Abstract
The paper deals with the current problems of developing and justifying technical solutions for the design of a long-base flat car for the transportation of high-capacity containers, which is associated with the need to improve the efficiency of container transportation under modern operating conditions. Based on the analysis of existing designs of flat cars, as well as the results of complex theoretical studies of the loading of their main components using modern engineering programs that implement the finite element method, an improved design of a long-base flat car is proposed and substantiated. The results of numerical modeling are confirmed by experimental studies conducted using the strain gauge method, which demonstrated a satisfactory correspondence between the calculated and experimental data. The developed design is characterized by improved technical and operational characteristics, reduced tare weight and increased load capacity by 1 ton, demonstrates a more uniform load distribution and increased durability under the considered loading conditions, which contributes to the competitiveness of the proposed flat car design. Thanks to the results obtained, at present, the car-building enterprises of the Republic of Uzbekistan have established the production of promising long-base flat cars, which contributes to improving the competitiveness of the proposed flat car design.
Keywords: Flat car, Frame, Loading, Stresses, Experiment, Strain gauge
Subject terms: Engineering, Mathematics and computing
Introduction
In the context of intensive growth of cargo transportation volumes and modernization of railway infrastructure, the improvement of rolling stock, which ensures an increase in the efficiency of transport processes, is of particular importance. Current trends in the organization of freight transportation are focused on increasing the carrying capacity of railway lines, reducing the turnover time of rolling stock and reducing operating costs, which is directly related to optimizing the design and operational characteristics of freight cars. In the world practice, research is actively carried out aimed at identifying ways to increase cargo turnover, the capacity of railway networks and the efficiency of transport systems in general, including through the rational use and improvement of the existing fleet of rolling stock1–3. It should also be noted that currently the industry is actively conducting research on the development of new models of railcars aimed at increasing the load capacity, reducing their own weight and increasing reliability when operating in various climatic and dynamic conditions.
One of the most promising areas in the development of railway transport is the creation and improvement of freight cars, the design of which ensures safe and efficient transportation of various types of cargo in accordance with modern industry requirements. In this regard, the application of modern methods of engineering analysis and computer modeling is particularly relevant, which make it possible to conduct a comprehensive assessment of the stress-strain state of structural elements at the design stage and justify the choice of rational technical solutions aimed at improving the strength, reliability and durability of railcars4–6.
Status of the issue, setting the research goals and objectives
One of the key stages in the design of freight cars is strength calculations and modeling of the stress-strain state of their structural elements, as well as the assessment of dynamic qualities under operating conditions7. Carrying out high-precision calculations allows not only to provide the required level of reliability and operational safety, but also to significantly optimize the design in terms of material consumption. This, in turn, is especially important in the context of increasing requirements for the economic efficiency of cargo transportation.
Studies8–10 performed using finite element methods (FEM), multi-body modeling (MBM), and spectral fatigue analysis methods are aimed at improving the accuracy of estimating the strength, service life, and reliability of key elements of freight cars and bogies. Within the framework of these works, a comparative study of the influence of suspension dynamics on the stress-strain state of the pin assembly liner was carried out, areas of maximum equivalent stresses were identified, the influence of the liner material (polymer, bronze, steel) on its strength and service life was established, and an experimentally confirmed method for predicting fatigue life was proposed. Additionally, a comparison of approaches to fatigue assessment of bogie frames—the endurance limit method at constant amplitude and the damage accumulation method at variable amplitude—is considered using both standard load spectra according to EN 13,749 and realistic spectra obtained by modeling a multi-body dynamic system. It is shown that taking into account real dynamic impacts, material properties, and variable load spectra can significantly improve the accuracy of predicting the durability and reliability of structural components and frames of railway rolling stock bogies.
It is necessary to mention a number of works in which the flat car is considered as a promising object of research aimed at improving the efficiency of intermodal and container transportation. In these studies, the main focus is on improving the design of long-base platforms, optimizing their load-bearing elements, as well as evaluating the strength and stress-strain state using finite element analysis methods11–13.
Separate works14–18 are devoted to modeling dynamic loads that occur during the movement of a flat car, and the development of structural solutions that reduce weight while maintaining the required strength characteristics, which makes flat cars one of the key areas of development of modern freight rolling stock.
A number of modern studies consider solutions aimed at expanding the functionality of existing freight cars by adapting them for container transportation. One of the most interesting directions is the use of gondola cars for container transportation by installing removable modules on them that ensure reliable cargo attachment. In the works of this direction, the design of a removable module of a rectangular profile is proposed, optimized according to the criterion of minimum material consumption while maintaining the required rigidity and strength. Computational studies19 have shown that the proposed design provides acceptable values of stresses and deformations under the action of both vertical and longitudinal loads, and the mass of the module can be reduced by about 1.5% compared to the traditional profile. The results of experimental tests confirmed the reliability of numerical models and showed a reduction in stresses in the elements of the gondola car body by more than three times when using the module. It is noted that the proposed solution has technological and economic advantages, as it allows the use of existing gondola cars without their complete reconstruction, which makes it a promising direction for increasing the flexibility and efficiency of container transportation.
Similar studies were carried out in20, which proposed the design of removable equipment in the form of two welded half-frames, which provides the possibility of transporting 20-and 40-foot containers without making changes to the basic design of a universal flat car. Calculations and experimental studies have confirmed the compliance of the overall dimensions of the modified car with regulatory requirements, while significant reserves in height and width have been identified. The inertial loads acting on removable equipment during transportation are determined, and its strength is evaluated. The simulation results showed that the maximum stresses in the most loaded areas of the structure do not exceed those allowed for the steel used, which indicates the reliability of the proposed solution and the possibility of its practical application for adapting open platforms for the transportation of high-capacity containers.
In21, the authors consider the effect of dynamic loads on containers placed on flat cars. In the course of the work, it was found that the accelerations acting on containers during shunting (impact) impacts significantly depend on the gaps between the container fittings and the platform thrust elements and can exceed regulatory values, which poses a potential threat to transportation safety. The authors came to the conclusion that ensuring safe operation requires limiting the relative movements of the container on the platform during collisions, and the resulting refined acceleration values should be taken into account when designing new-generation containers in order to increase their resistance to operational dynamic impacts.
In a number of studies, it is noted that the growth in the volume of container transportation, in particular, the transportation of refrigerated containers, requires the development of long-base flat cars capable of providing accelerated cargo delivery at speeds up to 140 km/h. Analysis of the existing four-axle flat cars with three-element bogies, designed for the transportation of containers with a length of 20 and 40 foot and operation at speeds up to 90 km/h, showed their non-compliance with modern requirements for the speed and conditions of transportation of perishable goods. Thus, in22, the technical and operational requirements for promising flat cars for high-speed transportation of refrigerated containers are formulated and the concept of a new six-axle flat car is proposed, which provides transportation of containers with a length of 20, 40 and 53 foot at increased speeds.
The same authors in a number of studies23,24 suggest the use of round pipes in the design of the flat car frame. To study the dynamic loading of the load-bearing structure of a flat car, mathematical modeling of both a separate four-axle platform and an articulated flat car made of round pipes was carried out. The results of research and calculations performed in MathCad and COSMOSWorks show that the accelerations that occur on the load-bearing structure of the flat car are 38.2 m/s2, and the second one is about 37.5 m/s2, and the maximum equivalent stresses occur in the cantilever parts of the ridge beam and are about 200 MPa, that is, they do not exceed acceptable values. Thus, the authors formulated recommendations for the design of modern structures of articulated railcars made of round pipes.
Despite a number of studies devoted to the strength characteristics of freight cars, the peculiarities of their stress-strain state, as well as the development of new design solutions for freight cars, in particular flat cars, and ways to improve the efficiency of container transportation, there are still a number of unsolved problems related to the rational use of their load capacity. One of the significant disadvantages of traditional flat cars produced by car-building enterprises of the Republic of Uzbekistan is the limited capacity in terms of the number of containers placed—as a rule, such cars are designed to transport one 40-foot or two 20-foot containers. At the same time, part of the loading length remains unused, as a result of which the estimated load capacity is not fully realized, which leads to irrational use of the car fleet and a decrease in the overall efficiency of container transportation.
In contrast, long-base flat cars can accommodate up to four 20-foot or two 40-foot containers with the possibility of additional load, which ensures a more complete use of the permissible load capacity and effective use of the overall parameters of the car. The transition to the use of such platforms contributes to increasing the capacity of rolling stock, reducing the cost of transportation per unit of cargo and, as a result, increasing the profitability of container transportation and overall improving the efficiency of cargo transportation in the Republic of Uzbekistan.
Based on the above, the aim of this study is to develop an improved structural design of a long-base flat car that enhances its operational performance and increases the efficiency of high-capacity container transportation. To achieve this aim, the study is focused on determining rational technical parameters and load-bearing structural elements of the improved flat car design; performing theoretical investigations using the finite element method to evaluate the stress-strain state and load distribution of the structure; conducting experimental investigations of a prototype long-base flat car through static and running tests; and comparing the experimental results with calculated data and relevant regulatory requirements in order to assess the reliability and structural soundness of the proposed design.
Selection of technical parameters and power-bearing structural elements of a long-base flat car
At the present stage of development of innovative freight cars, special attention is paid to reducing the tare weight and increasing the load capacity due to the use of high-strength and light materials in load-bearing structures. The design of the frames and power elements of flat cars has a decisive influence on their main technical characteristics. The load-bearing structure of such wagons, as a rule, is a system of beam elements united in stiffening units. Despite the similarity in the design of most of the flat cars in operation, they all differ in their final technical characteristics, which primarily include tare weight and load capacity. The ratio of tare weight to load capacity is the tare ratio, which is the main technical indicator of the efficiency of a freight car, including a flat car. In this regard, an important stage of research is to compare the technical characteristics of the most common models of flat cars, which allows us to identify trends in the development of rolling stock, determine the degree of mass optimization, evaluate the growth of load capacity and establish the relationship between the axle load and the efficiency of using the car.
To carry out this analysis, a sample of several popular production models that are in active operation and represent different approaches to improving technical and economic indicators was formed. Their key parameters-tare weight, load capacity, tare ratio and axial load-are combined in Table 1, and the existing variants of technical and structural frame solutions, differing in the cross-section of the longitudinal and pivot beams, as well as their height, are shown in Fig. 1, which provides a visual basis for further research on the efficiency of modern flatcars.
Table 1.
Serial models of flat cars with different parameters.
| No. | Flat car model | Load capacity, t | Tare weight, t | Tare ratio | Axle load, t |
|---|---|---|---|---|---|
| 1 |
13-4147 (Dneprovagonmash) |
68.0 | 26.0 | 0.382 | 23.5 |
| 2 |
13–644 (Barnaul wagon repair plant) |
69.0 | 25.0 | 0.362 | 23.5 |
| 3 |
Rens (Greenbrier) |
65.1 | 24.1 | 0.37 | 22.3 |
| 4 |
Rns 674 (Greenbrier) |
65.4 | 24.6 | 0.376 | 22.5 |
| 5 |
Sggns(s) 80’ (Containerwagen) |
67.5 | 22.5 | 0.333 | 22.5 |
| 6 |
Sggns(s) 80’ (Containerwagen) |
67.7 | 22.3 | 0.329 | 22.5 |
| 7 |
RTH08 (Railteco) |
61.0 | 23.0 | 0.377 | 23.5 |
| 8 |
RTH07 (Railteco) |
70.0 | 22.5 | 0.321 | 23.1 |
| 9 |
Rbnpss 189 (On Rail) |
61.5 | 28.4 | 0.461 | 22.5 |
Fig. 1.
Variants of technical and constructive solutions for the frames of flat cars: (a, b) design scheme; (c–f) variants of cross-sections of longitudinal beams; (g–j) variants of cross-sections of pivot beams.
Based on the analysis of existing models of flat cars shown in Table 1, the model of flat car 13-644 (manufactured by JSC “Barnaul wagon repair plant”) was chosen as a prototype for further research, which is due to a combination of operational and technological factors. First of all, this car is widely used in the space of railways with a gauge of 1520 mm, which ensures its full compatibility with the existing infrastructure and the relevance of the analysis results for the operating conditions of the Republic of Uzbekistan and neighboring countries.
It should be noted that among the considered models there are wagons with a lower tare weight and a higher load capacity. However, their reduced weight is achieved largely due to the use of high-strength and lightweight steels, as well as composite materials, the use of which can significantly reduce the tare coefficient, which is discussed in detail in25–27. Despite the obvious design advantages of such materials, their industrial production and widespread use in car building in the conditions of the Republic of Uzbekistan are still insufficiently developed. This limits the possibility of mass production of light railcars with high efficiency indicators.
Given these circumstances, as well as the need to ensure technological feasibility and compliance with production capabilities, the choice of model 13-644 seems to be the most reasonable. This car combines an acceptable level of tare weight, sufficient load capacity, optimal design (Fig. 2) and compliance with the requirements of the 1520 mm railway network, which makes it a rational starting point for further research.
Fig. 2.
Structural scheme of flat car model 13-644.
At the next stage, in order to improve the load-bearing structure in order to reduce the tare weight and increase the load capacity of the selected flat car, a number of possible configurations of welded I-beams used in long-base platforms were analyzed. The set of options was formed as a list of standard sizes rationally used in the industry, covering the following geometric dimensions: height – 600, 700, 960 and 1000 mm; cross-sectional parameters A×B×C – 14 × 10 × 12, 14 × 10 × 14 and 14 × 10 × 16 mm. All the beams under consideration are made of low-alloy structural steel grade 09G2S, widely used in building metal structures due to its increased strength, good weldability, and resistance to brittle fracture at low temperatures, with a yield strength of about 345 MPa, an ultimate tensile strength of 490-630 MPa, a Poisson’s ratio of 0.3 and an elastic modulus of approximately 2.0·105 MPa. This approach allowed us to consider structurally sound combinations of sizes without first limiting the specific profile type.
The optimal version of the I-beam was determined based on the results of strength calculations performed in modern engineering software complexes according to the calculation scheme (Fig. 3), taking into account the recommendations28. The calculations were carried out under a vertical load of 17.5 ton (175 kN) applied to a single load-bearing beam, which corresponds to the maximum payload capacity of 70 t uniformly distributed among four identical primary beams of the flat car. The calculation results are shown in Table 2.
Fig. 3.
Kinematic boundary conditions for strength calculation of welded I-beams.
Table 2.
Results of strength calculations of welded I-beams.
| Height, H, mm | Beam parameters, A×B×C, mm | Weight, kg | Permissible stress, MPa | Maximum stress, MPa | Estimated safety margin | Minimum safety margin | |
|---|---|---|---|---|---|---|---|
| 600 | 1 | 14 × 10 × 12 | 1873 | 293 | 231 | 1.26 | 1.8 |
| 2 | 14 × 10 × 14 | 1908 | 215 | 1.36 | |||
| 3 | 14 × 10 × 16 | 2052 | 205 | 1.43 | |||
| 700 | 1 | 14 × 10 × 12 | 2079 | 177 | 1.65 | ||
| 2 | 14 × 10 × 14 | 2112 | 165 | 1.78 | |||
| 3 | 14 × 10 × 16 | 2167 | 154 | 1.91 | |||
| 960 | 1 | 14 × 10 × 12 | 2249 | 152 | 1.93 | ||
| 2 | 14 × 10 × 14 | 2356 | 145 | 2.02 | |||
| 3 | 14 × 10 × 16 | 2443 | 141 | 2.08 | |||
| 1000 | 1 | 14 × 10 × 12 | 2366 | 149 | 1.97 | ||
| 2 | 14 × 10 × 14 | 2478 | 144 | 2.03 | |||
| 3 | 14 × 10 × 16 | 2565 | 140 | 2.09 | |||
The minimum weight of the beam and the minimum level of stresses that occur under standard loads (Fig. 4), as well as the final margin of safety, were used as criteria for choosing the optimal option.
Fig. 4.
Welded I-beam H = 700 mm, 14 × 10 × 16 mm (a) and its stress-strain state (b).
The obtained values of the stress-strain state, the safety margin coefficient, and the mass of beams are presented in the form of histograms for clarity (Fig. 5).
Fig. 5.
Dependence of the obtained equivalent stresses (a), safety margin (b) and mass of beams (c) on their height.
Based on the analysis of the calculated parameters and a comparative assessment of the considered options, it is established that the most rational design of a welded beam is a beam with a height of 700 mm. Its mass is 2167 kg, and the safety factor is 1.91, which meets the requirements of current technical and regulatory documents. In addition, the use of this beam in the construction of the flat car reduces its tare weight by 1 ton, which directly increases the load capacity by the same amount. In this regard, this beam is accepted as the base one and selected for further theoretical research and subsequent design stages.
Theoretical studies to determine the loading capacity of an improved design of a long-base flat car
At the next stage of the work, strength calculations of the flat car structure formed on the basis of the previously selected load-bearing elements were carried out. To perform theoretical studies aimed at determining the loading of structural elements under static and dynamic loads, taking into account the increased load capacity, a spatial calculation model was developed in the SolidWorks software environment (Fig. 6a) and imported into the ANSYS Workbench software package, where an updated plate-rod finite element model of the long-base flat car was formed (Fig. 6b). The finite element mesh was generated using second-order 20-node SOLID186 solid elements, providing increased accuracy in bending and stress concentration zones. The number of elements was selected based on a compromise between the required calculation accuracy and the available computational resources. Local mesh refinement was applied in critical areas, including the junctions of longitudinal, pivot and cross beams, connection nodes, cutouts and zones with abrupt changes in cross-section, while a coarser regular mesh was used in regions with a more uniform stress state. As a result, the final model comprised 53,043 elements and 219,330 nodes, which ensured numerical stability of the solution and reliable localization of maximum equivalent stresses at an acceptable computational cost.
Fig. 6.
Spatial calculation model (a) and refined finite element model (b) of a long-base flat car.
To assess the structural load and determine the stress distribution in the elements of the flat car, the design model provided cross-sections with virtual measurement points (Fig. 7). The choice of the location of these points was made based on the analysis of published scientific studies devoted to the assessment of the stress-strain state of flat car frames and similar welded structures29–31. In accordance with the recommendations of these works, virtual measuring points were placed in areas characterized by an increased concentration of stresses, typical load transfer paths and maximum bending moments, which ensures the correctness of subsequent stress comparison for various design options.
Fig. 7.
Layout of virtual measurement points in the flat car design elements: I–VI – control sections; 1–72 – virtual measurement points.
Setting up virtual measurement points allows to obtain individual stress values at each point and perform a local analysis of the stress-strain state according to two loading schemes:
scheme 1-load from four 20-foot containers (Fig. 8a);
scheme 2-load from two 40-foot containers (Fig. 8b).
Fig. 8.
Loading scheme of the flat car structure according to two schemes: a scheme 1 – four 20-foot containers; b scheme 2 – two 40-foot containers
Strength calculations of the flat car structure were performed in accordance with GOST 33211-201428 with a combination of loads acting on the frame, according to modes 1a, 1b, 1v, 1g (Table 3).
Table 3.
Loads acting on the flat car frame.
| Forces | Mode | |||
|---|---|---|---|---|
| 1a | 1b | 1v | 1g | |
| Longitudinal force, N, kN | 3500 | 2500 | 2500 | 2000 |
| Longitudinal acceleration, au, m/s2 | – | – | ||
| For scheme 1 | 37.5 | 26.8 | ||
| For scheme 2 | 59.0 | 42.2 | ||
| Longitudinal inertia force of the container, Ni, kN | – | – | ||
| For scheme 1 | 1313 | 938 | ||
| For scheme 2 | 2125 | 1518 | ||
| Container gravity, Q, kN | ||||
| For scheme 1 | 784.5 | |||
| For scheme 2 | 353.2 | |||
| Vertical force from the longitudinal inertia force of the container, PZ, kN | – | – | ||
| For scheme 1 | 290.6 | 207.6 | ||
| For scheme 2 | 256.7 | 183.4 | ||
| Transverse forces in curves, PN, kN | – | – | 200 | 58.5 |
| Force in case of non-central interaction of automatic coupling devices, P, kN | 175 | 138 | 125 | 111 |
| Longitudinal inertia force of car bogies, Nbi, kN | – | – | ||
| For scheme 1 | 182 | 130 | ||
| For scheme 2 | 286.3 | 204.5 | ||
Kinematic boundary conditions and the application of forces for the corresponding modes are shown in Fig. 9.
Fig. 9.
Kinematic boundary conditions and application of forces in the calculation of modes 1a, b (a) and 1v, g (b).
Mode 1a corresponds to the combination of forces acting on the frame of the flat car in the event of a collision when disbanding from the sorting hill, settling the composition of cars; mode 1b—when starting the composition; modes 1v and 1g—when braking and accelerating the composition moving in a curved section of track.
Figure 10 shows the stress-strain state of the flat car frame under the first loading scheme, which demonstrates the nature of the stress distribution and local zones of their concentration, which corresponds to the calculated values obtained and allows us to visually assess the operation of the structure under the influence of the most unfavorable combination of loads.
Fig. 10.
Plots of the distribution of maximum equivalent stresses in the load-bearing structural elements of a long-base flat car in modes 1a (a), 1b (b), 1v (c) and 1g (d) according to the first loading scheme.
The results show that in the first loading scheme, which corresponds to the placement of four 20-foot containers, the levels of maximum equivalent stresses in the load-bearing elements of the flat car significantly exceed the indicators obtained for the second scheme, which provides for the installation of two 40-foot containers. The increased values of stresses in the first scheme are explained by a more complex distribution of loads resulting from an increase in the number of points of application of vertical forces, as well as a smaller inter-container distance, which leads to an increase in local loads and a greater unevenness of the work of longitudinal and transverse elements.
The maximum equivalent and permissible stresses obtained in the main areas of the flat car structure during calculations based on two accepted loading schemes and their operating modes are summarized in Table 4.
Table 4.
Maximum equivalent stresses in the load-bearing elements of the flat car structure at modes 1a, 1b, 1b and 1g according to two loading schemes.
| Load-bearing | Stresses, MPa | Permissible stresses, MPa | |||
|---|---|---|---|---|---|
| Mode 1a | Mode 1b | ||||
| 1-scheme | 2-scheme | 1-scheme | 2-scheme | ||
| Ridge beam | 43.2 | 40.7 | 31 | 29 | 293 |
| Side longitudinal beams | 51 | 52.1 | 35.3 | 40 | |
| Pivot beam | 151.8 | 150 | 103.6 | 116.5 | |
| Cross beams | 65.5 | 71.3 | 52.2 | 57.9 | |
| Diagonal beams | 106.7 | 111 | 73.2 | 86.8 | 276 |
| End beams | 39.5 | 36.2 | 28.4 | 26.1 | 293 |
| Mode 1v | Mode 1g | ||||
|---|---|---|---|---|---|
| Ridge beam | 31 | 29.5 | 24 | 23.6 | 293 |
| Side longitudinal beams | 35.3 | 22.1 | 18.6 | 16.9 | |
| Pivot beam | 103.6 | 77.8 | 69.7 | 63.4 | |
| Cross beams | 52.2 | 82.4 | 58.7 | 76.7 | |
| Diagonal beams | 73.2 | 34.4 | 35 | 28.7 | 276 |
| End beams | 28.4 | 24.7 | 20.7 | 19.7 | 293 |
The presented data allow us to quantify the stress-strain state for each variant and determine how a change in the container load configuration affects the redistribution of forces between the longitudinal and transverse elements. The values shown in the table serve as a basis for comparing local stresses with the standard strength limits of the materials used, as well as for identifying the most loaded sections of the frame.
The analysis of the modeling results showed that the values of equivalent stresses that occur in the elements of the developed long-base flat car under the influence of standard operating loads do not exceed the permissible values and are characterized by a sufficient margin of safety. The data obtained indicate that the designed structure meets the requirements of the current regulatory and technical documentation, and also confirms its ability to ensure reliable and safe operation during the transportation of high-capacity containers in various loading modes.
Experimental studies of a long-base flat car for the transportation of high-capacity containers
At the final stage of the work, a program and methodology for conducting static and running dynamic tests using the strain gauge measurement method were developed, and experimental studies were performed on the basis of them to determine the load‑bearing structure of a prototype of an improved long‑base flat car manufactured at JSC “Foundry Mechanical Plant”.
When conducting static tests on the basis of JSC “Foundry Mechanical Plant”, a stand for loading wagons with longitudinal static loads was used to create longitudinal forces on the frame (Fig. 11). Strain gauges of the BBF200‑10AA‑A(11)‑BX30 type were used to register deformations, and measurements were carried out using the hardware and software complex MIC‑185 with recording of processes on the hard disk of a personal computer.
Fig. 11.
Installation scheme of the stand for static testing: 1 – loading stand; 2 – flat car; 3 – containers; 4 – jack.
Static tests were carried out in the following sequence in accordance with the requirements of GOST 33211-2014, clause 4.1, for each loading scheme: compression – 3.5 MN (mode 1a); stretching – 2.5 MN (jerk, mode 1b); compression – 2.5 MN (impact, mode 1v); stretching – 2.0 MN (as part of rolling stock, 1g mode).
The label of strain gauges on the prototype was made in accordance with the scheme shown in Fig. 7. The process of preparing for experimental studies of the prototype of a long-base flat car is shown in Fig. 12.
Fig. 12.
Sequence of preparation for experimental tests: a cleaning of the places for strain gauges; b labeling of strain gauges on the cleaned surfaces according to the program and method and the manual for labeling; c assembly of the stand for the effect of longitudinal forces around the prototype; d connection of strain gauges with the tensometric station using cables for processing the received signals.
Experimental static tests were carried out by applying a longitudinal static load through the elements of the automatic coupling device using jacks installed on the loading stand (Fig. 13).
Fig. 13.
Jacks on the loading stand.
The results of static experimental tests showing the most loaded sections of the structure are presented in Tables 5 and 6.
Table 5.
Maximum stress values obtained during static tests according to the first loading scheme.
| No. of strain gauges and sections | Stresses on the flat car elements, MPa | Permissible stress, MPa | |||
|---|---|---|---|---|---|
| Mode 1a | Mode 1b | Mode 1v | Mode 1g | ||
| No. 17, II sections | 143.41 | 105.19 | 85.94 | 66.84 | 293.00 |
| No. 19, II sections | 138.35 | 101.27 | 84.2 | 65.66 | |
| No. 25, III sections | 116.34 | 91.14 | 35.14 | 22.67 | |
| No. 29, III sections | 161.47 | 124.84 | 83.46 | 67.98 | |
| No. 31, III sections | 156.65 | 121.16 | 83.38 | 67.87 | |
| No. 35, III sections | 119.01 | 93.07 | 36.88 | 23.97 | |
Table 6.
Maximum stress values obtained during static tests according to the second loading scheme.
| No. of strain gauges and sections | Stresses on the flat car elements, MPa | Permissible stress, MPa | |||
|---|---|---|---|---|---|
| Mode 1a | Mode 1b | Mode 1v | Mode 1g | ||
| No. 17, II sections | 141.62 | 97.96 | 98.96 | 72.99 | 293.00 |
| No. 19, II sections | 137.26 | 95.00 | 72.99 | 70.78 | |
| No. 25, III sections | 114.29 | 78.26 | 79.69 | 36.85 | |
| No. 29, III sections | 163.31 | 111.53 | 111.61 | 82.87 | |
| No. 31, III sections | 156.82 | 106.6 | 106.8 | 72.86 | |
| No. 35, III sections | 114.82 | 78.86 | 79.82 | 37.71 | |
The highest values of equivalent stresses in the structural elements of the flat car, determined during static experimental tests in accordance with the requirements of GOST 33211-2014, are shown in Fig. 14. For a visual analysis of the stress-strain state, we identified those areas of the frame in which the maximum stress levels were observed. These diagrams reflect the highest stress values that characterize critical sections of the frame and allow us to assess the degree to which the structure approaches the permissible limits. This presentation of the results provides a visual comparison of the behavior of various structural elements under the action of standard operating loads.
Fig. 14.
Distribution of maximum equivalent stresses in the structural elements of the flat car under loading according to scheme 1 (a) and scheme 2 (b).
In the result of static experimental tests of a prototype of a long-base flat car, the maximum values of stresses were recorded on strain gauge No. 29 (the junction of the ridge and pivot beams) for each mode according to both loading schemes. Graphs of these dependencies are shown in Figs. 15 and 16 for clarity. According to the first loading scheme, the maximum stresses at the joints of the ridge and pivot beams were: on 1a mode – 163.31 MPa; 1b – 111.53 MPa; 1v – 111.61 MPa; 1g – 82.87 MPa. According to the second loading scheme, the maximum stresses in the same nodes were: 1a – 161.47 MPa; 1b – 125.34 MPa; 1v – 124.32 MPa; 1g – 69.41 MPa.
Fig. 15.
Maximum values of stresses in the joints of the ridge and pivot beams (sensor No. 29) under loading according to the first scheme in mode 1a (a), 1b (b), 1v (c) and 1g (d).
Fig. 16.
Maximum values of stresses in the joints of the ridge and pivot beams (sensor No. 29) under loading according to the second scheme in the mode 1a (a), 1b (b), 1v (c) and 1g (d).
Considering that the maximum equivalent stresses obtained during static tests at all control points of the frame do not exceed the permissible values established by regulatory documentation (including the requirements of GOST 33211-2014 for the strength of freight cars), we can conclude that the design of the prototype flat car has a sufficient margin of safety.
Running strength tests of the prototype were carried out on the test section of the railway track, which includes curved sections with a radius of R300 m, R600 m and a straight section of the railway track (Fig. 17) in accordance with the developed program and methodology on the track of the Khamza-Chukursai station, without precipitation, under climatic conditions from + 9 to + 15 °C using a traction locomotive.
Fig. 17.
Diagram of the railway track test section.
In view of the fact that during static tests, the maximum stresses were detected when loading the flat car with four 20-foot containers, running strength tests were carried out on a prototype with a similar load.
The conditions for passing straight and curved sections of railway track during running strength tests of the prototype are shown in Table 7.
Table 7.
Conditions for passing straight and curved sections of railway track during running strength tests.
| Track | Speed, km/h | |||||||
|---|---|---|---|---|---|---|---|---|
| Straight track section | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
| Curved track section | ||||||||
| R 300 | 10 | 20 | 30 | 40 | 50 | × | × | × |
| R 600 | 10 | 20 | 30 | 40 | 50 | 60 | × | × |
To conduct running strength tests, a prototype train was formed from a prototype of a flat car and a traction locomotive. The collection of the necessary and sufficient array of experimental data during the passage of straight and curved sections of the track by the coupling in each speed interval was performed in three passes according to GOST 33788-201632. For further processing and analysis, the average values of the obtained experimental data were selected, which are presented in Tables 8 and 9.
Table 8.
Maximum stresses on the frame of a flat car when passing a straight section of track, MPa.
| Sensor no. | Strain gauge installation zone | Speed, km/h | |||||||
|---|---|---|---|---|---|---|---|---|---|
| 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | ||
| 2 | Zone of the lower and upper shelves of the lateral longitudinal beams on the left side | 19.2 | 23.4 | 28.6 | 34 | 41.3 | 49.8 | 60.7 | 72.9 |
| 4 | Zones of the lower and upper longitudinal beams side shelves with right side | 20.1 | 24.2 | 29.3 | 35.5 | 42.9 | 51.9 | 62.8 | 73.5 |
| 5 | Zones of the lower and upper shelves sill on the left side | 19.3 | 23.3 | 28.2 | 34.1 | 41.2 | 49.9 | 60.4 | 72 |
| 6 | 20.9 | 25.2 | 30.5 | 36.9 | 45.7 | 54.1 | 65.1 | 76.4 | |
| 7 | Zones of the lower and upper shelves sill on the right side | 20.6 | 24.9 | 30.2 | 36.9 | 44.1 | 53.2 | 64.3 | 75 |
| 8 | 19.7 | 23.9 | 28.9 | 34.9 | 42.3 | 51.1 | 61.9 | 72.9 | |
| 10 | Zones of the lower and upper shelves of the lateral longitudinal beams on the left side | 20.1 | 24.3 | 29.5 | 35.6 | 43.1 | 52.2 | 63.1 | 73.8 |
| 12 | Zones of the lower and upper longitudinal beams side shelves with right side | 20.4 | 24.6 | 29.8 | 36.1 | 43.6 | 52.8 | 63.9 | 74.7 |
| 13 | Zones of the lower and upper shelves of the lateral longitudinal beams on the left side | 19.8 | 23.6 | 27.9 | 33.1 | 40.7 | 49.3 | 59.7 | 72.2 |
| 14 | 20.9 | 25.6 | 30.4 | 37.3 | 45.6 | 55.9 | 67.3 | 81.4 | |
| 15 | Zones of the lower and upper longitudinal beams side shelves with right side | 19.8 | 24.3 | 28.8 | 35.2 | 42.6 | 51.4 | 62.2 | 75.3 |
| 16 | 21.9 | 26.4 | 32.1 | 38.9 | 47.1 | 56.9 | 68.9 | 80.1 | |
| 17 | Zones of lower and upper shelves sill on the left side | 21 | 25.7 | 30.9 | 37.4 | 45.4 | 54.8 | 66.3 | 80.1 |
| 18 | 22.4 | 27.4 | 32.7 | 39.6 | 47.8 | 57.9 | 68.3 | 80.2 | |
| 19 | Zones of the lower and upper shelves sill on the right side | 22.6 | 27.2 | 33 | 40.7 | 48.2 | 58.3 | 69.5 | 80.7 |
| 20 | 22.1 | 26.8 | 32.4 | 39 | 47.4 | 57.1 | 68.1 | 81.8 | |
| 21 | Zone of the lower and upper shelves of the lateral longitudinal beams on the left side | 18.5 | 22.5 | 27.4 | 32.8 | 39.8 | 48.2 | 58.3 | 70.6 |
| 22 | 22.5 | 26.6 | 32.3 | 39.4 | 47.3 | 57.3 | 68.2 | 79.5 | |
| 23 | Zone of the lower and upper longitudinal beams side shelves with right side | 18.9 | 23 | 27.8 | 33.7 | 40.7 | 49.3 | 59.7 | 72.2 |
| 24 | 22.9 | 27.7 | 33.4 | 40.4 | 49.2 | 58.9 | 70.2 | 81.4 | |
| 25 | Zones of the lower and upper shelves of the lateral longitudinal beams on the left side | 22.4 | 27.4 | 32.7 | 39.6 | 47.8 | 57.9 | 68.7 | 80.2 |
| 26 | 21.4 | 25.9 | 31.7 | 39 | 46.8 | 55.5 | 66.9 | 80.5 | |
| 27 | Zones of the lower and upper longitudinal beams side shelves with right side | 21.6 | 26.2 | 31.7 | 38.2 | 46.5 | 56.1 | 67 | 80.6 |
| 28 | 22.1 | 26.6 | 32.3 | 39.2 | 47.3 | 57.3 | 67.6 | 79.9 | |
| 29 | Zones of the lower and upper shelves on the left side in the connections sill with pivot beam | 22.7 | 27.3 | 32.8 | 39.3 | 47.6 | 57.2 | 68.1 | 81.7 |
| 31 | Zone of the lower and upper shelves on the right side in the connections sill with pivot | 19.9 | 23.7 | 28.1 | 34.4 | 41.7 | 50.4 | 61.1 | 74 |
| 63 | Zones of lower and upper shelves of the side longitudinal beam on the right side | 57.5 | 66.7 | 76.71 | 88.5 | 102.1 | 117.9 | 136 | 157 |
| 65 | Zones of lower and upper shelves of the ridge beam on the left side | 59.9 | 69.13 | 79.77 | 92.06 | 106.2 | 122.6 | 141.5 | 164.7 |
| 67 | Zones of lower and upper shelves of the ridge beam on the right side | 59.01 | 68.1 | 78.59 | 90.69 | 104.6 | 120.7 | 139.4 | 160.8 |
| 69 | Zones of lower and upper shelves of the side longitudinal beam on the left side | 57.2 | 66.39 | 76.61 | 88.42 | 102 | 117.7 | 135.9 | 156.8 |
Table 9.
Maximum stresses on the frame of the flat car when passing curved sections of track, MPa.
| Sensor no. | Strain gauge installation zone | Curved section with R300 m, speed (km/h) | Curved section with R600 m, speed (km/h) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 20 | 30 | 40 | 50 | 10 | 20 | 30 | 40 | 50 | 60 | ||
| 1 | Zones of the lower and upper shelves of the lateral longitudinal beam on the left side | 18.7 | 23.7 | 30.1 | 38.2 | 48.5 | 18.7 | 23.2 | 28.8 | 34.1 | 39.2 | 45.1 |
| 2 | 20.3 | 25.7 | 32.3 | 40.82 | 52.7 | 20.3 | 25.3 | 31.4 | 37.4 | 42.8 | 49.4 | |
| 3 | Zones of the lower and upper shelves of the lateral longitudinal beam on the right side | 19.2 | 24.4 | 31 | 39.3 | 49.8 | 19.2 | 23.9 | 29.6 | 35.0 | 40.3 | 46.3 |
| 4 | 21.2 | 26.9 | 34.3 | 43.3 | 55.7 | 21.2 | 26.2 | 32.6 | 38.4 | 44.2 | 50.8 | |
| 5 | Zones of the lower and upper shelves of the ridge girder on the left side | 23.8 | 30.2 | 38.3 | 48.6 | 61.7 | 22.4 | 27.8 | 34.6 | 40.9 | 47.1 | 54.3 |
| 6 | 23.9 | 30.3 | 38.3 | 48.7 | 61.6 | 23.3 | 28.9 | 35.8 | 42.3 | 48.7 | 56.1 | |
| 7 | Zones of the lower and upper shelves of the ridge girder on the right side | 22.7 | 28.8 | 36.5 | 46.3 | 58.6 | 22 | 27.3 | 33.9 | 40.2 | 46.1 | 53.1 |
| 8 | 25 | 31.7 | 40.2 | 51 | 64.7 | 23.3 | 28.9 | 35.9 | 42.5 | 48.9 | 56.4 | |
| 9 | Zones of the lower and upper shelves of the lateral longitudinal beam on the left side | 19.7 | 24.9 | 31.6 | 40.2 | 51 | 19 | 23.6 | 29.3 | 34.6 | 39.9 | 45.9 |
| 10 | 22.2 | 28.2 | 35.8 | 45.4 | 57.6 | 22 | 27.3 | 33.9 | 40.2 | 46.1 | 53.1 | |
| 12 | Zones of the lower and upper shelves of the lateral longitudinal beam on the right side | 23.4 | 29.7 | 37.6 | 47.8 | 60.6 | 22.8 | 28.3 | 35.1 | 41.5 | 47.7 | 55.0 |
| 13 | Zones of the lower and upper shelves of the lateral longitudinal beam on the left side | 20.5 | 26.2 | 33.5 | 41.5 | 53.6 | 20.3 | 25.7 | 31.2 | 37.2 | 43.1 | 49.4 |
| 14 | 23.9 | 27.7 | 35.4 | 44.2 | 57.8 | 22.2 | 27.7 | 33.3 | 39.6 | 47.1 | 54.0 | |
| 15 | Areas of the lower and upper shelves of the lateral longitudinal beam on the right side | 21 | 26.7 | 34 | 43.6 | 54.9 | 21.8 | 26.4 | 32.5 | 38.2 | 44.2 | 50.7 |
| 16 | 22.1 | 28.8 | 36.5 | 46.4 | 58.9 | 23.2 | 28.7 | 35.8 | 42.4 | 48.5 | 55.8 | |
| 17 | Zones of the lower and upper shelves of the ridge girder on the left side | 26.1 | 33.1 | 42 | 53 | 67.76 | 24.6 | 30.5 | 37.9 | 44.9 | 51.7 | 59.5 |
| 18 | 25.6 | 32.6 | 41.2 | 52.4 | 66.5 | 25.8 | 32.3 | 39.1 | 46.2 | 53.3 | 61.5 | |
| 19 | Zones of the lower and upper shelves of the ridge girder on the right side | 24.3 | 30.9 | 39.1 | 49.8 | 63.2 | 24.6 | 30.5 | 38 | 44.9 | 51.5 | 59.2 |
| 20 | 28 | 35.4 | 45.1 | 56.9 | 72 | 26.3 | 31.9 | 39.9 | 47.4 | 54.6 | 62.9 | |
| 21 | Zones of the lower and upper shelves of the lateral longitudinal beam on the left side | 21.6 | 27.3 | 34.7 | 44.1 | 56 | 20.8 | 25.9 | 32.1 | 38.0 | 43.8 | 50.3 |
| 22 | 24.8 | 31.5 | 39.9 | 50.7 | 64.2 | 24.1 | 29.9 | 37.2 | 44.1 | 50.6 | 58.2 | |
| 23 | Areas of the lower and upper shelves of the lateral longitudinal beam on the right side | 20.5 | 26.8 | 33.6 | 41.9 | 53.2 | 20.5 | 25.4 | 31.6 | 37.4 | 43.1 | 49.4 |
| 24 | 26.1 | 33.2 | 41.9 | 53.3 | 67.5 | 25.1 | 31.5 | 38.5 | 45.5 | 52.3 | 60.3 | |
| 25 | Zones of the lower and upper shelves of the lateral longitudinal beam on the left side | 25.6 | 32.6 | 41.2 | 52.4 | 66.5 | 25.3 | 31.7 | 38.4 | 45.5 | 52.3 | 60.3 |
| 26 | 24.3 | 30.9 | 39.1 | 49.8 | 63.2 | 24.1 | 29.9 | 37.3 | 44.1 | 50.6 | 58.2 | |
| 27 | Areas of the lower and upper shelves of the lateral longitudinal beam on the right side | 27.5 | 34.8 | 44.4 | 56 | 71 | 25.8 | 31.3 | 39.2 | 46.6 | 53.7 | 61.9 |
| 28 | 79.8 | 92.1 | 106.3 | 122.7 | 141.6 | 58.2 | 67.2 | 77.5 | 89.5 | 103.3 | 119.2 | |
| 29 | The zones of the lower and upper shelves on the left side at the junctions of the ridge beam with the pivot beam | 77.4 | 89.1 | 103.1 | 119.8 | 137.4 | 54.8 | 63.6 | 74.3 | 85.8 | 99 | 114.3 |
| 31 | The zones of the lower and upper shelves on the right side at the junctions of the ridge beam with the pivot beam | 78.1 | 90.1 | 104.2 | 120.4 | 138.5 | 55.8 | 64.4 | 74.7 | 86.1 | 99.5 | 114.1 |
| 34 | Zones of the lower and upper shelves of the lateral longitudinal beam on the left side | 80.7 | 93.2 | 107.6 | 124 | 143 | 56.1 | 64.8 | 74.8 | 86.3 | 99.6 | 114.9 |
The results obtained in the course of running strength tests of the flat car using installed strain gauges are shown in Figs. 18, 19 and 20 for clarity. For further analysis, we selected the data of those measuring channels in which the highest stress values were recorded during the tests, which allows us to most fully evaluate the operation of structural elements under maximum load conditions. The graphs reflect the nature of stress changes over time and make it possible to compare experimental results with calculated data.
Fig. 18.
Maximum stresses on a straight section of track at a speed of 80 km/h, strain gauges No. 63 (a) and No. 69 (b).
Fig. 19.
Maximum stresses on the curved section of the track R300 m at a speed of 50 km/h, strain gauges No. 28 (a) and No. 31 (b).
Fig. 20.
Maximum stresses on the curved section of the track R600 m at a speed of 60 km/h, strain gauges No. 29 (a) and No. 31 (b).
Analysis of dynamic running tests showed that the greatest stresses occur in the following zones:
in section VI-VI – 195.73 MPa in the center of the lateral longitudinal beam on a straight section of track at a speed of 80 km/h;
in section III-III – 143.32 MPa on the inner sides of the upper shelves when moving in a curve with a radius of 300 m (50 km/h) and 119.23 MPa at a radius of 600 m (60 km/h).
The results of experimental studies to determine the load-bearing structure of a prototype of an improved flat car for the transportation of high-capacity containers, performed in accordance with the developed program and methodology of static and running dynamic tests, do not exceed the permissible standards established by GOST 33211-201428. These data confirmed the theoretically obtained calculations and indicate the high reliability of the developed finite element model and the design decisions made. At the same time, the conducted comparative analysis showed that the relative discrepancy between theoretical and experimental data does not exceed 8.1%, which meets the requirements of regulatory documentation and confirms the reliability and efficiency of the proposed design under operating conditions.
Limitations of the study
The obtained results are based on a combination of numerical simulations and full-scale experimental studies carried out for a prototype of a long-base flat car under specific loading and operational conditions.
The experimental tests were performed for defined speed ranges and track geometries, as well as for selected container configurations (20- and 40-foot containers). The stress-strain state of the structure was evaluated within these conditions.
The present study focused on strength and operational reliability. Issues related to long-term fatigue behavior, extreme accidental load cases, and operation under extended climatic conditions were not considered and require further investigation.
Therefore, the conclusions drawn in this work are valid within the scope of the conducted experimental program and the adopted assumptions.
Conclusions
The paper analyzes scientific studies devoted to the assessment of strength, stress-strain state and improvement of the design of freight cars, in particular long-base flat cars. It is established that the existing approaches and technical solutions do not fully meet a number of modern requirements for rolling stock intended for container transportation under current operating conditions, which indicates the relevance of developing an improved design of a long-base flat car that provides an increase in transportation efficiency, reliability and operational characteristics.
To carry out theoretical research, a plate-rod finite element model of a long-base flat car has been developed, which makes it possible to substantiate the selection of geometric parameters and rational dimensions of power-bearing elements, taking into account the analysis of the stress-strain state of the structure under the action of operational loads. Finite element calculations showed that the maximum equivalent stresses in the load-bearing elements do not exceed 151.8 MPa for the most unfavorable loading modes, while remaining below the permissible limits established by regulatory documentation. Based on finite element modeling, the dependences of the stress-strain state of the structure on its geometric parameters were established, which made it possible to determine the optimal dimensions and configuration of power elements that provide increased strength and reliability while reducing the tare weight.
The results of complex theoretical research using the finite element method served as the basis for the development of an improved design of a long-base flat car for the transportation of high-capacity containers. A distinctive feature of this design is the increased base and optimized layout, which provides increased capacity and improved operational characteristics and creates prerequisites for more efficient use of the car fleet in the context of growing container traffic volumes. A comparative analysis of two loading schemes demonstrated that the placement of four 20-foot containers leads to higher stress levels than the transportation of two 40-foot containers due to a more complex load distribution and increased local effects.
For the purpose of experimental verification of the calculated data, an improved program and methodology for conducting static and running dynamic tests of the flat car structure using the strain gauge method have been developed. Static strength tests of a prototype flat car showed that the maximum stresses were recorded at the junction of the ridge and pivot beams, reaching 163.3 MPa for the most unfavorable mode under the first loading scheme and 161.5 MPa under the second scheme. The conducted running dynamic tests established that the highest stress values occur in the lateral longitudinal beams and upper shelves of the structure and do not exceed 195.7 MPa on straight track sections at a speed of 80 km/h, as well as 143.3 MPa when moving in curves with a radius of 300 m.
The conducted experimental studies showed a high degree of correspondence between theoretical and experimental results: the relative discrepancy does not exceed 8.1%, which meets the requirements of regulatory documentation. The obtained results demonstrate the adequacy of the proposed finite element model and the validity of the adopted design decisions under the considered operating conditions.
The comprehensive theoretical and experimental studies made it possible to substantiate the proposed design solutions for a long-base flat car intended for transporting high-capacity containers. The developed design is characterized by improved technical parameters, including a reduced tare weight and an increased load capacity by 1 ton, as well as enhanced strength characteristics and operational reliability within the scope of the conducted studies. Based on the obtained results, the proposed design solutions were implemented in the development of a new flat car model 13-6991, manufactured by JSC “Foundry Mechanical Plant” in the Republic of Uzbekistan33, which contributes to improving the technical and economic performance of freight rolling stock used for container transportation. At the same time, the obtained results form a basis for further research aimed at refining the finite element model with a more detailed description of locally stressed zones, primarily in the areas of junctions of the ridge, pivot and cross beams, as well as for studying fatigue strength and durability of the load-bearing structure under variable operational loads corresponding to real operating conditions. In addition, further comparative analysis and optimization of container loading schemes and structural elements may reduce local stress levels and improve the uniformity of load transfer, while extended operational studies and long-term monitoring of the developed flat car design will allow validation of the calculated service life and further improvement of design solutions for the transportation of high-capacity containers.
Author contributions
All authors contributed equally to the theoretical and experimental investigations, numerical modeling, problem analysis, formulation of the research idea, and manuscript preparation. All authors reviewed the manuscript.
Funding
Not applicable.
Data availability
All data generated or analysed during this study are included in this published article.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Data Availability Statement
All data generated or analysed during this study are included in this published article.