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Vol. 28 (2025 year), No. 4, DOI: 10.21443/1560-9278-2025-28-4/1

Moskalev Yu. V.
A method for calculating the magnetic circuitof a synchronous salient pole machine using conformal mappings

Increasing the energy performance of a single-pole synchronous machine and reducing vibration during its operation can be achieved by optimizing the pole tips and ensuring a sinusoidal shape of the magnetic induction distribution curve in the air gap. The paper proposes a technique for calculating the magnetic circuit of a salient-pole synchronous machine using conformal mappings. The technique includes two methods – the finite element method and the conformal mapping method. To calculate the magnetic circuit of an electric machine for a pair of poles, a rectangular magnetic circuit is considered, for which a field problem is solved using the finite element method. The conformal mapping method allows you to transform a rectangular area into a sector corresponding to a magnetic circuit of a machine for a pair of poles, and to determine the strength and induction of the magnetic field at various points in this area. According to the known values of the magnetic field strength and induction at various points of the magnetic circuit sector for a pair of poles, these vector values can be calculated for other poles of the machine. An exponential function is used to conformal transform a rectangular area into an area corresponding to a sector of the magnetic circuit of a synchronous machine for a pair of poles. As an example of using the developed technique, the curves of the normal and tangential components of magnetic induction in an air gap per pair of poles for six-pole and eight-pole synchronous machines are calculated taking into account the uneven air gap between the pole tip and the stator core. To verify the calculation results, the magnetic field of the machine's magnetic circuit sector has also been calculated using the finite element method in the FEMM software package. The curves of the normal (tangential) components of magnetic induction in an air gap calculated according to the proposed method and using FEMM are compared. The relative largest margin of error does not exceed 0.47 %.

(in Russian, стр.10, fig. 7, tables. 0, ref 13, AdobePDF, AdobePDF 0 Kb)