Proceedings of the International scientific and practical conference ―Science at the Frontier of Civilizations: Challenges and Perspectives‖ (December 27-29, 2025) / Publisher website: www.naukainfo.com. – Helsinki, Finland, 2026. – 252 p.

187 dimensional problem for the average temperature and the temperature analogs of bending moments, taking into account convective heat exchange on the external surfaces and imperfect thermal contact in the slots. The obtained equations are used to analyze the temperature field of the barrel of a TGV-500-4 turbogenerator rotor with local overheating in one or several slots. The rotor is modeled as a beam with a piecewise constant cross section, hinged at both ends, and its deflections are determined on the basis of the equations of thermal bending. The influence of the orientation and number of overheated slots, as well as the thermal conductivity of intermediate layers, on the magnitude of thermal deflection and vibration level is investigated. It is shown that an increase in the thermal conductivity of the intermediate layers leads to an increase in the temperature analog of the bending moment, the maximum rotor deflection, and the corresponding rise in vibration levels. Keywords: thermo-stressed state, heat conduction, local overheating, turbogenerator rotor, multiply connected cross section, thermal deflection, vibrations, thermal bending of a beam. During the operation of turbogenerators, local overheating of rotors may occur due to various causes. This leads to thermal deflections and, consequently, to an increase in vibration levels, which in turn may result in serious emergency situations. It should be noted that under such conditions the turbogenerator rotor can also be considered as a rod-like structural element. A number of studies are devoted to the problem of determining thermal stresses in rod-type elements of engineering structures. The stresses in bimodular curved beams under the combined action of temperature effects and shear forces are investigated in works [1, 2]. Issues related to diagnostics and the development of methods for eliminating thermal imbalance of rotors are highly relevant. The effectiveness of the proposed measures significantly depends on the reliability of assessments of the influence of various thermal defects on rotor deflections. Since the turbogenerator rotor is a complex system, characterized by a multiply connected cross section and material