Article citation information:
Sakhno, V.,
Poliakov, V., Lyashuk, O., Murovanyi, I., Stelmashchuk, V., Onyschuk, V., Tson,
O., Rozhko, N. To the comparative evaluation of three-unit lorry
convoys of the different component systems by maneuverability. Scientific Journal of Silesian University of
Technology. Series Transport. 2023, 121,
189-201. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2023.121.12.
Volodymyr SAKHNO[1],
Viktor POLIAKOV[2],
Oleg LYASHUK[3],
Igor MUROVANYI[4],
Valeriy STELMASHCHUK[5],
Vasyl ONYSCHUK[6],
Oleg TSON[7],
Natalia ROZHKO[8]
TO THE COMPARATIVE EVALUATION OF THREE-UNIT LORRY CONVOYS OF THE
DIFFERENT COMPONENT SYSTEMS BY MANEUVERABILITY
Summary. The article
deals with the maneuverability of three-link road trains with various layout
schemes. If a train has more than three links, difficulties arise in that the
study of the movement of such a multi-link vehicle is significantly complicated
due to the need to take into account the influence of a significant number of
factors on the nature of the movement of all links. The interaction of
neighboring units in the movement of a train is eventually distributed to the
entire vehicle and causes certain deviations of the components of the train
(modules) from the direction of movement specified by the driving link
(tractor). Considering that a road train as a motor vehicle is a means of
increased danger, when solving problems about the possibility of operating
three- and multi-link road trains, it is one of the first to take steps towards
theoretical studies of their maneuverability, the results of which will be the
basis for answering many technical, organizational, and legal questions.
Analysis of the calculation results showed that in the established circular
path with the selected gear ratios of the control drives, none of the road
trains met the requirements of DIRECTIVE 2002/7 / EC. From this, it follows
that for three-link road trains, a fundamentally different control drive is
needed, which can be a double control drive.
Keywords: car
train, maneurability, folding angle, overall traffic band, control drive,
trajectory
1.
INTRODUCTION
Efficient and stable operation
of industry, agriculture, and the normal living conditions of the population
are ensured by a complex and extensive transport system, which includes
railway, automobile, air, sea, river, and pipeline transport. The general
purpose of all types of transport and the existing close relationship between
them allow us to consider them as a single transport system for the country.
The objective regularities and conditions of functioning of this system depend
on the influence of various socio-economic factors that change in a unique way
during the development of each individual country. A
coordinated and reliable transport system is so important for the state that it
receives special attention and is provided with state subsidies, even if
certain types of transport are materially unprofitable [1].
In order to increase the
efficiency of road transport and reduce fuel consumption and the toxicity of
exhaust gases per unit of transported cargo, since 1998, the Scandinavian
countries of Sweden and Finland have changed the requirements for the length and
total weight of juggernauts up to
The appearance of such road
trains, the useful body volume of which is about
The introduction of
long-distance road trains in countries is associated with three groups of
restrictions [4], in particular, restrictions on the geometric and
mass parameters of motor vehicles, safety requirements for the design of these
juggernauts, and the difficulties of intaking them at existing terminals and
logistics centers. UNECE Regulations No. 13
for three-link juggernauts also need further development due to the fact that
compatibility standards are established only for juggernauts with two transport
links, a tractor and a trailer (semi-trailer). In addition, with an increase in
the mass of the juggernaut, the traction-coupling devices of the tractor and
semi-trailer (trailer) will be more heavily loaded, and, of course, their
control regimes must be strengthened. This requirement will indirectly affect
the safety of the design of the rolling stock of three-link juggernauts.
Undoubtedly, it is much more
difficult for three-link juggernauts to comply with
the regulations regarding maneuverability in accordance with Directive
2002/7/EC and GOST R 52302-2004 [5, 6]
regarding the controllability and stability of the movement of motor vehicles
(MV).
If the juggernaut has more
than three links, difficulties arise in that the study of the movement of such
a multi-link MV is becoming significantly complicated due to the
need to consider the influence of a wide number of factors on the nature of the
movement of all links. The interaction of neighboring links during the movement
of the juggernaut eventually spreads to the entire
vehicle and causes certain deviations of the components of the juggernaut
(modules) from the direction of movement set by the leading link (tractor).
Taking into account the fact that the juggernaut as an MV is a recipe for
increased danger, while solving problems regarding the possibility of operating
three- and multi-link juggernauts, one of the first steps should be taken in
the direction of theoretical studies of their maneuverability and stability of
movement, the results of which will be the basis for answering many questions
of a technical, organizational, and legal nature [7].
2. MATERIALS
AND METHODS
For the
transportation of large consignments of cargo, it is advisable to use
three-link road trains of various layout schemes. In order to maximize the
compliance of road trains with specific operating conditions, the possibility
of forming high-capacity juggernauts from the existing rolling stock without significant
changes in its design is used. The modular principle of forming such MVs is
used [3]. That is, the
single system "juggernaut" can be represented as composed of two or
more subsystems, hingedly connected to each other - "tractor vehicle"
and "trailer link" = "semi-trailer", "trailer",
etc., depending on the layout scheme of the juggernaut. In the design of the
links of the juggernaut (tractor, trailer link) - complex
technical objects, it is possible to distinguish subsystems of a lower
hierarchical level: modules of undercarriages (controlled, uncontrolled),
carrier systems, cargo platforms, etc., Fig. 1,
from which a road train of a certain layout scheme is formed, Fig. 2.
Studies
of long two- and three-link road trains were carried out as early as the 60s of
the last century (in particular, in the Scandinavian countries, they became the
basis for the legislative approval of the maximum length of road trains of
As you
know, in the Scandinavian countries, road trains with a total length of
For
typical long-distance hauling, a long-distance combination can be used for most
of the mileage. Near destinations, the trailer can be detached, and the truck
can move on its own. And the semi-trailer can be transported further with
the help of a conventional semi-trailer tractor (or, if necessary, a three-axle
tractor).
Fig.
1. Components of a "modular" road train
In
addition to the use of standard bodies, trailers and semi-trailers,
"modular" transportation involves the use of containers that can be
transported by both sea and land transport. For such transport, the 25.25m
concept is the most efficient, as such a truck transports three containers
instead of the two that can be transported by a conventional road train and is
thus 30% more efficient [3,12].
Thus,
developments in the direction of the development of three-link road trains are
the main way to solve the problem of transportation both in Europe and in
Ukraine, which does not require significant capital investments and can be
implemented in the shortest possible time, provided that the issues of
maneuverability and stability of the movement of such road trains are resolved.
Maneuverability
of motor vehicles (MV) is a set of such properties that
ensure their unhindered movement on a support surface that has limitations both
in terms of area and shape [9]. Such restrictions in the movement of MV can be
spatial ones related to the length and height of the vehicle, as well as
restrictions on the shape and size of the road surface, which serves as a
support surface for the rolling of the wheels of its links.
The
curvilinear movement of the road train is characterized by such regime
parameters as the speed of movement, the turning radius and the turning angles
of the steered wheels, which do not remain constant during the operation of the
road train. Therefore, both kinematic and dynamic indicators are used to assess
the maneuverability of the MV.
Dynamic
indicators are provided by a three-axle tractor, which has a sufficient reserve
of power and is equipped with power steering.
Among the
kinematic indicators, two should be considered the main ones, namely:
-
overall traffic lane (OTL), equal to the difference between
the outer and inner overall turning radii. Also, worth considering is the
fact that the overall turning
radii are standardized (Rzg=12.5 m, Rвг=5.3 m), then the overall traffic lane will also
be standardized (Вг=7.2 m);
-
the ability to move in reverse.
The issue
the least studied today is the ability to drive a road train in reverse, which
was rarely considered theoretically for three-link road trains. The ability to
drive in reverse should be checked experimentally during the road tests of the
road train.
When
determining the OTL, the wheels of the road train are assumed to be
both rigid in the lateral direction and elastic.
For
wheels rigid in the lateral direction, the issues of maneuverability of a car
and a two-track road train were considered in detail by Y. Kh. Zakin in works [8, 9], and
for a three-track road train - by Ya. Ye. Farobin [10, 11]. In
[12, 13] a simplified analysis of the maneuverability and stability of vehicle
combinations, such as a tractor in combination with one or two semitrailers or
a truck and a full trailer, was carried out. Vehicle combinations are
considered linear dynamic systems with two degrees of freedom for each unit.
The motion equations are derived considering the effects of braking and
acceleration, and the characteristic equation for motion with constant speed is
obtained. They carried out detailed studies on the problems of
horizontal stability of road trains and their maneuverability using both
analytical and experimental methods.
We
should also not forget about the influence of tires on the vehicle's behavior [14].
Significant
studies of the maneuverability and stability of the movement of three-link
semi-trailer road trains, based on the solution of the system of differential
equations of plane-parallel motion of the road train, were conducted by
scientists [15]. Mathematical
models developed on their basis for studying the turning kinematics of a
three-link road train and a road train with a semi-trailer on a dolly on rigid
wheels in the lateral direction can also be used for a comparative analysis of
the maneuverability of three-link road trains and other layout schemes [16,
17]. It was adapted and improved on existing formulations
for the convoy movement problem, and new models and approaches were developed
to solve the GCMP more effectively [18]. Also, a robust adaptive
size-independent control protocol is designed to assure internal and string
stability in the presence of uncertain dynamics by using only relative
displacement information [19, 20]. The purpose of the work is a
comparative analysis of three-link road trains of different layout schemes
according to maneuverability indicators while they perform various turns.
3. DISCUSSION OF THE RESULTS OF
THE EXPERIMENT
The basis
of the three-link road trains that are in operation today are Scania tractors
as well as Krone trailer equipment - three-axle semi-trailers SD-27,
two-three-axle trailers with close axles ZZ-18 (ZZ-27), two-three-axle trailers
with spread axles with a front pivoting axle AZ-18 (AZ-27), two-axle
undercarriage "Dolly".
An
analysis of the layout schemes of modern three-link road trains, Fig. 2, which
are built according to the modular principle, shows that any layout scheme can
be turned into a scheme with a semi-trailer on a dolly
(hereinafter a road train). Such a train consists of a tractor, a dolly and a
three-axle semi-trailer.
The total
weight of such road trains is 60 tons, and the length exceeds 25 m. From the
point of view of kinematics, such a road train is transformed into a three-link
semi-trailer road train scheme, when the semi-trailer rests on the semi-trailer
coupling device of the tractor and the undercarriage turns into a trailer; in
the "B-double" scheme, when the dolly is transformed into a
semi-trailer; into a scheme with two trailers, when a dolly and a semi-trailer
are transformed into trailers (today such a scheme is almost not used due to
low traffic stability indicators).
To ensure
the necessary maneuverability, each element of the road train must fit into a
circle with an inner radius of 5.3 m and an outer radius of 12.5 m. Determining
the actual turning radii can be done for a road train with rigid wheels in the
lateral direction.
|
|
|
|
|
|
|
|
|
|
Fig.
2. Layout diagrams of three-link road trains
In
the works [8, 9] it is proved
that the maneuverability of vehicles at the previous stage can be determined on
wheels that are rigid in the lateral direction because of the mistake of the
overall traffic lane (OTL) calculations, which does not
exceed 10-12%. At the same time, the method of calculating the OTL is
based on the determination of the angles of assembly of the links of the road
train and the displacement of the trajectories of the driven links relative to
the trajectory of the tractor vehicle. This technique can also be used to
determine the OTL of three-link road trains with controlled trailer links.
During
one-way curvilinear movement, the road train goes through several stages [13]:
-
the stage of initial rectilinear movement (before
turning);
-
stage of entry into the turn;
-
circular rotation stage;
-
stage of exit from the turn;
-
exit of the tractor vehicle on a straight path.
For each
turning stage, the differential equations of the folding angles with unguided
trailer links were obtained, which were later used in determining the
displacement of the links' trajectories relative to the tractor and the OTL
of the road train. Analysis of the calculation results showed:
-
during a one-way turn, the trajectories of the trailing
links are shifted in relation to the trajectory of the leading link towards the
center of the turn, thereby increasing the overall traffic lane, and the
displacement of the trajectories and OTL increase with the increase in the base
of the trailing links;
-
the normalized value of the overall traffic lane under
real design parameters cannot provide a three-link road train for all the
considered layout schemes.
Fig. 3. A turning diagram
of a three-link trailer train with controlled trailers
Taking
into account the two expressions (1) mentioned above, we get [8]:
Equations
(2) and (3) after simple transformations are reduced to the form:
It can be
seen from expressions (4) and (5) that the resulting equations do not make up a
system because the first equation does not depend on the second at all. That
is, when there are no feedback links in the road train, the movement of
subsequent links does not affect the movement of previous links. Such a scheme
is very idealized, but considering that a three-link road train cannot make a
turn at high speed, in practice the differences between the calculated and
actual values are within acceptable limits [9].
Since, in
the general case, during the execution of a turn, the road train goes through
four stages (entering the turn, moving in a circle, exiting the turn, and
rectilinear movement until the return of all parameters to the initial state),
then equations (4) and (5) can be applied only for the first stage of
performing a turn.
During
movement along a circular trajectory with a radius R0MIN (if there
is such a section), the central angle jК. becomes the determining
parameter. Considering the ratio dg0 = R0MIN × Кp
× djК, as well
as the condition that g0 = const = g0МАХ we
obtain [8]:
When
exiting a turn, equations (4) and (5) are used, but since the steering wheel
rotates in the opposite direction, the KP coefficient has a negative value.
The last
stage is the rectilinear movement of the tractor until all the initial
parameters return to their initial state. Thus, at this stage, the angles of
assembly of the links of the road train no longer depend on the position of the
steered wheels, but only on the path taken by the tractor. At the same time,
g0 = 0.
So we
get:
The
integration of the folding angle equations for the considered road trains was
performed using Mathcad software. The transmission ratio of the direct drive of
the control of the trailer links was determined under the condition that the
main points of the undercarriage and the semi-trailer move along the trajectory
of the main point of the tractor vehicle [9, 15]. Fig. 4
shows the results of the calculation of the angles of assembly of the links of
road trains of various layout schemes, provided that the main points of the
trailer (roller) and semi-trailer move along the trajectory of the main point
of the tractor. The numbers indicate the following variants of road trains: No. 1: road train
with steered front axles of the car and a dolly and a steered rear axle of the
semi-trailer; No. 2: a road train with a steerable front axle of a car and a
steerable front axle of a semi-trailer; No. 3: a road train with a controlled
front axle of the car and controlled two extreme axles of the semi-trailer; No.
4: a road train with a steerable front axle of the car and a steerable rear
axle of the semi-trailer; No. 5: a road train with a controlled front axle of
the car and a controlled rear axle of the trolley.
The
analysis of the data, Fig. 4, shows the quite complex dependence of the angles
of assembly of the links of the road train on the angle of rotation of the
steered wheels of the front axle of the tractor. However, the rotation of the
wheels of individual links of the road train can be carried out not only by the
angle of rotation of the steered wheels of the front axle of the tractor
vehicle but also depending on the assembly angles. In Fig. 5, as
an example, the dependencies of the angles of rotation of the wheels of
individual axles of the trailer links and the transmission ratios of the
control drive to these axes depending on the assembly angles of the road train.
Trajectories
of the movement of the characteristic points of the links of the road train
were constructed based on the angles of assembly of the towing links and
transmission ratios of the control drive, and their displacement relative to
the trajectory of the main point of the tractor and the OTL of the
road trains was determined, Fig. 3-6 and Tab. 1.
Tab. 1
Dimensional traffic lane of three-link road trains of various layout
schemes
|
Types of the road train |
||||
|
No1 |
No2 |
No3 |
No4 |
No5 |
|
The gear ratio of the control drive |
||||
|
і0= 0,25;
і2= 0,60 |
і3= 0,75 |
і4= 0,32 |
і2= 0,83 |
і1= 0,74 |
|
Dimensional traffic lane with steady circular
traffic, m |
||||
|
7,38 |
7,93 |
7,41 |
7,53 |
7,83 |
Analysis
of the calculation results indicates that none of the road trains meets the
requirements of DIRECTIVE 2002/7/EC on the established circular trajectory with
the selected transmission ratios of the control drives.
4. CONCLUSIONS
The purpose of the work is a
comparative analysis of three-link road trains of various layout schemes in
terms of maneuverability while performing various turns.
Studies
proved that the maneuverability of vehicles at a preliminary stage can be
determined on wheels hard in the lateral direction since the error in
calculating the overall traffic lane does not exceed 10-12%.
It
was established that the angles of folding of the trailing links and the drive
ratios of the control drive. The trajectories of the characteristic points of
the articulated units were constructed, and their displacement relative to the
trajectory of the main point of the tractor and the OTL of the articulated
trucks were determined.
Conducted
studies of the maneuverability of road trains on wheels rigid in the lateral
direction have established that with direct drive control on the axis of the
trailer links, none of the road trains meets the requirements of DIRECTIVE
2002/7/EC. It follows that for three-link road trains, a second control drive
is fundamentally required, which can be a double control drive.
|
|
|
|
a) |
b) |
Fig. 4. Dependence
of the folding angles of the links on the angle of rotation of the front ones steered
tractor wheels for road trains of various layout schemes
|
|
|
|
a) |
b) |
Fig. 5.
Dependence of the angles of rotation of the wheels of the axles of the
undercarriage and semi-trailer on the angles' of assembly of links for road
trains of various layout schemes
Fig. 6.
Displacement of the trajectories of
the main points of the undercarriage (a) and semi-trailer (b)
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Received 09.07.2023; accepted in
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Scientific Journal of Silesian University of Technology. Series
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[1] Faculty of Automotive and Mechanical
Engineering, National Transport University, Mykhailа Omelianovycha -
Pavlenka 1 Street, 01010 Kyiv, Ukraine. Email: sakhno@ntu.edu.ua.
ORCID: https://orcid.org/0000-0002-5144-7131
[2] Faculty of Automotive and Mechanical
Engineering, National Transport University, Mykhailа Omelianovycha -
Pavlenka 1 Street, 01010 Kyiv, Ukraine. Email: poljakov_2006@ukr.net.
ORCID: https://orcid.org/0000-0001-7042-3066
[3] Faculty of Engineering of Machines, Structures
and Technologies, Ternopil Ivan Puluj National Technical University, Ruska 56
Street, 46000 Ternopil, Ukraine. Email: oleglashuk@ukr.net.
ORCID: https://orcid.org/0000-0003-4881-8568
[4] Faculty of automobiles and transport
technologies, Lutsk National Technical University, Lvivska 75 Street, 43018
Lutsk, Ukraine. Email: igor.murovanyi@lutsk-ntu.com.ua.
ORCID: http://orcid.org/0000-0002-9749-980X
[5] Faculty of automobiles and transport
technologies, Lutsk National Technical University, Lvivska 75 Street, 43018
Lutsk, Ukraine. Email: cdp@lntu.edu.ua. ORCID:
https://orcid.org/0000-0003-3813-3143
[6] Faculty of automobiles and transport
technologies, Lutsk National Technical University, Lvivska 75 Street, 43018
Lutsk, Ukraine. Email: fantom.root@gmail.com. ORCID: https://orcid.org/0000-0002-5316-408X
[7] Faculty of Engineering of Machines, Structures
and Technologies, Ternopil Ivan Puluj National Technical University, Ruska 56
Street, 46000 Ternopil, Ukraine. Email: tsonoleg@gmail.com.
ORCID: https://orcid.org/0000-0003-1056-4697
[8] Faculty of Engineering of Machines, Structures
and Technologies, Ternopil Ivan Puluj National Technical University, Ruska 56
Street, 46000 Ternopil, Ukraine. Email: rozhko18@googlemail.com.
ORCID: https://orcid.org/0000-0002-1400-9503