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Research Paper: PMPower and Machinery
Three-point hitch-mechanism instrumentation for tillage
power optimization
H. Bentahera,, E. Hamzab, G. Kantchevc, A. Maalejc, W. Arnoldd
aOlive-tree Institute, P.O. Box 1087, Sfax-3000, TunisiabNational Agronomic Institute of Tunis, Tunisiac
National Engineering School of Sfax, PBW, Sfax-3000, TunisiadFraunhofer-Institute for Non-Destructive Testing (IZFP), Campus E3.1, University, D-66123 Saarbrucken, Germany
a r t i c l e i n f o
Article history:
Received 29 December 2006
Received in revised form
28 November 2007
Accepted 29 January 2008
Available online 17 March 2008
In order to study tillage power optimization, a tillage-force measuring system has been
built with transducers in the three-point hitch mechanism, and then has been calibrated
and tested in the field. The uniqueness of this system is its ability to measure the three
orthogonal components of the tillage force despite using only three force sensors; this was
possible by using a three-dimensional analysis of the tractor linkage mechanism.
A dynamic calculus program was developed to take into consideration the changes of
the three-point hitch-mechanism geometry during the tillage operation. The calibration
results showed a linear relation between the applied and the measured forces. The
preliminary field tests proved the stability of the system results. The developed system can
readily be applied in studies to minimize tillage energy consumption.&2008 IAgrE. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Due to the rapid increase of energy cost, power optimization
is a common objective for many engineering devices. Tillage
is the biggest power consumer in an agricultural production
system, and hence the evaluation of tillage effort is a field of
great interest.
Researchers have proposed and built many systems to
measure the force and power requirements of tillage imple-ments. These systems can be classified into three types based
on the location of the force transducers. For the first type,
sensors are mounted on the tillage tool (Girma, 1989;Formato
et al., 2005). These systems give a precise idea about strain
distribution on the implement that helps in their design
optimization. However, they are expensive because each
tested tool has to be equipped with sensors. Moreover, the
transducers installation required some changes to imple-
ment global geometry which could modify the soiltool
interaction and the tool weight. The second category of
systems has separate frames in which transducers are
mounted. These frames are introduced between the tractor
and the implement. Because these systems are interchange-
able between different tractors and tools and are easy to
manufacture, the majority of researchers have investigated
such devices (Reece, 1961;Barker et al., 1981;Reid et al., 1985;
Clark and Adsit, 1985;ODogherty, 1986;Chaplin et al., 1987;
Thomson and Shinners, 1989; Palmer, 1992; Godwin et al.,1993; Hammada, 1998; Al-Jalil et al., 2001; Kasisira and du
Plessis, 2006). However, this approach presents many incon-
veniences: first, it requires a heavy frame to fix the
transducers which causes a change of the total weight and
requires a backward displacement of the implement. Second,
fixing the transducers and the frame to the tractor necessi-
tates many extra elements at the articulations that are a
source of error in the measurements. For these reasons, the
second type of system does not reflect real work conditions.
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1537-5110/$ - see front matter & 2008 IAgrE. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.biosystemseng.2008.01.008
Corresponding author. Tel.: +216 74 241589; fax: +21674 241033.E-mail address:[email protected] (H. Bentaher).
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The third type consists of installation of transducers in the
three-point hitch system of the tractor. Despite the fact that
this category preserves the real conditions of field work (e.g.
tool-tractor position), little research has been focused on it.
The efficiency of these systems is highly related to the
position of the sensors. On the one hand, some researchers
mounted the transducers on the top and the two lower links
(Bandy et al., 1985; Upadhyaya et al., 1985; Al-Janobi, 2000;
Bentaher et al., 2003). The load of the lower links is complex.
It entails tension, compression and flexure which prevent the
installation of force sensors. As a result, with such systems it
is not possible to measure the lateral effort generated by
asymmetrical implements. On the other hand, the installa-
tion of force transducers on the top and the two lift links
seems to be the best solution. To the best of our knowledge,
the only work that has been done on this type of system is by
McLaughlin et al. (1993). In that work, the three-point hitch
system was instrumented by five force sensors. A transfor-
mation matrix was derived to transform the force of these
transducers into orthogonal components of the tillage force.
Since the establishment of this matrix was based on a two-
dimensional kinematic study (Bandy et al., 1985), the in-
formation concerning the lateral tillage force was lost.
In the present work, a three-dimensional kinematic study was
developed to establish the transformation matrix. We instru-
mented a tractor with three force sensors (on the top and the two
lift links) and an angular transducer for the hitch rock shaft
(Fig. 1). A dynamic program, taking into consideration the
changes of the three-point hitch-system geometry, was estab-
lished to calculate the tillage effort. The developed system is able
to measure the three orthogonal components of the tillage force.
2. Materials and methods
2.1. Theoretical considerations
In the majority of the published work, researchers considered
the three-point hitch mechanism as a planar system. This
system was modelled in two dimensions to represent the forces
in the original geometrical configuration between the tractor
and the implement (Bandy et al, 1985; Al-Janobi, 2000). This two-
dimensional approximation, which causes the loss of the lateral
force, can be accepted for the studies of symmetric implements.
In order to evaluate the longitudinal, vertical and lateral
forces of a non-symmetric tillage tool, a three-dimensional
study of the tractor linkage mechanism is needed. The
mechanism consists of seven articulated beams. During field
work, this system is isostatic with one degree of freedom. The
angular position of the rockshaft is sufficient to determine the
exact geometry of this system.
To make the force calculation simpler, the three-point hitch
system is modelled by ties and pin joints. The coordinates of
each joint are calculated in a Cartesian coordinate system (X0,
Y0,Z0) with I0, the centre of the rear wheel, as the point of origin(Fig. 2). The calculus equations of all the pin-joint positions are
developed. The position of the tillage application point G in
reference to this coordinate system is given by the equations:
xG xDIHzKzD
IK HG
xDxKIK
(1)
zG zD HGzKzD
IK IH
xDxKIK
(2)
For a definition of the variables in these equations, see
Fig. 2. An Excel calculus program (CP1) was developed to
determine these coordinates. The inputs of this program are:
tractor characteristics: Cartesian coordinates of O, O0
, B, B0
,E, and the distances: AA0, L1, L01and L3;
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Fig. 1 Instrumented three-point hitch mechanism.
Nomenclature
AtoKandO positions of pin joints of the three-point hitch-
mechanism as defined inFig. 2
Cg gravity centre of the tillage tool chassis
G tillage application point
g gravitational accelerationl0 centre of the rear wheel
L1 length of the lower link
L01 distance between the joint of the lower link (tractor
side) and the pivot connection of the lift rod
L2 length of the lift rod
L3 length of the lift arm
L4 length of the upper link
m tillage tool masslRij reaction force in the point i at the direction j for
the left side of the hitch mechanismrRij reaction force in the point i at the direction j for
the right side of the hitch mechanismWx, Wy, Wz orthogonal components of the tillage force at
the pointG
Xi, Yiand Zi Cartesian coordinates of the point i
XG, YG, ZG Cartesian coordinates of the pointG
f rock shaft angular position
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adjustable lengths: L2and L4; tool triangular chassis characteristics: distances DD0, IK, IH
and HG;
rock shaft angular position f which is the variableparameter during the field work.
The tractor characteristics are measured and compared to
the Organization for Economic Cooperation and Development
(OECD) restricted code test report (CEMAGREF, 1995). The
equilibrium of the left lower link arm gives the following
system of equations:
lRDxl RBx
l RCx 0
lRDyl RBy
l RCy 0
lRDzl RBz
lRCz 0
lRCzyC yB lRCyzCzB l RDzyD yB lRDyzD zB 0
lRCxzC zB l RCzxCxB
l RDxzD zB l RDzxDxB 0
lRCyxCxB l RCxyC yB
l RDyxDxB l RDxyD yB 0
lRCxxA xC
lRCy
yAyC
lRCzzAzC
lRCL2
(3)
Here,Rijis the reaction force at the point i at the direction j,
xi,yiandzi, are the Cartesian coordinates of the point i andl
indicates the left side of the three-point hitch mechanism. The
equilibrium of the right lower link arm gave a similar system of
equations (r for the right side). From the equilibrium of the
tillage tool chassis (Fig. 3), this system of equations is derived:Wx l RDx r RDxRK
xKxEL4
Wy l RDy r RDy
Wz l RDz r RDz RKzKzE
L4mg
yDrRDz l RDz WyzGzD mgyCg
zKzDxKxE xKxDzKzE RKL4
WxzGzD WzxG xD mgxCg xI
Wy r RDx
lRDxxGxD
yD
8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:
(4)
Here, Wx, Wy and Wz are the orthogonal components of the
tillage force at the pointG,mis the tillage tool mass andgis the
gravitational acceleration. The last two of these equations arederived knowing the direction of the reactions in the two lift
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A1
O1
K
Z0 A2
O2E
B2B1
I0
D1 Wy
Wz
D2
Y0 I0
Z0
O
3A
EX0
B
1
C
2Z
K
45
H
X
Wz W
WxGD
Y0
I0 X0
EA2
B2C2 D2
Y
IKA1
B1
O1
C1 D1
X Wy
Wx
W
G
Line of attack
Fig. 2 Rear view (a), side view (b) and upper view (c) of the three-point hitch mechanism showing lower link 1 and its length
L1 BD; L01:the distance BC; lift rod 2 and its length L2 AC; lift arm 3 and its length L3 OA; upper link 4 and its length
L4 EK; tool triangle chassis 5; longitudinal component of tillage force Wx; lateral component of tillage force Wy; vertical
component of tillage force Wz.
Z0
I0
X0
B CRD D
mg
CgI
2
I
E
O
A 4
3
1
Rk K
5
W
Fig. 3 Force diagram of the three-point hitch mechanism,
Cgand mg are, respectively, the gravity centre and the
weight of the tool chassis,Wis the tillage force and Riis the
reaction force in the pointi.
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links and the top link: they are bi-articulated beams, and so
their reactions are parallel to the beam directions.
The solutions of these equations give the three orthogonal
components of the tillage force:
xi, yi and zi, are the Cartesian coordinates of the point i.
These equations show that the voltage responses of three
force transducers located in the two lift rods and the upperlink are sufficient to identify the tillage force. A second Excel
calculus sheet (CP2) was developed to evaluate the three
orthogonal components of the tillage effort. The inputs of this
program are the outputs of the first program (CP1) and the
responses of these transducers. The flow chart of the two
calculus programs is shown inFig. 4.
2.2. Instrumentation
The three-point hitch mechanism of a Massey Ferguson 6120
tractor was instrumented to evaluate the orthogonal compo-
nents of tillage implements without changing the dimensions
of the mechanism. Two HBM-U2B force transducers with a
range of 200 kN were incorporated into the two lift links. Four
simple thread shells were designed and manufactured to
make the assemblage of these transducers possible. A third
load cell with the same capacity and a lower weight was
designed and constructed for the top link (Fig. 1). The
incorporation of this transducer does not change the weight
of the top link much (less than 5%). More detailed information
concerning the design of this sensor and its calibration has
been presented by Bentaher et al. (2006). A rotary position
transducer functioning as a potential divider was mounted on
the rockshaft to monitor its movement. This transducer was
used to measure the angular position of the hitch mechanism
and to calculate the implement depth.
2.3. Data-acquisition system
The three load cells and the rotary position transducer wereconnected to four differential channels of the 21X Campbell
scientific data logger. This data logger was connected to the
RS232 port of a notebook via an optically isolated interface
SC32A. The whole acquisition system was mounted on a
platform behind the drivers seat. This system worked either
on its own batteries or on the 12 V power supply of the tractor.
The data logger was used to excite the transducers and to
sample and record their responses. The notebook was used
to control the in-field sampling, to collect the stored data and
to calculate the tillage effort using the developed calculus
programs CP1 and CP2. The software (PC208) was used to
prepare the data logger program and to run and test its
validity and the proper functioning of the acquisition system.The sampling frequency used for the preliminary tests was
1 Hz and the excitation voltage for the transducers was
500mV.
2.4. Calibration
The instrumented three-point hitch-mechanism was cali-
brated using a separate HBM-U9B force transducer with a
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Chassis dist.: D1D2,
IK, IH and HG
Input :
Coord. of O1,
O2, B1, B2, E
Distance: A1A2,
L1, L1, L3
Adj. length:
L2 and L4
Cartesian
Coord. of:
A1, A2,
C1, C2,
D1, D2,k,
and G
CP1
Angular position
(t)
CP2
Transducer
voltages
V1, V2and V3
Chassis Charact. : m
and XCg, YCg, ZCg
Tillage
components
Wx, Wyand Wz
Fig. 4 Flow diagram of the calculus programs; AA 0 is the distance between the two liftarm joints; L1 is the distance between
the joints of the lower link; L0
1 is the distance from the lower link joint to the lift rod joint; L2 is the lift rod length; and L3 isthe lift arm length.
Wx xKxExD xBzKzD xG xKxDxBzKzE xK xExGxDzDzB
xDxBzG zD xG xDzDzB
RKL4
xCxBzAzC xAxCzCzB
xD xBzGzD xGxDzDzB
xD xG
L2lRC
r RCh i
xD xBxGxCg
xD xBzG zD xGxDzDzBmg (5)
Wy xCxBzAzC xA xCzCzB
xDxBzGzD xGxDzDzB
yDL2
lRCr RC
h i
xBxDyCgxD xBzGzD xGxDzDzB
mg (6)
Wz xKxEzK zGzDzB xD xKzK zEzDzB xDxBzKzEzGzD
xDxBzGzD xGxDzDzB
RKL4
xCxBzAzC xAxCzC zB
xDxBzGzD xGxDzD zB
zD zG
L2lRC
r RCh i
xDxBzGzD xCgxDzDzB
xD xBzGzD xGxDzD zB
mg (7)
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capacity of 20 kN. The simulated effort was applied and varied
with a chain-hoist attached to a fixed point from one side,
and to the force transducer from the other side. This
transducer was fixed to the force application point (G) of the
triangular chassis with a cable. The tractor was placed on a
horizontal plane verified by an engineers spirit level. The
applied forces, given by the sheared cable, were located in the
horizontal and vertical planes; their modules were controlled
by an HBM-MVD 2510 control-panel measuring-amplifier.
Three principal forces, related to the orthogonal directions,
were applied: longitudinal (Wx), lateral (Wy) and vertical (Wz)
effort. The applied forces were increased stepwise and at
each value, the signals of the three sensors were logged for a
period of 1 min. The results of the calibration are presented in
Figs. 57.
3. Results and discussions
The calibration was done in the three directions in order to
prove that the developed instrumentation was able to detect
the three orthogonal components of the tillage force. The
results (Figs. 57) showed thatWxand Wzwere proportional to
the reaction force of the two lift links and the top link.
However, the lateral force Wy was proportional to the
difference between the reactions of the two lift links and
was independent of the top lift reaction.The calibration results showed a linear relation between
the applied force and the responses of the three force sensors.
The output of the calculus program CP2 (Wy) and its standard
deviation are displayed versus the applied force in Fig. 8and
similar curves are obtained for Wx and Wz. The measured
data fall very close to a straight line with a unit slope. The
least square fit with an R2 of 0.995 indicates that the force was
underestimated by approximately 0.5%.
The longitudinal measured force showed an error of 13%
for the lowest force (900N). This can be explained by the
sensitivity of the developed system. In fact, the use of trans-
ducers with a high capacity (200kN) represents a limitation in
the measurement of small forces (McLaughlin et al., 1993).
However, for higher forces, the maximal error was 0.82%. For
the lateral force, the highest error between the applied and
the measured forces was 7.6%. The error of the vertical force
was less than 2.8%.
In the design of this system we preserved the geometry of
the hitch mechanism and the position of the tillage tool to the
tractor because it will be used for two purposes. The first one
is to study the stability of the tractor and its characteristic
curves (power supply/fuel consumption) for different speeds.
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-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0
Sensorresponse,mV
Time, s
Left Link
Right Link
Top Link
50 100 150 200 250
Fig. 5 Sensors response to longitudinal applied force (Wx).
-0.1
-0.05
0
0.05
0.1
0.15
0
Sensorr
esponse,mV
Time, s
Left Link
Right Link
Top Link
100 200 300 400 500
Fig. 6 Sensors response to lateral applied force (Wy)
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0
Sensorresponse,mV
Time, s
Left LinkRight Link
Top Link
100 200 300 400
Fig. 7 Sensors response to vertical applied force (Wz)
0
1000
2000
3000
4000
5000
6000
0
Measuredforce,N
Applied force, N
1000 2000 3000 4000 5000 6000
Slope = 0.968
R2= 0.995
Fig. 8 Lateral measured force (Wy) versus applied force(solid curve is 1:1 line).
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In fact, the change of the tool position gives unreal results
concerning the tractor reactions which are not directly
transposable. The second purpose is to measure the power
demand of different tillage tools in relation to the type of soil,
its mechanical characteristics and the work parameters
(depth and speed). These kinds of results are very useful for
the evaluation of different tillage tools, the decision in the
choice of the tool (e.g. according to the tractor power,
availability on the farm, to calculate the number of plough
shares) as well as the design of new tools adapted to the type
of soil.
The developed system gives us reliable results directly
exploitable for research and for manufacturers in order to
optimize power consumption.
The field tests were conducted at the Tunisian agriculture
institute farm (361480N, 101100E), where the soil was silty
consisting of 63.69% silt, 36.16% sand and 0.15% clay. The
mean water content (dry basis) and the cone index for the
upper horizon (020 cm) were 14% and 2.2 MPa, respectively.
A 50.8cm (2000) locally manufactured mouldboard with one
ploughshare was used for the tests. The tractor speed used for
these tests was 1kmh1 with a slip less than 2%. A tillage
depth of 20cm was chosen. The registered data are repre-
sented inFig. 9. This figure shows good stability of the three
orthogonal components of the tillage force. The means of the
horizontal, lateral and vertical forces generated by the tested
mouldboard are, respectively, 4105 N,40N and 295N. The
negative values indicate that the forces are in the opposite
direction to the Cartesian coordinate system. The obtained
data are in agreement with those given by several researchers
working on a similar type of soil (McLaughlin et al., 1993;Al-Janobi, 2000;Al-Jalil et al., 2001).
4. Conclusion
Instrumentation of the three-point hitch mechanism allowed
the force generated by tillage implements to be measured
using just three force transducers. The system was calibrated
and tested in the field and the results showed its capability to
measure the three orthogonal components of the tillage force.
The three-dimensional study of the hitch mechanism of the
tractor demonstrates that the technique allows the difference
in the reaction of the two lift arms to be measured whenusing non-symmetric tools like mouldboards. Their differ-
ence is proportional to the lateral component of the tillage
force. The developed calculus programs gave this system
flexibility in the interpretation of the logged data in relation to
the tool penetration in the soil.
The three components of the tillage force have been measured
using a system that allows the natural positions of tool and
tractor to be retained. This will allow the energy consumption of
different tillage tools to be measured during natural operation, so
that steps can be taken to optimize their design. More investiga-
tions would be needed to study the influence of work parameters
such as tillage speed, tillage depth and soil type on the measured
forces to achieve this optimization.
Acknowledgements
The authors would like to thank the Agence Universitaire de
la Francophonie for the financial support of the researchersmobility between the laboratories: IZFP in the Saarland
University LASEM in the Engineering school of Sfax and
LAPOAF in Olive-tree institute of Tunisia.
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0 5 10
Time, s
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Fig. 9 Measured data of the forces Wx,Wy, and Wzacting on the ploughshare of a 50.8cm (2000) mouldboard.
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