# Calculation Schemes for Determining Contact Stresses in Railway Rails
## 4 Conclusions  
Forecasting contact fatigue endurance, wear and destruction of railway rails and wheels of rolling stock is based on estimates of the stress-strain state of parts, which is associated with the need to solve boundary value problems of contact interaction. Such calculations are also necessary for understanding the physical processes of damage accumulation, the occurrence and development of defects in rails and wheels. These processes are influenced by many factors, which can be conditionally divided into three groups--structural (geometric parameters of the rail and wheel, types of fasteners, types of sleepers, rail inclination angles, rail elevation in curves, track width, etc. ), technological (material, heat treatment, residual stresses, wheel and rail hardness ratio, etc. ), and operational (speed, slippage, temperature, lubrication, etc.). The complexity of the comprehensive analysis of the influence of the specified groups of factors is associated with the synergistic effects of their action, and therefore such an analysis is very complex and requires multivariate calculations. In this work, the authors deliberately limited themselves to considering the influence of only some design parameters of the rail track and wheels on the magnitude and distribution of stresses in the contact zone. This work presents the basic formulas for a simplified analytical solution to the contact problem based on [PERSON]'s theory, which is still widely used in many regulatory documents to assess the magnitude of stresses in the contact of parts for various purposes, including rails and wheels. The modern approach to solving contact problems is to use numerical methods, in particular, the finite element method (FEM). When using numerical methods, the accuracy of calculating the stress-strain state depends on several factors: software capabilities, computer processing power, and the accuracy of the calculation scheme. The FEM calculation scheme consists of a geometric model, a model of force and kinematic conditions, and a model of physical and mechanical properties of the material. In this work, the main attention is paid to the consideration of the features of constructing a geometric model of the MSE, which would allow assessing the influence of some factors related to the design of the track (in particular, the rigidity of the sub-rail base, the inclination of the rail sole to the sub-rail base, the amount of elevation of the outer rail in curved sections of the track, the track width and the profiles of the contact surfaces) on the magnitude of the contact stresses. This possibility is provided only by a sufficiently complete geometric model, which is shown in Figure 6. Consideration of the contact interaction using 2D and 3D fragments of the wheel and rail gives only qualitative results; therefore, such problems should be used for modeling surface plastic deformation under conditions of rolling with slipping, analyzing the influence of surface roughness on the stress-strain state of the surface layers of parts, stress concentrations on defects (inclusions and microcracks) of the material, etc. It is obvious that the level of contact stresses can be controlled to some extent by using certain combinations of rail inclination, rail elevation in curves, and wheel and rail profiles. These issues should be reflected in new editions of regulatory documents related to the design of railway infrastructure elements. At present, it is problematic to expect from such contact interaction models results that would exactly correspond to the real stresses in the wheel-rail pair. In this work, the influence of only five different design parameters on the magnitude of contact stresses was estimated. The use of superposition methods to assess the joint influence of these factors is currently impossible, since contact problems are nonlinear even for elastic materials. Therefore, the search for optimal values of the factors considered in the work is a very difficult task from a mathematical point of view.