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The paper discusses the design and principle of operation of the elastic-friction absorbing device of the automatic coupler. The results of a study of the force characteristic of the elastic-friction absorbing device of the automatic coupler, which takes into account the operating modes of the device and the deformation of the structural elements involved in the transmission of longitudinal force from the automatic coupler body to the absorbing device, are presented. It is proposed to consider the force characteristic of the absorbing device as a piecewise linear loop characteristic consisting of nine sections. Equations have been obtained for determining the static force characteristic for each deformation section of the corresponding structural element of the absorber apparatus of the automatic coupler. The force characteristic has been described using a single system of equations. The main numerical parameters characterizing the operation of the absorber apparatus, such as the stiffness and deformation of the structural elements of the apparatus, the automatic coupler body, and the spring, have been refined and determined. The developed mathematical model of the spring-friction absorber of the automatic coupler takes into account all modes of its operation and deformation of the structural elements that transmit the longitudinal force from the automatic coupler body to the absorber. The results obtained in the work specify the form of the power characteristic of the absorbing device, bringing it closer to the experimentally obtained graphs. The presented mathematical description of the power characteristic can be used in the development of a multi-mass train model, which is a system of rigid bodies connected to each other by nonlinear elastic-frictional bonds. The results of this study can be used to determine the maximum forces in the absorbing devices of automatic couplers when modeling longitudinal vibrations in freight trains, which occur when the locomotive operating modes and train movement modes change as the train passes through the longitudinal track profile changes.

The problem of optimizing train driving modes continues to be relevant for a long time, despite a large number of scientific research and development in this subject area. This is due both to the general complexity of the implementation of the technological process of running the train, and to parametric uncertainty and significant variations in the parameters of the control object itself and the external environment. Well-known methods for calculating energy-optimal train driving modes (calculus of variations, the maximum principle, dynamic programming) and auto-driving systems based on them assume some simplifications of the original problem, and, as a result, implement quasi-optimal control in practice. In this regard, the development of methods for searching for the global extremum of a functional defined on the set of permissible trajectories of a train as a dynamic system is both theoretically and practically a significant task. The aim of the work is to create a computationally efficient metaheuristic algorithm for searching for energy-optimal control as a global extremum of the objective function, the values of which are calculated using a reference model of the control object. The authors have developed a problem-oriented evolutionary algorithm for calculating the optimal control of train movement based on the theory of random search. Its features are the proposed specialized operators of local random search, taking into account the specifics of the control object as a multi-mode system; combined procedures of local and global optimization based on the concept of a multi-island population algorithm with superpopulation, as well as a method of selection (selection) of promising options based on the clustering algorithm. Computational experiments have shown good convergence of the algorithm and repeatability of the calculation results. Based on the solutions obtained, a train running time controller can be implemented that implements asymptotically optimal control.