concentric two-layer sections cannot create insurmountable technological problems. It is necessary to formulate a technical task, carry out optimization calculations, carry out experimental design studies and work out the bending technology - pressing the winding sections, with baking the coils in an adhesive compound. It can be assumed that the winding with curved sections will certainly be stronger, since stiffening ribs will appear. Another disadvantage may seem to be the lack of an electromagnetic reverse of the inductor with an inclined arrangement of the windings, when powered by a frequency converter. However, this drawback can be corrected by using an electromechanical reverse [16]. Indeed, to place the inductor in the technological pit, an electromechanical lift is often used. Therefore, the inductor of obviously smaller mass will be easier to lower and deploy under the furnace by mechanical means in automatic mode.
Conclusion. The paper presents a constructive solution for the inductor of a flat linear MHD machine, which makes it possible to increase the traction efficiency, and therefore to reduce the weight, dimensions and power consumption. Judging by the results of preliminary study and simulation, the low-pole inductor with an inclined arrangement of the windings can be made shorter. Removing excess steel elements makes the inductor more economical by the amount of tooth loss. Due to the absence of teeth, it is possible to optimize the cooling system, to increase the current density and linear current load. The weakening of magnetic couplings between the windings of adjacent phases, associated with a decrease in the effect of nonlinearities, helps to reduce the asymmetry of the three-phase current system. This allows you to improve the modes of typical power supply systems. The use of a massive external magnetic circuit provides an improvement in the electromagnetic environment due to the shielding of the windings and the creation of a magnetic circuit closed with the mixer body.
References
1. RF patent No. 2524463. Induction unit for stirring liquid metals. Timofeev V., Lybzikov G., Khat-syuk M., Eremin M. Published on July 27, 2014.
2. US Patent, №» 9901978B2. Metod and aparatus for moving molten metal. Pavlov E., Ivanov D., Gas-sanov P., Gulayev A. Published on Feb. 27, 2018.
3. Aliferov A., Vlasov D., Promzelev V. & Morev A. (2018) MHD steering of aluminum melt in cylindrical bath by means of permanent magnets system. EDM 2018 - Proceedings. International Conference of Young Specialists on Micro/Nanotechnologies and Electron Devices. Erlagol, Altai, Russia: IEEE Computer Society.
4. RF patent No. 2683596. Inductor of a linear induction machine. Timofeev V. Registered on 29.03.2019.
5. RF patent No. 2712676. Device for electromagnetic stirring of molten metals. Goremykin V., Prikhodko S. Registered 30.01.2020.
6. Sokolov I., Shvydkiy E., Bolotin K., Bychkov S. & Losev G. (2019) The influence of traveling magnetic field inductor asymmetric power supply on the
liquid metal flow. 11th winter school on continuous media mechanics. Perm, Russia: Institute of Physics Publishing.
7. Timofeev V. & Khatsyuk M. (2017) Analysis of electromagnetic processes of magnetohydrodynamic mixing of liquid metals. Electricity, 1, 35-44.
8. Bychkov S., Nazarov S., Tarasov F. & Frizen V. (2017) Windings of induction machines of rotational and translational motion. Ekaterinburg, Russia: UrFU.
9. Korobova N., Aksenenko A., Tarasov F., Frizen V., Luzgin V. & Fatkullin S. (2013) On the electromagnetic effect on the aluminum melt during its modification. Metallurgy of mechanical engineering, 1, 008-011.
10. ANSYS 2019 R1. Updates and Changes / ANSYS, Inc. 2019, 81 p.
11. Frizen V., Chernykh I., Bychkov S. & Tarasov F. (2014) Methods for calculating electric and magnetic fields. Ekaterinburg, Russia: UrFU.
12. RF patent No. 2708036. A method for stirring a metal melt and an electromagnetic stirrer for its implementation. Golovenko E., Avdulov A., Kinev E., Timoshev V. Registered 03.12.2019.
13. Tyapin A., Kinev E. & Bezhitsky S. (2019) Approach to optimization of the magnetic circuit of a threephase induction plant. Siberian Journal of Science and Technology, 20(3), 398-408. Doi: 10.31772/25876066-2019-20-3-398-408.
14. Timofeev V. & Khatsayuk M. (2016) Theoretical design fundamentals for mhd stirrers for molten metals. Magnetohydrodynamics, 52(4) 495-506.
15. Maksimov A., Khatsyuk M. & Timofeev V. (2018) Analysis of the influence of the normal component of electromagnetic forces in the process of MHD mixing of the melt. Light alloy technology, 4, 106-112.
16. Kinev E.S., Tyapin A.A., Golovenko E.A., Avdulov A.A., Efimov S.N. Universal MHD Device for Automation of Casting Control of Aluminum. In the collection of articles: IOP Conference Series: Materials Science and Engineering. Krasnoyarsk Science and Technology City Hall of the Russian Union of Scientific and Engineering Associations. Krasnoyarsk, Russia, 2020. pp. 32019.
