Design Features of a Removable Module Intended for Securing Containers When Transported in an Open Wagon

Abstract

The design of a removable module is proposed in order to enable the use of open wagons for container transportation. This module secures a container placed on an open wagon considering conditions for its strength under conditions of the operational load. The use of rectangular pipes was proposed as profiles for the removable module. The possibility of optimizing the cross-section parameters of the beams of the removable module frame was investigated. The optimization was carried out according to the criterion of a reduction in the material consumption of the removable module frame. It was established based on the preformed calculations that this optimization contributes to reducing the unit mass of the frame beam by 1.5% compared to using a typical rectangular profile. A spatial model of the removable module was built, and its strength was calculated considering the results of the optimization process. The results of the calculations show that the strength of the removable module is ensured under the considered load schemes. Moreover, within the framework of the research, an experimental study of the hatch cover strength of an open wagon when loaded by the removable module was carried out. At the same time, experimental tests were carried out in laboratory conditions using the method of the electrical strain gage. It was established that the strength of the hatch cover is maintained. The conducted research will contribute to the creation and development of the use of open wagons for container transportation and, accordingly, to increasing the efficiency of containerized cargo transportation, including in international traffic.

1. Introduction

There are several kinds of transport of goods. Regarding land transport, railway transport is a very important kind of transport for goods and passengers for shorter as well as for long distances [1,2,3]. Rail vehicles as a means of railway transport are subjected to strict requirements from their designs’ point of view [4]. The proper design of wagons influences their dynamic behavior [5,6] and running properties. Moreover, it significantly influences the preservation of required functional and structural properties during their long-term operation [7]. The minimization of the dynamical effects of rail vehicles running along a railway track helps to ensure the good quality of transport infrastructure [8,9,10,11,12]. Further, there are applied materials [13], new technologies in production and operation of rail vehicles to reduce negative effects on the environment [14,15,16]. Additionally, modern systems are also used for monitoring rail vehicles during their movement on a railway track to ensure operational safety [17,18,19,20].

Railway transport is characterized by certain characteristics that provide it with advantages compared to road transport as another type of land transport [21]. It has a high axleload and low rolling resistance [22,23,24,25]. Further, wagons can be included in a long train, which contributes to lower drag [26]. In the case of freight railway transport, this advantage is obvious. Further, these advantages come to the fore when containers are used as cargo transport units. Ensuring the efficiency of the transport industry, including in international and intermodal transport [27,28,29], necessitates the introduction of container transportation. This is explained by the mobility of containers as a means of transport. Containers are the most important transport unit used in the intermodal transport of goods [30,31]. The increase in container transportation has led to a shortage of platform wagons, which can be replaced by open wagons, which need to be technologically modified to be used for container transportation. As they do not have a roof, they can be applied for container transportation. However, the design of the open wagon is not adapted to fasten a container, because these wagons were not previously used for these purposes. Due to the absence of container fastening in the open wagon, mutual damage may occur during transportation. This damage often includes damage to the goods transported in the containers. In addition, this may lead to accidents and violations of the environmental safety of transportation. Therefore, there is a need for technical adaptation of open wagons for container transportation.

It is important to note that the creation and modernization of wagons for container transportation are urgent issues. Thus, the authors of publication [32] studied the issues of container transportation safety using the example of the Rgs wagon. An interesting point is the fastening of containers in such a wagon. It is provided by bolts, not fitting stops. The authors conducted the appropriate calculations and proposed the use of the most rational bolted connection. However, the authors studied neither the strength of this solved wagon structure nor the container, considering the use of such a fastening scheme.

The authors of [33] propose the modernization of a universal flat wagon for container transportation by rail. Its objective is to increase the efficiency of container transportation. Such modernization consists of installing fitting stops on its frame. The authors present the results of experimental tests of the modernized design of a flat wagon.

The modernization of a universal flat wagon for container transportation by using a removable frame is also proposed in [34]. This frame is attached to the flat wagon, and it is a kind of a pallet on which the containers are placed. At the same time, the modernization proposed in [33,34] does not fully resolve the issue of providing the railway industry with vehicles for transporting containers.

The issues of the situational adaptation of an open wagon for container transportation are considered in [35]. The authors proposed a removable module in the form of a flat frame to enable the fastening of containers in an open wagon. The corresponding scientific justification for the use of such a scheme for securing containers is provided. However, the design features of the removable module structure are not covered.

The GreenBrier Europe company has developed a wagon designed for the transportation of wheeled equipment and containers [36]. The peculiarity of the wagon is the special fastening devices installed on it, depending on the goods being transported. This wagon was designed considering international standards, allowing for its use in international transport. However, the creation of such a wagon requires significant capital investment. These costs limit its implementation in operation.

The authors of [37] present research focused on improving the strength of the side walls of an open body. It is proposed to strengthen them with additional belts. At the same time, it is reinforced by diagonal belts in three sections of the body from the console side. Further, reinforcing belts are applied in the middle section at a height of 1/3 from the lower strapping with a horizontal belt. The strength of the open body under the main load modes was calculated. It was established that the resulting stresses are lower by 10.3% than those occurring in a typical open-body wagon design. However, the authors did not consider the possibility of transporting containers in the proposed open wagon design.

The design features of a freight wagon designed for the transportation of heavy goods are covered in [38]. Some hypotheses and assumptions are indicated when this kind of wagon is designed. The results of determining its stress state under the main operating conditions are presented. However, the features of the load of the wagon structure during the transportation of containers are not specified.

The authors of [39] considered the possibility of utilizing an open wagon for container transportation. Its floor is formed by the covers of unloading hatches. The corresponding calculations of the hatch cover for strength are presented. It has been proved that its strength is not ensured. The stresses in its structure significantly exceed the permissible ones. However, the authors did not propose solutions for the technical adaptation of the open wagon for container transportation.

A floor of open wagons is formed by hatch covers. Therefore, it is important to consider issues related to ensuring their strength. For example, the authors proposed a new design of the unloading hatch cover in a publication [40]. It is provided with special reinforcing belts that contribute to increasing the rigidity of the most loaded areas of its structure.

A study of the strength of the unloading hatch covers of open wagons under excessive load conditions is conducted in [41]. A solution was proposed to improve the hatch cover, including the introduction of energy-absorbing material into its design.

The authors of the works mentioned above did not investigate the possibility of container transportation in open wagons equipped with such hatch covers or floors.

A new design for the hatch cover is also proposed in [42]. The hatch cover is formed by two metal sheets interacting around the perimeter through a W-shaped strapping. An energy-absorbing material is placed in the cavity between the sheets. This ensures a reduction in the load on the hatch cover in operation. However, the authors did not study the strength of the hatch cover when loaded via a container.

A new design for the hatch cover of an open wagon was also proposed in [43]. A feature of the proposed hatch cover is its convex configuration. This solution allows us to increase the load capacity of the open wagon by 0.9 t compared to a prototype. The results of strength calculations proved the rationality of the proposed design of the hatch cover. However, the authors of the article considered only one calculation mode of its loading.

A review of literary sources proves that the issues of the technical adaptation of open wagons for container transportation are quite relevant and require further research.

The purpose of this research is to highlight the features of designing a removable module for transporting containers in an open wagon. This will contribute to increasing the efficiency of containerized cargo transportation by rail, including international transport. The following tasks are defined to achieve this goal:

• To optimize the cross-section parameters of the beams of the removable module frame according to the criterion of minimum material consumption;
• To calculate the strength of the removable module;
• To conduct an experimental study of the strength of an open wagon hatch cover under load from the removable module.

2. Materials and Methods

The design of a removable module is proposed (Figure 1) to enable the use of open wagons for container transportation. This module works as an intermediate adapter between the open wagon body and the container.

In this case, we plan to install fitting stops on the floor of the open wagon body floor, which will ensure the module fixing on the wagon body (Figure 2). The corner fittings of the removable module have a recess that ensures the transmission of the vertical load (marked by red arrows) to the wagon body floor through the entire area of the removable module’s contact with it (Figure 3). The vertical load is further transmitted to a wagon bogie [44,45].

The justification of such a container fastening scheme is given in a previous publication by us [46]. Based on the previous studies, the use of rectangular pipes as the profile of the removable module was proposed. This is explained by the manufacturability of the module’s manufacturing and maintenance, as well as the possibility of further use of fillers in the module components to reduce its load in operation.

The calculations show that from ensuring the strength of the removable module point of view, it is advisable to use a pipe with dimensions of a cross-section 30 × 30 × 5 and a moment of resistance of the cross-section W = 561.13 cm³. In order to reduce the container of the removable module, the parameters of its profile were optimized. A cross-section of the beam of the removable module frame is shown in Figure 4.

The geometric dimensions of the cross-section of a longitudinal beam are optimized to reduce material consumption.

To solve the optimization problem of finding the geometric dimensions of the cross-section components, the objective function and constraints have the following form:

$$\begin{array}{l}m\left(\overline{X}\right)\to \min \\ \overline{X}\in D_x\in D\end{array}.$$

(1)

$$\begin{array}{l}D=\left\{t_1,t_2,b,h{|}_{4mm\le t_1\le 8mm;4mm\le t_2\le 8mm;180mm\le b\le 340mm;180mm\le h\le 300mm}\right\}\\ D_x=\left\{t_1,t_2,b,h{|}_{4mm\le t_1\le 8mm;4mm\le t_2\le 8mm;180mm\le b\le 340mm;180mm\le h\le 300mm}^{m\to \min ;W_x\le \left[W_x\right];4mm\le t_1\le 8mm}\right\}\end{array}.$$

(2)

where m—the mass of one linear meter of the longitudinal beam of the removable module (the main criterion indicator); $\overline{X}$—the vector of controlled variable parameters, the components of which are considered; t₁, t₂, b, h—the variation intervals, which determine the area of possible solutions D, in which the area of permissible solutions D_x is distinguished by functional limitations [W_x].

The permissible values of the moment of resistance of the longitudinal beam cross-section of the removable module relative to the horizontal axis x are accepted according to the calculation results for the 1st calculation mode and are [W_x] = 546.8 cm³.

The solution for the problem is performed in the following sequence.

(1) The initial data are formed for this research in the form of specified intervals of variation in controlled variables (factors of the mathematical plan): t₁ = 0.004 to 0.008 m, t₂ = 0.004 to 0.008 m, b = 0.18 to 0.34 m, h = 0.18 to 0.3 m.

(2) The transition from the actual values of the variables t₁, t₂, b, h to their normalized parameters is performed.

The transition to normalized parameters $x_{t_1}$, $x_{t_2}$, x_b, x_h determines the relationship with the actual values of the controlled variables t₁, t₂, b, h (

Table 1. A list of correspondence of normalized parameters to actual values of controlled variables [m].

Parameters	Initial Value [m]	Average Value [m]	Final Value [m]
t1	0.004	0.006	0.008
t2	0.004	0.006	0.008
b	0.180	0.260	0.340
h	0.180	0.240	0.300
$x_{t_1}$$, x_{t_2}$, xb, xh	–1.000	0	1.000

), which allows us to draw up a mathematical plan with the appropriate planning matrix.

(3) Based on the planning matrix (

Table 2. A second-order orthogonal mathematical design for four variables varying at three levels.

Mode No.	${\mathit{x}}_{{\mathit{t}}_1}$ [m]	${\mathit{x}}_{{\mathit{t}}_2}$ [m]	xb [m]	xh [m]
1	1	1	1	1
2	1	1	1	−1
3	1	1	−1	1
4	1	1	−1	−1
5	1	−1	1	1
6	1	−1	1	−1
7	1	−1	−1	1
8	1	−1	−1	−1
9	−1	1	1	1
10	−1	1	1	−1
11	−1	1	−1	1
12	−1	1	−1	−1
13	−1	−1	1	1
14	−1	−1	1	−1
15	−1	−1	−1	1
16	−1	−1	−1	−1
17	0	0	0	0
18	1	0	0	0
19	−1	0	0	0
20	0	1	0	0
21	0	−1	0	0
22	0	0	1	0
23	0	0	−1	0
24	0	0	0	1
25	0	0	0	−1

), an orthogonal second-order mathematical plan is compiled for four controlled variables that vary at three levels (

Table 3. A second-order orthogonal mathematical design for four variables with real parameters varying at three levels (m).

Mode No.	${\mathit{x}}_{{\mathit{t}}_1}$ [m]	${\mathit{x}}_{{\mathit{t}}_2}$ [m]	xb [m]	xh [m]
1	0.008	0.008	0.34	0.3
2	0.008	0.008	0.34	0.18
3	0.008	0.008	0.18	0.3
4	0.008	0.008	0.18	0.18
5	0.008	0.004	0.34	0.3
6	0.008	0.004	0.34	0.18
7	0.008	0.004	0.18	0.3
8	0.008	0.004	0.18	0.18
9	0.004	0.008	0.34	0.3
10	0.004	0.008	0.34	0.18
11	0.004	0.008	0.18	0.3
12	0.004	0.008	0.18	0.18
13	0.004	0.004	0.34	0.3
14	0.004	0.004	0.34	0.18
15	0.004	0.004	0.18	0.3
16	0.004	0.004	0.18	0.18
17	0.006	0.006	0.26	0.24
18	0.008	0.006	0.26	0.24
19	0.004	0.006	0.26	0.24
20	0.006	0.008	0.26	0.24
21	0.006	0.004	0.26	0.24
22	0.006	0.006	0.34	0.24
23	0.006	0.006	0.18	0.24
24	0.006	0.006	0.26	0.3
25	0.006	0.006	0.26	0.18

).

For each mode of the mathematical plan, the values of the controlled indicators are calculated: mass of 1 linear meter of the longitudinal beam, the value of the moment of resistance of the longitudinal beam section W_x:

$$m=\left(b\cdot h-b_1\cdot h_1\right)\cdot l\cdot \gamma .$$

(3)

$$W_x={\displaystyle \frac{\left(b\cdot h^3-b_1\cdot h_1^3\right)}{6\cdot h}}$$

(4)

where l—the length of one linear meter of the longitudinal beam of the removable module (100 cm); γ—the specific mass of considered steel (0.0078 kg/cm³).

(4) Problem (1), (2) is solved.

The gradient descent method was used for numerical minimization of the function with size restrictions. In this case, only those points were considered for which the value of the resistance moment was not less than the given value: W_x ≥ [W_x].

When optimizing all four parameters, the values obtained were: t₁ = 0.601 cm, t₂ = 0.773 cm, b = 23.3 cm, h = 27.6 cm, m = 52.50 kg, W_x = 598.1 cm³. This is marked by letter E in Figure 7. It should be noted that the geometric parameters of the profile were set in cm in the calculation, because the moment of resistance is measured in cm³.

When the fixed values of the parameters b = 23.3 cm, h = 27.6 cm are given for optimization, a graphical method can be applied. For this purpose, the functions m and W_x on the grid 100 × 100 were calculated, and the isolines of these functions were constructed (Figure 5, Figure 6 and Figure 7) using the obtained approximations. These isolines are functions of two parameters that vary on a given grid with dimensions t₁ (0.4 to 0.8 cm) and t₂ (0.4 to 0.8 cm). At the same time, the value of the function W [m] is recognized as constant value in each graph depicted in Figure 5, Figure 6 and Figure 7.

It is clear from the analysis of the graph shown in Figure 7 that the optimal parameters at point B are: t₁ = 0.4 cm, t₂ = 0.8 cm, b = 23.3 cm, h = 27.6 cm. The research carried out in the area of admissible solutions D_x made it possible to determine the following values of the parameters under consideration as optimal: t₁ = 0.4 cm, t₂ = 0.8 cm, b = 23.3 cm, h = 27.6 cm. Such a solution is justified by the established normalized values of sheet metal (δ = 4 mm, 5 mm, 6 mm, 7 mm, 8 mm…). With these parameters, the values of the mass and moment of resistance are: m = 45.3 kg, W_x = 570.1 cm³.

Figure 5. A graph of isolines W_x = f(t₁, t₂) for b = 23.3 cm, h = 27.6 cm.

Figure 5. A graph of isolines W_x = f(t₁, t₂) for b = 23.3 cm, h = 27.6 cm.

Figure 6. A graph of isolines m = f(t₁, t₂) for b = 23.3 cm, h = 27.6 cm.

Figure 6. A graph of isolines m = f(t₁, t₂) for b = 23.3 cm, h = 27.6 cm.

Figure 7. A graph of a definition of optimal structure parameters t₁ and t₂. ABCD is an area of acceptable decisions, E is the point of the optimal solution.

Figure 7. A graph of a definition of optimal structure parameters t₁ and t₂. ABCD is an area of acceptable decisions, E is the point of the optimal solution.

3. Results

Considering the determined parameters of the frame profile, its spatial model was built, and its strength was calculated. When calculating the strength, the finite element method was used, which was implemented in SolidWorks Simulation 2018. When creating the model, the welds between the individual components of the frame were not considered. The finite element model of the frame was formed by tetrahedra elements, and it is depicted in Figure 8, since the finite element mesh was created on a solid body [46,47,48,49,50]. The number of tetrahedra that formed the mesh was calculated graphically. Taking this into account, the number of nodes was 40,688, and the number of elements was 110,331. The largest element had a size of 100 mm, and the smallest element had a size of 20 mm. The calculation was implemented for two load schemes of the removable module:

• An action of the vertical load P_V (Figure 9);
• An action of the vertical P_V and longitudinal loads P_L (Figure 10).

It was established that the maximum stresses in the removable module structure occur in the zones of interaction of the transverse beams with the longitudinal ones (Figure 11).

The maximum stress that arose in these zones was 112.5 MPa (Figure 12), which is lower than the permissible ones for steel grade 09G2S, which are 310.5 MPa.

Maximum displacements occur in the upper parts of the module structure, and they are about 1 mm (Figure 13).

For the case of perception of the vertical and longitudinal loads by the removable module, the most loaded zones are the zones of interaction of transverse beams with longitudinal ones, which are located on the side of the loaded fittings (Figure 14).

The maximum stress that arose in these zones was 287.6 MPa (Figure 15). These values are lower by 7.4% than the permissible ones.

The maximum displacements of the removable module structure occur in the end wall located on the side, where the load acts on it (Figure 16). These displacements amounted to a value of 2.16 mm.

Bench tests were conducted in the research laboratory of the “Center for Diagnostics of Transport Structures” at the Ukrainian State University of Railway Transport (Kharkiv) in order to experimentally substantiate the use of the removable module. This study was conducted on an example of the unloading hatch cover of an open wagon, which is a component of its floor.

The determination of the stresses that arise in the hatch cover structure was carried out using the method of measurement by means of the electrical strain gauges. The installation of strain gauges was carried out according to a gauge scheme. The locations of the strain gauges on the hatch cover were determined based on the theoretically obtained stress fields that arise in the hatch cover, and they are shown in Figure 17.

The strain gauges were calibrated (Figure 18) before their installation in the hatch cover structure. Strain gauges with a base of 10 mm and a resistance of 100 Ohms were used.

The strain gauges were mounted using cyanoacrylate-based glue (Figure 19). Before this, the mounting locations were cleaned and degreased.

The hatch cover was secured using hinges. Metal pins were used for this purpose (Figure 20). On the opposite side, the hatch cover was secured in the areas of its interaction with the locking mechanisms. For this purpose, supports were installed under the brackets.

The load was transmitted on the hatch cover through a metal plate. Its width equaled the width of the longitudinal beam of the removable module (Figure 21). The load on the plate was transferred through an I-beam, which, in turn, perceived the load from the jack. The load was controlled by a dynamometer. In this case, the maximum load was taken as equal to a value of 6 t (60 kN), which corresponds to the maximum loaded state of the 1CC size container.

The largest deformation obtained during the tests was recorded by the third group of the strain gauge (Figure 22).

It can be seen from Figure 22 that the dependence of relative deformations on the load is linear. The stresses that arose in the hatch cover are given in

Table 4. Stresses in the hatch cover in the area of the location of the third group of strain gauges.

Load [kN]	Stress [MPa]
5	9.4
10	19.5
15	27.6
20	37.5
25	46.4
30	53.2
35	65.4
40	75.3
45	84.1
50	94.5
55	106.2
60	115.4

and also in Figure 23.

The maximum stresses recorded in the hatch cover were 115.4 MPa. These stresses are lower than the allowable ones by 45%. The difference between the results of computational calculations of the hatch cover strength and experimental studies is shown in Figure 24.

It can be concluded based on the results achieved that the largest percentage of differences is 10.4%, and it is recorded when the load on the hatch cover is 20 kN. This percentage of discrepancy may be caused by the geometric parameters of the tested hatch cover, which had insignificant deviations from the nominal ones. This is explained by the fact that the tests were carried out on the hatch cover, which was already in use on the open wagon.

The proposed scheme for fastening containers on open wagons allows us to reduce the stress in the hatch cover by 3-times compared with the typical scheme of interaction of fittings with fitting stops.

4. Discussion

The main idea in this research is to utilize open wagons for container transportation. Experimental measures were proposed for the technical adaptation of open wagons to transport containers. We proposed the use of a special removable module, which is installed on an open wagon body, and it provides the possibility of fastening a container on it (Figure 1). The use of a rectangular profile is proposed as the profile of the removable module. To reduce the mass of the removable module, the parameters of the frame beam cross-section were optimized according to the criterion of minimum material consumption. The calculations made it possible to establish the optimal parameters of the beam cross-section of the removable module from the point of view of the minimum mass while observing the corresponding moment of resistance of its section (not lower than W = 561.13 cm³). Taking this into account, the mass of 1 m of the frame beam of the removable module is 45.3 kg, which is lower than the mass of a typical rectangular profile by 1.5%. The results of the strength calculations confirmed that the strength of the removable module is maintained (Figure 12 and Figure 15). Experimental studies were conducted in order to study the strength of the open wagon body in interaction with the designed removable module. In this case, the unloading hatch cover, which forms the floor of the wagon, was subjected to testing. The results of the experimental studies confirmed the feasibility of using the removable module from the point of view of ensuring the strength of the open wagon body (Figure 22).

The results of this study have advantages in comparison with the known ones. Thus, in comparison with the results of other studies [32,33,34], the authors proposed specific solutions for the technical adaptation of an open wagon for container transportation. Unlike in [35], the authors not only proposed a solution for the situational adaptation of an open wagon for container transportation but also provided a justification for the design of the removable module for the implementation of this solution. Unlike the technology of container transportation specified in [36], the solution proposed by the authors can be implemented by modernizing wagons and not by creating its new design. The solutions proposed in [37,38] for improvements in wagons contribute to improving their durability in operation, but, at the same time, the authors of the specified works did not study the possibility of involving such open wagons for container transportation. The advantage of the results obtained over those specified in [39,40,41,42,43] is that the authors investigated an additional loading mode of the hatch cover. It has not been considered so far, and it was proven that its strength is ensured during container transportation. It is important to note that the use of the proposed container fastening scheme has advantages compared to existing technologies for their transportation in open wagons. The authors carried out a set of calculations of an open wagon when transporting containers considering various schemes of their interaction. The results of the calculation of the strength of the open wagon body when transporting containers on it without considering their fastening showed that the maximum stresses arise in the zone of interaction of the transverse belts of the end wall with the corner posts and are 371.3 MPa. The achieved stresses are almost twice as high as the permissible ones.

The calculation of the strength of the open wagon structure was also carried out considering the fastening of containers by means of fitting stops. The maximum stresses in this case are identified in the fitting stops and they equal 142 MPa. These stresses do not exceed the values of permissible stresses. At the same time, the calculation of the strength of the container considering such a fastening scheme showed that the strength of its structure is not ensured. Attention was paid to the calculation of the container strength when it is fastened on an open wagon using pneumatic shells. The maximum stresses arise in the middle part of the side beam, and they amount to 326.4 MPa. The results of the calculation allow us to conclude that the strength of the container under the applied loads is not ensured. Therefore, the proposed scheme for fastening containers on an open wagon is more appropriate in comparison with existing schemes. Preliminary calculations of the economic feasibility of implementing the results showed that the economic effect can be achieved by annual savings in the dependent part of operating costs compared to the basic option of using open wagons and one-time costs for their structural re-equipment for transporting containers in an empty direction.

The limitations of this work can be noted, including that the authors considered the case of transportation in a removable module of a dry cargo container; i.e., the option of transporting a tank container in it has not been studied yet. This will be carried out in subsequent studies by the author’s team. The main drawback of this study is that, when calculating the strength of the removable module, the authors did not consider the welds between its individual components; i.e., the module was considered as a monolithic structure. It is important to note that the proposed design of the removable module for fastening dry cargo containers is designed considering the international standard size. In this regard, this solution can also be used for fastening tank containers on open wagons. However, the presence of the degree of freedom of the bulk cargo requires the creation of an appropriate mathematical model for studying the dynamic load and strength of the removable module. It is also necessary to consider the influence of the use of such transportation technology on the traction properties of the locomotive [51,52,53,54]. Moreover, we also plan to consider the possibility of transporting containers on open wagons by means of railway ferries in international transportation [55]. A special unit for interaction with chain ties will be mounted on the open wagon frame pivot beam for this purpose (Figure 25).

In this case, special attention will be paid to the issue of the container’s stability against capsizing during ship rolling. The conducted studies will contribute to the development of the involvement of open wagons for container transportation and, accordingly, to increasing the efficiency of cargo transportation in containers, including in international transport.

5. Conclusions

1. The parameters of the cross-section of the beams in the frame of the removable module were optimized according to the criterion of minimum material consumption. The gradient descent method was used to numerically minimize the function with size restrictions. The research carried out in the area of allowable solutions made it possible to determine the following values of the parameters under consideration as optimal: t₁ = 0.4 cm, t₂ = 0.8 cm, b = 23.3 cm, h = 27.6 cm. This solution is justified by the established normalized values of sheet metal (δ = 4 mm, 5 mm, 6 mm, 7 mm, 8 mm…). The values of the mass and moment of resistance align with these parameters as follows: m = 45.3 kg, W_x = 570.1 cm³, respectively.

2. The strength of the removable module was calculated. Two loading modes of its structure were considered: the action of the vertical load and the action of the vertical and longitudinal loads. It was established that for the case of perception of the vertical load by the module, the maximum stresses in its structure are 112.5 MPa. These stresses are concentrated in the zones of interaction of transverse beams with longitudinal ones. The maximum displacements occur in the upper parts of the superstructures, and they are equal to a value of about 1 mm.

For the case of perception of the vertical and longitudinal loads by the removable module, the maximum stresses in its structure were 287.6 MPa. These stresses are indicated in the zones of interaction of transverse beams with longitudinal ones, which are located on the side of the loaded fittings. The maximum displacements of the structure occur in the end superstructure located on the side of the load application to the removable module. These displacements were 2.16 mm. Therefore, the strength of the removable module for the considered load schemes is ensured.

3. An experimental study of the strength of the hatch cover of an open wagon under load from the removable module was carried out. At the same time, the maximum stresses in the hatch cover were 115.4 MPa, which do not exceed the permissible values. The largest percentage of differences between the results of computer modelling of the hatch cover strength and experimental studies was 10.4% and it was recorded at the load on the hatch cover of 20 kN. The results of experimental studies of the hatch cover strength allow us to conclude that the proposed scheme of fastening containers on an open wagon using a removable module allows us to reduce the stresses that arise in the hatch cover by three-times compared to the typical scheme of interaction of fittings with fitting stops.

6. Patents

• Freight unit: Patent 156991 Ukraine, MPK B65D 88/12 (2006.01); u202400568. Application 2 February 2024; Publication 28 August 2024. Bulletin No. 35.
• Open wagon for container transportation. Patent 157214 Ukraine, MPK (2024.01) B61F 1/00 B61D 3/00; u202400795. Application 16 February 2024; Publication 18 September 2024. Bulletin No. 38.
• Modular cargo unit: Patent 157156 Ukraine, MPK B65D 88/12 (2006.01); u202400565. Application 02 February 2024; Publication 11 September 2024. Bulletin No. 37.