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RESEARCH IF INDUCTION COEFFICIENT OF MAGNETIC CIRCUIT AND CHARGE OF INDUCTOR
! A.P. Kislov, N.M. Kabdualiev
Pavlodar State University named after S. Toraighyrov
ABSTRACT. Induction smelting crucible furnaces have the advantage of optimal management of the process, regulation of the capacity and have high technical indices. The research of electrical and energetic correlation of induction smelting crucible furnaces is necessary in order to analyze the work and elucidate the optimal condition of exploitation, to work out the methods of projection and determine the optimal constructions of magnet wires. The authors worked out the methods of calculating the energy of electromagnetic field according to the sections of the space of the induction system, to the
- selection and installation of magnet wires in order to meet the technological requirements in the best way and to achieve high energetic and exploitation indices when building the induction crucible furnaces. The work represents the influence and interrelation of the inductor and the charge with the magnet wire depending on geometrical correlation of the induction system.
Introduction
Calculation of electromagnetic field for induction system of inductor-charge for melting pot furnaces is especially complicated. Because of determination of the magnetic field in surround area. The goal of research is the_analysis of distribution of electromagnetic field and reactivity power on the areas of space of inductor-charge. Investigation was completed by means of mathematical model for space of inductor-charge.
Mathematical model
Calculation of energy of field is the base of mathematical model that allows to part thejesearch external space of the inductor-charge system per tores of rectangular section and to define the tension of magnetic field H in it and the energy of electromagnetic field in given area. The whole energy of the inductor-charge defines as sum of energy that localized in the every particular tore.
Because of complexity of induction cylindrical axis symmetrical system, during calculation of radial and axis components of magnetic field tension, the real
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induction system is substituted to idealized - real torsions is substituted by thread circular contours and it is considered that thickness of circular contour is equal to depth of penetration of current into metal of inductor, and current in every circular contour is equal to the current of inductor, besides that the assumption of sinusoidal change of electromagnetic values at the frequency 50 GHz.
Lets note expression for components of tension of magnetic filed [1,2] that was created by circular thread current at the point with coordinates rk - zk for cylindrical system of coordinates:
Hrt = — '■J 2n
zu
L +*)+<;} d) ttJ
-K + -T^—\ •[ -E + z?j
2 2 2 v ri,j ~rk ~ZiJ
u ■j+zb
(2)
K and E are full elliptical integral of first and second types of circular contours with current; indices I and j are contours that is equal to inductor and charge.
Modules of elliptical integrals k and e is equal to:
Using expressions for components of tension of magnetic field Hri,j and H zi,j of circular turn with current and utilizing the principle of imposition of fields we would obtain formulas that define components of tension of magnetic field induction system inductor-charge:
Hru (4)
¡=1 7=1
Hz = ±± Hzij (5)
w M
(6)
N and m are the quantity of thread contours with current in inductor, charge.
So components of tension of magnetic field Hr and Hz in investigated point of space defines as sum of tension, created by all elemental of thread contours of current inductor and charge.
In order to find energy of electromagnetic field concentrated at the volume dV we use following expression:
dW = ^\x0H2dV (7)
Formula of determination of reactivity power in the given volume is given in the following way:
dPq = 2n\iQfH2dV (8)
In accordance to principle of imposition at the determination of components of tension of magnetic fields 4-6 of system inductor- charge, energy of electromagnetic field is defined by the integration of expressions 7, 8 in all investigated system volume.
The expression for energy of electromagnetic field is:
■I r2 271 Z2
fF = —¡j,0JrJcosaIH2dr da dz (9)
n 0 z,
We use the following expression for reactivity power:
r2 2j[ z2
Pq =27t(i0/jr j cos a |if2i/r da. dz (10)
r, 0 z,
After the integration by variable a, the rewriting of expression (9)-(10) comes in the following way:
'l z2
W = тг|д0 J JH2rdrdz (11)
ч ч
P?=47tV0/j | H2rdrdz (12)
n zi
Then the calculation just comes to determination of investigated space V, integration by this volume with respect to obtained components of tension of magnetic fields Hr and Hz so that the field would be homogeneous in the given volume and calculation of specific reactivity energy of electromagnetic field of system inductor-charge, as a sum of energy, localized in each particular investigated tore:
X 03)
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The expression for reactivity power in investigated space system of inductor-charge would be following:
(14)
4=1
Conclusions
Investigation of distribution of energy of electromagnetic field of induction system comes to the calculation and quantity value of energy in the areas of space with the aim of selection of place magnetic circuit and determination its influence on energy indices of plants, for axis symmetrical cylindrical system of inductor-charge of distribution of energy of electromagnetic field in the area of space the calculation of section of magnetic circuit might be done and its influence on the energy indices of all the system
Bibliography
[1] Method of calculation of reactivity power for axis symmetrical system of inductor-charge. Kislov A.P. Thesis of the report of the conference MUandC. Pavlodat 1985, page 10-12.
[2] Kislov A.P. Mathematical model for calculation of energy of electromagnetic field of axis symmetrical system of inductor-charge. Scientific work of MEI, 1987. Issue-11, page 18-23.
Тушндеме
Авторы статьи разработали методы расчета энергии электромагнитных полей согласно площадям индукционной системы. Данная работа представляет влияние и взаимодействие индукторов и зарядов с обмоточным проводом электромагнита влияющего на геометрическое соотношение индукционной системы.
Resume
The authors of the article worked out the methods of calculating the energy of electromagnetic field according to the sections of the space of the induction system. The work represents the influence and interrelation of the inductor and the charge with the magnet wire depending on geometrical correlation of the induction system.
