# Mathematical Model of Magnetic State of Permanent Magnet Direct Current Motor

2019;
: pp. 10 - 16
Authors:
1
Lviv Polytechnic National University

There is a tendency of replacement of small direct current motors with electromagnetic excitation on permanent magnet direct current (PMDC) motors nowadays. PMDC motors are widely used and that is why a task of creation of mathematical models of this type of motor is actual. The aim of the article is creation of mathematical model of magnetic state of PMDC motors on the basis of theory of electric and magnetic circuit. This mathematical model gives an opportunity after these values of curve of demagnetization of the magnet and instantaneous values of currents of armature to find distribution of magnetic flux (inductions) in all parts of magnetic core of motor. The mathematical model of PMDC motor is created on the basis of the ramified equivalent circuit of magnetic core with the concentrated parameters and with the high level of working out in detail of magnetic core. The magnetic core of PMDC motor is conditionally divided in to separate areas. In every area consider the magnetic field homogeneous. To the areas of magnetic core from electrical engineering steel and tooth layer of armature on a equivalent circuit is corresponded by nonlinear magnetic resistance. These resistance is set by descriptions of F[Ф] as by dependences of magnetomotive forces on magnetic flux. Areas with an air gap are corresponded by permanent magnetic resistance. A permanent magnet appears the concentrated magnetomotive force that is set by description of demagnetization curve of Fм[Фм]. The armature with an air gap divide radial planes into s = m + n areas within the limits of pole pitch. From them m of even areas corresponded part of armature, that is under a magnet and n of even areas — in space between magnets. The initial system of equations is written for one pole pitch after the method of contour flux that are primary unknown. The initial system of equations transforms — the magnetomotive forces on nonlinear resistance are presented by dependences on the flux of branches. Description of demagnetization of the magnet is presented equations of line that is located in the second quadrant and crosses the axis of X in the point of remaining magnetic flux of Фr, and axis of Y in a point that corresponded complete magnetomotive force of the magnet — Fc. The nonlinear system of equations of algebra it is expedient to decide an iteration Newton method. Mathematical model of magnetic state of PMDC motors can be fixed in basis of creation of mathematical models of calculation of transients and steady state of this type of motor.

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