Due to the simplicity of the design and the possibility of obtaining significant rotation frequencies (up to 20,000 - 30,000 rpm) and large starting torques, single-phase commutator motors (SPCM) with series excitation continue to be promising for use in household electrical appliances and hand-held electric tools. During the design of new samples of SPCM, as well as modernization of existing engines of this type, it is necessary to use adequate mathematical models of SPCM, which determines the relevance of the study. The purpose of the article is the development of a mathematical model of transient processes in SPCM based on circular methods. The basis of the mathematical model is a branched substitute scheme of the magnetic circuit with concentrated parameters, which makes it possible to find the distribution of magnetic fluxes in the loops based on the dimensions of the magnetic circle, winding data and the instantaneous value of the current. The system of nonlinear equations of the magnetic state, composed by the method of contour magnetic flux, corresponds to the substitute scheme of the SPCM magnetic circuit. In this system, the primary unknowns are the loop magnetic fluxes, and the secondary ones are the magnetic fluxes in the branches of the scheme. Relationships between fluxes in branches and contour fluxes are established using connection matrices. The nonlinear system of equations of the SPCM magnetic circuit is written in vector form. The algorithm for solving this system by Newton's iterative method is presented. Equilibrium equations of voltages and equations of armature motion are recorded, which must be integrated by a numerical method to calculate transient processes in SPCM. An explicit method of numerical integration is used, which involves solving the system of equations of the magnetic state at each step of integration, i.e. finding the magnetic fluxes in the branches of the substitute circuit. On the basis of the solution of the system of equations of the magnetic state, the working magnetic flux in the air gap, the electromotive force of the armature winding, the electromagnetic moment and the differential inductances of the armature and excitation windings are determined - quantities that are included in the equations of the balance of voltages and moments. The proposed mathematical model of transient processes of SPCM can be used for the analysis of these processes, as well as during the design of SPCM.
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