УДК 625.143.482 ДАРЕНСЬКИЙ О. М., д.т.н., професор (Український державний університет залізничного транспорту), ШРАМЕНКО В. П., к.т.н., доцент (Український державний університет залізничного транспорту), ТУЛЕЙ Ю. Л., заступник начальника філії «Південна залізниця» (ПАТ «Укрзалізниця»), ДУДІН О. А., к.т.н., доцент (Український державний університет залізничного транспорту), ЛЕЙБУК Я. С., аспірант (Український державний університет залізничного транспорту) Математична модель колії, яка має інерційні характеристики, під дією швидкісного рухомого складу Розроблено моделі і методи визначення приведеної вертикальної жорсткості рейкової нитки в точці контакту колеса і рейки, яка враховує пружні і геометричні характеристики рейок, жорсткості опор, відстані між ними і розподілену масу колії. Величина цієї жорсткості змінна в часі для кожного колеса у будь-який момент часу і відрізняється для різних коліс екіпажу. Запропонована математична модель реалізована в програмному комплексі Matlab і дасть змогу надалі виконати чисельні дослідження динаміки взаємодії колії і рухомого складу. Ключові слова: балка на опорах, математична модель, динамічна система, "екіпаж-колія", приведена жорсткість. Визначення мети та задачі дослідження Проблема, вирішенню якої присвячено цю роботу, полягає у відсутності на сьогодні математичної моделі колії як балки на багатьох пружно-дисипативних опорах з урахуванням інерційних характеристик колії. Розроблення такої моделі істотно підвищить точність розрахунків.

The article defines the parameters and working conditions for the final restoration of the integrity of the rail beams of a continuous gauge rail by electrocontact welding, as well as when welding rails with each other when they are elongated in the field by the method of preliminary bending. This involves the process of welding rails at temperatures above the temperature of their fixation. In this connection, an appropriate calculation scheme has been considered in relation to which the necessary parameters have been determined to ensure the conditions for straightening the residual curvature and, as a consequence, the formations of the corresponding stress state. To ensure the self-straightening conditions, the resulting formula for determining the residual bending arrow, the elimination of which under the influence of its own weight leads to the appearance of compressive stresses in the weld zone. In addition, a formula has been derived for determining the compressive stresses in the weld zone arising in the rail after the elimination of residual curvature. This means that when performing welding operations without forced straightening of the rails, you can restore not only their integrity, or weld them together. Thereby form a corresponding temperature-stress state.

The purpose of this article is to perform the calculation of this design for the strength of the sleepers in compression according to the “The Strength and Stability Calculation Rules for Railway Track”, which has not been used before. Wooden sleepers in the subway tunnel are encased in track concrete with 2/3 of their length resting on the concrete base. Under the action of rolling stock, stresses and deformations occur in the upper track structure elements. Their dependence on the forces affecting the track is complicated and hard to define. To solve the strength calculation problem, some prerequisites were assumed, and a design diagram and model were created. The magnitude of the vertical modulus of elasticity of the rail pad of the non-ballast track on wooden sleepers in the subway tunnel, the horizontal modulus of elasticity of the track rail, the dynamic vertical pressure of the wheel on the top of the rail, as well as estimated normal stress in the sleeper under the pad were calculated to determine the vertical forces acting on the rail pad of the intermediate rail fastening. The results obtained from the calculation of the wooden sleeper using the “The Strength and Stability Calculation Rules for Railway Track” showed that its bearing capacity is ensured.

The article uses the software complex Lira for the calculation of wooden sleepers, in which the finite element method in the form of displacements is used. FEM provides for making a system of equations that is solved by considering each individual finite element, which is very easy to implement and thus is an important advantage of the method. The purpose of its use is to calculate the wooden sleepers for strength and to determine its bearing capacity. The following types of finite elements were chosen to simulate the upper track structure in the subway tunnel: universal rod-type spatial finite element (type 10) and universal finite element of spatial problem of the elasticity theory (type 31). To design a spatial model, a section of the rail with seven sleepers in the subway tunnel was simulated and loaded with one axle of the car, since the influence of the adjoining sleepers on the estimated sleeper is negligible. They were divided into eight-node tetragonal parallelepiped-shaped finite elements. In order to simulate a sleeper encased in track concrete, a movement restriction was introduced at its points of contact with track concrete. The loads are applied to the rail above the middle sleeper symmetrically relative to its middle and are assumed as concentrated forces on each track line. The part of the sleeper above the culvert is not supported by track concrete and can move freely in all directions. To obtain the values of stresses, the maximum-stress theory of strength is used.