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Tyapin Alexey Andreevich, Postgraduate student, Siberian Federal University E-mail: Mishinskaya_AS@tamerlan-krk.ru Kinev Evgeny Sergeevich, Candidate of technical sciences, Director Thermal Electric Systems LLC E-mail: kinev_es@ontecom.com
FOUR-ZONE LINEAR INDUCTION MACHINE WITH TWO-PHASE POWER
Abstract. Linear induction MHD machines with a low-frequency power supply inverter form a complex of electromagnetic stirring of liquid aluminum in melting furnaces. The article discusses the classification features and characteristics of four-zone inductors of a longitudinal magnetic field with a two-phase power supply. 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. The study shows the main directions of optimization of the low-pole induction machine mode to obtain the best current distribution in the windings and to estimate the equivalent linear current load. 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.
Keywords. Induction MHD machine, inductor of longitudinal magnetic field, electromagnetic stirrer, running magnetic field, multiphase magnetic circuit model, vector magnetic flux diagram, two-phase power supply system, frequency inverter.
For stirring metal melts in furnaces, linear in- These design features appropriately characterize duction machines of transverse and longitudinal the pole position of the inductor and the magnitude magnetic fields are used [1, p. 2]. The cost of each of the synchronous velocity of the runnling magnetic technical solution, along with the technological and field in the melt [4, p. 26]. The following designa-energy efficiency of induction machines and power tions are used as constructive and operational pa-sources, is a decisive factor in the decision to mod- rameters in the description: ernize production or to develop design solutions for 2p - is the number of poles of the inductor;
new construction of smelting furnaces [2, p. 217]. As Z - is the number of teeth of the core; induction machines for stirring aluminum alloys in q - is the number of grooves of the core per pole
mixers and furnaces, in addition to transverse field and phase;
inductors, high-tech shortened inductors of the lon- a - is the phase zone of the inductor; gitudinal field are used [3, p. 65]. Among the simplest m - is the number of phases of a multiphase flat induction MDG machines, two constructive so- winding inductor; lutions can be distinguished, which determine the A - is the working gap.
type of machine, according to the number of force The classical induction MHD machine of a longi-inducing windings (inducing zones). tudinal magnetic field can have 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 [5, p. 86].
1. Four-zone inductor with two-phase power supply.
2p = 2, Z = 5, q = 1, m = 2, a = 90 °
2. Four-zone inductor with a three-phase power supply.
2p = 4/3, Z = 5, q = 1, m = 3, a = 60 °
3. Three-zone inductor with a two-phase power supply.
2p = 3/2, Z = 4, q = 1, m = 2, a = 90 °.
4. Three-zone inductor with a three-phase power supply.
2p = 1, Z = 4, q = 1, m = 3, a = 60 °.
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).
Figure 1
The inductor has four windings 1, denoted 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, in the middle part of which a thickening is provided, designed to reduce saturation. Between the windings 1 are placed steel teeth 3, which serve as magnetic field concentrators. In the windings connected to the inverter, alternating currents occur at a frequency of about 1 Hz, which create a traveling magnetic field in the surrounding space and capacitance 4 with aluminum melt 5 [6, p. 50].
For this design of the inductor, a two-phase power supply from the transistor inverter of the modified voltage can be applied, and the inductor becomes a four-pole, with a corresponding change in the traction characteristics. By inverting the phases of a pair of windings, they change the polarity of the induc-
tion machine (IM). The presence of four windings allows to increase the raster of the coating of the molten metal, located in the region of the dentate zone, by magnetic flux [4; 5].
For presented in fig. 1 letter designation of the A x ByXaYb windings is obtained by a system of balanced voltages in a two-phase configuration with a phase shift of voltages of about n / 2. There is an effect of the mutual influence of currents and distortion of the field pattern due to edge effects and the open-ended configuration of the magnetic circuit, as well as power transfer between the windings due to mutual inductance. Due to the proximity of the windings on the common magnetic core, the phase shifts of currents differ from a=n /2, therefore the refined distribution of magnetic fluxes is estimated by calculation and experiment, and to control the amplitude-phase relations, measures
of modal regulation, special circuit solutions and algorithmic control of the transistor state inverter [7, p.54].
An example of a spatial phase representation of the mode characteristics for the steady state of an idealized inductor with a power source is shown in (Fig. 2).
a)
b)
Figure 2.
The use of phase coordinates allows us to show vector diagrams of currents, voltages and magnetic fluxes more clearly. The nature of the multi-phase power supply system is largely determined by the wiring diagram of the inducing windings. It should be noted that in the considered two-phase configuration of the MHD inductor, the IM power supply system, in contrast to the three-phase one, is balanced, therefore the side effects caused by the pulsating component of the magnetic field are significantly weakened compared to the use of three-phase power supply. In addition, the power and vibration loads on the metal structures of the inductor and frequency converter, as well as additional losses, are significantly less [3; 5; 8].
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 n/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.
Figure 3.
Changing the polarity certainly leads to a change in the traction characteristics, therefore, for each configuration of a longitudinal magnetic field inductor, the effectiveness of the effect on the melt is estimated in advance and recommendations are made for the use of each type of induction machine [3; 6].
Judging by the scheme, each pair of windings of one phase is connected in series with each other. Such a connection provides the specified distribution of the magnetomotive forces, according to the initial vector diagram, in (fig. 2). It should be noted that the presence of edge effects causes distortion of the field pattern, therefore, the given initial distribution should be considered idealized. If necessary, advanced regulation of the linear current load inductor, the connection diagram of the windings of (fig. 3) can be modified
and transferred to the mode of separate connection of phases to the inverter with an increased number of half-bridges, or a parallel connection of windings is realized. However, such decisions are made in advance, since they require additional research and coordination on the current of the inductor mode with the inverter. For parallel connection of the windings, a design solution with a reduced cross-section of the copper bus is required in order to preserve favorable proportions of the inverter utilization ratio by voltage.
An example of the distribution of the integral working flows of the dentate zone in a longitudinal axial section of the inductor is shown in (Fig. 4, a). The distribution diagram for the teeth of the MDS vectors of the balanced system of currents in the reverse order of the phase rotation is shown in (Fig. 4, b).
->-------. —4----------------------4
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! r^TTT*.....11 ! r^n
Oa tfi.j 1 m. _ ! ! !
Ou
) !
oA2 I- O
'CI
T I
A3-!
oAi Tr
0A
JA4 jOB5 M
o-
'2 A
O
'4 A
y//////\ r ~| y//////[ r ~1 y/////'1 f ~l
art
0A3 OB OA 0B3 OB PAS
A x 12IbA hJx 4 Y b
a)
b)
Figure 4.
The calculation of the electromagnetic mode of the induction machine of the longitudinal magnetic field is conveniently performed using a multiphase model of a magnetic circuit [4; 9]. The structure and parameters of the model are determined by the actual geometry of the inductor and the winding mode. The specified magnetizing effects take the values of equivalent sinusoid currents, taking into account saturation for a given inductor mode. According to the results of the parametric optimization of the distribution of integral fluxes of teeth, increased values of the magnetizing forces of the extreme windings can
be applied, according to the condition of the greatest achievable uniformity in a circular raster [9; 10]. Optimization criteria may be different, more complex, directly taking into account the developed tractive effort in the molten aluminum.
A fragment of the spatial circuit model of a two-phase nonlinear magnetic circuit is shown in (Fig. 5). The construction and determination of the parameters of a detailed magnetic circuit model is considered in [9; 10]. A feature of the presented model can be considered the use as magnetizing sources, controlled four-pole links. The principle of analogy of electrical
and magnetic circuits [4; 10] is used. 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. 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 a formal analogy of electric and magnetic circuits, we are talking about sources of magnetic voltage (magnetomotive force), controlled by magnetic flux or magnetic voltage.
Figure 5.
The solution of the nonlinear problem is performed by the methods of the theory of chains, using a modified nodal analysis. Therefore, a matrix image corresponds to each element of the circuit model, and a system of equations of 5-6 orders of magnitude is formed for each controlled source, and a second order for passive elements in the conducive format. When using n-sensors of magnetic flux in the circuit structure, the dimension of the system increases proportionally by 2n. It can be noted that the final dimension of a nonlinear iterative problem is not decisive, since modern computing resources have overcome possible limitations [11; 12]. Practical iterative calculations showed that in the steady state in the center of the magnetic circuit, the relative magnetic permeability can be reduced to 20-30 units with a corresponding increase in the magnetic resistance (H-1) of the chain section. The order of complexity of the model can be quite significant, but 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 chain model, does not lead to
a significant increase in the accuracy of the calculation [12, p. 208].
The description of the mathematical model is formed manually, in a text format in ASCII code, similar to some versions of the Ansys software package. Repeat fragments can be declared models and grouped in a compact form.
The results of an iterative calculation of the electromagnetic mode of IM are presented in the form of a vector diagram. The distribution diagram for the teeth of the amplitude vectors of the working magnetic fluxes is shown in (Fig. 6). The diagram shows the expanded raster of the magnetic field vectors above / 6, with a circular movement counterclockwise from the 01 vector to the 05 vector. This suggests that the raster leaves the magnetic poles of the four-zone inductor with a two-phase power supply beyond the full circle for the case of 2p = 2.
Regulation of the magnetizing force of the windings carry out the redistribution of tooth flows, changing their intensity and phase shifts. Naturally, with a pair of head-on switching windings of differ-
ent phases, the possibilities of regulation are limited, even if there is software and algorithmic control of the inverter mode.
Figure 6
It should be noted that a detailed study ofthe possibility of controlling the shifts of magnetic fluxes is the subject of parametric optimization. In this case, the optimization criteria can be set significantly different, both for uniform distribution of the prong flows, and for extremely non-uniform. An additional parameter in the design of the optimization target function is the tractive effort in the melt developed by these flows [12-14]. 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 statement of the problem
and a first approximation to the calculation of the electromagnetic mode in the development format of an induction MHD machine of the above configuration.
Conclusion. When building energy-efficient 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 effective winding switching circuit, controlling the number of poles and the speed of a traveling magnetic field should also be considered as a task in the field of research into flat induction machines of a longitudinal magnetic field. In addition, it should be understood that the standard three-phase inverters of a rotating asynchronous electric drive are unsuitable for powering metallurgical equipment, the modes of which are sharply asymmetric and extreme. Therefore, when constructing complexes of various dimensions intended for electromagnetic mixing of the melt, it is necessary to create a series of economical and reliable power sources for induction machines, with a different number of phases and various circuitry for switching windings. Each of the indicated tasks for the whole variety of designs of induction machines is rather complicated and it is necessary to devote a separate study to it.
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