683
1 INTRODUCTION
The increase in the volume of freight transportation
through international transport corridors has resulted
in the development of combined transport systems.
The possibility for European states of entering
international transportation through the waters of the
Black, Azov, Mediterranean, and Baltic Seas has led to
the emergence and successful operation of train ferry
transportation (Figure 1).
The loading of wagons on the train ferry is carried
out by rolling them through the ramp to the deck
(Figure 2).
For the safe rolling of wagons on the deck, it is im-
portant to minimize the gap in the contact areas be-
tween the bridge and the ferry deck. However,
techno-logically it is quite difficult to ensure the
complete ab-sence of such a gap. In this regard, when
passing this area, there may be a load of the structure,
which can lead to the derailment of the wagon.
2 ANALYSIS OF RECENT RESEARCH AND
PUBLICATIONS
The study of dynamic loads on the wagon bodies
during transportation by train ferries is carried out in
[1]. A mathematical model for determining the
dynamic loads on the wagon body in the conditions of
the main types of oscillations of the train ferry is
given. The obtained results of theoretical research
were verified by computer simulation of oscillations
for the train ferry loaded with wagons. The studies
made it possible to obtain refined values of
Determination Of The Loading On The Open Wagon
Body When Rolling On The Train Ferry
J. Gerlici
1
, G. Vatulia
2
, A. Lovska
1,3
, O. Kravchenko
1,4
, J. Harušinec
1
& A. Suchánek
1
1
University of Zilina, Zilina, Slovak Republic
2
O.M. Beketov National University of Urban Economy, Kharkiv, Ukraine
3
Ukrainian State University оf Railway Transport, Kharkiv, Ukraine
4
Zhytomyr Polytechnic State University, Zhytomyr, Ukraine
ABSTRACT: The higher efficiency of international transportation necessitates the introduction of combined
transport systems. One of the most successful among these is train ferry transportation. And in order to provide
safe transportation of wagons by sea, it is important to formulate the operational requirements for railway-sea
transportation. And one of the loading modes for wagons is rolling on the train ferry.
The article presents the results of determining the dynamic load of the open wagon body when rolling on the
train ferry. The calculation was made for the open wagon placed on 18-100 bogies. A mathematical model was
formed, which made it possible to determine the main dynamic indicators that characterize the movement of
the wagon. The results of the calculations were used to determine the permissible inequality amplitude in the
zone of interaction between the rail tracks of the bridge and the ferry deck so that the indicators of the car
dynamics would be within the permissible values. The permissible value of the inequality amplitude was 0.021
m. The conducted studies will contribute to the database of developments on ensuring the operational safety of
wagons used for international railway-sea transportation.
http://www.transnav.eu
the
International Journal
on Marine Navigation
and Safety of Sea
Transportation
Volume 18
Number 3
September 2024
DOI: 10.12716/1001.18.03.2
3
684
accelerations on the wagon bodies during
transportation by train ferries.
a)
b)
Figure 1. Train ferries with wagons on board
a) Greifswald;
b) Heroes of Sevastopol
An assessment of the external forces acting on the
wagons during transportation by the train ferry is
given in [2]. The accelerations acting on the wagon
bodies in the conditions of the sea wave are
determined on the basis of the calculation of the trail
ferry rolling with six degrees of freedom at irregular
three-dimensional rough sea and movement at a
speed of 6.5 knots.
It is important to note that the studies pay no
attention to the dynamic loads acting on the wagon
bodies when loading on the train ferry, namely when
the wagon passes over the zone of interaction
between the ramp and train ferry.
The methodology for determining the dynamic
loads acting on the wagon bodies during
transportation by train ferry is given in [3]. At the
same time, the accelerations acting on the wagon were
determined by differentiating the law of motion of the
sea wave. The calculations are made for the train ferry
Soviet Azerbaijan, which connected Azerbaijan with
Dagestan and Turkmenistan (Baku with
Makhachkala, Baku with Turkmenbashy). It should be
noted that the study of dynamic loads acting on the
wagon when rolling on the train ferry is not carried
out.
a)
b)
Figure 2. Loading of railway vehicles on train ferry
a) Heroes of Shipka;
b) Greifswald
In publications [4, 5], the authors determine the
dynamic load and strength of the bearing structures of
wagons transported by train ferries. The solutions
proposed are aimed at adapting wagons to secure
fastening on the deck. At the same time, the authors
only focus on sea transportation of wagons. That is,
the dynamic load of wagons when loading on the ship
was not studied.
The loads acting on the wagon body when
transported by the train ferry are determined in [6]. A
technique that allows determining the pressure of
bulk cargo on the wagon walls is proposed. However,
the loading the wagon body when rolling on the train
ferry was not studied.
Documents [7, 8] shows the loads that act on a
wagon when transported on a rail ferry by sea.
Possible schemes for fixing the car on the deck are
indicated. The requirements for securing wagons are
given. However, the issues of rolling wagons onto a
ship are not considered in this publications.
Therefore, to ensure the safety of train ferry
transportation, it is necessary to study the dynamic
loads acting on the bearing structure of the wagon,
and take into account their specified values at the
design stage. Thus, studies on the determination of
the dynamic load of wagons during train ferry
transportation are quite relevant.
The objective of the research is to determine the
load of the open wagon body when rolling on the
train ferry. To achieve this objective the following
tasks were set:
685
− to conduct mathematic modelling of the dynamic
load on the open wagon body when rolling on the
train ferry; and
− to determine the permissible inequality amplitude
in the zones of interaction of the rail tracks
between the bridge and the ferry deck.
3 MATHEMATIC MODELLING OF THE
DYNAMIC LOAD ON THE OPEN WAGON
BODY WHEN ROLLING ON THE TRAIN FERRY
To study the dynamic loads acting on the wagon body
when passing over the zone of interaction between the
bridge and the train ferry, the mathematical model
given in [9-11] was used. The model describes the
oscillation process for the wagon when it passes over
an inequality; it takes into account the delay of the
disturbing effect on the structural elements of the
wagon. In this study the model has been modified
taking into account an additional degree of freedom
in the longitudinal plane. It is taken into account that
the rail track has elastic-viscous properties and the
track responds proportionally to both the deformation
and the speed of this deformation.
The design diagram of the open wagon when
passing over the zone of interaction of the rail tracks
between the ramp and the train ferry is shown in
Figure 3.
Figure 3. The design diagram of the wagon when passing
over the zone of interaction of the rail tracks between the
ramp and the train ferry
The system of nonlinear differential equations,
which describes the oscillations of the wagon when
passing the zone of interaction of the rail tracks
between the bridge and of the train ferry, has the
form:
22
1 11 3
22
,
′
⋅ + ⋅⋅ =
l
dd
M q Mh q Р
dt dt
(1)
2
1 1 1,1 1 1,3 3 1,5 5
2
12
,
δδ
⋅ + ⋅+ ⋅ + ⋅ =
=−⋅ +
FR
d
M qCqCqCq
dt
dd
F sign sign
dt dt
(2)
2
2 2 2,2 2 2,3 3 2,5 5
2
12
,
δδ
⋅ + ⋅+ ⋅+ ⋅ =
= ⋅⋅ +
FR
d
M qCqCqCq
dt
dd
F l sign sign
dt dt
(3)
2
3 11
2
,⋅=
d
M qH
dt
(4)
( )
2
3 3 3,1 1 3,2 2 3,3 3 3,3 3
2
1 11 2 1 1 2
,
δ ηη β η η
⋅ + ⋅+ ⋅ + ⋅ + ⋅ =
=⋅ + ++ +
FR
dd
M q CqC q C q B q
dt dt
d dd
F sign k
dt dt dt
(5)
2
4 12
2
,⋅=
d
M qH
dt
(6)
( )
2
4 4 4,4 4 4,4 4
2
11 2 1 1 2
,
ηη β η η
⋅ + ⋅+ ⋅ =
=− − − ⋅⋅ −
dd
M qCq B q
dt dt
dd
ka
dt dt
(7)
( )
2
5 5 5,1 1 5,2 2 5,5 5 5,5 5
2
2 13 4 1 3 4
,
δ ηη β η η
⋅ + ⋅+ ⋅ + ⋅ + ⋅ =
=⋅ + ++ +
FR
dd
M q CqC q C q B q
dt dt
d dd
F sign k
dt dt dt
(8)
( )
2
6 6 6,6 6 6,6 6
2
1 34 1 3 4
,
ηη β η η
⋅ + ⋅+ ⋅ =
=−⋅⋅ − − ⋅⋅ −
dd
M qCq B q
dt dt
dd
ka a
dt dt
(9)
where М
1, М2 – the mass and the moment of inertial of
the wagon body; М
3, М4 – the mass and the moment
of inertia of the first bogie facing the engine; М
5, М6 –
the mass and the moment of inertia of the second
bogie facing the engine; С
ij – the elasticity
characteristics of the oscillation system elements
determined by the values of the stiffness coefficients
of the springs; k
b; Bij – the dissipation function; а – the
half of the bogie base; k – the track stiffness; β – the
damping coefficient; η
i(x) – the function describing the
track inequality; δ
i – the deformation of elastic
elements of the spring suspension; F
FR – the friction
force in the spring group; Н
1, Н2 – the values of
horizontal forces applied to the centre plates of first
and second bogies; h – the height of the centre of mass
of the bearing structure of the wagon.
1 1 35
2
( ),
⋅
′
=+++
nI
M M MM
r
(10)
where n – the number of axles in the bogie; I – the
moment of inertia of the wheel set; r – the wheel
radius.
686
The study was carried out on the example of an
open wagon based on 18-100 bogies. It was assumed
that the freight was distributed evenly relative to the
horizontal plane, i.e., without a heap, and did not
move relative to the open wagon body. That is, the
own degree of freedom of the freight was not taken
into ac-count when modelling the dynamic load of the
wagon.
The differential equations were solved with the
Runge–Kutta method in MathCad [12 – 14]. The initial
displacements and speeds were taken equal to zero
[15 – 17].
The dependence of the acceleration of the wagon
body in the centre of mass on the inequality
amplitude in the interaction zone of the rails is shown
in Figure 4.
Figure 4. Dependence of the wagon body acceleration in the
centre of mass on the inequality amplitude
The results of the study made it possible to
determine the inequality amplitude in the zone of
interaction between the ramp and the train ferry,
which can ensure the permissible dynamic load of the
open wagon body in accordance with document [18].
The permissible value of the inequality amplitude is
0.021 m.
The main dynamic indicators of the open wagon,
which characterize its movement, when passing over
the interaction zone of the rail tracks between the
ramp and the train ferry at the given inequality
amplitude, are shown in Figure 5.
In this case, the coefficient of vertical dynamics is
determined as follows [9]
,=
sp
dv
b
P
k
P
(11)
where Р
sp – the force arising in the spring suspension
of the bogie; Р
b – the load force of the bogie from the
wagon body.
a)
b)
Figure 5. Indicators of dynamics of the open wagon when
passing over the zone of interaction of the rail tracks
between the ramp and the train ferry
a) acceleration at the centre of mass;
b) coefficient of vertical dynamics
To determine the force in the spring suspension,
formula [9] was used
,
δδ
= ⋅+ ⋅
sp b FR
P k F sign
(12)
where
,
δδ
– the deformation of the elastic
elements of the spring suspension and the speed of
deformation, respectively.
Thus, analysing the dependencies shown in Figure
4, it can be concluded that the maximum acceleration
value acting on the open wagon body at the given
inequality amplitude is 6.4 m/s², and the coefficient of
vertical dynamics is 0.65. These indicators of
dynamics correspond to the permissible movement of
the wagon.
4 CONCLUSIONS
1. A mathematic simulation of the dynamic load on
the open wagon body when rolling on the train
ferry is carried out. The dependences of
accelerations acting in the centre of mass of the
body on the inequality amplitude in the zone of
interaction of the rail tracks between the ramp and
the ferry deck are obtained.
2. The permissible inequality amplitude in the zone of
interaction of the rail tracks between the ramp and
the ferry deck, so that the indicators of the wagon
dynamics are within the permissible values, is
determined. The permissible value of the
inequality amplitude is 0.021 m.
The conducted study will contribute to the
database of developments on ensuring the
operational safety of wagons used in international
railway sea transportation, including the creation
of an improved loading scheme by modernizing
the transition bridge.
687
ACKNOWLEDGEMENTS
This contribution was elaborated within execution of the
projects VEGA 1/0513/22. Investigation of the properties of
railway brake components in simulated operating
conditions on a flywheel brake stand; KEGA 036ŽU-4/2021.
Implementation of modern methods of computer and
experimental analysis of the properties of vehicle
components in the education of designers of future means
of transport.
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