MATHEMATICAL MODEL OF INDUCTION RHEOSTAT TWO COIL DESIGN

Abstract

The vast majority of research is devoted to induction rheostats (IR) of disk design with a single coil. IRs of this design have a number of disadvantages: increased resistance at low current frequencies and a significant aperiodic current component in transient conditions. The elimination of these shortcomings gives IR with two coils. In this design, the coil is divided by a ferromagnetic plate into two equal halves, which are included in the circuit in concert. With this connection of the coils, their magnetic fields are directed oppositely. At a current frequency of 50 Hz, the depth of field penetration into the metal is insignificant and the magnetic flux passes through the plate from both sides. With a decrease in the current frequency, the depth of penetration of the flow increases and the field of one coil displaces the field of the other. To study the electromagnetic parameters of ІR, their mathematical model in the field formulation has been developed. In this case, the following assumptions are made: there are no gaps at the joints of structural elements (the steel parts of the body are a ferromagnetic screen) and coil insulation, the influence of the temperature effect on the specific conductivity, magnetic permeability is neglected, and the hysteresis of steel is not taken into account. The relationship between magnetic induction and magnetic field strength appears to be a normal magnetization curve. Since the IR construction has the property of symmetry about the central axis of rotation, the equations are written in cylindrical coordinates relative to the vector magnetic potential. A mathematical model is presented in the form of a system of differential equations, for the solution of which the finite element method was used. Dependences of the current ІR on time and the distribution of magnetic induction in the cross section of the coils are obtained. A comparative analysis showed that a two-fold decrease in the thickness of the inner ring of the structure made it possible, at a frequency of 5 Hz, to reduce the total resistance of the rheostat by 1,74 times. To conduct experimental studies of IR, a laboratory installation was created, which made it possible to remove the dependences of resistance on the magnitude and frequency of the current in the coils. The experimentally obtained dependences of the impedance ІR on frequency at fixed values ​​of currents are compared with the calculated points. It is shown that the discrepancy between them is 510 %. The obtained accuracy is sufficient for engineering calculations.