*Periodicity.:*

**Special Edition PDATU-2019, May- 2019***e-ISSN......:*

**2236-269X**### INVESTIGATION OF THE
TRICYCLE TRACTOR INCLINE INFLUENCE ON ITS STABILITY UNDER THE CONDITIONS OF
WORK AT THE OF SLOPE FIELDS

*Victor Sheychenko*

*Poltava State Agrarian Academy, Ukraine*

*E-mail: victorseychenko@gmail.com*

*Gedal Hailis*

*Uman National University of Horticulture, Ukraine*

*E-mail: vsheychenko@ukr.net*

*Ihor Dudnikov*

*Poltava State Agrarian Academy, Ukraine*

*E-mail: dudnikovigor17@gmail.com*

*Pavlo Fedirko*

*State Agrarian and Engineering University in Podilya, Ukraine*

*E-mail: rmo@pdatu.edu.ua*

*Submission: 24/11/2018*

*Revision: 14/12/2018*

*Accept: 08/02/2019*

ABSTRACT

The
theoretical calculations carried out by the authors made it possible to
establish the stability conditions for a tricycle tractor on the slope of the
field. The research methodology was based on a theoretical solution of a static
problem and the establishment of stability of a tricycle tractor depending on
its layout and the angle of the field to the horizon. The layout of the
tricycle tractor, which has one steerable wheel in front and two wheels in the
rear, is considered. The conditions of the steady state of the tractor for the
selected scheme are determined. The stability of the tractor will be ensured
when the vertical line lowered down from its center of gravity crosses the
surface inside the supporting quadrilateral. The surface of the supporting
quadrilateral is formed as a result of connecting the outer points of the
wheels. The
dependence of the influence of the rim width and the wheel radius on the
maximum angle of inclination of the tractor with one front wheel is
established. The scientific problems posed in the work are solved in the
developed theoretical bases for determining the stability conditions of a
tricycle tractor. The theoretical foundations have been developed taking into
account the layout of the tractor and the angle of inclination of the field to
the horizon. The dependencies of the maximum angle of inclination of the
tractor were theoretically determined, which made it possible to establish the
conditions for its safe operation. The scientific background for increasing the
safe operating conditions of tricycle tractors has been further developed.

**Keywords**: stability
of a tricycle tractor, tractor weight, slope angle, slope angle of the tractor,
conditions of stable balance of a tricycle tractor

**1. ****INTRODUCTION**

As it
is known, the stability of any object on the reference plane will be ensured if
the object is located on at least three supports that are not in a straight
line (HAILIS et al, 2017) Taking into account
the above, if you consider the machine's stability on two wheels (for example,
a drill-machine), then this machine must have one more (the third) support.
This support may be a tractor hitch component to which the machine is attached.
For such a machine, it is important that if operated it does not slide along
the sloping plane of the field towards its slope and does not bowl over to the
same side (PRYSHLIAK, 2010).

**1.1.
****Analysis
of recent studies and publications**

The
work of tractors and agricultural machines depends on their design, the size of
the fields where they operate, and the incline of these fields. In this regard,
it is important to investigate the effect of the field slope angle to the
horizon on the tractor stability during operation (KYRYIENKO et al., 2010).

The paper (USENKO, 2014) presents the results of a study
of the stability of a four-wheel tractor, which is located on a field with a
slope in either direction. The conditions of non-displacement of the front and
rear wheels of the tractor in the direction of the slope have been established.
According to these conditions it is necessary that the sum of the maximum
frictional forces of both resting pairs of tractor wheels on the ground was
greater than the force of the weight that falls on the axle.

The
theoretical substantiation of the condition of transverse stability of a
combine harvester during operation on slopes is given in (SMOLINSKYI, 2013).
According to the results of the research, the analysis of the position of the
static and dynamic stability of the combine on transverse slopes has been
carried out and the stability conditions for combines have been established
both with and without the frame leveling system. The obtained dependencies are
recommended to be used in the design of self-propelled bunker combine
harvesters in order to determine its parameters under steady state conditions
on the slopes.

The paper (MAKHAROBLIDZE et
al, 2017) calculating formula for lateral displacement of the tractor on the; down-hill
side of the slope, considering: angle of the slope; mass of the tractor;
coefficient of; leading away of wheels; speed of displacement and traveled
path, is deduced. In accordance; with this, some traction and exploitation
indices of the tractor aggregates are made more exact at; operating on the
slope. The research results can be used in developing of new mountain tractors.

High
clearance tractors are often operated on rough terrain with high rollover risk,
which would result in operator injury. This paper introduces high clearance
tractor rollover detection and risk prediction system, developed with
multi-sensing technologies and embedded device. Mathematical model was firstly
established and coded to calculate the stability index of tested machine. GPS
and inertial sensors were utilized to obtain the machine parameters for index
calculation. Mobile software was developed with the function of image and sound
warning for machine operator. Experiments were conducted to identify the effect
of velocity, slope angle, rotation velocities on tractor stability. Obtained
results indicated the validity of developed model and prediction system (SUN et
al, 2016).

In
order to investigate the effects of forward speed, ground slope and
wheel–ground friction coefficient on lateral stability of tractor at the
presence of position disturbances, a tractor dynamic model was developed (AHMADI, 2011). In this model two types of instability were
considered: instability due to overturn and skid and for each case the stability
index was determined. Different geometries and mass specifications of tractor
MITSUBISHI-2501D were used to examine the model. According to the results of
this model forward speed and ground slope had a reverse effect on all stability
indexes. Moreover stability of this tractor was more affected by tractor
skidding than overturning. Therefore to improve the overall stability of this
tractor, preference should be on increasing the tractor stability index derived
from skid dynamics of tractor.

The paper (MUNESHI et
al, 2016)** **assumed a possible case that a
tractor operator has several spare tires of different types and service
condition. Additionally, the ballast weight, track width, and implement
position can usually be controlled before operation. A scale model tractor was
thus developed allowing changes to these factors. The model tractor was
designated to pass over typical farming road surfaces. Moreover, the tractor
lateral stability was evaluated in terms of the roll angle, lateral-load
transfer ratio, and Phase I overturn index.

Employing
the Taguchi method, we arranged experiments and assessed the applicability of
the three kinds of indexes regarding tractor Phase I overturn. Results revealed
that the roll angle did not well reflect the initiations of overturns. Compared
with the lateral-load transfer ratio, the Phase I overturn index had more
convincing factorial effects on tractor stability. Further investigation of the
suggested tractor configuration supported this conclusion by comparing predicted
and experimental results. In practical cases, this approach may provide a
reference for engineers to help operators improve driving safety with limited
spare parts. An optimized tractor configuration is suggested through this
approach.

The paper** **(GOBBI
et al, 2014) the analytical mathematical
relations governing the anti-dive and anti-lift characteristic of the farm
tractor are derived by considering both the common brake architecture and
either the cases of two or four wheel drive systems. The effect of the very
complex driveline of farm tractors on anti-dive and anti-lift characteristic is
dealt with. It turns out that, to obtain an anti-dive behavior, in case of
four-wheel-drive, the non-statically determined torque distribution between
front and rear axles requires a proper tuning of the geometry of the front
arms, particularly of their slope.

A
geometrical model for predicting the rollover initiation angle and tire contact
forces under quasi-static conditions for tractors fitted with front axle pivot is presented (GUZZOMI, 2012). The model uses a kineto-static approach
based on two rigid bodies which correspond to: an anterior body, comprising the front axle and wheels
(assumed of negligible inertia and mass), and a posterior body, comprising the
rear wheels and the remaining machine (with significant inertia and mass). As
developed, the model is more suited to fixed-chassis tractors with non-massive
front wheels and swing axles. The most significant result is that the model
suggests that activation of full-brake lock on all four tires may hinder progression into Phase II rollover and
this is consistent with the Kutzbach criterion.

This
study (SUN et al, 2017)** **was
conducted to develop a numerical program to predict the effective height and
width of a safety frame, or tip-over protective structure (TOPS), for a
three-wheeled agricultural carrier. To hasten program development, the main
algorithm of computation in the original program for a tractor with protective
structure laterally rolling over was not modified for this study. The target
carrier was assumed to be safe when the successive rollover on the slope was
prevented by the adoption of TOPS with sufficient height and width.

Based
on catalogue data of commercially available carrier, the accuracy of the
developed program was investigated. Results showed a predicted height of TOPS
that is reasonable with respect to the carrier dimensions. Then, a small
carrier model was constructed to verify the accuracy of analysis by comparing
the experimentally obtained result of overturning and the numerical result of
the model carrier. Results showed that the developed program had qualitatively
sufficient accuracy for predicting the TOPS height. For more precise prediction
of the necessary TOPS height for three-wheeled agricultural carrier, a computer
program based on the contact physics should be developed to include rolling or
sliding of vehicles.

A
general model to predict quasi-static articulated tractor instability on a
slope has been derived using kineto-static modeling (BAKER; GUZZOMI, 2013).
Under simplifying assumptions, it is possible to model fixed-chassis tractors
and, in particular, include the effect of front axle-wheel mass. The model is
therefore used in this paper to investigate the effect of front body mass on
tractor stability and behavior during Phase I rollover.

The
results are of particular relevance to four-wheel-drive (4WD) tractors. It is
shown that the stability of a tractor depends on the position of the centre of
gravity (COG) of the main (posterior) body. For tractors with massive front
wheels, tires and beam axles, this COG is likely not to be the same as that
found from the standard COG methods currently adopted.

Numerous
investigations have been made concerning the work of agricultural machines on
the field slopes (ARIKO; MOKHOV, 2010), but the issue of a tricycle tractor
stability on the slope fields is not sufficiently developed.

**1.2.
****Statement
of the objective and tasks of the study**

The
objective of the study is to increase the safety of operating tricycle tractors
due to theoretically established conditions for their stable operation on the
slopes of the fields.

To
achieve this goal, the following tasks were solved:

·
to conduct theoretical studies of tricycle tractors
under conditions of their operation on the slopes of fields and to determine
the influence of the slope angle of the field on the conditions of stable
operation of the machine;

·
to establish the theoretical dependence of the maximum
angle of inclination of the tractor on the width of the wheel rim, wheel
radius;

Theoretical studies were carried out using the provisions
of higher mathematics, theoretical mechanics, the theory of mechanisms and
machines, and mathematical modeling.

**2. ****RESULTS**

Let's
consider the work of a tractor that rests on three wheels under conditions when
one of them is a front wheel, and two are the rear wheels. Scheme of this
machine is shown in Figure 1. The front wheel of this tractor is a steering
wheel.

This
tractor has such a peculiarity. Its weight, which falls on the front wheel,
should be heavy enough to ensure the pressure of this wheel against the ground
when the machine is moving on the road with a slope upward. Under these
conditions, due to the transfer of tractor weight to the rear wheels, the load
falls on the front wheel.

Under
such a location of the tractor wheels, shown in Figure 1, it can be assumed
that the *ABDE* rectangular quadrilateral is located below the tractor,
which includes the lower support line *AB* of the front wheel and the
lower lines *DD*_{1} and *EE*_{1} of the rear wheels
(on the straight line *DE*).

Inside
of this quadrilateral under the condition of a stable condition of a tractor
there is a trace of its gravity center *C*, that is, the point of
intersection of the vertical axis, passing from the tractor gravity center *C
*down to the intersection with the horizontal surface of the ground. If the
gravity center *C *is located on the ground inside the quadrilateral *ABDE*,
the tractor is in a stable condition; if the trace does not lie inside the
quadrilateral, it means that there is no stability.

In
the Figure1 it is shown that the weight of the tractor front element, which is
indicated as_{}, is transmitted to the front wheel. Under the machine
operation on the slope of the field, the tractor wheels will turn, and the
tractor will also turn. The diagrams of the tractor front wheel rotation on the
slope are shown in Figure 2.

If
the field is inclined horizontally to a small angle α (Figure *a*_{} will be deviating from the median plane dividing the
cylindrical part of the wheel rim into two equal parts, also on the angle α (Figure *a*_{}action begins at the point *C*_{1} and
acts vertically downwards to the left of the extreme lower point *A* of
the wheel rim; this means that the force _{} action does not
lead to the forward wheel shift to the right.

Figure 1. Scheme of the
three wheel tractor: *1* - front wheel (steering wheel); *2 –
left rear wheel; 3 - right rear wheel;4 - cabin; 5 - hitch; A, B, D, D _{1},
E and E_{1} are the lower supporting points of the wheel rims*.

If
the angle α of
the field deviation _{}upwards from the horizontal line _{}is larger than the angle α in the previous
case (Fig. *a**b*, then the vertical force_{}_{, }going from point *C*_{1}
downwards (Fig. 2, *b*), crosses the line of the field to the right of the
extreme lower point *A* of the wheel rim.

In
this case, it would be possible to roll over the point *A* of the right
wheel, but this is impossible due to the fact that the wheel is connected to
the other part of the tractor, which has not yet been brought to such a
position as to rollover (for the rollover of the tractor it is necessary, as
already being noted, that the trace of the center *C* of its weight on the
ground appeared outside the quadrilateral *ABDE *in Figure 1).

Figure 2. Scheme of the axle
load of the sole front wheel of the tractor by force on the field slope at a small angle α (a) and at a
large angle α (b) of the field incline.

Under
the circumstances where the force _{}of a point *A* is safe, it does not mean that
such a force action is always safe; it is advisable to check this state of
force_{}taking into account the above recommendations. Thus,
working with such a tractor on the field slopes is better than the scheme in
Fig. _{} acts on the *C*_{1}*K*_{1}
or *C*_{1}*K*_{2} line on the same Fig. *a*_{}action (Fig. 2) passes through point *A*, is
called the limiting angle of the wheel α_{Kex}; it is determined by following
dependence:

_{} (1)

where b is the width of the wheel rim, *r*_{к} is the wheel
radius

The _{}force of tractor weight can be divided into two
components parallel to it, namely_{} and _{}(Fig. *a*_{}has already been mentioned above. The force_{}is applied at the point *С*_{2},
representing the projection of the *С*_{2}rear wheels axis on a vertical
plane passing through the center of gravity *С*_{2} of
the rear element of the tractor.

Let’s
assume that if the position of the machine changes, the position of the center
of gravity *С*_{2 }does
not change, that is, we assume that the moving of materials inside the machine during
its movement does not occur, and the distance from the weight center *С*_{2} to
its reference plane and the wheels does not change.

At
such a turn of the tractor on the angle α, the force _{}will act on the surface of the field perpendicular to
this surface with force _{}(Figure 3) and parallel to the field surface with a
sloping force_{}, that is, the force _{}can be expanded into two such components as_{} and _{} that equal to:

_{} (2)

As a
result of action of the _{}component, the rear part of the machine is pressed
against the soil surface (Figure 3), and under the action of the constituent _{}the machine tends to move to the right, overcoming the
resistance to the friction created by the soil in the zones of its contact with
the lower wheel surface, where the points *О*_{2}and*О*_{3}situated
(Figure 3). All force of soil friction on the lower parts of the rear wheels we
indicated as *F*, this force consists of two components *F*_{2}
and *F*_{3}, the component *F*_{2} operates in the
zone of point *О*_{2}, and component *F*_{3 }operates in the
zone of point *О*_{3}. The component* F*_{2 }equals to *f*_{p}*N*_{2}, and
the component *F*_{3} equals to *f*_{p}*N*_{3},
where *f*_{p}is the friction coefficient at rest, and *N*_{2}_{ }and *N*_{3}are
the normal forces of the soil reaction in the zone of points*О*_{2}and *О*_{3}.
Then the condition of the absence of wheel slip on the soil will look like:

_{} (3)

or

_{} (4)

where *f*_{p max} is the maximum value of
the soil friction coefficient at rest on the wheel rim.

Figure 3. Rear
view of a turned three-wheel tractor and forces acting on a transversal
vertical plane where the center С2 is located

Figure 1, 2, 3 and 4 shows the weight force_{}of the tricycle tractor which is applied to the center
*C* of its weight, as well as the components of the force_{} and _{} acting on the
point *С*_{1} of
the front wheel axis*1* and at the point *С*_{2} on
the rear axle *2* and *3*. Dependence of forces _{}and _{} on the force _{}and distance *a* and* b* between the axes
(Fig. *a*

_{} (5)

Taking into
account these two equations we find:

_{} (6)

_{} (7)

If
the three-wheeled tractor is in such position on the field slope shown in Fig.
4 (rear view), then the tractor will be influenced by such forces, which will
increase the pressure of the right wheel to the ground, and the pressure of the
left wheel on the ground will decrease. Under such conditions a soil pressure
force on the lower part of the front wheel also changes a bit (Figure 4, *b*).

Figure 4. The
rear view of a turned three-wheeled tractor and the forces acting on it in a
transverse vertical plane, where its gravity center is located.

As
can be seen from Fig. 4 on the field slope, the gravity force _{}, acting on the whole tractor, is divided into two
components_{} and _{}. The component _{}presses the tractor to the inclined surface of the
field, and the component _{}seeks to move the tractor to the right and down. This
is prevented by friction forces *F*_{1}, *F*_{2 }and *F*_{3},
acting from the side of the soil on all tractor wheels.

The
force *F*_{1} = *f*_{p}*N*_{1}*, **F*_{2} = *f*_{p}*N*_{2}, and
force *F*_{3} = *f*_{p}*N*_{3}, where *N*_{1}, *N*_{2 }and *N*_{3 }are
the normal forces of the soil reaction on the rim of wheels 1, 2 and 3, and *f*_{p}
is the coefficient of soil friction at rest on the wheel rim. Force_{} under these conditions acts vertically down.

The
forces_{},_{}and_{}, are in such conditions in a transverse vertical
plane.

**3. ****RESULTS AND DISCUSSION**

According
to the results of the theoretical studies of the interaction of the movers of a
tricycle tractor with the surface of the field, the conditions for the stability
of the tractor depending on the layout and the angle of inclination of the
field to the horizon were established. Note that determine stability conditions
can be used in the study of self-propelled tricycle tractors, machines and
units.

The three-wheel layout has several advantages over the traditional four-wheel. The most important advantages include maneuverability, better control conditions, lower indicators of specific pressure on the soil and metal capacity. For certain operating conditions (mountainous terrain, fields with a complex profile), a three-wheel layout scheme has advantages over a four-wheel one.

For
the selected layout scheme, the conditions for the steady state of the tractor are
established. The stability of the tractor will be ensured when the vertical is
lowered down from its center of gravity and crosses the surface inside the
reference quadrilateral. The surface of the supporting quadrilateral is formed
as a result of connecting the outer points of the wheels.

The
determined conditions of sustainability coincide with the well-known conceptual
recommendations for ensuring the steady state of the machine. We distinguish
the main ones: an increase in the surface of the supporting, as well as a
decrease in the distance from the center of gravity of the machine to the soil
surface. The dependence of the influence of the rim width and the wheel radius
on the maximum angle of inclination of the tractor with one front wheel is established.

The
scientific problems posed in the work are solved in the developed theoretical
bases for determining the stability conditions of a tricycle tractor. The
theoretical foundations have been developed taking into account the layout of
the tractor and the angle of inclination of the field to the horizon. According
to the results of the research, the scientific background for increasing the
safe operating conditions of tricycle tractors was further developed.

**4. ****CONCLUSION**

1)
The theoretical calculations carried out by the
authors made it possible to establish the stability conditions for a tricycle
tractor on the slope of the field. The stability of the tractor will be ensured
when the vertical line lowered down from its center of gravity crosses the surface
inside the supporting quadrilateral. The surface of the supporting
quadrilateral is formed as a result of connecting the outer points of the wheel
rims.

2)
The dependence of the influence of the rim width and
the wheel radius on the maximum angle of inclination of the tractor with one
front wheel is established. The dependencies of the maximum angle of
inclination of the tractor were theoretically determined, which made it
possible to establish the conditions for its safe operation.

3) The
theoretical foundations have been developed taking into account the layout of
the tractor and the angle of inclination of the field to the horizon. The
scientific background for increasing the safe operating conditions of tricycle
tractors has been further developed.

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