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

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.