315
1 INTRODUCTION
The growth of liquid cargo transportation through
international transport corridors leads to the
commissioning of tank containers. The demand for
tank containers in the transportation process is due to
their mobility as vehicles and intermodality. Trade
flows should be regarded as a key driver of demand
and development for container services in seaports
[20]. In work [12] the influence of global container
market development on global logistics supply chains
has been estimated.
Recently, the efficiency of the operation of tank
containers has also been traced on railway ferry routes
as part of combined transport trains. At the same time,
the transportation of tank containers can also be
carried out on roll trailers.
It is important to note that the process of loading
the carrying structures of tank containers during
transportation by rail ferries by sea differs
significantly from the operation relative to main lines.
As a result of the action of loads that are inherent in
these operating conditions, the stability of tank
containers relative to vehicles may be disturbed. This
situation endangers safety to damage the stability of
the railway ferry and its traffic safety.
In this regard, to ensure the safety of the
navigation of tank containers by sea, it is necessary to
study their stability during oscillations of a railway
ferry.
Determination of the dynamic loading of a tank
container under operating conditions of loading was
carried out in [24]. The obtained values of dynamic
loads were taken into account when calculating the
strength of the tank container in the Ansys software
environment. However, the work does not pay
attention to the study of the dynamic loading of a tank
container during transportation on a railway ferry.
Stability Study of Tank Containers Placed on a Roll-
Trailer During Transportation by 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, Kharkov, Ukraine
3
University of Zilina, Zilina, Slovak Republic
ABSTRACT: The article presents the results of determining the dynamic load of the load-bearing structure of
the tank container placed on a roll-trailer during transportation by railway ferry. For this purpose, a
mathematical model was developed, which takes into account the dynamic loading of the tank container during
angular displacements of the railway ferry. It is taken into account that the roll trailer is rigidly fixed on the
deck, and the tank container and the liquid cargo in the boiler have their own degrees of freedom. The obtained
accelerations are taken into account when calculating the stability of the tank container on the roll trailer. Thus
the stability of the tank container is provided at lurch angles to 240. The carried-out researches will allow
increasing safety of transportations of tank-containers on railway ferries by the sea, and also the efficiency of
functioning of combined transportations in the international communication.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 15
Number 2
June 2021
DOI: 10.12716/1001.15.02.06
316
The results of determining the stress state of the
tank container are given in [1]. The work is carried out
to determine the deviations of the frame and the
boiler under operating load conditions.
The study of the strength of the T11 tank container
under operating load conditions is carried out in [18].
The paper analyses the effect of the density of a finite
element mesh on the accuracy of calculating the
stress-strain state of a tank container, and also carries
out field studies of its strength under shock loads.
It is important to say that the strength calculations
did not take into account the loads that can act on the
tank container when transported by railway ferry.
The specifics of calculating the strength of the
carrying structure of a tank container for transporting
food products are highlighted in [15]. Strength
analysis was carried out using the finite element
method [5, 15, 23]. Recommendations for the design of
tank containers of this type are given [15].
The results of optimization of the supporting
structure of the tank container are given in [21].
Improvement of the design of the tank container for
the transportation of light oil products.
However, when carrying out strength calculations,
no account was taken of the loads that may act on the
carrying structure of a tank container when
transported on a roll-trailer by a railway ferry.
The study of the dynamic loading and strength of a
tank container during transportation as part of a
combined train on a rail ferry is carried out in [9, 10].
Recommendations for the safe operation of tank
containers are given.
At the same time, no attention was paid to the
study of the dynamic loading and stability of the tank
container during transportation on a roll-trailer by rail
ferry.
The purpose of the article is to highlight the
features of the dynamic loading and stability of a tank
container placed on a roll-trailer during
transportation by a railway ferry. To achieve this goal,
the following tasks have been set:
− to determine the dynamic loading of a tank
container placed on a roll-trailer during
transportation by a rail ferry.
− to determine the stability of a tank container
placed on a roll-trailer during transportation by a
rail ferry.
2 PRESENTATION OF THE MAIN MATERIAL OF
THE ARTICLE
To determine the dynamic loading of a tank container
placed on a roll-trailer during transportation by a
railway ferry, a mathematical model was created (1),
созданная авторами статьи,which takes into account
the movement of the system "railway ferry - tank
container - liquid cargo" during angular
displacements relative to the longitudinal axis (Fig. 1).
The model takes into account that the roll-trailer,
on which the tank container is located, is rigidly fixed
to the deck of the railway ferry and moves along with
it. It is important to say that the design diagram
shown in Fig. 1 and model (1) were developed by the
authors of the article.
The calculations were carried out to the Greifswald
railway ferry moving along the Black Sea. As a
prototype, a tank container of 1СС standard size was
chosen, which is placed on a roll-trailer 6.09 m long
and with a carrying capacity of 20 tons.
Figure 1. Diagram of displacements of a tank container with
a liquid cargo during oscillations of a railway ferry
The shock effect of sea waves on the body of the
railway ferry was not taken into account. When
compiling the model, the trochoidal law of motion of
the disturbing action [17, 19] (sea wave) on the
railway ferry and the dissipative component, which
arises during oscillations of the railway ferry under
sea rolling conditions, as well as the heading angles of
the sea wave concerning the body of the railway ferry
(χ = 0 - 180 [4]) and wind load acting on its surface
projection.
( )
( )
22
2
2 3 2
1 1 1
3 2 3
4 Λ Λ ,
12 2 2 2
0,
g
k k k
i ij ij ij ij ij i ci ij ij
j j j
ij ij ij ij ij ij
D B h B
B z q q p F t
g
I m c m c l g m z m c
I m c l g m l
= = =
+ + = +
+ + − +
− + =
. (1)
where q1 = θ1, q2 = θ2, q3 = θ3 – generalized coordinates
corresponding to the angular displacement relative to
the longitudinal axis, respectively, of the railway
ferry, tank container and liquid cargo. The origin of
the coordinate system is at the centre of mass of the
rail 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;
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
317
the tank wagon boiler of a part of the liquid cargo
does not participate in the movement relative to the
boiler, Fk - moment of forces between tank container
and roll trailer.
The movement of the liquid cargo in the boiler of
the tank container is described by the oscillations of a
mathematical pendulum [2]. The determination of the
hydrodynamic characteristics of the liquid cargo was
carried out according to the methodology given in
[14]. Gasoline was adopted as a liquid cargo. The
determination of the hydrodynamic characteristics of
the liquid cargo was carried out taking into account
the maximum permissible load of the tank container
boiler - 95% of its total capacity.
The calculation of the mathematical model was
carried out in the MathCad software package [6–8,
25]. In this case, the initial displacements and speeds
are set equal to zero [11, 16, 25]. The Runge-Kutta
method [3, 13, 22] was used as a calculation method.
The total acceleration value includes the
acceleration that acts concerning the nominal position
of the tank container placed on the roll trailer, as well
as the horizontal component of the gravitational
acceleration due to the roll angle of the rail ferry. It is
taken into account that the lurch of the rail ferry is
caused by wind loads on the surface of the rail ferry.
With the value of wind pressure P = 1.47 kPa [27], the
resulting lurch angle θ = 18.80. The results obtained
by the authors of the article are shown in Fig. 2. From
the side of the ordinate axis, the heading angles of the
wave concerning the body of the railway ferry are
taken out. In this case, the acceleration values are
about 0.46g.
Figure 2. Acceleration of a tank container placed on a roll
trailer
The obtained accelerations were taken into account
when determining the stability of a tank container on
a roll-trailer during transportation by a rail ferry. The
design scheme created by the authors of the article is
shown in Fig. 3.
In this case, the equilibrium condition has the form
[10, 26]:
1,
res
c
o
M
k
M
=
(3)
where Mres - the value of the restoring torque; Mo - the
value of the overturning moment.
At the same time, the article authors have derived
analytical dependencies for determining the
overturning (4) and restoring (5) moments.
( )
2
sin ,
22
kk
o k gr
hh
M p M g
= + +
(4)
( )
( )
cos g sin ,
22
f
k
res gr f gr k
h
B
M P n M q
= + +
(5)
where Mgr is the gross mass of the tank container; Рgr -
gross weight of the tank container; Vs - the width of
the tank container; nf is the number of fitting stops on
which the tank container is supported during angular
displacements relative to the longitudinal axis; hf - the
height of the stop fittings.
Figure 3. Calculated diagram of a tank container
Based on the studies carried out, the dependence
of the stability coefficient of a tank container on a roll-
trailer on the lurch angle of a railway ferry was
obtained (Fig. 4). The stability threshold is set when
the values of the restoring and overturning moments
are equal to each other.
Figure 4. Dependence of the stability coefficient of a tank
container on a roll-trailer from the lurch angle of a railway
ferry
It was found that the stability of a tank container
on a roll-trailer, taking into account the typical scheme
318
of interaction (fitting stops - fittings), is ensured at
lurch angles up to 240.
3 CONCLUSIONS
1. The dynamic loading of a tank container placed on
a roll-trailer during transportation by a railway
ferry has been determined. For this, a
mathematical model has been created that takes
into account the movement of the railway ferry
around the longitudinal axis. It was found that in
the absence of movements of the roll-trailer
relative to the deck and the presence of movements
of the tank-container on the roll-trailer, the
maximum accelerations acting on the tank-
container are equal to 0.46g.
2. The stability of the tank container placed on a roll-
trailer during transportation by rail is determined.
It was found that the stability of a tank container
on a roll-trailer, taking into account the typical
interaction scheme, is ensured at lurch angles up to
240.
To ensure the safety of combined transport in
international traffic, it is important to clarify the
regulatory documents, which indicate the loads acting
on vehicles. At the same time, it is necessary to note
additional conditions for loading tank containers
when transported on roll trailers by rail ferries. The
results obtained can contribute to the creation of
recommendations for the design of tank containers.
ACKNOWLEDGEMENTS
This publication was issued thanks to supporting the
Cultural and Educational Grant Agency of the Ministry of
Education of the Slovak Republic in the project No. KEGA
036ŽU-4/2021: Implementation of modern methods of
computer and experimental analysis of properties of vehicle
components in the education of future vehicle designers.
The research is also supported by the state budget of
Ukraine from 2020 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.
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