321
1 INTRODUCTION
The development of foreign economic relations
between European countries necessitates reforming
the transport sector. One of the most promising
solutions in this direction is the creation of combined
transport systems. In countries that have access to
international traffic through sea areas, rail-ferry
transportation has been developed. A feature of such
transportation is the ability to move wagons by sea on
ships specially equipped for this - railway ferries [17].
At the same time, there is a trend towards an increase
in the transportation volume of liquid cargo by rail
ferries. Transportation of such goods is carried out
mainly in tank wagons (Figure 1). The stochastic
process of container loading is described in [24] with
special emphasis to ship motion when she is lying at a
quay.
To ensure the stability of tank wagons relative to
the decks, they are fastened using a complex of multi-
turn means: chain ties with lanyards, stop-jacks and
brake pads. To keep the tank wagons from moving in
the longitudinal direction, the wagons that are
extreme in the connections are connected to dead-end
stops.
It is important to note that the carrying structures
of tank wagons do not provide for special elements
that are designed to be fixed relative to the decks of
railway ferries. Therefore, when transporting tank
wagons by sea, their interaction with the fixing means
is carried out for any component of the structure. This
situation leads to damage to the carrying structures of
tank wagons during their transportation by sea and
the need for unscheduled repairs. Besides, the
disruption of the tank wagon's stability on decks can
contribute to the disruption of the railway ferry
stability and its overturning.
In this regard, it is important to conduct research
on the dynamic loading and strength of the carrying
structures of tank wagons during transportation on
Determination of the Loading of the Carrying Structure
of a Tank Wagon During Transportation by a Railway
Ferry
O. Fomin
1
, G. Vatulia
2
, A. Lovska
2
, J. Gerlici
3
& K. Kravchenko
3
1
State University of Infrastructure and Technologies, Kyiv, Ukraine
2
Ukrainian State University оf Railway Transport, Kharkiv, Ukraine
3
University of Zilina, Zilina, Slovak Republic
ABSTRACT: A study of the dynamic loading of the carrying structure of a tank wagon during transportation on
a railway ferry was carried out. The studies were carried out with the angular displacements of the railway
ferry around the longitudinal axis (lurch), as the case of the highest load on the carrying structure of the tank
wagon. It was found that the acceleration total value that acts on the outermost tank wagon from the bulwark is
0.31g. The resulting value of acceleration, as a component of the dynamic load, was taken into account when
calculating the strength of the carrying structure of the tank wagon, taking into account the typical scheme of
interaction with chain ties. The research carried out will contribute to the creation of recommendations for the
safe operation of tank wagons in international rail and water traffic and increasing the efficiency of rail
transport functioning.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 15
Number 2
June 2021
DOI: 10.12716/1001.15.02.07
322
rail ferries and to create measures to ensure the safety
of their transportation.
At the present stage of development of the railway
industry it is necessary at the stage of designing cars
to implement new innovative solutions for their
design [5, 6, 28]. The results of determining the
maximum equivalent stresses and deformations in the
tank wagon boiler taking into account different levels
of its workload are given in [29]. Recommendations
for improving the boiler strength characteristics were
formed.
a)
b)
Figure 1. Transportation of tank wagons on railway ferries
a) the approach of a rail ferry loaded with tank wagons to
the ramp;
b) securing tank wagons on the deck
Improvement of the carrying device design of the
tank car for the transportation of liquid cargo is given
in [30]. The strength calculation was conducted by the
finite element method, implemented in LIRA
software.
However, the strength calculations did not take
into account the loads that can act on the carrying
structure of the tank wagon during transportation on
a railway ferry.
Determination of the dynamic loading of the
carrying structure of a tank wagon during shunting
operations is presented in [1]. When compiling a
mathematical model, the compliance of the liquid
cargo in the boiler of the tank wagon was taken into
account. The critical speeds of the tank wagon
movement are determined.
The study of the tank wagon dynamics taking into
account the liquid cargo movements in the boiler
under operating conditions is given in [26]. A
mathematical model has been formed that allows one
to determine the effect of tank ullage with a liquid
cargo on its dynamic loading.
It is important to say that no attention was paid to
the study of the dynamic loading of the carrying
structure of the tank car during transportation by a
railway ferry.
The development of a calculation and
experimental methodology for predicting the reliable
operation of freight rolling stock is covered in [33].
The studies were carried out concerning the tank
wagon, taking into account the residual operating
time.
The work [7] is devoted to the definition of the
main aspects of safety in the transportation of liquid
cargo by rail. The presented results of modelling the
emissions of dangerous goods from railway tank
wagons.
However, these works did not take into account
the issues of transportation of tank wagons on railway
ferries by sea.
The study of the dynamic loading and stability of
flat wagons loaded with tank wagon under operating
conditions of loading is carried out in [12, 14].
Proposed measures to reduce the dynamic loading of
flat wagons in operation. At the same time, no
attention was paid to the issue of the dynamic loading
of tank wagons in these works.
The purpose of the article is to determine the
dynamic loading and strength of the carrying
structure of a tank wagon during transportation on
the rail ferry. To achieve this goal, the following tasks
have been identified:
− to determine the dynamic loading of the carrying
structure of a tank wagon during transportation on
a rail ferry;
− to determine the strength of the carrying structure
of a tank wagon during transportation on a rail
ferry.
2 DETERMINATION OF THE DYNAMIC
LOADING OF THE CARRYING STRUCTURE OF
A TANK WAGON DURING TRANSPORTATION
ON A RAIL FERRY
To determine the dynamic loading of a tank wagon
during transportation by railway ferry, a
mathematical model was created (1). At the same
time, the absence of the tank wagon movements
relative to the deck during ferry oscillations is taken
into account, that is, the case when only liquid cargo
is involved in the oscillation process, the movement of
which is limited by the walls of the boiler. The
angular displacements of the railway ferry relative to
the longitudinal axis (lurch) are taken into account.
The design diagram of the carrying structure of the
tank wagon located on the railway ferry deck is
shown in Figure 2.
In this case, the mathematical model of the
dynamic loading of the tank wagon has the form:
323
( )
( )
22
11 1
2 1 2
4 Λ Λ ,
12 2 2 2
0,
g
ij ij ij ij ij ij
D B h B
B z p F t
g
I m c l g m l
+ + = +
− + =
(1)
where θ1, θ2 – generalized coordinates corresponding,
respectively, to the angular displacement of the
railway ferry and liquid cargo in the tank wagon
boiler around the longitudinal axis passing through
the centre of mass of the railway ferry. The coordinate
system origin is located at the centre of mass of the
railway ferry.
Figure 2. Design diagram of the carrying structure of the
tank wagon located on the railway ferry deck
For the railway ferry: D - weight of displaced
water; B - width; h - board height; Λθ is the coefficient
of resistance to vibrations; zg - coordinate of the
gravity centre; p´- wind load; F(t) - law of the force
action that excites the movement of the railway ferry
with the wagons placed on its decks.
For the tank wagon: Iij - moment of inertia of the
pendulum; mij - the pendulum mass in the tank wagon
boiler; cij - the distance from the plane zi=0 to the
fixation point of the pendulum in the tank wagon
boiler; lij - the pendulum length; Iθ - the reduced
moment of inertia of the liquid tank wagon boiler,
does not participate in the movement relative to the
boiler; zci - the centre height of tank wagon gravity; mi
- body weight equivalent to the tank wagon boiler of a
part of the liquid cargo does not participate in the
movement relative to the boiler.
It is important to say that in the previous studies of
the article authors, no attention was paid to the
transportation of tank wagons by sea. At the same
time, the issue of transportation of open wagons,
covered wagons, platform wagons and tank
containers by ferry was considered. In addition, this
model takes into account the rigid fastening of the
tank wagon on the deck, i.e. the liquid cargo takes
part in the oscillatory process, and the tank wagon is
considered as an “item of cargo”. This assumption
also distinguishes this study from previous ones.
Since the tank wagon weight is much lower (more
than 600 times) than the rail ferry weight, the system
of equations (1) did not take into account the effect of
the liquid cargo movements in the cistern on the rail
ferry movements. At the same time, it is taken into
account that tank wagons located on the deck have the
same loading with liquid cargo. In view of this, the
accelerations that act on tank wagons located on the
same ferry rail track will have the same values. In this
connection, the research is carried out to determine
the acceleration of one tank wagon during
transportation on a rail ferry.
The determination of the resistance coefficient to
vibrations of a railway ferry was conducted according
to the methodology given in [2].
When determining the accelerations acting on the
tank wagon, the heading angles of the wave
concerning the railway ferry body were taken into
account [4].
cos ,kL
=
(2)
where kλ - coefficient depending on the shape of the
ship lines; L - length of the ship; α - the angle of the
wave to the ship body.
When compiling the model, the shock effect of sea
waves was not taken into account. The wave motion
was described in the form of a trochoidal law [20].
( )
( )
sin ,
cos .
kb
kb
x a Re ka t
z b Re ka t
= + +
= − +
(3)
where a and b - the horizontal and vertical coordinates
of the trajectory centre on which the particle currently
has the coordinates x and z rotates; R - the trajectory
radius along which the particle is rotated; ω - sea
wave frequency; k - the trajectory frequency of
exciting force.
The movement of the liquid cargo in the boiler is
described in accordance with [3]. The determination
of the hydrodynamic characteristics of the liquid
cargo was conducted according to the method
described in [18]. Gasoline is accepted as liquid cargo.
The calculations take into account the case of the
maximum allowable load of the tank wagon boiler
with liquid cargo per [25].
The solution of the mathematical model was
conducted in the MathCad software package by the
Runge-Kutta method [10, 11, 15, 19].
The input parameters of the mathematical model
are the technical characteristics of the railway ferry,
liquid cargo, as well as hydrometeorological
characteristics of the cruising areas. The initial
displacement and velocity are taken equal to zero.
The results of the calculations are shown in
Figure 3.
The total amount of acceleration acting on the
carrying structure of the tank wagon also takes into
account the horizontal component of the gravitational
acceleration. Taking this into account, the total
acceleration that acts on the tank wagon, which is
outermost from the bulwark, was 0.31g. The resulting
value of acceleration does not exceed the normative
one acting on the carrying structure of the wagon
when moving on the main track with "satisfactory
running" [8, 16].
324
Figure 3. Acceleration acting on the outermost tank wagon
from the bulwark
3 DETERMINATION OF THE STRENGTH OF
CARRYING STRUCTURE OF THE TANK
WAGON DURING TRANSPORTATION BY
RAILWAY FERRY
To determine the strength indicators of the carrying
structure of a tank wagon during transportation on
the railway ferry, model 15-1443 was chosen as the
base (Figure 4).
Figure 4. Tank wagon model 15-1443
The spatial model of the carrying structure of the
tank wagon was created in the SolidWorks software
package (Figure 5). Strength analysis was conducted
using the finite element method in the SolidWorks
Simulation software package [13, 31, 32].
Figure 5. The carrying structure of the tank wagon
The finite element model of the carrying structure
of the tank wagon is shown in Figure 6. When
constructing a finite element model, isoparametric
tetrahedrons were used. The optimal number of grid
elements was determined using the graphical-
analytical method [20-23]. The number of grid
elements was 778286, nodes - 253823. The maximum
size of a grid element is 40.0 mm, the minimum is 8.0
mm, the maximum side ratio of elements is 105.21, the
percentage of elements with a side ratio of less than
three is 18.4, and more than ten is 0.371. The
minimum number of elements in the circle - 9, the
ratio of increasing the element size - 1.7.
Figure 6. Finite-element model of the carrying structure of a
tank wagon
The value of pressure on the inner surface of the
boiler was determined based on the hydrostatic
dependence [27]:
,
s ekv
p p h
= +
, (4)
where ps - saturated steam pressure; ρ - density of
liquid cargo; αeqv - equivalent acceleration of liquid
cargo; h - the distance from the point located on the
inner surface of the tank wagon boiler to the free
surface plane.
One of the most unfavourable cases of fixing the
tank wagon relative to the deck, recorded during field
research, is taken into account (Figure 7). In this case,
two chain ties were attached to the towing bracket.
Figure 7. The scheme of fixing the tank wagon relative to
the railway ferry deck
Figure 8 shows a diagram of the application of
loads to the carrying structure of the tank wagon
during transportation on a railway ferry. It is taken
into account that the carrying structure is affected by
the vertical loading Рv, the side loading Рw (wind), the
325
liquid cargo pressure on the boiler Рр, as well as the
loading from the chain ties Рt. Due to the spatial
arrangement of chain ties, the load that will be
transmitted through them to the carrying structure
was decomposed into components taking into account
the placement of the ties in space [4]. The calculated
values of the loads acting on the carrying structure of
the tank wagon during transportation on the railway
ferry are given in table 1.
Figure 8. Calculated scheme of the carrying structure of the
tank wagon with angular displacements around the
longitudinal axis
Table 1. Loads acting on the carrying structure of the tank
wagon during transportation by railway ferry
_______________________________________________
Forces acting Vertical loading, kN py = 137.2
on the wagon pz = 634.7
body Side loading (wind) 74.57
Liquid cargo pressure, kPa 190
Loading from the chain ties, 54
kN
_______________________________________________
Components of Dynamic loading, kN XY px = 17.15
the load acting py = 29.7
on the wagon YZ py = 17.15
body from pz = 19.7
chain ties XZ px =17.15
pz = 29.7
Wind loading, kN XY px = 9.32
py = 16.14
YZ py = 9.32
pz = 16.14
XZ px =9.32
pz = 16.14
Forces from tension XY px = 27
of chain ties, kN py = 47
YZ py = 27
pz = 47
XZ px =27
pz = 27
_______________________________________________
The calculation results showed that the maximum
equivalent stresses in the carrying structure of the
tank wagon are about 480 MPa (Figures 9, 10). The
maximum displacements occur in the area of the
loading hatch and are 5.4 mm (Figure 11). The
maximum deformations were 3.8 · 10
-2
.
The obtained values of the maximum equivalent
stresses exceed the allowable for a given grade of steel
metal structures of the tank car [8, 9, 16]. That is, a
typical fixing scheme for a tank wagon does not
contribute to ensuring the strength of the carrying
structure during transportation on a railway ferry and
endanger the safety of its movement by sea.
This necessitates the creation of measures to adapt
the carrying structures of tank wagons to reliable
interaction with the means of fixing rail ferries to
ensure the safety of their transportation by sea.
Figure 9. Stress state of the carrying structure of a tank car
during angular displacements relative to the longitudinal
axis
Figure 10. Maximum equivalent stresses acting in the
towing bracket
Figure 11. Displacement in the units of the carrying
structure of the tank wagon during angular displacements
relative to the longitudinal axis
4 CONCLUSIONS
1. The dynamic loading of the carrying structure of a
tank wagon during transportation on a railway
ferry has been determined. In this case, the angular
displacements of the railway ferry relative to the
longitudinal axis are taken into account, as in the
case of the highest loading of the carrying structure
of the tank car. It was found that the total value of
acceleration that acts on the outermost tank wagon
from the bulwark is 0.31g. The obtained value of
acceleration does not exceed the normative one
acting on the carrying structure of the wagon when
moving on the main track with "satisfactory
running".
2. The strength of the carrying structure of a tank
wagon during transportation on a railway ferry
has been determined. The calculation is
implemented using the finite element method in
326
the SolidWorks Simulation software package. The
maximum equivalent stresses in the carrying
structure of the tank wagon are about 480 MPa and
are fixed in the towing bracket. The maximum
displacements occur in the area of the loading
hatch and are 5.4 mm. The maximum deformation
was 3.8 · 10
-2
. The obtained stresses exceed the
permissible values for the caused steel grade of the
metal structure of the tank wagon. This makes it
necessary to improve the carrying structure of the
tank wagon for reliable interaction with the means
of fixing railway ferries.
The conducted research will contribute to the
creation of recommendations for the safe operation of
tank wagons in the international rail-water service
and increase the efficiency of railway transport.
ACKNOWLEDGEMENTS
These studies were carried out within the framework of the
scientific theme of young scientists "Innovative foundations
for the creation of resource-saving wagon constructions by
taking into account the refined dynamic loads and
functional adaptive flash concepts", which is performed at
the expense of the state budget of Ukraine from 2020.
This research was supported by the Slovak Research and
Development Agency of the Ministry of Education, Science,
Research and Sport of the Slovak Republic in Educational
Grant Agency of the Ministry of Education of the Slovak
Republic in the project No. VEGA 1/0558/18: Research of the
interaction of a braked railway wheelset and track in
simulated operational conditions of a vehicle running in a
track on the test bench.
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