Influence of unsupported sleepers on flange climb derailment of two freight wagons

Jan Matej; Jarosław Seńko; Jacek Caban; Mikołaj Szyca; Hubert Gołębiewski

doi:10.1515/eng-2022-0544

Article Open Access

Influence of unsupported sleepers on flange climb derailment of two freight wagons

Jan Matej , Jarosław Seńko , Jacek Caban , Mikołaj Szyca and Hubert Gołębiewski

Published/Copyright: March 30, 2024

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From the journal Open Engineering Volume 14 Issue 1

Abstract

Two freight platform wagons connected together conventionally or in the form of so-called rigid connection were taken into account to investigate the influence of unsupported sleepers on climb flange derailment on transition curve. Presented results are related to the freight wagons equipped with two-axle Y25 standard bogies, entering at an acceptable speed in the transition curve of the track with the radius of 150 or 1,000 m. Three cases have been analyzed: only the inner rail, only the outer rail, or both rails had unsupported sleepers. Simulation models were prepared using the VI-Rail software and nonlinear wheel–rail contact model. The dynamic calculations showed that wheel flange climb derailment caused by unsupported sleepers will only occur if deflection of the rail or track on transition curve is deep enough. These tests allowed us to determine the relationship between the radius of curvature and the depth of the trough causing derailment of the wagons. Calculation results allowed us to answer also the questions whether the method of connection and the weight of freight wagons have a significant impact on the wheel flange climb derailment.

Keywords: transport safety; transition curve; unsupported sleepers; wheel flange climb derailment

Notation

μ: coefficient of friction
H derail: vertical deflection of the rail creating conditions for derailment
Q 0 lim ̅: magnitude of the static load, necessary to achieve the vertical deflection of the rail creating conditions for derailment
W1, W2, W3: length dimensions of the trough
I _x, I _y, I _z: moments of inertia of the model components
L, V: projections of the resultant tangential T and normal N forces in the wheel-rail contact area, respectively, in transverse and vertical directions
γ _max: maximum contact angle
Δ_Z: lifting of the wheel in relation to the rail head
E: the Young’s module for steel
J _x: inertia moment of transverse section of the 60E1 rail
l: distance between two supported sleepers located closest to each other
T, N: resultant tangential and normal forces in the wheel-rail contact area
L, V: projections of the resultant tangential and normal forces in transverse and vertical directions, respectively

1. Introduction

Rail transport is one of the branches of transport that is responsible for the transport of a large amount of goods, including dangerous goods (RID), and has a large impact on the national economy. Providing railway infrastructure is a prerequisite for achieving high-quality freight transport, which can be considered as the backbone of the entire transport system [1]. System failures in rail transport operations of industrial centers result in a rapid increase in transportation time expenditures, material resource consumption, the number of incidents, and environmental degradation [2]. In the event of damage to the track and railway subgrade, an important issue is the incorrect location of the railway sleepers supporting the rails.

There are many aspects associated with the problem of unsupported sleepers. Unsupported sleepers mostly do not touch the ballast and then increase the risk of train derailment. Very important is the number and size of the gap between an unsupported sleepers and the ballast. This article presents the results of numerical calculations allowing to answer the questions below.

How big must be the gap between an unsupported sleepers and the ballast for occur wheel flange climb derailment of freight wagons entering at an acceptable speed in the transition curve?
How does the position of unsupported sleepers on transition curve affect the course of the wheel flange climb derailment?
Does the way the freight wagons are connected and the state of their loading has significant impact on wheel flange climb derailment of freight wagons entering at an acceptable speed in the transition curve with unsupported sleepers?

2. Literature review

Rail transport is one of the safer modes of transport. Nevertheless, in the literature, one can find a lot of scientific studies devoted to the issues of rail transport safety [3,4,5,6,7,8,9,10]. Some of these works are devoted to the issues of rail vehicle dynamics on safety [4,7,8,9] and travel comfort [5,6]. Analyzing the available literature, it can be concluded that safety in rail transport is strongly influenced by transport infrastructure [1,3,11,12,13,14], various technical defects [15,16,17,18,19,20,21,22], and the human factor [23,24,25]. From the viewpoint of safety on the railway network, the most dangerous place is a rail crossing for the railway track and road (railway-crossing or level-crossing) as practically the only place of direct physical contact between otherwise relatively isolated transport modes [26,27]. Various damages to the railway rail have a significant impact on the operational safety and service life of the railway infrastructure [28]. In addition, some researchers deal with the issues of monitoring the condition of infrastructure [29,30,31] and modeling rail vehicles [32,33,34,35,36,37].

Good technical condition of the railway infrastructure is essential for the safety of rail transport. The essential elements are the railway rail, sleeper, fasteners, and track. The task of fastening rails to railway sleepers can be performed by elastic fastenings [38,39,40,41]. The fastening of the rails to the sleepers is required for structural integrity and for transferring loads arising in the railway track. In the case of the sleepers, there are various defects that affect safety [42], e.g., cracking of a railway sleeper. Lack of contact between the sleepers and the ballast results in the effect of the so-called “hanging sleeper” or “mud outflow,” resulting in a gap between the sleepers. Bednarek [43] has shown that the zone of lack of contact between the track and the ground can reach even up to 5 m. Results of Li and Sun [44] research indicate that on heavy haul freight lines in China, up to 50% of all sleepers could be considered as unsupported and the largest length of track with unsupported sleepers was equal to 4 m. Shi et al. [45] have shown that the vertical sleeper displacement may be greater than the size of the gap if three or four unsupported sleepers occurred consecutively. Dusza [46] has shown that dangerously high vertical deflection will occur over the distance of three or more neighboring sleepers that have lost their support.

3. Cases of unsupported sleepers

Solkowski and Jamka [47] showed that on the length of loaded track section with unsupported sleepers, a characteristic trough of about one meter long at the base is formed with depth depending on the number of consecutive unsupported sleepers. The depth and main dimensions of the trough, resulting from vertical force Q, are indicated by H, W1, W2, and W3, respectively (Figure 1).

Figure 1

Characteristic dimensions of the trough for three consecutive unsupported sleepers.

4. Tested freight wagons

The group of two interconnected freight platform wagons intended for carry containers was investigated. They were connected together in two ways: conventionally, by the means of screw coupling device and buffers or customized by the means of intermediate bogie in the form of so-called stiff, articulation connection. In both ways, the freight wagons were equipped with the Y25 standardized freight bogies. Molatefi et al. [48] suggested that when the play between the axle box and the bogie frame in longitudinal direction is exhausted, the values of longitudinal stiffness of primary suspension may increase even to 1 × 10⁸ N/m.

Stiffness values coefficients of primary suspension elements are shown in Table 1. The values of dry friction coefficients for side friction blocks and central pivot surface have been used according to Jendel [49] and Kisilowski [50]. The masses and moments of inertia of the model components are shown in Table 2.

Table 1

Stiffness and damping values coefficients of primary suspension elements

Parameter	Value (N/m)
Longitudinal stiffness of primary suspension springs (empty/loaded wagon)	(0.89/13) × 10⁶
Lateral stiffness of primary suspension spring (empty/loaded wagon)	(0.43/2.2) × 10⁶
Vertical stiffness of primary suspension spring (empty/loaded wagon)	(0.85/17) × 10⁶
Damping of primary suspension in x, y, and z directions (Ns/m)	1 × 10⁴ Ns/m

Table 2

Mass and Inertia parameters of the freight wagon model elements

Component of the model	Mass (kg)	Moments of inertia (kg m²)
Component of the model	Mass (kg)	I _x	I _y	I _z
Car body (empty/full)	11,000/34,000	8,000/25,000	150,000/500,000	150,000/500,000
Bogie frame	2,200	1,900	1,500	2,800
Wheelset	1,700	810	810	150

5. Simulation models of interconnected freight platform wagons

Simulation models of two freight platform wagons were prepared using the VI-Rail engineering software and nonlinear wheel–rail contact theory – Kalker [51]. In the first variant, two wagons were connected by the means of screw coupling device and buffers (Figure 2). In the second variant, wagons were connected by the means of intermediate bogie in the form of the so-called stiff connection (Figure 3). Car body (platform frame and container), bogie frames, wheelsets, and axle-boxes were considered to be perfectly rigid bodies. The position of a given element toward an immovable, global reference system was described by three Cartesian coordinates, and the attitude of each element was defined by three Euler angles.

Figure 2

Elements of the simulation model with conventional connection of two wagons.

Figure 3

Elements of the simulation model with stiff connection of two wagons.

Model parameters were as follows: masses, the locations of the center of gravity, and the main inertia moments of the individual rigid elements. Characteristics of the 105 mm buffer stroke and draw gear shock absorber were consistent with the UIC 526-1 Leaflet [52]. Mathematical model of the coupling device has been implemented from the doctoral thesis Seńko [53]. The regular track with 60E1 rails profile, gauge of 1.435 m, and the 0.025 radians angle of track inclination was considered. Track geometry has been described by three sections of railway: straight part, transition curve, and curve of constant radius. The track substitute parameters were in accordance with the specification of VI-Rail 15.0 Documentation [54] and Iwnicki [55]. The nominal radius of the wheels with S1002 profile was assumed to be 0.460 m, while the bases of wagons and bogies were equal to 9 and 1.8 m, respectively.

Contact angles between wheels and rails as a function of lateral wheelset displacement are shown in the Figure 4. To solve the so-called normal and tangent tasks the RSGEO and modified FASTSIM procedure proposed by Kik and Piotrowski [56] were used.

Figure 4

Contact angles between wheels with nonlinear S1002 profile and rails with nonlinear UIC60E profile as a function of lateral wheelset displacement – VI-Rail program report.

6. Criteria for assessing the risk of wheel flange climb derailment

Three different criteria were taken into account. First, the safety criterion resulting from the forces acting in the wheel–rail contact area under dynamic conditions was considered. The danger of derailment appears when the rim of the wheel starts to climb the rail head. The border value of the derailment coefficient was estimated according to the Nadal formula in the following way:

(1) | L / V | border = tg γ max − μ 1 + tg γ max .

According to Figure 4, the value of 57.95 degrees for the maximum contact angle γ _max was used. The L and V are the projections of the resultant tangential T and normal N forces in the wheel–rail contact area, in transverse and vertical directions, respectively (Figure 5). The value of 0.4 for coefficient of friction μ between wheel and rail was established. In the derailment process, oncoming wheel rises in relation to the rail head and the contact angle between the wheel increases. The final phase of derailment occurs when the contact angle reaches its maximum value γ _max. According to formula (1), the border value of the |L/V|_border is equal to 0.73. None of derailment coefficient value, calculated during the simulation, may be greater than the border value |L/V|_border. As a second, the safety criterion resulting from the lifting of the wheel in relation to the rail head was considered. According to document EN 14363 [57], the calculated maximum value Δz _max of the lifting of the wheel in relation to the rail head must not exceed the border value Δz _border equal to 0.005 m:

(2) Δ z max ≤ Δ z border = 0.005 .

Figure 5

Lifting of the wheel in relation to the rail head and forces determining the wheel flange climb derailment.

The third criterion was based on the control of the time duration of the y _max value. The time duration should be no more than 50 milliseconds – Elkins and Carter [58]. If all three criteria were not met, it was only then that the wheelset was found to have derailed.

7. Calculation results

This article considers the situation in which the railway track bends to the right in horizontal plane and three consecutive unsupported sleepers are at the point where the straight track turns into transition curve (Figure 6).

Figure 6

Sections of the railway track and the location of trough.

Three cases concerning the location of unsupported sleepers have been considered: only inner rail (Case 1), only outer rail (Case 2), and both sides of the track (Case 3). Dip Analytical Irregularities function of the VI-Rail program was used. Simulation tests were performed for empty and fully loaded wagons, for different curved track radii with transition curves ranging from 150 to 2,000 m. The curve R = 150 m is the smallest of the curves on which dynamic calculations should be carried out in accordance with EN-14363 [57]. The relationship between the vertical deflection of the rail H _derail, creating conditions for wheel flange climb derailment on the transition curve, and the known radius of curvature R is presented in Figure 7.

$Figure 7 Relationship between the vertical deflection of the rail H derail {H}_{{\rm{derail}}} , creating conditions for wheel flange climb derailment on the transition curve, and the known radius of curvature R.$

Figure 7

Relationship between the vertical deflection of the rail H derail , creating conditions for wheel flange climb derailment on the transition curve, and the known radius of curvature R.

If we treat a single rail as a freely supported bending beam with a force concentrated at half the distance between the two consecutive sleepers being in contact with the ground, we can calculate vertical static forces Q ₀ exerted by a single wheel on the rail (Table 3).

Table 3

Vertical static force Q ₀ exerted by a single wheel on rail

Variant of wagon connection	Empty wagon (kN)	Loaded wagon (kN)
Conventional	27.222	55.426
Stiff	40.119	97.119

The magnitude Q 0 lim ̅ of the static load, necessary to achieve the vertical deflection of the rail H derail creating conditions for derailment, was determined from the known pattern according to the strength materials:

(3) Q 0 lim ̅ = 48 E J x 1 l 3 H derail ,

where E means the Young’s module for steel, J _x is the inertia moment of transverse section of the 60E1 rail, and l is the distance between two supported sleepers located closest to each other (Table 4).

Table 4

Relation between the magnitude Q 0 lim ̅ of the static load and vertical deflection of the rail H _derail creating conditions for derailment

Q 0 lim ̅ (kN)	H derail (m)
133.586	0.060
66.793	0.030

The vertical static forces Q ₀ are smaller than expected values of Q 0 lim ̅ . However, the results of Shi et al. [45] research indicate that the dynamic forces may increase to 220% approximately of static load, when there are four consecutive unsupported sleepers. Droździel et al. [59] and Dyniewicz et al. [60] show that in a particular case, the dynamic vertical forces may be even greater. On the other hand, Zhang et al. [61] presented simulation studies of unsupported sleepers which indicate that the spacing between unsupported sleepers and ballast masses has a large influence on normal wheel and rail loading.

For the radius of curvature equal to 150 meters, the depth H derail of the trough, causing the wheel flange climb derailment of the simulation models on transition curve with three consecutive unsupported sleepers, takes the value equal to 0.060 m, while for the radius of curvature equal to 1,000 m, the depth H derail of the trough was equal to 0.030 m. The most attention was paid to the Case 1 (results are presented in Figures 8 and 9) and to the Case 2 (results are presented in Figures 10 and 11) realized for the transition curve connected to the track with the radius of curvature equal to 150 m. The drawings below describe the wheelset positions in the transition curve at the point, where the individual wheelsets have been derailed. Figure 8 shows the wheelsets positions in critical phase of derailment of two wagons connected by means of screw coupling device and buffers on the transition curve with three unsupported sleepers located only under the inner rail. Results obtained for empty and fully loaded wagons are identified by the letters E and F, respectively. Derailed wheelsets are shown in red and bold. Wheelsets, that have not derailed, are black and are drawn with a thinner line. At the top of the drawing, the successive wheelset numbers are shown. At the bottom of the drawing, order of derailment of wheelsets in the time is presented. The letter L or R informs that the given wheelset has derailed to the left or to the right side of the transition curve. Additional information according to the order of derailment of wheelsets in the time for empty or fully loaded wagons is given in Table 5. These include the start time t ₀ of derailment, interval time duration Δt and distance duration Δs in the critical derailment phase plus distance s from the beginning of the straight track section to the derailment site.

$Figure 8 Wheelsets positions on the transition curve for empty and fully loaded wagons connected by means of screw coupling device and buffers: Case 1, R = 150 m, v = 15 m/s, and H derail {H}_{{\rm{derail}}} = 60 mm.$

Figure 8

Wheelsets positions on the transition curve for empty and fully loaded wagons connected by means of screw coupling device and buffers: Case 1, R = 150 m, v = 15 m/s, and H derail = 60 mm.

$Figure 9 Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of screw coupling device and buffers: Case 2, R = 150 m, v = 15 m/s, and H derail {H}_{{\rm{derail}}} = 60 mm.$

Figure 9

Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of screw coupling device and buffers: Case 2, R = 150 m, v = 15 m/s, and H derail = 60 mm.

$Figure 10 Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie: Case 1, R = 150 m, v = 15 m/s, and H derail {H}_{{\rm{derail}}} = 60 mm.$

Figure 10

Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie: Case 1, R = 150 m, v = 15 m/s, and H derail = 60 mm.

$Figure 11 Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie: Case 2, R = 150 m, v = 15 m/s, and H derail {H}_{{\rm{derail}}} = 60 mm.$

Figure 11

Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie: Case 2, R = 150 m, v = 15 m/s, and H derail = 60 mm.

Table 5

Order of derailment of wheelsets in the time for fully loaded wagons according to Figure 8

Layout	Wst 8	Wst 7	Wst 1	Wst 4	Wst 3
t ₀	9.568	9.503	8.928	8.64	8.488
Δt	0.296	0.401	0.056	0.176	0.072
Δs	4.44	6.015	0.84	2.64	1.08
s	201.32	202.145	216.52	201.4	200.92

Figure 9 shows the wheelset positions on the transition curve with three unsupported sleepers located under the outer rail in critical phase of derailment for two wagons connected by means of screw coupling device and buffers. We can note that some of the wheelsets have derailed to the left side of the transition curve and other to the right side. The next two figures relate to the wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie (stiff connection). If only the inner rail had unsupported sleepers and wagons were empty, then two of the wheelsets have derailed to the left side of the transition curve and only one to the right side (Figure 10). For fully loaded wagons, all of the wheelsets have derailed to the left side of the transition curve.

If only the outer rail had unsupported sleepers and wagons were empty, then all of the wheelsets have derailed to the right side of the transition curve and only one to the right side for fully loaded wagons (Figure 11). In accordance with the applicable regulations, the train operating speed must be reduced in curved track. At the speed of 39 m/s (140.4 km/h), allowed on a curved track with a curve radius R equal to 1,000 m, only specially designed freight wagons are able to move.

Examples of such solution are, for instance, the bimodal freight wagons and the prototype bimodal train, designed in Poland. Data on this construction can be found, among others, in Medwid et al. [62]. The calculation results for two wagons with intermediate bogie, which derailed on the transition curve connected to the curved track with the radius of 1,000 m, are presented in Figures 12 and 13. Similar calculation results were also obtained for Case 3, when two rails had three consecutive unsupported sleepers.

$Figure 12 Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie: Case 1, R = 1,000 m, v = 39 m/s, and H derail {{\rm{and}}H}_{{\rm{derail}}} = 30 mm.$

Figure 12

Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie: Case 1, R = 1,000 m, v = 39 m/s, and H derail = 30 mm.

$Figure 13 Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie: Case 2, R = 1000 m, v = 39 m/s, and H derail {H}_{{\rm{derail}}} = 30 mm.$

Figure 13

Wheelset positions on the transition curve for empty and fully loaded wagons connected by means of intermediate bogie: Case 2, R = 1000 m, v = 39 m/s, and H derail = 30 mm.

8. Conclusions

The safety of rail transport depends on several factors [63], but above all, these are the human and technical factors (means of transport and infrastructure). In this study, the impact of the proper technical condition of the track (proper foundation of railway sleepers) on the safety of wagons was considered.

The dynamic calculations have confirmed that wheel flange climb derailment of the group of two freight platform wagons, entering at an acceptable speed in the transition curve with unsupported sleepers of the track with the radius of 150 or 1,000 m, will only occur if vertical deflection of degraded track is deep enough. It was also found that the real cause of wheel flange climb derailment may be a trough of the rails created as a result of the load exerted by the wheel on the track with consecutive unsupported sleepers. The group of platform wagons will derail regardless of whether the trough is formed on inner, outer, or on both rails of the transition curve. However, the necessary condition must be met, i.e., the trough must be deep enough. For the speed equal to 15 or 39 m/s, the critical rail deflection, at which wheel flange climb derailment occurs, shall not be less than 60 and 30 mm, respectively. In each of the tested cases of the transition curve with unsupported sleepers, the state of loading of the wagons affects the number of de-railed wheelsets, the order of the derailment in time, and the way of derailment (to the left or to the right side of the transition curve). This happened regardless of how the wagons were connected. It was also confirmed that on transition curve without unsupported sleepers, the wheel flange climb derailment will not occur if the freight wagons under the test do not exceed an acceptable speed.

It is possible to conduct research on a larger group of wagons and a group of wagons equipped with central couplers, which are to be introduced into freight transport in Europe in the near future. Therefore, future research should focus on this issue, which will be the subject of further research.

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Funding Information: Authors state no funding involved.
Conflict of interest: Authors state no conflict of interest.
Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

[1] Stopka O, Chovancova M, Kampf R. Proposal for streamlining the railway infrastructure capacity on the specific track section in the context of establishing an integrated transport system. In Proceedings of the MATEC Web of Conferences, 8th International Scientific Conference, LOGI 2017, České Budějovice, Czech Republic, 19 October 2017. EDP Sciences Ceske Budejovice, Czech Republic, MATEC Web Conf., 2017;134:00055.10.1051/matecconf/201713400055Search in Google Scholar

[2] Kagramanian A, Aulin D, Trubchaninova K, Caban J, Voronin A, Basov A. Perspectives of multifunctional integrated suburban-urban rail transport development. Sci J Sil Univ Technol Ser Transp. 2023;120:105–15.10.20858/sjsutst.2023.120.7.Search in Google Scholar

[3] Alvarenga TA, Carvalho AL, Honorio LM, Cerqueira AS, Filho LMA, Nobrega RA. Detection and classification system for rail surface defects based on eddy current. Sensors. 2021;21:7937.10.3390/s21237937Search in Google Scholar PubMed PubMed Central

[4] Bao YL, Li YL, Ding JJ. A case study of dynamic response analysis and safety assessment for a suspended monorail system. Int J Env Res Public Health. 2016;13:1121.10.3390/ijerph13111121Search in Google Scholar PubMed PubMed Central

[5] Hlavatý J, Ližbetin J. Innovation in rail passenger transport as a basis for the safety of public passenger transport. Transp Res Procedia. 2021;53:98–105.10.1016/j.trpro.2021.02.013Search in Google Scholar

[6] Kardas-Cinal E. Statistical analysis of dynamical quantities related to running safety and ride comfort of a railway vehicle. Sci J Sil Univ Technol Ser Transp. 2020;106:63–72.10.20858/sjsutst.2020.106.5Search in Google Scholar

[7] Koziak S, Chudzikiewicz A, Opala M, Melnik R. Virtual software testing and certification of railway vehicle from the point of view of their dynamics. Transp Res Procedia. 2019;40:729–36.10.1016/j.trpro.2019.07.103Search in Google Scholar

[8] Ližbetin J, Vejs P. Dynamic weighing to improve rail freight traffic safety: a case study from the Czech Republic. Transp Telecommun. 2022;23(3):220–6.10.2478/ttj-2022-0018Search in Google Scholar

[9] Mikhailov E, Semenov S, Shvornikova H, Gerlici J, Kovtanets M, Dižo J, et al. A Study of improving running safety of a railway wagon with an independently rotating wheel’s flange. Symmetry. 2021;13:1955.10.3390/sym13101955Search in Google Scholar

[10] Nozhenko O, Kravchenko K, Loulová M, Hauser V. Double treaded wheelset riding regime change in strongly curved track from the derailment-safety point of view. Manuf Technol. 2018;18:303–8.10.21062/ujep/96.2018/a/1213-2489/MT/18/2/303Search in Google Scholar

[11] Andrusca M, Adam M, Dragomir A, Lunca E. Innovative integrated solution for monitoring and protection of power supply system from railway infrastructure. Sensors. 2021;21:7858.10.3390/s21237858Search in Google Scholar PubMed PubMed Central

[12] Andruşcă M, Adam M, Dragomir A, Lunca E, Seeram R, Postolache O. Condition monitoring system and faults detection for impedance bonds from railway infrastructure. Appl Sci. 2020;10:6167.10.3390/app10186167Search in Google Scholar

[13] Janas L. Experimental study on vibration and noise characteristics of steel-concrete railway bridge. Sensors. 2021;21:7964.10.3390/s21237964Search in Google Scholar PubMed PubMed Central

[14] Ngamkhanong C, Kaewunruen S, Afonso Costa B. State-of-the-art review of railway track resilience monitoring. Infrastructures. 2018;3:3.10.3390/infrastructures3010003Search in Google Scholar

[15] Cho H, Park J. Study of rail squat characteristics through analysis of train axle box acceleration frequency. Appl Sci. 2021;11:7022.10.3390/app11157022Search in Google Scholar

[16] Dižo J, Blatnický M, Steišunas S, Falendysh A. Investigation of ride properties of a rail vehicle with wheel defects. Transport Means - Proceedings of the International Conference; 2018, 2018-October. p. 104–9.Search in Google Scholar

[17] Hu X, Dong K, Zheng P, Sun Z. Failure case analysis of fastening bolts for trolley rail of quay crane. Eng Fail Anal. 2023;144:106984.10.1016/j.engfailanal.2022.106984Search in Google Scholar

[18] Kanis J, Zitrický V. Automatic detection of track length defects. LOGI - Sci J Transp Logist. 2022;13(1):13–24.10.2478/logi-2022-0002Search in Google Scholar

[19] Kishore M, Park J, Song S, Kim H, Kwon SG. Characterization of defects on rail surface using eddy current technique. J Mech Sci Technol. 2019;33:4209–15.10.1007/s12206-019-0816-xSearch in Google Scholar

[20] Loulová M, Suchánek A, Harušinec J, Strážovec P. Analysis of a railway vehicle with unevenness on wheel. Manuf Technol. 2018;18:266–72.10.21062/ujep/89.2018/a/1213-2489/MT/18/2/266Search in Google Scholar

[21] Opala M, Korzeb J, Koziak S, Melnik R. Evaluation of stress and fatigue of a rail vehicle suspension component. Energies. 2021;14:3410.10.3390/en14123410Search in Google Scholar

[22] Šťastniak P, Smetanka L, Drozdziel P. Computer aided simulation analysis for wear investigation of railway wheel running surface. Diagnostyka. 2019;20:63–8.10.29354/diag/111569Search in Google Scholar

[23] Papadimitriou E, Schneider C, Aguinaga Tello J, Damen W, Vrouenraets ML, ten Broeke A. Transport safety and human factors in the era of automation: What can transport modes learn from each other. Accid Anal Prev. 2020;144:105656.10.1016/j.aap.2020.105656Search in Google Scholar PubMed

[24] Shepherd A, Marshall E. Timeliness and task specification in designing for human factors in railway operations. Appl Erg. 2005;36(6):719–27. 10.1016/j.apergo.2005.05.005.Search in Google Scholar PubMed

[25] Shipunova O, Berezovskaya I, Efremenko O. Transport risk factors and personal potential safe behavior of the railway operator. Transp Res Procedia. 2022;63:1163–70. 10.1016/j.trpro.2022.06.120.Search in Google Scholar

[26] Bulková Z, Gašparík J, Mašek J, Zitrický V. Analytical procedures for the evaluation of infrastructural measures for increasing the capacity of railway lines. Sustainability. 2022;14:14430.10.3390/su142114430Search in Google Scholar

[27] Dedík M, Mašek J, Gašparík J, Ľupták V. Assessment of the perspective ratios in rail crossings as an important evaluation factor of rail crossings. Appl Sci. 2022;12:7489.10.3390/app12157489Search in Google Scholar

[28] Fedorko G, Molnar V, Blaho P, Gasparik J, Zitricky V. Failure analysis of cyclic damage to a railway rail – A case study. Eng Fail Anal. 2020;116:104732.10.1016/j.engfailanal.2020.104732Search in Google Scholar

[29] Chudzikiewicz A, Bogacz R, Kostrzewski M, Konowrocki R. Condition monitoring of railway track systems by using acceleration signals on wheelset axle-boxes. Transport. 2018;33:555–66.10.3846/16484142.2017.1342101Search in Google Scholar

[30] Saga M, Jakubovicova J. Simulation of vertical vehicle non-stationary random vibrations considering various speeds. Sci J Sil Univ Technol Ser Transp. 2014;84:113–8.Search in Google Scholar

[31] Turabimana P, Nkundineza C. Development of an onboard measurement system for railway vehicle wheel flange wear. Sensors. 2020;20:303.10.3390/s20010303Search in Google Scholar PubMed PubMed Central

[32] Deng CX, Zhou JS, Thompson D, Gong D, Sun WJ, Sun Y. Analysis of the consistency of the Sperling index for rail vehicles based on different algorithms. Veh Syst Dyn. 2021;59:313–30.10.1080/00423114.2019.1677923Search in Google Scholar

[33] Dižo J, Blatnický M, Harušinec J, Suchánek A. Assessment of dynamics of a rail vehicle in terms of running properties while moving on a real track model. Symmetry. 2022;14:536.10.3390/sym14030536Search in Google Scholar

[34] Muñoz S, Aceituno JF, Urda P, Escalona JL. Multibody model of railway vehicles with weakly coupled vertical and lateral dynamics. Mech Syst Signal Process. 2019;115:570–92.10.1016/j.ymssp.2018.06.019Search in Google Scholar

[35] Pavlik A, Gerlici J, Lack T, Hauser V, Šťastniak P. Prediction of the rail-wheel contact wear of an innovative bogie by simulation analysis. Transp Res Procedia. 2019;40:855–60.10.1016/j.trpro.2019.07.120Search in Google Scholar

[36] Wu Y, Zeng J, Qu S, Shi HL, Wang QS, Wei L. Low-frequency carbody sway modelling based on low wheel-rail contact conicity analysis. Shock Vib. 2020;2020:71049.10.1155/2020/6671049Search in Google Scholar

[37] Yu YW, Zhao LL, Zhou CC. A new vertical dynamic model for railway vehicle with passenger-train-track coupling vibration. Proc Inst Mech Eng Part K-J Multi-Body Dyn. 2020;234:134–46.10.1177/1464419319879790Search in Google Scholar

[38] Ivaskovska N, Mihailovs F. Reliability and profitability of rail fastenings. Procedia Comput Sci. 2019;149:349–54.10.1016/j.procs.2019.01.147Search in Google Scholar

[39] Sung D, Chang S. Nonlinear behavior of rail fastening system on slab track at railway bridge ends: FEA and experimental study. Eng Struct. 2019;195:84–95.10.1016/j.engstruct.2019.05.098Search in Google Scholar

[40] Zhang N, Fu C, Jiang B, Sun L, Liu Y. Failure analysis of fatigue fracture for 60Si2Mn steel fastening clip in the track of high-speed railway. Eng Fail Anal. 2022;142:106757. 10.1016/j.engfailanal.2022.106757.Search in Google Scholar

[41] Zhang P, Li S, Núñez A, Li Z. Vibration modes and wave propagation of the rail under fastening constraint. Mech Syst Signal Process. 2021;160:107933.10.1016/j.ymssp.2021.107933Search in Google Scholar

[42] Hřebíček Z, Lupták V, Stopková M. Determining lateral resistance of sleeper in railway ballast. MATEC Web Conf. 2018;235:00007.10.1051/matecconf/201823500007Search in Google Scholar

[43] Bednarek W. The analysis of chosen imperfections of rail subgrade on rail deflection of CWR track. Arch Inst Civ Eng. 2017;25:19–34.10.35117/A_ENG_16_11_05Search in Google Scholar

[44] Li ZF, Sun JG. Maintenance and cause of unsupported sleeper. Chin Railw Build. 1992;2:15–7.Search in Google Scholar

[45] Shi J, Chan AH, Burrow MPN. Influence of unsupported sleepers on the dynamic response of a heavy haul railway embankment. Proc IMechE Part F: J Rail Rapid Transit. 2013;227(6):657–67.10.1177/0954409713495016Search in Google Scholar

[46] Dusza M. Rail vehicle model dynamics of motion along straight track with vertical irregularity. Railw Probl. 2018;181:91–7.10.36137/1812eSearch in Google Scholar

[47] Solkowski J, Jamka M. Deformation of the surface and substructure at bridge object-tests and diagnostics. Transport Overv. 2016;4:46–60.10.35117/A_ENG_16_04_06Search in Google Scholar

[48] Molatefi H, Hecht M, Kadivar MH. Critical speed and limit cycles in the empty Y25-freight wagon. Proc Inst Mech Eng, Part F: J Rail Rapid Transit. 2006;220(4):347–59. 10.1243/09544097JRRT67 Search in Google Scholar

[49] Jendel T. Dynamic analysis of a freight wagon with modified Y25. bogies. TRITA-FKT report 1997:48, Royal Institute of Technology, Department of Vehicle Engineering, Railway Technology. Stockholm; 1997.Search in Google Scholar

[50] Kisilowski J. Dynamika układu mechanicznego pojazd szynowy-tor. Warszawa: PWN; 1991.Search in Google Scholar

[51] Kalker JJ. Three-dimensional elastic bodies in rolling contact. Dordrecht/Boston/London: Kluwer Academic; 1990.10.1007/978-94-015-7889-9Search in Google Scholar

[52] UIC 526-1 Card. Wagons - Buffers with a stroke of 105 mm.Search in Google Scholar

[53] Seńko J. Metodyka badań obciążeń pociągu towarowego wyposażonego w zderzaki z dodatkowym segmentem rozpraszającym energię. Rozprawa doktorska, Politechnika Warszawska, Wydział SiMR. Warszawa; 2007.Search in Google Scholar

[54] VI-Rail 15.0 Documentation. VI-grade engineering software & services, 2013.Search in Google Scholar

[55] Iwnicki SD. The Manchester benchmarks for rail vehicle simulation. Suppl Veh Syst Dyn. 1998;30:295–313.10.1080/00423119808969454Search in Google Scholar

[56] Kik W, Piotrowski J. A fast approximate method to calculate normal load at contact between wheel and rail and creep forces during rolling. Proc. 2nd Mini Conference on Contact Mechanics. TU Budapest: Ed. I. Zobory; 1996.Search in Google Scholar

[57] European Document EN 14363:2016. Railway applications - Testing and Simulation for the acceptance of running characteristics of railway vehicles - Running Behaviour and stationary tests.Search in Google Scholar

[58] Elkins JA, Carter A. Testing and analysis techniques for safety assessment of rail vehicles. Veh Syst Dyn. 1993;2:185–208.10.1080/00423119308969026Search in Google Scholar

[59] Droździel J, Sowiński B, Szulczyk A. Equivalent track stiffness determination. Int Virtual J Sci, Tech Innov Ind. 2011;4(1):16–8.Search in Google Scholar

[60] Dyniewicz B, Bajer C, Matej J. Mass splitting of train wheels in the numerical analysis of high speed train–track interactions. Veh Syst Dyn. 2015;53:51–67.10.1080/00423114.2014.982659Search in Google Scholar

[61] Zhang SG, Xiao XB, Wen ZF, Jin XS. Effect of unsupported sleepers on wheel/rail normal load. Soil Dyn Earthquake Eng. 2008;28:662–73.10.1016/j.soildyn.2007.08.006Search in Google Scholar

[62] Medwid M, Stawecki W, Czerwiński J, Cichy R. Bimodal transport system adopted to traffic „S” and „SS”. Rail Veh. 2011;4:23–8.10.53502/RAIL-139535Search in Google Scholar

[63] Kaczor G, Szkoda M, Machno M. Hazard and risk analysis of railway vehicle control systems according to safety integrity levels. Transp Probl. 2023;18(1):179–92.10.20858/tp.2023.18.1.15Search in Google Scholar

Received: 2023-07-11

Revised: 2023-10-17

Accepted: 2023-10-30

Published Online: 2024-03-30

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2022-0544

Keywords for this article

transport safety; transition curve; unsupported sleepers; wheel flange climb derailment

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