Siberian Federal University

Issue

Journal of Siberian Federal University. Engineering & Technologies. 2026 19 (5)

Authors

Zhakatayev, Toksan A.

Contact information

Zhakatayev, Toksan A.: Astana International University (Astana, Kazakhstan);

Keywords

iterative algorithm; computational program; compound magnetic circuits; Lagrangian interpolation; cubic spline; magnetomotive force; magnetic circuit; electrical circuit; electric machine

Abstract

Autonomous, simple algorithms and computational schemes for iterative calculations have been developed. This allows you to calculate the distribution of magnetic fluxes in closed circuits of electrical machines (EM). These allow for the calculation of magnetic flux distributions in closed circuits of electric machines (EMs). These calculations can be used to calculate induced emfs, adhesion forces, and braking forces arising between the rotor and stator. The computational algorithms are implemented in C++. Is devoted to the issue of developing and implementing new iterative schemes and models for the calculation of magnetic and electric circuits in the most diverse types and designs of electrical machines. Which are available in simple manual programming mode. And they can be implemented on the simplest PCs. In other words, our work and our results are intended for engineers – developers of new electrical machines, structures and equipment. In the new conditions of technological progress for mass and widespread use. Solved a problem of analysis in the theory of calculating magnetic circuits using automation of the computational algorithm. Based on numerical computer calculations. According to it, for a given magnetizing force F = Iw, the induced induction Bi is calculated over all sections of a complex nonlinear magnetic circuit and BA in the air gap. In the scientific and educational literature, this problem is also called the inverse problem, or also the second Kirchhoff’s law for a contour of a magnetic circuit. Features of interpolation formulas application in calculation of magnetic characteristics of various circuits are shown. Clarifications were made when using them. It is shown that the Lagrange interpolation formula to the third power (the cubic Lagrange polynomial) in some places exceeds the accuracy of the cubic spline calculation. When calculating magnetic fields, we believe this is due to the error in determining mi and mi + 1 at the extreme nodal points for the cubic spline. An algorithm has been implemented in which the program dynamically determines the required interpolation point ZC. It then selects two symmetrical nodal points to the left of this point (j; j‑1) and to the right of it (j+1; j+2). This flexible algorithm, with dynamically changing nodal points for a third‑degree polynomial, guarantees improved Lagrangian interpolation accuracy. This is facilitated by the fact that the steps for the function arguments change quickly and dynamically during the calculations. This ensures the following principles: convenient, simple, accessible, easy, and reliable

Pages

668–681

EDN

AGKSUH

Paper at repository of SibFU

https://elib.sfu-kras.ru/handle/2311/159306

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).