# Situational Adaptation of the Open Wagon Body to Container Transportation

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## Abstract

**:**

## 1. Introduction

## 2. Objective and Main Tasks of the Research

- To determine the dynamic load and the strength of the open wagon body when transporting containers;
- To offer the detachable module design for securing containers in the open wagon body;
- To determine the dynamic load and the strength of the open wagon body during container transportation by taking into account the proposed fastening diagram.

## 3. Determination of the Dynamic Load and the Strength of the Open Wagon Body When Transporting Containers

_{l}= 2.5 MN [17] was applied to the front stops of the couplers, which corresponded to the “stretch–jerk” mode, as one of the most unfavorable in terms of the force action. It should be noted that there is an international document that is similar to the normative document [17]; however, it contains the values of longitudinal loads [18] that are mainly applicable for 1435 mm gauge wagons. As far as the work deals with the transportation of containers in 1520 mm gauge wagons, this stage of the study was based on standards from [17].

_{W}is the weight of the open wagon; M

_{W}is the weight of the bearing structure of the open wagon; h is the height of the center of gravity of the body; I

_{W}is the moment of inertia of the open wagon relative to the longitudinal axis; P

_{l}is the value of the longitudinal force to the coupler; P

_{fr}is the friction force emerging between the container fittings and the open wagon floor; l is a half of the open wagon base; P

_{FR}is the absolute value of the dry force in the spring group; k

_{1}, k

_{2}are the rigidities of springs in the spring group of the open wagon bogies; m

_{c}is the container weight; z

_{ci}is the height of the center of container weight; I

_{c}is the moment of inertia of the i-th container; x

_{W}, ϕ

_{W}, and z

_{W}are the coordinates corresponding to the longitudinal, angular around and transverse axis, and vertical displacements of the open wagon, respectively; x

_{i}, ϕ

_{i}, and z

_{i}are the coordinates corresponding to the longitudinal, angular around the transverse axle, and vertical displacements of the container, respectively; and F

_{z}is the vertical force arising between the container and the wagon body.

^{2}, and the wagon base was 8.65 m. The rigidity of the spring suspension of the bogie was 8000 kN/m, and the relative friction coefficient was 0.1 These parameters of the spring suspension correspond to the standard parameters of the bogie model 18-100; i.e., they correspond to its technical characteristics.

^{2}. The height of the container was 2.35 m.

^{2}, and those on the open wagon—about 36 m/s

^{2}(Figure 3). The resulting acceleration value can be explained by the fact that the container was not fastened in the body and had its own degree of freedom. This acceleration value is consistent with that presented in the research by Prof. Bogomaz [16]. However, this concerned the longitudinal dynamics of the flat wagon loaded with tank containers. Moreover, his calculation included the displacements of the tank containers due to the gaps between the fittings and the fitting stops.

_{v}, longitudinal P

_{l}

^{st}applied to the end wall, as well as longitudinal P

_{l}applied to the stops of the coupler and balanced on the opposite side by the forces of the inertia of the wagon weight.

_{v}was applied to the wagon bottom through the plates, the geometry of which was identical to the geometry of the container fittings. It was taken into account that the bearing structure of the open wagon was loaded with four 1CC containers. In this case, the total value of the vertical load P

_{v}from one container to four plates was taken equal to 240 kN, which corresponded to the gross weight of one container. The load was applied to the entire surface of the plates. In these zones, the longitudinal frictional forces P

_{fr}, which emerged due to the displacement of the container relative to the floor, were taken into account. The value of these forces per container was taken equal to 94.2 kN, and the “steel–steel” friction coefficient was 0.4.

_{l}

^{st}, which acted on the end wall, was determined using the value of the longitudinal acceleration acting on the container. This force was considered to be evenly distributed over the end wall. The longitudinal force P

_{l}, which was applied to the stops of the coupler, was taken equal to 2.5 MN. This force was also considered to be evenly distributed over the vertical surface of the stop.

## 4. Structural Features of the Detachable Module for Securing Containers in the Open Wagon Body

^{2}. The acceleration value obtained was 13% lower than that acting on it if containers were not fastened to the body.

_{l}, caused by the forces of inertia, acted on the telescopic cantilever part (Figure 13). This load was applied on one side of the module; i.e., it simulated its leaning against the end wall of the open wagon. The calculation was carried out under the condition that the module was loaded with a 1CC standard container.

^{2}is obtained with a safety margin of n = 2.0. It is advisable to use a square pipe with a width and height of 110 mm, which has a cross-sectional area of 8.5 cm

^{2}[39,40]. The weight of 1 m of pipe is 25.14 kg. With this in mind, the weight of the detachable module is about 960 kg.

_{v}acting on the detachable module from the weight of the containers (Figure 16), the longitudinal loads, P

_{l}and P

_{l}

^{f}, conditioned by the forces of inertia and applied, respectively, to the fitting stops from the containers, as well as to the fittings from the fitting stops placed in the open wagon body. The value of the vertical force P

_{v}was taken to be equal to 240 kN. The longitudinal force P

_{l}was about 187 kN. Since the force P

_{c}was the reaction to the force P

_{l}, their values were equal.

_{c}in the zones of interaction between the module and the end wall of the open wagon body.

## 5. Determination of the Dynamic Load and the Strength of the Open Wagon Body during Container Transportation by Taking into Account the Proposed Fastening Diagram

_{v}acted on the open wagon body and was transferred to it through the module fittings. This load was taken to be equal to 24 kN and evenly distributed over four plates, which simulated the zone on the floor on which the module rested in the open wagon. Also, the longitudinal load P

_{l}, caused by the forces of inertia, was applied to the end wall in the direction of the movement. This load was determined taking into account the acceleration obtained by means of mathematical model (2) and applied to the end wall through the plate and simulated the zone of interaction between the module and the wall.

## 6. Results and Discussion

^{2}(Figure 3). The resulting acceleration was taken into account when calculating the strength of the open wagon body. The finite element method was used for the calculation. It was implemented in SolidWorks Simulation. It was found that the strength of the open wagon body, which was not technically adapted for the transportation of containers, was not ensured. The maximum equivalent stresses were 387.2 MPa (Figure 6), which exceeds permissible values.

## 7. Conclusions

- The dynamic load and the strength of the open wagon body when transporting containers are determined. It was found that the maximum accelerations acting on the container are about 34 m/s
^{2}, and on the open wagon—about 36 m/s^{2}. The results of the strength calculation for the open wagon body show that the maximum stresses in its structure arise in the zone of interaction between the transverse belts of the end wall and the corner posts; they are 387.2 MPa. The resulting stresses are almost twice as high as the permissible ones, which, for design mode III, are 210 MPa. - The design of a detachable module for securing containers in the open wagon body is proposed. This module can operate on the principle of the detachable open-type module FLAT RACK, which increases its functionality in operation. To determine the profile of the detachable module, it was calculated as a rod system in LIRA-SAPR. A square pipe with a width and height of 110 mm, which has a cross-sectional area of 8.5 cm
^{2}, was proposed as the detachable module profile. With this in mind, the weight of the detachable module will be about 960 kg. - The results of the strength calculation for the detachable module show that the maximum stresses occur in the areas of fittings, and they are 176.1 MPa; that is, they do not exceed the permissible values. The maximum displacements are recorded in the longitudinal beams of the removable module and amount to 2.78 mm.
- The dynamic load and the strength of the open wagon body during the transportation of containers were determined using the proposed fastening diagram. It was found that the maximum stresses occur in the lower part of the end wall and are 196.2 MPa, which does not exceed the permissible values. The maximum displacements are recorded in the end wall of the body, and they amount to 4.84 mm.
- The conducted studies will contribute to improving the efficiency of container transportation and the transport industry as a whole. Also, the results of the research will be useful developments for designing modular vehicles.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Gerlici, J.; Lovska, A.; Vatulia, G.; Pavliuchenkov, M.; Kravchenko, O.; Solčanský, S.
Situational Adaptation of the Open Wagon Body to Container Transportation. *Appl. Sci.* **2023**, *13*, 8605.
https://doi.org/10.3390/app13158605

**AMA Style**

Gerlici J, Lovska A, Vatulia G, Pavliuchenkov M, Kravchenko O, Solčanský S.
Situational Adaptation of the Open Wagon Body to Container Transportation. *Applied Sciences*. 2023; 13(15):8605.
https://doi.org/10.3390/app13158605

**Chicago/Turabian Style**

Gerlici, Juraj, Alyona Lovska, Glib Vatulia, Mykhailo Pavliuchenkov, Oleksandr Kravchenko, and Sebástian Solčanský.
2023. "Situational Adaptation of the Open Wagon Body to Container Transportation" *Applied Sciences* 13, no. 15: 8605.
https://doi.org/10.3390/app13158605