Development of a method for calculating the optimal mode of conducting a train in terms of energy saving meet the safety requirements and schedules. The method of calculation must solve the assigned tasks without significant time spent on the calculation. To implement this method of calculation was used a simplified model of the train as a controlled system. The existing mathematical and algorithmic methods for solving isoperimetric problems of finding the optimal solution in the presence of restrictions on resources were the information base for methodology development. Scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodical and normative materials, currently in force on Ukrainian Railways. The results of these studies were used to create simulators on the basis of computer technology for the training of locomotive drivers. The scientific novelty of the proposed calculation method consists in applying the simplified calculations of the status of the train as a controlled system, without the use of differential equations of motion that allows to significantly increase the speed of the calculations. This, in turn, will solve the problems of finding optimal control in real time, taking into account changing conditions during the movement of the train. The practical significance of the obtained results is the use of such a calculation method that does not require significant time for its implementation and can be used as a subsystem of the on-board train control system capable of per-forming calculations taking into account changes in the current train situation.
Purpose. Using scientific publications the paper analyzes the mathematical models developed in Ukraine, CIS countries and abroad for theoretical studies of train dynamics and also shows the urgency of their further improvement. Methodology. Information base of the research was official full-text and abstract databases, scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodological materials of ministries and departments. Analysis of publications on existing mathematical models used to solve a wide range of problems associated with the train dynamics study shows the expediency of their application. Findings. The results of these studies were used in: 1) design of new types of draft gears and air distributors; 2) development of methods for controlling the movement of conventional and connected trains; 3) creation of appropriate process flow diagrams; 4) development of energy-saving methods of train driving; 5) revision of the Construction Codes and Regulations (SNiP ΙΙ-39.76); 6) when selecting the parameters of the autonomous automatic control system, created in DNURT, for an auxiliary locomotive that is part of a connected train; 7) when creating computer simulators for the training of locomotive drivers; 8) assessment of the vehicle dynamic indices characterizing traffic safety. Scientists around the world conduct numerical experiments related to estimation of train dynamics using mathematical models that need to be constantly improved. Originality. The authors presented the main theoretical postulates that allowed them to develop the existing mathematical models for solving problems related to the train dynamics. The analysis of scientific articles published in Ukraine, CIS countries and abroad allows us to determine the most relevant areas of application of mathematical models. Practical value. The practical value of the results obtained lies in the scientific validity and applied orientation of theoretical studies using mathematical models, the improvement of which will expand the range of problems to be solved, and increase the level of reliability of the results obtained. ботаны существующие математические модели для решения задач динамики поезда. Проведенный анализ научных статей, опубликованных в Украине, странах СНГ и за рубежом, позволяет определить наиболее актуальные области применения математических моделей. Практическая значимость. Практическое значение полученных результатов заключается в научной обоснованности и прикладной направленности теоретических исследований с использованием математических моделей, совершенствование которых позволит расширить круг решаемых задач, повысить уровень достоверности получаемых результатов.Ключевые слова: длинносоставные поезда; динамика поезда; математические модели продольных колебаний поезда; моделирование межвагонных соединений; научные статьи; продольные силы в поезде; тренажеры машинистов локомотивов ISSN 2307-3489 (Print), ІSSN 2307-6666 (Online) Наука та прогрес транспорту. Ві...
The paper studies the possibility of using previously developed by the authors spatial mathematical model of the modern diesel train DPKr-2 for parameters determination, with the help of which the dynamic properties of the mechanical part are evaluated. The dependences of maximum accelerations of the body in the vertical and horizontal planes, the coefficients of vertical and horizontal dynamics both in the primary and in the secondary suspension on the speed of the car movement, the amplitude and the length of geometrical unevenness of the railway track were obtained. It is established at what speeds, depending on the parameters of geometrical unevenness of the railway track, the phenomenon of resonance and danger for the diesel train car movement appears. For a particular length of geometrical unevenness, the maximum permissible value of its amplitude over the entire range of speed movement, where the coefficients of vertical and horizontal dynamics in the primary suspension do not exceed permissible limits, has been studied. The adequacy of the mathematical model is checked by comparing the results obtained during calculations with the experimental ones.
The description of the developed computer system possibilities and its use to solve problems of motion safety and stability is given.
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