Journalof
www.elsevier.com/locate/jterra
TerramechanicsJournal of Terramechanics 41 (2004) 187–198
Development of a vehicle to study the tractiveperformance of integrated steering-drive systems
B.C. Besselink
Agricultural Machinery Research and Design Centre, University of South Australia,
Mawson Lakes, SA 5095, Australia
Available online 18 May 2004
Abstract
This paper describes a test-bed vehicle for studying the integration of the steering system of
a wheeled vehicle with the drive system. The vehicle was produced in order to determine
whether such an integrated system is practical; to investigate tractive performance compared
to other steering-drive systems; and to determine under which conditions such a system has
better performance. The integrated steering-drive system of the test-bed vehicle uses a com-
puter to co-ordinate the independently driven wheel speeds of the drive system (which is also
the primary steering system) with the steer angles of the non-driven steerable wheels to pro-
duce a beneficial secondary steering effect. The secondary steering system assists the primary
steering system when side forces act on the vehicle, while producing minimal conflict. This
concept can be applied to agricultural vehicles such as tractors, harvesters, mowers, sprayers
and self-propelled windrowers. The test-bed vehicle is able to be configured for the following
steering-drive systems types: open differential drive with steerable wheels, independent drive
wheels with castors, locked differential drive with steerable wheels and a computer integrated
steering-drive system. The capacity of the test-bed vehicle to be configured as described is a
significant advantage when measuring tractive performance, as the results obtained will be
more valid due to the vehicle parameters being the same.
� 2004 ISTVS. Published by Elsevier Ltd. All rights reserved.
Keywords: Tractive efficiency; Zero turn radius vehicle; Steer by wire; Computer control; Drive systems
1. Introduction
The two basic conventional two-wheel-drive configurations for wheeled vehicles
are independent drive and differential drive.
0022-4898/$20.00 � 2004 ISTVS. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.jterra.2004.02.001
188 B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198
With an independent drive system, the left-drive wheel and right-drive wheel are
driven independently by means of a variable ratio transmission. Examples of
wheeled vehicles that use this system are garden tractors, ride-on mowers and self-
propelled windrowers. In these vehicles, the non-driven wheels must be castors:
otherwise, significant ground damage and handling problems occur when turning.
Compared to a vehicle with a differential, these vehicles have a high degree ofmanoeuvrability and traction. When both the left-drive wheel and right-drive wheel
are driven forward at the same speed, the vehicle moves straight ahead. On the other
hand, when both the left-drive wheel and right-drive wheel are driven at equal and
opposite speeds the vehicle rotates about the centre of the drive axle (a zero turn
radius (ZTR) vehicle). The independent drive means that if one drive wheel loses
traction, the other drive wheel is not affected and the vehicle is still able to move.
This contrasts with the behaviour of vehicle with an open differential.
However, when traversing steep slopes, the castors cannot exert a sideways force,so the end of the vehicle with the castors tends to move down the slope due to the
gravitational turning moment acting on the vehicle (where the centre of gravity is
substantially forward of the drive wheels). This presents a significant limitation in this
situation. In order to maintain the direction across the slope, a counteracting moment
must be provided by increasing the difference in drive speeds to produce a difference in
thrust between the two drive wheels. Thus, there is a decrease in tractive capability in
order to increase steering capability. This may lead to a loss of traction and control.
As well, on flat slippery terrain, castors also have a disadvantage: a sudden loss oftraction on one drive wheel will cause a sudden steering deviation. The castors
cannot contribute any steering effect to reduce or eliminate the deviation since they
cannot hold a side force.
The most common drive system for a two-wheel-drive vehicle is one that has a
differential. It is a relatively simple mechanical drive system that provides equal
torque to both drive wheels and produces minimal scuffing in turns. In this case,
the drive wheels cannot provide a steering effect, as they are not independent. The
vehicle is steered by changing the rolling direction of the non-driven wheels. Thebenefit when traversing slopes is that the non-driven wheels can hold a side force.
The steering behaviour of a vehicle with a differential is more stable under changing
tire-surface conditions than a vehicle with independent drive wheels. With a differ-
ential, although total thrust is reduced when the traction conditions are different for
each drive wheel, the driving torques will be equal; and if the rolling resistances are
equal, the thrusts will be equal. Hence, there is no turning moment induced under
these different conditions.
However, when one wheel has lower traction, a vehicle using a differential hasdisadvantages. Differences in traction characteristics may come about from different
tire-surface characteristics or weight distribution. Since a differential delivers equal
torque, the wheel with better traction characteristics can only deliver the same
amount of torque as the wheel with the lower traction. To overcome this problem,
various forms of differential locking or drive shaft braking techniques are used.
These result in poor handling. For example, locking the differential enables the
steering effect from wheel speeds, and the equal wheel speeds create a tendency to
B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198 189
move the vehicle straight ahead. The application of a braking effect to a drive wheel
produces energy losses. Generally, manoeuvrability is reduced and handling is
impaired. As well, vehicles in an agricultural context require traction control on an
ongoing basis since the drive wheels of an agricultural vehicle usually operate with
high longitudinal slip. Whereas with road vehicles, traction control is only required
for a small percentage of the time.A wheeled vehicle having the tractive advantages of two independent drive wheels
but having steerable non-driven wheels has greater design possibilities with respect to
weight distribution, space considerations, and wheel sizes. It should also have
improved tractive ability, mobility and safety on slopes and slippery surfaces.
The aim of the author�s current research is to integrate the steering and drive
systems of a wheeled vehicle having two independently driven wheels. The steering
and drive systems are to be integrated using a computer with an appropriate algo-
rithm. Another objective of the research is to investigate the performance of such avehicle, particularly in turning and especially on slopes and slippery terrain, and to
compare it with conventional systems.
Contrary to conventional two-wheel-drive vehicles, the two-wheel-drive vehicle
developed will have a steering system at one end from wheel direction (steerable
wheels) and at the other end from wheel speeds (independent drive wheels).
The purpose of this paper is to describe the design of the test vehicle and control
system hardware being used for this research.
2. Background
Besselink and Spark [4] have described a computer controlled steering-drive
system for four-wheeled vehicles having two independently driven wheels. The
steering-drive system is proposed to be achieved by replacing the two castors of the
conventional system with two steerable non-driven wheels. These are positively
turned to steer angles appropriate to the radius of curvature produced by the wheelspeeds of the two independently driven wheels. A microprocessor is used to deter-
mine the appropriate steer angles. The microprocessor uses an algorithm based on
the mathematical relationship between the wheel speeds of the two independently
driven rear wheels and the Ackerman steer angles of the two front steerable wheels.
Sensors are used to determine the speed and direction of the two driven rear wheels
and the microprocessor controls the actuators that turn the non-driven wheels to the
appropriate steer angles.
Further mathematical relationships have been developed for vehicles having morethan two driving wheels and more than four wheels [3,5,6].
The paper by Spark and Besselink [4] presents the mathematical relationships and
some analysis of the motion of the vehicle. However, the analysis for the develop-
ment of a practical computer algorithm was not presented. The presence of the in-
verse tangent function in the mathematical expressions presented some problems
with instability for a steerable wheel as Blair and Spark [2] highlighted (but did not
solve). The other references do not disclose a computer algorithm either.
190 B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198
Besselink [1] presented an analysis of the motion of a vehicle with two indepen-
dently driven rear wheels and described a computer algorithm which solves the in-
stability problem and which emulates and improves upon the motion of a zero turn
radius vehicle with two drive wheels.
3. Theory
3.1. Steering effects
The radius of the turning circle of a wheeled vehicle is a result of either or both of
the following two steering effects:
• the radius of curvature produced by the independent wheel speeds of the left drive
wheels and the right drive wheels; and/or• the radius of curvature produced by the rolling direction of thewheels of the vehicle.
However, for a conventional four-wheeled vehicle in a turn, when both of these
steering effects are operating there is conflict between them. An extreme example of
this conflict occurs with a skid-steer vehicle, such as a four-wheeled skid loader. The
wheels of the vehicle are always directed straight ahead and hence would produce an
infinite radius of curvature if acting alone. However, this steering effect conflicts with
the dominant effect: the radius of curvature resulting from the different independent
wheel speeds selected by the operator. The actual turn radius will be a compromisebetween the two radii of curvature. The conflict results in extreme scuffing, ground
damage, tire wear, fuel wastage and, in some cases, reduced manoeuvrability.
The traditionalmethod toavoid this conflict is todisableone steering effect.Zero turn
radius vehicles donot haveany steering conflict because the non-drivenwheels aremade
inoperative as steerable wheels by turning them into castors. The steering is solely from
the independent drive wheel speeds. With a conventional motor vehicle, the steering
effect of the drive wheel speeds is eliminated by the inclusion of a differential, which
removes their independence. As a result, there is no conflict between the two systems.
3.2. Integrated steering-drive systems
For a two-wheel-drive vehicle of typical configuration with equal front and rear
tracks, the mathematical relationship between the speeds of the drive wheels and the
steer angles for the steerable wheels is detailed as follows (Spark and Besselink [4]):
/L ¼ tan�1 bt
1
��� xR
xL
��; ð1Þ
/R ¼ tan�1 bt
xL
xR
��� 1
��; ð2Þ
where b is the wheel base of the vehicle; t, the track of the vehicle when front and reartracks are equal;xL andxR are the rotationalwheel speeds of the rear left and rear right
drive wheels of the primary steering system respectively;/L and/R are the steer angles
of the front left and front rightwheels of the secondary steering system respectively. It is
B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198 191
assumed that the drive wheels have equal wheel diameters. An understanding of the
terms used may be obtained from Fig. 1 (which is for unequal track).
Fig. 1 depicts a vehicle with a primary steering system using two independently
driven wheels and a secondary steering system using the wheel direction of the front
non-driven wheels. tB is the track of the rear wheels; tF is the track of the front
wheels; R is the radius of the turning circle of the vehicle. Clockwise rotations areregarded as positive and have a positive radius of curvature.
The following equations for the general case, where the track of the front wheels is
different to the track of the rear wheels, were developed by Besselink [1]. The un-
derlying assumptions in all these equations is that there are no slip angles on any
wheels and that longitudinal slip is the same on each drive wheel.
For the front left steerable wheel,
/L ¼ tan�1 2bðxL � xRÞxLðtB þ tFÞ þ xRðtB � tFÞ
� �: ð3Þ
Similarly, for the front right steerable wheel,
/R ¼ tan�1 2bðxL � xRÞxLðtB � tFÞ þ xRðtB þ tFÞ
� �: ð4Þ
We can see that if tB ¼ tF, the equations simplify to the equations developed by
Spark and Besselink [4].
For a vehicle using two independently driven wheels and only one steerable wheel
at the front, we have the case where tF ¼ 0. Hence, the equation for the steer angle is
as follows:
/ ¼ tan�1 2bðxL � xRÞtBðxL þ xRÞ
� �; ð5Þ
Fig. 1. Geometry of a 2WD2WS vehicle with unequal track.
192 B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198
where / is the steer angle of a lone non-driven wheel. This relationship is used as the
basis for the computer algorithm of the test-bed vehicle described later.
3.3. Measures of performance
Drawbar performance is the most important performance indicator for off-roadvehicles that are designed to pull or push various types of working machinery, e.g.,
tractors. The main measures are as follows.
Drawbar pull, Fd, is the force available at the drawbar, and is equal to the dif-
ference between the driving force, F , developed by the wheels and the resultant re-
sisting force,P
R, acting on the vehicle:
Fd ¼ F �X
R: ð6Þ
Drawbar power, Pd, is the product of drawbar pull and vehicle speed and rep-
resents the potential productivity of a vehicle. It is defined by the following:
Pd ¼ FdV ; ð7Þ
where V is the actual forward speed.Tractive efficiency (or drawbar efficiency) is usually defined as the ratio of the
output power of a tractive device to its input power. The equation for tractive effi-
ciency may be expressed as follows:
gd ¼PdPW
; ð8Þ
where PW is the power inputted to the driven wheels.
Generally, all the traditional performance measures are for vehicles travelling in a
straight-line and on level ground. Performance characteristics in turns will be mea-
sured in this project; and due to the presence of slip angles, the component of tire
force in the direction of motion needs to be considered in these expressions. How-
ever, it is not possible to investigate these considerations in this paper.
3.4. Test-bed vehicle
The requirements of the test-bed vehicle were as follows:
• to provide a practical example of a computer integrated steering-drive system;
• to allow instrumentation of the vehicle for measuring tractive performance;
• to be capable of being instrumented to assist in the validation of the computer
models developed in the project; and
• to provide comparisons between different conventional vehicle configurations.
The basis of the test-bed vehicle is a John Deere Z-Trak 757 (Fig. 2). This is a zeroturn radius (ZTR) lawn mower. Although it is a ride-on mower, at 25 hp, it has a
power rating near to that of a small tractor but with the benefit of a hydrostatic drive
system. Being a hydraulically driven vehicle, it is capable of being converted to a
vehicle with different drive configurations by changing the arrangement of the hy-
draulic lines. Thus, the tractive efficiency of different drive configurations may be
Fig. 2. John Deere Z-Trak 757.
B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198 193
compared directly on the same vehicle. As well, when modified to include a drawbar,
it should be able to handle moderate to high drawbar loads.Since the computer-integrated concept can be extended from a three-wheeled
vehicle to a four-wheeled vehicle, the three-wheeled vehicle design was selected over a
four-wheeled vehicle. It eliminates problems resulting from uneven load distribution
when the terrain is uneven. A suspension system was considered, but this would
make the vehicle too complex without entirely removing the weight distribution
problem. It also provides a close emulation of a tractor-type vehicle since the usual
trunnion mounted front axle of a tractor has a stability that is similar to a three-
wheeled vehicle. Hence, the two castors were removed and replaced with a frontwheel module with a single wheel.
3.5. Front wheel module
The front wheel module had to have a wheel which was steerable: in some cases,
manually and in other cases automatically by the computer (depending on the
configuration chosen). Therefore, a 12 V 130 W electric motor was connected to the
vertical axis of the front wheel via a chain and two sprockets. Using this arrangementinstead of linkages allows the possibility of an infinite number of turns. The position
sensor for feedback to the computer is described in a later section.
The front wheel module was made to be configurable as a conventional castor, as
well as a steerable wheel. Thus, the original zero turn radius configuration could also
be compared with the other configurations (see Fig. 3).
In order to obtain the characteristics for a specific tire of a steerable wheel for use in
computer models, the front wheel module can be detached and mounted with a dyna-
mometer on a rolling trolley device with guides. This device allows side force and rollingresistance to be measured for different vertical loads, tire pressures and slip angles.
Fig. 3. Steerable wheel and castor configuration of front wheel module.
194 B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198
The module is also adapted for the mounting of a specially designed dynamom-
eter for the measurement of forces along any of the three axes. Spacers are used when
the dynamometer is not present.
3.6. Control system
The control system consists of the following:
• a computer,
• a data acquisition card,
• relays and electronics, and
• control sensors.
The program for the control of the steering-drive system is loaded in a notebook
computer that is interfaced with the control sensors via a data acquisition card(National Instruments DAQCard-1200). The data acquisition card has 24 digital
inputs/outputs, eight analog inputs, two analog outputs and three counter/timers.
One counter may be used to generate a pulse output.
The steering motor on the front wheel module is switched on and off by a set of
relays triggered from the digital outputs of the data acquisition card.
3.7. Control sensors
The computer program compares the appropriate steer angle for the front wheel
to the current steer angle. The current steer angle is measured with an angular po-
sition sensor. This is a Hewlett Packard HEDS-5701#E10 optical encoder rated at
200 pulses per turn; but since it also has quadrature encoding, further electronics
produces 800 pulses per turn. This encoder is an incremental encoder and not an
absolute encoder, and so some further electronics (which includes an up/down
counter) produces an absolute encoder for the time it is powered on. The use of an
encoder allows an infinite number of turns to be made by the steerable wheel, as well
B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198 195
as allowing a complete rotation to be measured. Potentiometers generally do not
cover 360�, and if capable of infinite rotation have a discontinuity between the ends.
The drive wheel rotational speeds are measured for inputting into the control
program by optical encoders (Allen-Bradley Bulletin 845T Optical Incremental
Encoder 360 pulses per turn) mounted on each drive wheel. The pulses from the two
encoders are used to gate two counters on the data acquisition card: one counter foreach drive wheel. The third counter is used to the generate the set frequency of pulses
which are gated by the encoders. Hence, the drive wheel rotational speeds are in-
versely proportional to the counts. This system is able to produce estimations of
speed more rapidly than by counting the pulses outputted by the encoders.
The above sensors are required for a basic control system. Further sensors are
required for a more sophisticated system.
3.8. Performance measurement sensors
Various sensors are required in order to determine tractive performance. The
power input and power output are required for efficiency measurement. For power
input, the input torque to the wheels and rotational speed need to be measured.
In conventional tractor experiments, torque load cells are used (and rotational
velocity measured) on an input shaft. These are not be able to be applied in the test-
bed vehicle as it is hydraulically driven. Since the rotational speed of each of the
drive wheels is already required for the computerised steering-drive control system, itis advantageous to measure the torque at each drive wheel as well. With the test-bed
vehicle, this is conducted by measuring the pressure drop across each hydraulic drive
motor using pressure sensors. The pressure drop across a motor is a function of
torque and rotational speed. With a set of calibration curves, the torque can be
determined from the measured pressure drop and the rotational speed. One pressure
sensor (Measurement Specialties Inc. MSP-600-350) is on the inlet and the other on
the outlet of each motor. The pressure sensors input data to the data acquisition card
via the analog inputs. Since the torque input is measured for each drive wheel, anextra benefit, in terms of analysis, is that the torque distribution between the drive
wheels is able to be determined.
For output power, the drawbar pull and velocity at the drawbar hitch is required
for drawbar efficiency. In a straight line, the velocity at the drawbar hitch is the
vehicle velocity. For turning, the velocity of the hitch needs to be determined either
directly or by deduction. Drawbar pull is measured with a load cell. When turning,
the draw angle also needs to be known and this is measured using a potentiometer
connected to an analog input of the data acquisition card.When the instrumentation is set up for tractive (drawbar) efficiency, other com-
mon measures of performance, such as drawbar power, can also be calculated.
3.9. Dynamometer
A dynamometer was designed and constructed for mounting on the front wheel
module (see Fig. 4). It consists of a S-type load cell sandwiched between two 10 mm
Fig. 4. The dynamometer designed for measuring forces on the front wheel.
196 B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198
plates with five small roller bearings and guides. It has overall dimensions of 200
mm� 200 mm� 70 mm.
The dynamometer or a number of dynamometers can be mounted in the front
wheel module to measure force in the vertical axis (vertical load), lateral horizontal
axis (side force) and longitudinal horizontal axis (rolling resistance). The amplified
load cell output is inputted via an analog input of the data acquisition card to the
computer. The forces on the front wheel are not necessary for standard tractive
efficiency measurement. However, the forces are needed to validate computer sim-ulations developed in the project for each of the steering-drive systems.
3.10. Comparison of configurations
An aim of the research is to compare the tractive performance of the computer
integrated steering-drive system with conventional steering-drive systems. In order to
compare like with like (experimentally, rather than with computer simulations), it
was desirable to have a test-bed vehicle that was able to adapt to different steering-drive configurations. Hence, factors such as track, wheelbase, tire type, vehicle
weight, weight distribution, and power would be the same for each configuration.
The front wheel module (as described already) is one element of the adaptable
steering-drive configuration concept used in this research (note that the castor option
produces a slightly varying wheel base in turns). The other element is the adaptable
hydraulic circuit that was fitted.
An hydraulically driven vehicle was chosen because of its potential for re-con-
figuration compared to a mechanically driven vehicle. The original drive system ofthe test-bed vehicle is an independent drive system with one variable displacement
hydraulic pump matched with one fixed displacement hydraulic motor for each drive
wheel.
Fig. 5 shows the three different hydraulic circuits that can be configured with two
pumps and two motors: independent, open differential and locked differential (1:1
speed ratio) drive systems. These are the three configurations of interest. This allows
Fig. 5. Independent drive, open differential and locked differential hydraulic configurations obtained using
the hydraulic circuit designed for the project.
B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198 197
the comparison of following steering-drive systems: open differential drive with
wheel direction steering, independent drive with wheel speed steering (and castor),
locked differential drive with wheel direction steering, and the computer integratedsteering-drive system.
The original hydraulic pipes were removed and replaced with an arrangement of
hoses and valves that can be configured to these three drive systems relatively easily.
Opening two valves switches the circuit from independent drive to differential drive.
To obtain the locked differential drive two short hoses are disconnected, and a longer
hose installed between the outlet of one motor and the inlet of the other. For the
locked differential configuration, it was considered that a system with valves was too
complex and not necessary.The John Deere Z-Trak 757 as it appears after modification is shown in Fig. 6.
Fig. 6. John Deere Z-Trak 757 after modification.
198 B.C. Besselink / Journal of Terramechanics 41 (2004) 187–198
4. Conclusion
The test-bed vehicle outlined in this paper demonstrates the feasibility of an im-
proved wheeled vehicle that uses a computer integrated steering-drive system and
that has two independent drive wheels and steerable non-driven wheels. This vehicle
has all the tractive advantages of two independent drive wheels with none of thedisadvantages. The secondary steering system assists the primary steering system
(from the drive wheel speeds) when side forces act on the vehicle, while producing
minimal conflict.
As it is hydraulically driven, the test-bed vehicle can be instrumented in a unique
way to measure the parameters required for tractive performance, in particular,
tractive efficiency. This is achieved by utilizing the outputs of the sensors of the
control system and providing additional measurement sensors.
The capacity of the test-bed vehicle to be configured to emulate a range ofsteering-drive systems provides a significant advantage when measuring tractive
performance, due the vehicle parameters being the same. Hence, since like is com-
pared with like, the performance comparisons are more valid than if different ve-
hicles using these steering-drive systems were compared.
The major advantage of a vehicle using a computer integrated steering-drive
system, as described, is the improved ability to traverse steep slopes and the ability to
have larger non-driven wheels. The latter allows improved load carrying capacity.
The presence of a steering system at each end of the vehicle allows greater variationof load distribution while maintaining the same level of steering capability.
References
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[3] Lu J, Spark IJ, Vains GG, Spriggs KR. Computer integrated steering/drive systems with steering wheel
control. In: Proceedings of I.E. Aust. Conference on Control Engineering, Sydney, Australia, 1997. p.
236–41.
[4] Spark IJ, Besselink BC. Zero turn radius vehicle incorporating computer-controlled �intelligentcastors�. In: ASME Computers in Engineering Conference, Minneapolis, USA, 1994. p. 825–27.
[5] Spark IJ, Ibrahim MY. Integrated mechatronics solution to maximise tractability and efficiency of
wheeled vehicles. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics,
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