Improvement of dynamic wheel loads and ride quality of heavy
agricultural tractors by suspending front axles
G. RILL, D. SALG and E. WILKS, Regensburg, Germany
The development of agricultural tractors clearly shows the tendency towards faster vehicles. Heavy
agricultural tractors driving on uneven roads at 40 or 50 km/h do not offer any ride comfort at all. High
wheel load variations generate stresses and strains in roads and reduce ride safety to critical values. By
means of a newly developed suspended front axle it is possible to considerably improve ride safety and
ride comfort. The proven standard design of tractors is maintained. Field tests and computer calculations
prove the effectiveness of a suspended front axle.
INTRODUCTION
1. Today the farm tractors are all working machines
mostly destined for
agricultural use. Business
developments, however, s how an increas ing tendency
to
multi-purpose
vehicles.
Besides
the
usual
agricultural service, transport work is also carried out
to an increasing extent. This way of using tractors
gains in importance. The vehicle speed has an
increasing influence on the economy of a tractor.
2. Vehicle speeds of 30 km/h are usual to date, but,
vehicle speeds of 40 km/h are prevailing in those
countries where permissible by law. Today some
vehicles are even offered with permissible maximum
speeds of 50 km/h or 70 km/h resp., Fig. 1.
3. The permissible maximum speed is first of all
limited by the ride comfort and the the ride safety. The
ride comfort is mostly increased by suspended driver
seats and in some cases suspended driver cabs are
used.
4. Ride comfort and ride safety can be improved by
actively influencing the three-point hydraulics. Of
course, this is only possible if a heavy-duty mounted
implement, e.g. a plough is attached.
5. Currently the non-suspended design causes high
wheel load variations at the tractors. Due to this there
are high stresses and strains in the road and the ride
safety is severely affected.
Fig. 1. JCB FASTRAC
116
6. With a suspended axle, as currently in development
by ZF Passau, the ride comfort and ride safety of a
tractor with or without mounted implements are clearly
improved. For a perfect adjustment of the suspension,
field tests
are
made together with computer
calcul ations.
STANDARD TRACTOR
Concept
1. Today most tractors are made acc. to the so-called
modular design. Rear axle, transmission and engine
are rigidly connected to each other. For equalizing
extreme ground unevenesses the front axle is movable
round an axis in longitudinal direction of the vehicle.
2. The suspension of the tractor and the damping of
the vehicle vibrations is exclusively made by large
volume tyres. Different tyre sizes on front and rear
axles as well as the driver's cab located in the rear
third of the vehicle are the essential features of these
vehicles, Fig. 2.
3. Various mounted implements can be located both
in the rear and front area. Hydraulic lifting devices
ensure an exact positioning of the implements. By
means of P.T.O. shafts driving is also possible on these
two main mounting areas. In practical service this
results in a variety of loading alternatives, Fig. 3.
Frg.2
Standard tractor
Heavy vehicles and roads: technology, safety and policy. Thomas Telford, London. 1992.
DYNAMIC LOADS
4.
With an empty tractor the axle loads are
rather evenly distributed on front and rear axle. In
the case of heavy mounted front or rear units the
. relating axle is loaded up to 80% of the total
weight,[1J. The Consequencies of these extremely
axle loads are considerably reduced ride safety, a
lower ride comfort and high loads on roadways.
Dynamic Wheel Loads and Ride Quality
5.
Fig. 4 shows the driving behaviour of a
standard tractor on an uneven roadway (country
road) at a speed of 50 km/h. The road profile is
shown in Fig. 6. The front and rear-mounted
implements result in a static load of 47 kN at the
front axle and of 44 kN at the rear axle.
6.
Considerably reduced
ride safety
and
enormous
load
on
the
roadway
are
the
consequencies
of
these
high
wheel
load
variations.Furthermore the high shock load values
in the vehicle body are unhealthy to the driver.
Fig.3. Some loading alternatives
60
60
front
50
40
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Ride characteristics of standard tractor
at high speed (50 km/h)
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o
234
5
6
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9
time (s)
10
Ride characteristics of standard tractor
at low speed (20 km/h)
117
HEAVY VEHICLES AND ROADS
6
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2
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0
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14
28
42
56
70
84
98 112 126 140
space coordinate (m)
Fig. 6.
Road profi le
7.
A vehicle speed decrease, e.g. to 20 km/h,
obviously reduces the wheel load variations and improve the ride comfort, Fig. 5.
8.
Longer transport times due to lower driving
speeds, however, will reduce the economy of a
tractor. Due to the installation of suspended front
axles more ride safety and ride comfort can be
obtained.
TRACTOR WITH SUSPENDED FRONT AXLE
State of the art
1. The characteristics required for a suspension
system
in
the tractor
are based
on
other
objectives
than
for
passenger
cars
or
for
commercial
vehicles.
The
variety
of
possible
combinations of mounted implements results in a
large range of static axle loads in service.
Furthermore rigidity as well as no influence at all
on
the
control
hydraulics
of
the
mounted
implements are the main demands.
2.
Due to the modular design there are very
few possibilities to suspend the rear axle. The
tractor manufacturers have realized in time the
necessity to use at least a suspended front axle.
MAN and Fendt e.g. already offered corresponding
vehicles in 1950, Fig. 7. In this case the front axle
was connected with the body by means of a leaf
spring, as done by other manufacturers. However,
this concept could not penetrate the market, [5J.
Fig. 7.
118
MAN tractor with suspended front axle
Fig. 8.
MB-Trac
3.
Only in 1972 a vehicle with front axle
suspension was produced in the Federal Republic of
Germany, i.e. the MB-Trac, Fig. 8. Also in this
case a mechanical suspension is obtained by two
coil springs.
4.
A new vehicle in Trac-design is the
JCB-FASTRAC, Fig. 1. Depending upon the vers ion
this vehicle reaches driving speeds up to 80 km/h.
With a mechanically suspended front axle and a
hydro-pneumatic suspension on the rear axle this
vehicle reaches a relatively high ride comfort.
Rear-mounted implements directly attached to the
axle will certainly result in too high dynamiC wheel
loads on this axle.
ZF-Axle Layout
5. The modern tractor design includes all-wheel
drive and level control. The newly developed front
axle APL -2000 from ZF Passau fully meets these
requirements, Fig. 9.
6. The axle carrier is supported at the body by
two hydro-pneumatic spring cylinders. Driving and
braking forces are absorbed by the torque tube.
The torque tube joins the body on one end and the
axle carrier on the other end via a ball joint. The
lateral guiding of the axle is made by a Panhard
rod.
Fig. 9.
Torque Tube Axle
DYNAMIC LOADS
60
I
I
I
front
50
HD High pressure storage element (main
sprin~)
~D
40
Low pressure storage element
(additional spring for load compensation)
30
DR Pressure regulator
- Pressure regulator
- Limitation of max. and min. prt'ssure
- Damping valves
- Shifting spring suspension/oscillation
:\'R Level regulator
FP Switch: Spring suspension/osciDation
P.T Encrg)', supply central hydraulic unit
.,.
20
z
20
0
60
(\j
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40
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,!A,~oI.
,!Ui!
!j~,
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30
Dynamic Wheel Loads and Ride Comfort
10.
Fig. 11 shows the driving behaviour of a
tractor with suspended front axle on an uneven
roadway at the speed of 50 km/h. Even driving at
high speed the wheel load variations at the front
axle are considerably lower than for the standard
tractor at a lower speed. The wheel load variations
at the rear axle are also lower in comparison with
those non suspended vehicles.
11.
First of all the driver, almost sitting over
the rear ax le in standard tractors, profits from
the suspended front axle by the reduction of the
body pitching. Since the rear axle remains nonsuspended, the shock loads at the driver's seat
are only insignificantly affected by the suspended
front axle. In this case a suspended driver's cab
would compliment the effectiveness of a suspended
front axle.
12.
As the hydropneumatic suspension system
automatically adjust to different static axle loads
the advantage of a suspended front axle holds for
any loading condition, Fig. 12.
!A
rear
50
Hydro-pneumatic suspension
7. The axle suspension is makes the spring
engagement and disengagement possible as well as
the free movement round the torque tube axle.
8.
If the panhard rod is not attached to the
axle carrier but to the wheel body, the axle
carrier moves in lateral direction when steering. By
means of the pivoted torque tube at the body, an
additional
steering
movement of
the
axle
is
produced. Due to the lateral displacement of the
axle more clearance between vehicle body and the
inner tyre wall is obtained, such that a larger
steering angle is possible. As a result the turning
circle of the vehicle can still be reduced. Steering
is alternativly made through double-acting steering
cylinders or a turning lever steering.
9. The suspension is hydro-pneumatic, Fig. 10.
The spring accumulators are filled with nitrogen.
By
means
of a special
regulating
valve the
pressure is adjusted to the static axle load. A
level control valve is compensating the different
vehicle loads. The axle movements are absorbed by
a throttle valve. This design ensure good vibration
damping
characteristics
even
under
extreme
different
axle
loads,
For
special
work
the
suspension can be locked. The axle will then
behave like a standard swing axle.
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o
2
3
4
5
6
7
8
9
10
time (s)
Tractor with suspended front axle
at high speed (50 km/h)
Fig. 11.
z
50
suspended
axle
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standard
axle
40
50
static
wheel
load
60
static front axle load (kN)
Fig. 12.
Effect of suspended front axle at
different loading conditions.
Driving over an obstacle (25 km/h)
119
HEAVY VEHICLES AND ROADS
SIMULATION MODEL
Concept
1. The tractor body, the front axle and the four
wheels are considered as rigid bodies, Fig. 13.
2.
The coordinates x R ' YR' zR' "'R' I3 R , YR
describe the location of a reference frame fixed in
the tractor body with respect to the inertial
frame. The movements of the
tractor body are
unconstrained. Rear axle and driver's cab are
rigidly connected with the body. The angular
speeds of the wheels are described by ° 1, ° 2 , 03
and 04 . At point G the front axle is pivot
mounted with the body. The remaining possibilities
of axle movement a.A' ~A' YA are limited by a
panhard rod.
3. If the panhard rod is fixed at the wheel body, a constraint condition for the yawing movement
of the axle is obtained in form of
YR
=
YR
(a. R
'
~R ' 8 1 ) .
(1)
Where 8 1 describes the rotation of the left front
wheel (wheel 1) round the king pin. Steering kinematics entail another constraint condition
=
(2)
4.
Thus the tractor model has f=9 degrees of
freedom, which are summarized in the position
vector
y
=
[ xR'YR,zR'
a.R'~R,'YR' a.A'~A'
T
81
J.
(3)
By means of generalized speeds the equations of
motion can be simplified, see [2]. In this case it
is adequate to apply as generalized speeds the
components of
=
(3)
and
=
The vectors vOR' wOR describe the velocity and the
angular velocity of the reference frame with
respect to the inertial frame O. The subscript R
separated by a comma means that the components
of vOR and wOR are expressed in the reference
frame.
5.
By means of Jourdain's principle, see [3],
the equations of motion are obtained in form of
K(y)
=
w
= z ,
Q ( y, z, w )
=
(4)
R ( y, z, w ) .
The vector of the generalized speeds is given by
. T
Z = [vRx,VRy,VRZ' WRx,WRy,WRz' a.A'~A' 81
(5)
J
The kinematic matrix K(y) directly results from the
generalized speeds chosen.
6.
Due to the skilled choice of generalized
speeds, the mass matrix M(y) only depends very
slightly on the position vector y. Hence, M can be
considered as constant for the simulation. The.
remaining state variables, like the angular wheel
speeds ° 1, ° 2 , ° 3 , 04 and the lateral tyre
deflections
YRE1'
YRE2'
YRE3'
YRE4
are
summarized in the auxiliary vector
w = [° 1,°2 ,°3 ,°4 , YRE1'YRE2'YRE3'YRE4
JT .
(6)
The lateral tyre deflections are making possible a
dynamic description of the lateral forces, see [2].
7.
The tractor model is described by a set of
26 non-linear first order differential equations. The
nonlinearities are resulting from kinematics (steering and front axle suspension) and from the forces (tyres and hydro-pneumatic suspension).
8. During simulation random road unevennesses
are generated by means of presettable spectral
densities and wavinesses via interferences of band
limited noise processes, see [4].
9.
Numerical solution is made by means of a
modified semi-implicit Euler-formula, [3]. Due to
this a run-time minimized computer code is making
possible the optimization of the axle suspension.
Model Quality
10.
Fig. 14 and Fig. 15 show a comparison
between calculations and measurements. A tractor
with suspended front axle and an axle distribution
as indicated above is driving on an uneven roadway
with a speed of v = 50 km/h.
3
04t
*Y
M(y)* z
60
measurement
50
40
J
°3
30
•.Mo,
.~,
z
~
20
..
~JIi
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l~ ~ rfII\J
V.
10
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'¥
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YA
'{
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(ij
J.,. 81
QJ
.£:
~
I
~A
0
60
30
lli,~
J
wheel 1
Fig. 13.
120
Tractor model
°1
I
I
simulation
40
20
wheel 2
I
50
L~.I
'" LA ...
AAIA
"l1li. ~A
k!UJA I,Ud, 11 .. ,I.
10
00
2
3
4
5
6
7
8
time (s)
Fig. 14
Front axle wheel loads
9
10
DYNAMIC LOADS
5.
Paul, M.; Wilks, E.
Driven Front Axles for
Agricultural Tractors. ASAE (American Society of
Agricultural
Engineers)
Distinguished
Lecture
Series, Tractor Design No. 14, 1989.
6. Wimbeck, M. Vergleich zwischen Messung und
Fahrsimulationsrechnung
am
Beispiel
eines
vorderachsgefederten Schleppers. Diplomarbeit an
der FH Regensburg, Regensburg 1991.
6
4
2
C\J
Vl
0
S
-2
"'c
0
:;:;
III
L
-4
-6
Q)
u
u
6
4
.0
::J
2
>.
0
Qj
III
.£
"U
0
.0
-2
simulation
lA A ~~ ~AI ~.J,"VU lA f1 11,.., i\.-IA lA N\ A, ~
11..""
V V
V V V\ V '''\ V ~yv
ItJ V
V\
~'
-4
-6
Fig. 15
o
234
5678910
time (s)
Body accelerations above front axle
11.
The results of simulation are in good
conformity with the measurements. Both the wheel
load variations as well as the body accelerations
are correctly represented. The somewhat higher
acceleration
values
of
the
measurement
are
supposed to be due to friction in the axle
suspension.
12. With a tractor model verificated at a prototype now the front axle suspension can be adapted
to each tractor version without any essential work
to be done.
CONCLUSION
1. This paper shows that by use of a suspended
front axle the ride comfort and the ride safety of
heavy
agricultural
tractors
are
considerably
improved. Even at high driving speeds an improved
ride safety and almost the same ride comfort are
obtained as with non-suspended tractors at a
lower driving speed by means of the perfectly
adjusted hydro-pneumatic front axle suspension. An
increase of the driving speed , however results in
a higher economy, since times to be spent only for
transport work are reduced.
2. The front axle developed by ZF Passau offers
a
nu mber of advantages.
By
means
of the
simulation
program
ATRACTION
(Agricultural
Tractor Simulation) The front axle is perfectly
adaptable to all vehicles.
REFERENCI ES
1.
Ehrlinger, F.; Carlson, R.
Improved Economy
and Mobility in FWD Axles. SAE Technical Paper
Series 821064, 1982.
2.
RILL G.
Steady State Cornering on Uneven
Roadways. SAE Technical Paper Series No 860575,
1986.
3.
RILL G.
Vehicle Dynamics in Real-Time
Simulation. In: The Dynamics of Vehicles on Roads
and
on
Tracks.
Ed.:
Apetaur,
M.,
Lisse:
Swets-Zeitlinger 1988.
4. RILL G. Demands on Vehicle Modeling. In: The
Dynamics of Vehicles on Roads and on Tracks. Ed.:
Anderson, R.J., Lisse: Swets-Zeitlinger 1990.
121