J. ugric.
Res. (1989)43,
Engng
11-21
Dynamic Characteristics of Large Tyres
A.
H.
KISING:
GGHLICH*
To optimise the vibrational behaviour of tractors it is necessary to have detailed
information on the dynamic properties of tyres. To be able to make statementsabout the
vibrational responseof tyres, the vibrational characteristicsof the tyres must be ascertained
under field and laboratory conditions. A flat-belt tyre test stand has been developed which
makesit possibleto simulatethe essentialoperating conditions of tractor tyres for speedsof
up to 60 km/h and to investigate spring and damping characteristics as well as other
performance characteristics.
Experiments have been carried out which show that there is a decreasein the tyre stiffness
and especiallyof the damping values with an increasein speed.Non-uniformities in the tyre,
such asnon-circularity, can significantly affect the vibration characteristicsof large tyres.
1. Introduction
As the development of agricultural vehicles changes from the purely functional
approach to a more human-orientated one, requirements of safety and comfort
increasingly come to the fore.
In view of the fact that tractors are used frequently (up to 50% of the time) for
transport purposes and that the road conditions in agricultural areas have improved, the
maximum speed of tractors has increased to 40 or 50 km/h. This increase in speed has led
to some new problems in tractor ride dynamics, caused primarily by the lack of a
suspension system. To solve these problems, new developments are being pursued in
respect of axle suspensions, pitch movement reduction and tyre characteristics.
The significance of the damping behaviour of tractor tyres with regard to dynamic
wheel loads is illustrated in Fig. 1, which shows how the wheel vibration, expressed by the
ratio of Fdyn/Fsta,,depends on the damping ratio, over the usual damping range between
D = 0.02 and D = 0.06 and a typical spring rate of the tyre.
To optimize the dynamic behaviour of tractors, it is absolutely necessary to choose the
parameters of the tractor and the tyres with regard to stiffness, damping and selfexcitation on the basis of acceptable experimental data.‘” A greater appreciation is also
needed of the self-excitation of tyres, caused particularly by non-uniformities, which can
lead to additional vibrational effects. The digital simulation of tractor models offers the
opportunity to calculate and predict the dynamic behaviour of tractor tyres by driving
over simulated obstacles and uneven roads. In order to make real simulation possible, it is
necessary to consider the enveloping effects of the tyre contact area and the nonlinear
characteristics of stiffness, damping and non-uniformities.
2. Aims of the investigation
These were as follows: (1) to determine experimentally, accurate tyre characteristics
under different operational conditions up to 40 km/h; (2) to examine the self-excitation
* Institut
fiir
Zoppoter
Strasse
Maschinenkonstruktion,
35, loo0
Berlin
Received
5 March
Presented
at AG
1988;
ENG
accepted
88,
Paris,
33.
Federal
Landtechnik
Republic
in revised
France,
und
Baumaschinen,
of Germany
form
2-6
28 January
March
Technische
Universitlt
Berlin,
1989
1988
11
0021-8634/X9/05001
I + I1 $03.(K)/O
@ IYHY The
British
Society
for
Research
in Agricultural
Eneineerine
12
DYNAMIC
CHARACTERISTICS
OF
TYRES
Notation
c stiffness, N/m
damping ratio, 1
; pyY’
11s
s absorption capacity, %
f time, s
T time period, s
u velocity, m/s
damiing coefficient, Ns/m
mass, kg
n dynamic load factor, 1
pi inflation pressure, N/m2
8 moment of inertia, kg x m2
0 natural frequency, l/s
& frequency of excitation, l/s
D
k
m
effects, particularly those caused by non-uniformities
of rolling tyres under load; (3) to
examine the behaviour of tyres rolling over obstacles; (4) to develop tractor tyre models.
The realistic evaluation of the dynamic behaviour of tyres can be achieved by a
thorough investigation in three steps (Fig. 2).
Experiments on roads, in the laboratory and computer/simulation
are closely connected. The development
and validation of tyre models are dependent on a suitable
laboratory test, whereas road tests can be used for the validation of the laboratory results.
3. Test equipment
3.1. Road experiments
Free oscillation tests were carried out on a smooth road by rolling the tyre over an
obstacle (Fig. 3) and by measuring the sinusoidal amplitude of the axle relative to the
ground, during the decay of the vibration.
L
v = 30-50
km/h
I
F=Fstat
+ Fdyn
Voigt
-Kelwn
Model
0.02
0.06
0.2
Domplng
Fig. 1. Dynamic wheel load as a function
of damping
0.3
rotlo,
D
ratio (D)
A.
KISING;
H.
13
GijHLICH
ROAD EXPERIMENT
-
oscillation
over obstacles
nlth
different
weeds
on an even road
1. Validation of the
laboratory results
accordlng to the road
tests
Test by free
on dlfferent
2.
1. Test
by free
by Passing
2.
LABORATORY
EXPERIMENT-
oscillation
field
condltlons to examine
the wheel-ground
interaction
3. Orlve tests on roads
ADDkiCatlOn
COMPUTER
SIiWLATION
1. Search of sultable
mathematical models
In order to simulate
tyre behaviour as an
Integrated Dart of
the vehicle
Of different
excitation modes to
determlne the tyre
characteristics
3. Measurementof the static
at
and dynamic DrODertleS
dlfferent ooeratlonal
condltlons
2. Slmulatlon of different
ooerational condltlons
and comoarlson nlth the
exoerlmental results
3. Further adaotatlon to
lmorove tne rellablllty
4. Oetermlnatlon of tvre
non-unlfomltles
Fig. 2. Investigation
of dynamic
behauiour
Fig. 3. Road experiments
of tyres in three steps
14
DYNAMIC
/hg.F&d
CHARACTERISTICS
OF
TYRES
,/,-I
Excltatlon
unit
Fig. 4. Diagram
of the fiat band tyre test rig
3.2.
experiments
Laboratory
A new test rig permitted the examination of numerous different properties of large
tyres under different operating conditions.4 The mounting arrangement of the flat band
tyre stand in an electrohydraulic
vibration test rig, permits vertical excitation of the tyre
with harmonic or random signals. The tyre test rig consists of three structural components
(Figs 4 and 5), namely a test frame to guide and load the wheel, a flat band tyre test stand
to simulate road speed and to support the vertical wheel loads and a hydraulic excitation
system in the vertical direction. Details of the tyre test rig are given in Table 1.
Fig. 5. The tyre test rig
A.
KISING;
H.
15
GijHLICH
Table
Tyre
1
test rig details
Static-dynamic
load capacity
Roiling
speed
Supported
area of the steel
Vertical
oscillation
amplitude
Frequency
range
Camber
angle
up to 3.0 t
60 km/h
0.6 m x 1 m
f90
mm
O-10 Hz
band
O-4”
The dynamic experimental data are gathered by servo-acceleration transducers installed
at the vibrating test band and at the test-wheel. The static deflection behaviour is
measured by a load transducer installed at the wheel bearings. Further details are given
by Kising and Gohlich.’
4. Results
of measurements
4.1. Static spring characteristics
The relationship between the load and the displacement of a non-rolling and a rolling
radial tyre for three different inflation pressures is shown in Fig. 6. Both the non-rolling
tyre and the rolling tyre display nonlinear characteristics of increasing stiffness with
deflection. Whereas the non-rolling
tyre has an evident damping hysteresis loop, the
rolling tyre shows periodical load changes which are mainly caused by tyre nonuniformities.
Increasing inflation pressure changes the gradient of the curves; both are
important in characterizing the properties of a tyre.
The relationship between wheel load and tyre deflection is conventionally
represented
by the static curves. The dynamic behaviour is considered in the following sections.
lnflotion
0
20
pressu
40
60
Deflection,
00
100
mm
Fig. 6. Comparison of the stiffnesscharacteristicsof a non-rolling and a rolling tyre for three different
inflation pressures
16
DYNAMIC
CHARACTERISTICS
OF
TYRES
Test by free oscillotmn
Y
I
Harmonic
0
c=F”4”.T?
2
I
excitation
s,F f
I
Hormontc/stochostnc
ezcitotion
Fig. 7. Various methods to determine tyre characteristics stiffness (c) and damping ratio (D)
4.2. Measurements to determine stiffness and damping behaviour of fyres
To investigate the dynamic behaviour of tyres, measurements were made of dynamic
spring rate and damping ratio, using three different methods of excitation (Fig. 7).
The first method is the well known test by free oscillation. The second method uses a
harmonic excitation signal. This method can be used for examining the linear or nonlinear
behaviour of a non-rolling or slowly-rolling tyre. Furthermore, it is possible to obtain the
complete dynamic relationship
between wheel load and deflection of a rolling tyre.
Non-uniformities
disturb the hysteresis loops in such a way that damping information is
obtainable only for non-rolling
and slow-rolling conditions. The third method is well
known in the field of signal analysis of the dynamic behaviour of machines. The vibration
system is excited by a limited random noise in an adequate frequency range. From the
input and output acceleration signals, it is possible to calculate the transfer function of a
tyre. This method has the advantage of exciting the system in a realistic range and
linearizes the tyre characteristic in the range of static load. Moreover, the simultaneously
calculated coherence function offers a remarkable
criterion for the quality of the
measurements.
In principle, the measurements show no significant difference in tyre stiffness and
damping between the different methods. However, measurements of the transfer function
obtained on the laboratory test rig are the most reliable ones, particular for high
velocities. For that reason this method is prefered to calculate the dynamic behaviour of
tyres.
4.3. Dynamic characteristics of two radial tyres of different size
The dynamic stiffness is shown as a function of velocity and inflation pressure in Fig. 8.
The stiffness of the tyres is found to decrease at the beginning of rolling and thereafter
remains relatively constant at higher speeds. In general the stiffness values of rolling tyres
are about 25% lower than for non-rolling tyres. Increasing the inflation pressure increases
the stiffness.
A.
KISING;
H.
17
GOHLICH
600
Fig. 8, Measured
stiffness us a function
of veloci~
and inflation
pressure far two tyres
Damping decreases substantially with increasing speed and decreases slighly with
increasing inflation pressure (Fig. 9). It is apparent that the tyre damping is constant
above 30 km/h. Above this speed, all types of tyres yield equal values independent of
their structural construction and tyre size. As a result it can be concluded that damping
only improves
the dynamic behaviour below 30 km/h and that above 30 km/h better
dynamic behaviour can be achieved only by reduced tyre stiffness.
4.4.
Obstacle
roll-over
properties
The absorption capacity (s) of a tyre can be defined as follows
(obstacle height -wheel lift)
100%
s=
obstacle height
6-9834
1300
kq load
2-4
Fig. 9. Damping
rutio us II function
of velocity and in&tion
pressure for two tyres
18
DYNAMIC
CHARACTERISTICS
_. _.
.:_.
_.
_:.
OF
_,
TYRES
.:
_.
_:
.f
f. . . . . . . . . .
f .
.
.
.
.f
.
.._...
.
.
.:
.I
.I.
,
30
Velocity,
Fig. 10. Absorption
capaciQ
,
40
:
50
60
km/h
of front wheel tyre as a function
(Tyre 13.6 R24, m = 968 kg)
of velocity
and inflation
pressure
-3
0
I
2
3
4
5
Time,
Fig.
11. Rolling
test of a cross-ply
6
7
6
9
IO
s
tyre under load
p = 180kPa)
(Tyre
13.6 R24,
m = 952kg,
v = Skm/h,
A.
KISING;
H.
19
GijHLICH
As an example, a front tyre was examined when passing over a rectangular obstacle of
40 mm in height and 70 mm in width. The expected results are, that s increases with
higher velocities and lower inflation pressures and Fig. 10 shows this to be the case. This
provides a method of comparing the dynamic behaviour of different tyres.
4.5. Tyre non-uniformities
Because tyres are often not absolutely circular, additional dynamic forces are excited
during each revolution. The resulting periodic vehicle vibrations are dependent on the
speed. If the excitation frequency caused by the non-uniformities
is equal to the
natural-frequency of the vehicle, high resonance amplitudes can be induced.
The radial deflection during rolling of a cross-ply front tyre is shown in Fig. 11. This
tyre shows a non-uniformity
characterized by a variation of the rolling radius of about
3 mm. The variation of deflection during the course of rotation of the radial tyre in Fig. 11
is limited to one local region of the tyre periphery. Apart from the effects of mass
unbalance, such a variation is responsible for high changes in the dynamic axle load.
To evaluate the load changes at different speeds, it is advantageous to divide the
maximum load by the static load. Then the dynamic load factor n can be calculated as
follows.
F
n=l+
=Inmax
L stat
If the value of n is greater than 2, the tyre will lose contact with the ground.
In the speed range between 5 and 50 km/h the factor n was calculated from force
measurements (Fig. 12). It is evident that at 37 km/h the tyre was very strongly excited.
At the half frequency, a second resonance could be observed. The resonance ratio at
37 km/h is caused by the first harmonic of the free rolling tyre and can easily be calculated
from the tyre radius and the speed.
2
““““““‘.““‘.‘........
1.8
_.
.I.
.I.
.;.
.:.
.I..
. . . ..
:.
..:
1.6
1..
.*.
.:.
.: ._......_._
.:.
.:.
..
..
+
h
i
,.a...
1.2
,
..
,*,
. .I
1
0
i.
IO
t.;.........
.I.
,j,
,y,
I . . . . . . . . . .. . . . . . . . . .. . .
,
20
load factor
(n) as a function
f
.
30
Veloctty,
Fig. 12. Dynamic
..: . . . . . . . . . .. . . . . . . .._.
.I,
J,
40
f
50
.
,
. ;
60
km/h
of velocity (Tyre 13.6 R24, m = 952 kg, p = 160kPa)
20
DYNAMIC
CHARACTERISTICS
OF
TYRES
10.
2
N’
Pi<
5
6.
4 ‘.
2
0
0
100
Frequency,
Fig. 13. PSD of a freely rohg
150
Hz
cross-ply lyre (Tyre 13.6 R24,
m
= 952 kg, p = 160 kPa)
12
N
6
5
N
c
E
6
=:
a
4
Fig. 14. PSD of a freely rolling
radial tyre (Tyre 136 R24, m = 968 kg, p = 160 kPa)
A.
KISING;
H.
21
GZjHLlCH
4.6. High frequency
properties
A survey of the tyre vertical excitation
frequencies caused by the tyre lugs is shown in
for a
cross-ply tyre. Both the tyre lug frequency and the half tyre lug frequency cause speed
dependent resonances. In the range between 0 and 50 Hz the opposite lugs produce
resonances in the roll mode. The PSD spectrum shows the excitation of the radial mode
and the vertical components of the roll mode. Between 50 and 100 Hz, successive lugs
excite the system in the roll mode.
There also exist considerable differences between PSD curves and cross-ply (Fig. 13)
and radial tyres (Fig. 14). The latter measurements show lower PSD peaks for radial
tyres and missing resonances in the range between 50 and 100 Hz.
The experiment suggests that radial tyres will give a smoother ride than cross-ply tyres.
A reason for this significant difference is the more flexible side wall of radial tyres and the
type of lugs.
Fig. 13 for a cross-ply tyre. The power spectral density (PSD) curves are typical
5. Conclusions
1. The newly developed flat band tyre test rig, fixed in a vertical vibration test rig is an
excellent tool to determine the essential characteristics of agricultural tyres.
2. Rolling and non-rolling tyres possess nonlinear stiffness characteristics; non-rolling
tyres more so than rolling tyres.
3. Measurements of the tyre dynamic stiffness show a decrease of 15-25% at the onset
of rolling but this tends to become constant with increasing speed.
4. In the frequency range between 0 and 30 km/h the damping decreases by about
60-70%. Cross-ply tyres and low inflation pressures cause higher damping. Up to
30 km/h all types of tyres have a constant damping ratio of about O-02.
5. The absorption capacity of a tyre increases with velocity and as the inflation pressure
is decreased.
6. Tyre non-uniformities
are mainly responsible for resonance vibrations at higher
velocities.
7. Tyre lugs cause excitation of vehicles at high frequencies. Cross-play tyres show two
significant frequency ranges caused by the mutual and successively arriving tyre lugs
in the contact area. Radial tyres give a smoother ride, because the resonance
intensities are less severe and the resonance frequencies caused by successively
arriving lugs have less effect.
References
M. Dynamik der Kraftfahrzeuge (Dynamic of motor vehicles) Band B, Springer Verlag
Berlin, Hamburg, Heidelberg 1984
* Kutzbach, H. D.; Schrogel, H. Dynamic behaviour of rolling tractor tyres. International Society
for Terrain Vehicle Systems,9th International Conference, Barcelona CongressHall 1987 pp.
457-464.
3 Kising, A.; Giihlich,
H. Kenndatenermittlung von AS-Reifen fur hohere Geschwindigkeiten
(Determination of characteristics of agricultural tyres for higher speeds). Grundlagen der
Landtechnik 1988,38(3): 78-87
’ Giihlich, H.; Kising, A. Flachbahnreifenprtifstand zur Kennwertermittlung von grol3volumigen
Traktor- und Baumaschinenreifen(Tyre band test stand for large tractor and wheel loader
tyres). Forschungaktuell, TU Berlin 1987, pp. 52-54.
’ Mitschke,