Introduction. Currently, the development of transport highways is strictly linked to urban agglomerations, regional and international logistics corridors, therefore, the urgency of creating multi-level transport interchanges near main hubs is growing. At the same time, it is important to ensure static and kinematic dimensions at various levels of overpasses and underpasses. The article proposes to avoid default usage of beam, arched or truss superstructures and considers a two-support superstructure as an element on which the load from the vehicle is applied to the middle part of the height of the cross-section.
Materials and methods. Several standard superstructure designs for automobile and railway transport modes were considered. According to the available engineering solutions, proposals were developed for dividing the cross-section of the superstructure into an upper and lower part relative to the plane of application of the train dynamic load. The stiffness parameters of the superstructure section are represented as a function of orthogonal spatial coordinates. Linearisation method is used as the solution method of the desired functions on elementary time intervals in order to solve the defining differential equations.
Results. Dynamic vertical displacements of the superstructure cross-section points are obtained depending on the type of section and the distribution of the stiffness function over height. Variation of the geometric parameters of the bridge span cross-section in the range of permissible values enables to change the maximum movements of the cross-section points to keep them in the line of standard values, which may be in demand during calculation of the structure for the f irst and second groups of limit states.
Discussion and conclusion. The presented model is simplif ied and does not consider a number of factors, such as damping in the structural material, irregularities on the surface of the traff ic area and the interaction of the rolling stock wheels with the superstructure. Further research may be aimed at developing more accurate mathematical models that take into account a wide range of factors affecting the dynamic behaviour of bridge crossings. It also seems promising to conduct experimental studies on real structures, which would allow to verify the calculated obtained data and develop practical recommendations for optimising the design of bridge crossings with the distribution of bending and torsional stiffness over the height of the superstructure.

Introduction. The research was conducted by the specialists of the Railway Research Institute in 2018–2019 on the condition of wagon wheels in operation and included an assessment of the form of wear of their working surfaces. At the same time, wheels with worn ridges of unfavorable shape were identified. In combination with other factors, such forms of wear may pose a threat to traffic safety and, in particular, wheels rolling onto contact tongue of turnout switch when moving along the point. The safe passage of a wagon is influenced by the thickness of wheel ridges and their shape, characterised by the inclination angle of ridge generatrix.
Materials and methods. The research was carried out on the basis of data on the actual geometry of wheel pairs and working surfaces of rail elements of the turnout switches. Measurements of geometric parameters of the turnout switches and the rolling surface of wagon wheels on the Russian Railways were performed using a laser profilometer.
Results. Analysis of the conditions for wheels rolling onto contact tongue of the turnout switch when moving along the point was performed and calculation scheme was defined to assess the possibility of wheel derailment due to the wheel rolling onto contact tongue. Mathematical calculations carried out on the basis of a variety of values of geometric parameters of wheel pairs and turnout switches from operation allowed to analyse their unfavorable combinations and showed that the value of the parameter of the maximum permissible inclination angle of ridges of wagon wheels should be normalised.
Discussion and conclusion. The results of dynamic strength tests and mathematical calculations show that the safe passage of wagon is influenced by wheels with ridges with inclination angle tending to 90°, and a sharp flange close to its vertex. The mutual dependence of geometric parameters in the “wheel pair — rail track” system on the turnout switches is shown. The proposals are made to normalise the maximum inclination position of the wheel ridges of wagons to ensure the safety of wheel pairs passage of turnout switches.

Introduction. The probabilistic approach allows to obtain a fatigue assessment considering loading history and characteristics of the fatigue resistance spread and is widely used to calculate the service life of bearing structures of the undercarriage. The approach is based on the application of linear damage summation rule and the transition to the loading limit block. However, approach is presented differently in regulatory documents for different types of rolling stock. The objective of the study is to demonstrate the possibility of unification of probabilistic regulatory methods used for fatigue assessment of different types of rolling stock.
Materials and methods. The regulatory documents data on the strength and dynamic qualities assessment of locomotivehauled cars, EMU cars and locomotives were analysed.
Results. The methods for fatigue assessment under irregular loading are considered, using the concept of equivalent stress and the concept of transition to the loading limit block. A comparison of methods for the values of fatigue safety factors with identical values of the coefficients of variation of the fatigue limit and maximum stress in the block is performed. It is shown that with statistically reliable data on loading and fatigue limit, the smallest fatigue safety factor is included in regulatory documents for the strength assessment of locomotive cars. The author proposes to use an approach in which stress amplitudes are normalised by the fatigue limit value. Conservatism of the deterministic approach is shown in comparison with the probabilistic one.
Discussion and conclusion. The proposed approach allows simplifying the calculations of durability of the rolling stock bearing structures and solving several types of problems: assessing the durability corresponding to a given failure probability, calculating the failure probability at a given durability, assessing the values of the fatigue safety factor. This allows to consider it as a unified approach for different types of rolling stock.

Introduction. The article considers the issues of improving the operation of equipment for vibration diagnostics of rotary mechanical units of rolling stock, and determining objective criteria for assessing the efficiency of the diagnostic process. Industry regulatory documents have significant shortcomings in terms of determining the efficiency indicators of diagnostic equipment. Examples of calculating the “certainty” indicator, performed using different methods, showed that the results of calculating this indicator depend on the sample size of the diagnosed units. The purpose of the article is to analyse existing methods for assessing the quality of operation of vibration diagnostic equipment and to develop an additional criterion for assessing quality based on the likelihood function.
Materials and methods. The samples of diagnostic results of axle boxes of wheel pairs of wagons (selected as an example) are the source material for the discussed problem. The employed methods relate to the sections of mathematical statistics and probability theory. A mathematical method for estimating parameters based on the calculation of the likelihood function is analysed. An example of calculating the likelihood function on simulated data is given.
Results. The result of the work performed is a methodology that allows to determine the certainty limit of diagnostic results of a given degree of probability (“reliability”).
Discussion and conclusion. The authors propose to introduce interval estimates of the “certainty” parameter. It is proposed to use three intervals with specific boundary values. Along with the assessment of the certainty (confirmability) of diagnostic results the authors propose to assess the quality and efficiency of operation of vibration diagnostic equipment by calculating the likelihood function. It is noted that the results of the study could be used in various industries.

Introduction. The authors conducted valid accounting methods choice of complex stress-strain state and mean stress in the calculations of elastic clamps of intermediate rail fastenings nodes connected with the localisation of potentially critical sites under the condition of fatigue durability. Methods that enable to most accurately localise places of fatigue fractures has been determined.
Materials and methods. The elastic clamp CP 369.102 (clamp ZhBR-65) was chosen as the clamp under study. The selection of potential methods for accounting complex stress-strain state and mean cycle stress for the origin of a fatigue crack in an elastic clamp localisation was carried out through a review and analysis of existing approaches. A finite element model of the elastic clamp was developed for conducting virtual tests. Full-scale fatigue tests of the elastic clamps were performed according to the developed test procedure. In order to compare the results of the full-scale fatigue tests and the virtual experiments, 3D scanning of the fractured clamp fragments was employed.
Results. It was established that samples of the elastic clamp CP 369.102, when subjected to full-scale fatigue life tests, failed in two distinct zones with probabilities of 5 % and 95 %, respectively. The results of calculations performed using combined methods for accounting complex stress-strain states and the influence of mean cycle stress demonstrated satisfactory correlation with the experimentally determined locations of fatigue crack initiation in the clamps.
Discussion and conclusion. Combinations of methods for accounting for complex stress-strain states and the influence of mean cycle stress were identified, which allow to localise potentially critical zones of the elastic clamp in terms of fatigue durability during calculations. Further research is planned and aimed at developing a model for the elastic clamp that would enable a sufficiently accurate assessment of its service life based on the current results.

Introduction. Rail damages represented by railhead cracks in the area of joints and bolt holes prevail on railway sections with heavy traffic density and harsh climatic conditions. This is proved by the statistics of withdrawal of severely defective rails on the Trans-Baikal Railway. The analysis of scientific publications shows that in terms of increasing reliability the joint has an advantage with pin and link design of fishplates, which reduces stresses in the rail neck due to the modified support on the rail gorge. The aim of the study is to confirm the hypothesis about the possibility of reducing stresses in the rail neck by using a new fishplate design. In order to confirm the effectiveness of the construction the authors conducted com- parative operational tests with wedge-shaped fishplate construction.
Materials and methods. Strain gauge method was used to measure the stress-stain state of the rail neck at the joint. Fishplates were tested at various bolt tightening torques. During tests, the mounting stresses around the bolt hole were recorded first, and additional dynamic loads occurring during the passage of the train were measured after.
Results. The results show that the pin and link fishplates reduce the assembly tension stresses in the rail neck and increase the fatigue strength of the rails with an increase in the tightening torque of the butt bolts compared to the wedge-shaped design. Vertical loads have little effect on bolt tightening, and the stresses in the fishplates remain within safe limits. Joint monitoring also confirms the reliability of the pin and link design: bolt tightening torques decrease over time, but no defects or damage have been detected.
Discussion and conclusion. The advantages of the pin and link design of a fishplate are proposed and discussed. It is shown that it provides increased reliability of rail joints, reduces stresses in the rail neck and has an increased margin of fa- tigue strength. It was found that this construction retains a higher stability of bolt tightening during operation compared to wedge-shaped fishplates. This increases the durability of the butt joint, reduces the frequency of maintenance, and reduces operating costs. The solution is especially effective for areas with high traffi c density and severe climate.