Develop a method for determining and evaluating the stress-strain state, particularly the distribution of thermomechanical stresses in the materials of individual rotating parts of vehicles.The proposed method is based on the principle of gradual approximations of the solution when the boundary conditions are satisfied on the curvilinear limiting surfaces of the disk body.The proposed method of determining and estimating the distribution of thermomechanical stresses in the disk material makes it possible to take into account the variable geometry: thickness and presence of a hole in the central part of the disk, also correctly determine stress-strain state at any point of unevenly heated rotating axial body.The work uses generally accepted assumptions and limitations for thermomechanical calculations.It is proved that in real disks, the stress-strain state is spatial, and the well - known method based on the hypotheses of the plane-stress state does not provide the possibility of calculating the values of stresses in the thickness of the disk. The obtained results can be used to improve the methodology of auto technical examination of road accidents. In addition, they can be taken into account by bus drivers on urban routes when choosing a safe distance in heavy traffic, as well as design engineers of car brake systems.

Purpose: Ensuring the required operational reliability of disc brakes by forecasting their technical condition taking into account thermomechanical processes. Design/methodology/approach: Differential equations of rotation of a rigid body around a fixed axis are solved, it is established that the equations of motion and the equations of thermal conductivity are indirectly related. The use of these analytical dependences provides a better understanding of thermomechanical transients. Findings: The solution is obtained on the basis of the differential equation of thermal conductivity of the hyperbolic type, which does not allow an infinite velocity of propagation of temperature perturbations in contrast to the differential equation of thermal conductivity of the parabolic Fourier type. The obtained analytical dependences provide a better understanding of thermomechanical transients and develop a theoretical basis for determining stresses and heat fluxes in solving problems of reliability and durability of disc brakes. Research limitations/implications: The work uses generally accepted assumptions and limitations for thermomechanical calculations. Practical implications: It is shown, that transients in a mechanical system - a brake disk at impulse loadings cause emergence of thermal effects which arise under the influence of external loadings. Originality/value: The application of these analytical dependences provides a better understanding of thermomechanical transients and develops a theoretical basis for solving problems of reliability and durability of disc brakes.