Mathematical Modeling of the Thermal Stability of Permanent Magnets under External Demagnetizing Fields for Traction Rolling Stock

Aleksandra S. ZHevak; Dmitry Kurilkin

doi:10.20295/1815-588X-2026-3-830-841

UDC 537.622 UDC 621.313.323

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MATHEMATICAL MODELING OF THE THERMAL STABILITY OF PERMANENT MAGNETS UNDER EXTERNAL DEMAGNETIZING FIELDS FOR TRACTION ROLLING STOCK Mathematical Modeling of the Thermal Stability of Permanent Magnets under External Demagnetizing Fields for Traction Rolling Stock

АА Аа

Published in Proceedings of Petersburg Transport University · Volume 23, Issue 3, 2026 · Pages 830–841 · Rubric: СОВРЕМЕННЫЕ ТЕХНОЛОГИИ — ТРАНСПОРТУ

DOI: https://doi.org/10.20295/1815-588X-2026-3-830-841

Received: 11.06.2026 Accepted: 09.07.2026 Published: 07.10.2026 Language of publication: RUS

Authors

Aleksandra S. ZHevak

Dmitry Kurilkin

Aleksandra S. ZHevak

Tashkent State Transport University, 1 Temiryulchilar Assistant

Dmitry Kurilkin

Academic degree: doctor of technical sciences

Science rang: docent

Emperor Alexander I Petersburg State Transport University Head of the Department · Head of the Department of Locomotives and Locomotive Engineering · Russian Federation · St. Petersburg

ABSTRACT

Objective: to develop a method for assessing the residual life of permanent magnets in traction synchronous motors of locomotives based on Nd–Fe–B alloys, taking into account the temperature dependence of magnetic properties. Methods: the study is based on a thermodynamic analysis of the temperature evolution of magnetic properties using analytical models of the temperature dependence of residual magnetic flux density, incorporating both linear and nonlinear relationships. Results: an analytical model describing the reduction of coercivity in Nd–Fe–B magnets under heating has been derived based on a power-law dependence of magnetocrystalline anisotropy on temperature. A dimensionless thermal stability criterion is introduced, enabling the determination of irreversible demagnetization conditions through the ratio of the operating demagnetizing field to the temperature-dependent coercivity. A method is proposed for converting motor operating conditions into an equivalent demagnetizing field via the d-axis component of the stator current. A comparative analysis of magnets of different commercial grades shows that an increase in energy product is not accompanied by improved thermal stability. An integral measure of degradation accumulation under cyclic heating is also introduced. Practical significance: the results can be used to assess thermal degradation of permanent magnets in traction synchronous motors of locomotives and to predict their residual life under various operating conditions, taking into account accumulated damage.

KEYWORDS

permanent magnets, nd-fe-b magnets, magnetocrystalline anisotropy, coercivity, thermal degradation, thermal stability criterion, permanent magnet synchronous motors, locomotive traction motor

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Editor-in-chief

Oleg S. Valinskiy

Deputy Editor-in-chief

Dmitry Kurilkin

It@pgups.ru

Science editor

Andrey Evstaf'ev

elt@pgups.ru

Edition

zhurnala P. Redakciya

izvestia@izvestiapgups.org

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GOST

ZHevak A. S., Kurilkin D. N. Mathematical Modeling of the Thermal Stability of Permanent Magnets under External Demagnetizing Fields for Traction Rolling Stock // Proceedings of Petersburg Transport University. 2026. no. 3. pp. 830-841. DOI: https://doi.org/10.20295/1815-588X-2026-3-830-841. (Date of access 13.10.2026).

MLA

Aleksandra S. ZHevak, Kurilkin D. N.. "Mathematical Modeling of the Thermal Stability of Permanent Magnets under External Demagnetizing Fields for Traction Rolling Stock." Proceedings of Petersburg Transport University 23.3 (2026): 830-841. DOI: https://doi.org/10.20295/1815-588X-2026-3-830-841.

APA

ZHevak A. S., Kurilkin D. N. (2026). Mathematical Modeling of the Thermal Stability of Permanent Magnets under External Demagnetizing Fields for Traction Rolling Stock. Proceedings of Petersburg Transport University, 23(3), 830-841. https://doi.org/10.20295/1815-588X-2026-3-830-841

Chicago

Aleksandra S. ZHevak, Kurilkin D. N.. "Mathematical Modeling of the Thermal Stability of Permanent Magnets under External Demagnetizing Fields for Traction Rolling Stock." Proceedings of Petersburg Transport University 23, no. 3 (2026): 830-841. https://doi.org/10.20295/1815-588X-2026-3-830-841.

WIKI

{{cite journal | author = ZHevak A. S., Kurilkin D. N. | title = Mathematical Modeling of the Thermal Stability of Permanent Magnets under External Demagnetizing Fields for Traction Rolling Stock | journal = Proceedings of Petersburg Transport University | year = 2026 | volume = 23 | issue = 3 | pages = 830-841 | doi = 10.20295/1815-588X-2026-3-830-841 }}

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MATHEMATICAL MODELING OF THE THERMAL STABILITY OF PERMANENT MAGNETS UNDER EXTERNAL DEMAGNETIZING FIELDS FOR TRACTION ROLLING STOCK Mathematical Modeling of the Thermal Stability of Permanent Magnets under External Demagnetizing Fields for Traction Rolling Stock

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