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The method of determining the durability indicators of wheel pairs of locomotives is considered on the example of diesel locomotives of the 2TE25KM series operated on the Volga railway. For this purpose, the 90% resource of the wheel pairs of the studied series of locomotives was determined, and it was compared with the accepted standard indicator. In addition, a controlled parameter of the wheelset is selected, limiting the reliability of this node. To conduct the study, methods of mathematical statistics and probability theory were used, in particular, the Laplace distribution function, the Student's criterion, as well as the results of calculations of the dependencies of the mean value and the standard deviation of the controlled parameters, the initial values of developments and operating time corresponding to the probability of failure 0.5. In this study, a mathematical model for assessing the durability of wheelsets from the point of view of reliability theory was developed. The evaluation of the durability indicators of the wheelset elements was carried out on the basis of the type of random variable distribution law with its parameters obtained on a computer and adopted according to the Pearson criterion. As a result of the calculations, 90% of the life of the wheelset was obtained according to two controlled parameters, which amounted to 476.6 thousand km for the thickness of the bandage, and 282.6 thousand km for the thickness of the ridge. The results obtained were compared with the values adopted in the Technical Specifications for this series of locomotives (800 thousand km). km), as well as with statistical data on the values of controlled parameters obtained during processing and analysis - 240 thousand km. Due to the fact that in operation the average life of the wheelset is determined by a larger number of controlled parameters, taking into account unscheduled repairs, and in this study - only on the basis of the thickness of the bandage and the ridge, it is not possible to talk about full compliance with the calculated and actual data. According to the results of calculations, the limiting reliability of the wheelset is such a controlled parameter as the thickness of the ridge. For a more accurate assessment of the durability of wheelsets, it should also be taken into account that the intensity of wear of rolling stock equipment is affected by specific operating conditions, in this regard, inter-repair runs should be adjusted taking into account the influence of external factors during operation. In order to fully assess the durability of wheelsets in the future, it is necessary to take into account additional factors, in addition to those that affect the parametric change of random variables, as well as the fact that takes into account the monitoring and analysis of all controlled parameters of this node during the operation of locomotives.

Optimization of insulation of walling of building walls is proposed, taking into account the relationship of structural, heat engineering, operating parameters and economic indicators. The purpose of research is to determine the optimal value of the thickness of the insulation with the heat-insulating material of the object, taking into account the thermal energy released to it. The study used methods of mathematical modeling of heat transfer, an optimization problem. The results of the study of the influence of the thickness of the insulating material on the technical and economic efficiency of the building's consumption of energy resources and material costs are presented. The results showed a decrease in heat losses through the building envelope, consumption of heat and electric energy for the heating, ventilation system and reduced costs.