MODEL ESTIMATION OF LONGITUDINAL DYNAMIC FORCES CARGO TRAIN ON STEEP SLIDES

ABSTRACT

In this article, the process of synchronous electrodynamic braking of locomotives located at the beginning and end of the train is modeled. Based on the developed mathematical model, a computer model of train movement was created in MSC.ADAMS software. After 3 out of 4 parts of the train went down the slope, during the transition of the two locomotives to the synchronous electrodynamic braking mode, longitudinal-dynamic forces generated in the connections between the locomotive and the wagons were evaluated. The evaluation of longitudinal forces in inter-car connections of trains with trains of 40 cars and gaps of 50 mm was made.

АННОТАЦИЯ

В данной статье моделируется процесс синхронного электродинамического торможения локомотивов, находящихся в начале и в конце поезда. На основе разработанной математической модели создана компьютерная модель движения поезда в программе MSC.ADAMS. После того, как 3 из 4 частей поезда сошли под уклон, при переходе двух локомотивов в режиме синхронного электродинамического торможения оценивались продольно-динамические сил, возникающие в межвагонных соединениях и локомотивами. Произведена оценка продольных сил в межвагонных связях поездов с составами из 40 вагонов и зазорами 50 мм.

Key words: track gradient, model, train movement, longitudinal dynamic force, automatic coupler, inter-car connection, electrodynamic braking, AV-RT systems.

Ключевые слова: уклон пути, модель, движение поезда, продольно-динамическая сила, автосцепное устройство, межвагонное соединение, электродинамическое торможение, системы АV-RT.

The most effective way to reduce the longitudinal forces in the interwagon connections during train movement and shunting operations is the use of modern impact absorbing devices with a large energy capacity. However, these new devices require significant financial costs for purchasing and re-equipping the fleet of wagons with them.

To date, one of the main conditions for increasing the reliability of train longitudinal dynamics modeling is the accuracy of mathematical models of train movement and traction equipment in locomotive and wagon connections, along with properly organized computational experience and computational algorithms of model implementation.

The analysis of studies of the dynamics of train movement modes has shown that the effect of longitudinal compressive forces on interwagon connections is the cause of rolling stock derailment in most cases. The maximum values of these forces should be limited, especially in curved parts of the track, in order to avoid compression of the crews, expansion and displacement of the rail under the train [2].

Thus, the train movement model should provide an opportunity to evaluate the longitudinal-dynamic interaction of the wagons in the composition both in their movement with different characteristics and in different longitudinal profiles of the track. Taking into account the variety of rolling stock used in railway transport and the fact that its characteristics significantly affect the longitudinal dynamics, it is important to consider the characteristics of each wagon separately for the model.

Modern computer technologies allow solving complex systems of differential equations with high accuracy.

In order to approximate the process of train motion modeling to a real object, it is recommended to consider the train as a chain of rigid bodies connected by connections with nonlinear properties. In studying the longitudinal dynamics of the train, it is possible to limit the consideration of longitudinal components only and not to take into account the spatial vibrations of the carriages. Taking spatial vibrations into account complicates the process of building a train model and research, but it has an insignificant effect on the accuracy of measuring longitudinal forces in interwagon connections. Such a simplification has been accepted by world scientists and the legality of its application has been experimentally confirmed [1, 5].

Currently, "Uzbekistan Railways" is using new 2OʻZ-ELR electric locomotives in mountainous sections in order to increase the efficiency of cargo transportation. These locomotives have an AV-RT system, which allows simultaneous control of two locomotives in electrodynamic braking and traction modes during operation when the locomotive is placed at the head and tail of the locomotive (Fig. 1).

Figure 1. AV-RT system of mutual radio control of two locomotives

This AV-RT system makes it possible to reduce the longitudinal dynamic forces in interwagon connections on sections with different profiles due to the increased mass and length of rolling stock. Accordingly, the following scheme was developed (Fig. 2).

Figure 2. Scheme of descent from the slope of a train model with two locomotives

According to the scheme, the mathematical description is expressed as a system of balance equations [4]

                (1)

where: m_л1, m_л2, m_аi, m_i, m_а(n+1) - is the mass of the locomotive, i is the connection between cars; including i – th car (i = 1, 2, …, n); , ,  , ,  – longitudinal acceleration of the locomotive, i – connection between cars, i – connection between cars; W_л1, W_i, W_л2 - the main resistance forces to the movement of the locomotive and the i-th car; T_л1, T_л2 T_i, Tʹ_i - forces acting on the absorption devices of the locomotive and i-wagon; T_аi, Tʹ_аi, T _а(n+1), Tʹ_а(n+1)– the forces acting on the trailers of the i-th interwagon connection; B_л1, B_л2 – electrodynamic braking and traction power of locomotives; g - acceleration of free fall; α_л1, α_i, α_аi, α_л2, α_а(n+1) – the slope of the track on which the locomotive moves i – in the interwagon connection and i – the car; n is the number of wagons in the train.

In the above mathematical models, trains are a chain of rigid bodies connected by parts that reflect the characteristics of trailers. When using a spring shock absorption device, the forces in the interwagon connections were determined according to the following expression.

                        (2)

where, С_н, С_р– are the coefficient of stiffness of the absorber during loading and unloading, respectively; q - compression of the shock absorbing apparatus; p, k – indicator of the level of loading and unloading, depending on the design of the hammer absorption apparatus; K - damping coefficient;  – compression speed of the punching device; T_0н –is the excitation and initial clamping force of the absorption apparatus; T_0р is the minimum return force of the punching device;

Δ - intermediate distance of connection between cars. С_н = 1.5‧105 kN/m²; p = 2;

С_р = 1.0‧103 kN/m; k = 1; K = 200 kN‧s/m; T_0н = 50 kN; T_0р = 20 kN.

The forces of resistance to movement depend on many factors, such as rolling stock and type of road, curvature of the road profile, speed of movement, weight load falling on the axle, air temperature, wind, etc. The developed model takes into account the resistance forces constantly acting on the rolling stock during movement and is called the main movement resistance [3]. The effect of non-constant factors (wind, air temperature, operation of undercarriage generators) is not taken into account in the model, but can be easily taken into account if necessary.

Based on the developed mathematical models, the results of calculation of longitudinal dynamic forces in inter-car connections during electrodynamic braking when 3 out of 4 of the weight of the content is lowered in the MSC.ADAMS software complex are shown in Fig. 3.

For calculations, we accept the conditions:

1. The length of the car is assumed to be conditional - 13.92 m;

2. The maximum mass of locomotives is 276 tons + 276 tons;

3. Speed - 40 km/h;

4. Mass of the train - 3600 tons.

Figure 3. Graph of changes in longitudinal dynamic forces in inter-car connections of a train with two locomotives during synchronous electrodynamic braking when ¾ of the train passes through a slope

Thus, it can be concluded from the theoretical studies conducted during the movement of two-locomotive trains, that is, if the braking force is uniformly increased in the mode of two-locomotive synchronous electrodynamic braking, the effect of longitudinal forces will be reduced. At the same time, it is necessary to carry out these theoretical studies on sections with a broken road profile.

References:

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