This paper presents the results of the International Benchmarking of Longitudinal Train Dynamics Simulators which involved participation of nine simulators (TABLDSS, UM, CRE-LTS, TDEAS, PoliTo, TsDyn, CARS, BODYSIM and VOCO) from six countries. Longitudinal train dynamics results and computing time of four simulation cases are presented and compared. The results show that all simulators had basic agreement in simulations of locomotive forces, resistance forces and track gradients. The major differences among different simulators lie in the draft gear models. TABLDSS, UM, CRE-LTS, TDEAS, TsDyn and CARS had general agreement in terms of the in-train forces; minor differences exist as reflections of draft gear model variations. In-train force oscillations were observed in VOCO due to the introduction of wheelâ\u80\u93rail contact. In-train force instabilities were sometimes observed in PoliTo and BODYSIM due to the velocity controlled transitional characteristics which could have generated unreasonable transitional stiffness. Regarding computing time per train operational second, the following list is in order of increasing computing speed: VOCO, TsDyn, PoliTO, CARS, BODYSIM, UM, TDEAS, CRE-LTS and TABLDSS (fastest); all simulators except VOCO, TsDyn and PoliTo achieved faster speeds than real-time simulations. Similarly, regarding computing time per integration step, the computing speeds in order are: CRE-LTS, VOCO, CARS, TsDyn, UM, TABLDSS and TDEAS (fastest)

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The development of the methods for modeling the processes of accumulation of the rolling contact fatigue damage and wear of the wheels of the railway rolling stock and the rails is particularly relevant due to the increase in the number of damage in the recent times. The work is underway to improve the chemical composition and the technology of production of the wheel and rail steels in order to improve their mechanical properties and ability to resist the action of the cyclic loads. The methods of modeling allow predict the possibility of initiation of the fatigue cracks during operation with the sufficient accuracy in the short time. The selection of the contact fatigue criterion and the mathematical apparatus for calculating the stresses at points in the area adjacent to the contact patch to obtain the numerical values of the criterion components is the most important task in the development of modeling methods. The article focuses on the approaches based on the Dang Van criterion and the shakedown diagram for a material undergoing to the action of cyclic loads, which are widely used to assess the rolling contact fatigue of the wheels and rails. The assumptions that are used in the development of the algorithms concerning the models of the contacting bodies, the shape of the contact patch, the distribution of the contact pressures and the tangential forces are considered. The approach using the criterion — the amplitude value of the maximal shear stress is also considered. The example of modeling the process of accumulation of the rolling contact fatigue damage in the wheel of the freight car is given. The results of modeling are presented in the form of the isolines of the criterion values and the accumulated damage in the area adjacent to the contact patch. This work was supported by the Russian Foundation for Basic Research under Grant [17-01-00815A].