# Calculation Schemes for Determining Contact Stresses in Railway Rails
## 3 Results and Discussion  
Railways with the corresponding infrastructure are the most important part of the transport industry in most countries. The problem of ensuring their safe operation and sustainable functioning and development is a complex and multifaceted task. The life cycle of a track, as one of the most important elements of the railway infrastructure, depends on many factors, which can be divided conditionally into several groups. The factors influencing the external environment include daily temperature fluctuations, humidity, dustiness and others, which are associated with the climate zone, terrain characteristics, and soil. The influence of such factors (for example, changes in climatic conditions and large-scale natural disasters) can be spontaneous and difficult to foresee, and even more difficult to predict their impact on the life cycle of a track [63]. Organizational factors include the quality of management, the level of automation on the railway, professional training of personnel, traffic, the organization and volumes of passenger and freight transportation, as well as their documentation, excess loads of  
Figure 11: Force interaction scheme of a wheel and rail. trains, the availability of modern lubrication equipment, etc. Only some of the listed factors can be formalized and used as parameters of mathematical models for resource forecasting. It is sometimes quite difficult to foresee the consequences of some management decisions related to the organization of railway transportation or the implementation of railway construction and reconstruction projects [64]. Economic factors (affiliation with private, joint-stock or state structures, the volume and distribution of financing, etc.) are closely related to organizational factors and have a significant impact on the development of railways. The factors combined into the operational group, unlike those listed above, are mostly subject to formal description and their influence can be modeled, which allows the improvement of the methods of predicting the life cycle of the track. These include the geometric characteristics of the elements of the track superstructure, the design features of the rolling stock, the physical and mechanical characteristics of the main materials, train movement modes, and others [29; 30; 31; 32; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66]. The influence of these factors can be assessed by means of natural, laboratory, and numerical experiments. To conduct field experiments on existing road sections, it is necessary to obtain permission from the administration, since this is related to traffic safety and often to changes in traffic. In addition, such experiments can last for several months and are often very expensive. Difficulties in conducting laboratory experiments are often associated with the impossibility of reproducing the operating conditions of individual structural elements with sufficient accuracy. For example, many methods are used to assess the level and nature of contact stress distribution: electrical tensometry, the coordinate grid method, polarization-optical methods, methods of applying brittle or optically transparent coatings, hardness measurements, and others. However, all of them provide only qualitative results. Therefore, at present, increasing the accuracy of predicting the durability and residual life of railway infrastructure elements is associated mainly with the use of numerical calculation methods. To obtain reliable results in numerical modeling of the contact interaction of the wheel and rail, it is important to correctly specify or formulate all components of the finite element method calculation scheme--a geometric model, a model of force and kinematic conditions, and a model of physical and mechanical properties of the material.