This document summarizes research on modeling the dynamic characteristics of off-road tires. It describes various testing methods used to measure tire stiffness, damping, and lateral force properties. Results showed stiffness and damping values varied with factors like tire pressure, load, and speed. Models were developed to predict vertical and lateral force responses to different inputs. The research highlighted the importance of direct measurement for simulation accuracy and limitations of existing tire models.

1. Agrartechnik
Hohenheim
9th European Conference of the ISTVS
Harper Adams , September 8 – 11, 2003
The dynamic characteristics of off road tyres
Volkmar Schlotter Alex Keen
Hohenheim University Harper Adams University

2. Agrartechnik
Hohenheim
General purpose agricultural tractor

3. Agrartechnik
Hohenheim
High mobility tractor with full suspension

4. Agrartechnik
Hohenheim
Introduction
Introduction
The two main characteristics of stiffness and
damping are required to simulate the dynamic
behaviour of off road tyres

5. Agrartechnik
Hohenheim
Introduction
Some major differences between off road tyres and
on road tyres are:
Off road tyres generally have:
larger diameters,
larger sections,
large tread bars
Often operate at low rotational speeds
with large deflections,
and large changes in deflection,
They operate on a wide range of hard and soft
surfaces.

6. Agrartechnik
Hohenheim
Introduction
This paper considers:
Vertical (radial), lateral and longitudinal characteristics
The factors that affect their values
The main models used to represent tyres
Methods of determining tyre characteristics used by the authors
Some limitations of using tyre data in simulation models
Some new vertical tyre data and a new model on tyre dynamic
lateral characteristics

7. Agrartechnik
Hohenheim
The Silsoe wheel tester

8. Agrartechnik
Hohenheim
The Silsoe wheel tester

9. Agrartechnik
Hohenheim
Silsoe wheel tester vertical input, vid 1

10. Agrartechnik
Hohenheim
Silsoe wheel tester longitudinal input, vid 2

11. Agrartechnik
Hohenheim
Silsoe wheel tester lateral input, vid 3

12. Agrartechnik
Hohenheim
Hohenheim moving belt test stand, vid 4

13. Agrartechnik
Hohenheim
Hohenheim single wheel tester, vid 5

14. Agrartechnik
Hohenheim
The variation in agricultural tyre stiffness
under normal operating conditions
(Lines and Murphy, 1991)

15. Agrartechnik
Hohenheim
The variation in agricultural tyre damping
under normal operating conditions
(Lines and Murphy, 1991)

16. Agrartechnik
Hohenheim
Ground-tyre contact models

17. Agrartechnik
Hohenheim
Tyre models
Tyre representations: standard tyre model (left),
proposed by Crolla et al (1990) (right)

18. Agrartechnik
Hohenheim
The Harper Adams single wheel tester
on the steel plate bumpy track

19. Agrartechnik
Hohenheim
The HA single wheel tester on the soil tank

20. Agrartechnik
Hohenheim
The coil spring and damper and lock out links

21. Agrartechnik
Hohenheim
The flat steel plate bumpy track

22. Agrartechnik
Hohenheim
1.5 bar tyre pressure and 1606 kg load
on the steel bumpy track close to resonance. Vid 6

23. Agrartechnik
Hohenheim
1.5 bar tyre pressure and 1606 kg load
on the steel bumpy track
close to resonance
Example acceleration time histories
for the wheel on the test tracks
20
10
0
10
20
time, s
Acceleration,m/s2

24. Agrartechnik
Hohenheim
1.5 bar tyre pressure and 1606 kg
load on the soil surface close to resonance. Vid 7

25. Agrartechnik
Hohenheim
1.5 bar tyre pressure and 1606 kg
load on the soil surface close to resonance
20
10
0
10
20
time, s
Acceleration,m/s2
0.5
0
0.5
Figure 2a soil accelerometer trace
time, s
Acceleration,m/s2

26. Agrartechnik
Hohenheim
3 bar tyre pressure and 1606 kg wheel load
on the steel bumpy track close to resonance, vid 8

27. Agrartechnik
Hohenheim
3 bar tyre pressure and 1606 kg wheel load
on the steel bumpy track close to resonance
20
10
0
10
20
Figure 2a soil accelerometer trace
time, s
Acceleration,m/s2

28. Agrartechnik
Hohenheim
T
1 2  


2
1


2 2
2  


2
Amplitude transmissibility calculated
from maximum acceleration
Amplitude transmissibility for a
one degree of freedom system
Tyre radial damping coefficient
Tyre radial stiffness
Data processing
k m 
2

29. Agrartechnik
Hohenheim
Cutting the sine wave on the soil surface

30. Agrartechnik
Hohenheim
Rolling the sine wave surface

31. Agrartechnik
Hohenheim
The effect of four tyre pressures on vibration
transmissibility on the steel plate bumpy
track with the suspension not operating
0 1 2 3 4 5 6
0
2
4
6
8
10
12
Input frequency, Hz
Transmissibility
0.5 bar
1 bar
1.5 bar
2 bar
124 kN/m
469 kN/m
Tyre stiffness
Max tyre stiffness = 645 kN/m at 3 bar

32. Agrartechnik
Hohenheim
The effect of four tyre pressures on vibration
transmissibility on the steel plate bumpy track
with the suspension not operating
0 1 2 3 4 5 6
0
2
4
6
8
10
12
Input frequency, Hz
Transmissibility
0.5 bar
1 bar
1.5 bar
2 bar
1270 Ns/m
247 Ns/m
Damping coefficient

33. Agrartechnik
Hohenheim
The effect of tyre load on vibration
transmissibility at 1.5 bar tyre pressure
on the steel plate bumpy track
no suspension
x – experimental data
0 1 2 3 4 5 6
0
2
4
6
8
10
12
Input frequency, Hz
Transmissibility 1106 kg
1606 kg
2106 kg

34. Agrartechnik
Hohenheim
A comparison with the tyre stiffness
prediction of Lines and Murphy
0 0.5 1 1.5 2 2.5 3 3.5
0
200
400
600
800
Tyre pressure, bar
Tyrestiffness,kN/m
k = 172 – 1.77 Ra + 5.6 Ag + 0.34 W Ra P
Lines & Murphy
prediction
Measured data

35. Agrartechnik
Hohenheim
The effect of three tyre pressures on vibration
transmissibility on the soil surface with the
suspension not operating
0 1 2 3 4 5 6
0
1
2
3
4
5
6
Input frequency, Hz
Transmissibility
1 bar
1.5 bar
2 bar

36. Agrartechnik
Hohenheim
The variation in agricultural tyre damping
under normal operating conditions

37. Agrartechnik
Hohenheim
Tractor and load frame with 1000 kg against the
headstock

38. Agrartechnik
Hohenheim
A lumped mass multi-body model of the
tractor, linkage and load frame
cc kkF F R
k - tyre stiffness
c - damping coefficient
m - mass
mF
subscripts: F - tractor front
R - tractor rear
I - implement
mR
R
top link
rods
lift mI

39. Agrartechnik
Hohenheim
The Working Model screen display

40. Agrartechnik
Hohenheim
Right rear tyre characteristics with
transmissibility equation fitted
0 1 2 3 4 5 6
0
1
2
3
4
5
6
7
8
b) 1.6 bar tyre pressure
Input frequency, Hz
0 1 2 3 4 5 6
0
1
2
3
4
5
6
7
8
a) 2.1 bar tyre pressure
Input frequency, Hz
Transmissibility
Transmissibility

41. Agrartechnik
Hohenheim
0 0.5 1 1.5 2 2.5 3 3.5 4
0
5
10
15
20
25
30
35
40
1000 kg, position 2, 1.6 bar
Track input frequency, Hz
Toplinkmaximumforcevariation,kN
Maximum force variation: measured
and predicted
Top link
Out of phase
In Phase

42. Agrartechnik
Hohenheim
Wheel tester and tractor collected data
Rear tyre
Front tyre
Rear tyre
Tyre pressure, bar

43. Agrartechnik
Hohenheim
Tractor and load frame with 1000 kg against the
headstock

44. Agrartechnik
Hohenheim
Hohenheim single wheel tester, vid 5

45. Agrartechnik
Hohenheim
Hohenheim single wheel tester
lateral force measurement, Vid 9

46. Agrartechnik
Hohenheim
Hohenheim single wheel tester
ramp function input,vid 10

47. Agrartechnik
Hohenheim
Sinusoidal slip angle excitation
and lateral force response
40 50 60 70 80
0.0
1.5
3.0
4.5
6.0

FY
kN °
s
lateralforceFy
time t
0.0
1.5
3.0
4.5
6.0
A
AFY
slipangle

48. Agrartechnik
Hohenheim
Sinusoidal slip angle excitation
and lateral force response
-15
-12
-9
-6
-3
0
3
6
9
dB
15
amplituderatio|F(j)|®Fy
0.1 1 10
-90
-75
-60
-45
-30
°
0
Eck
Eck
tyre 20.8 R38
FZ
= 20 kN; pi
= 0.8 bar
v = 10 km/h; asphalt
rad/s
slip angle excitation frequency log
phaseshift
approach with amlitude ratio
approach with phase shift

49. Agrartechnik
Hohenheim
Lateral force response for a step function and
a ramp function of the slip angle
slipanglelateralforceFY
time t time t

50. Agrartechnik
Hohenheim
Influence of the slip angle changing speed on
the lateral force response
0 2 4 6 8
0
2
4
6
FY
v = 2 km/h
asphalt
step
 = 10°/s
 = 5°/s

°
s
lateralforceFY
time t
0
1
2
3
tyre 520/70 R34
FZ
= 10 kN; pi
= 0.8 barkN
slipangle

51. Agrartechnik
Hohenheim
Course of the lateral force for a ramp change
of the slip angle
0 2 4 6 8 10
0
2
4
6
Reifen 20.8 R38
FZ
= 10 kN; pi
= 0.8 bar
v = 2 km/h;  = 10°/s
asphalt
°
s
lateralforceFy
time t
0
1
2
3

FY
measured
FY
calculated
kN
slipangle

52. Agrartechnik
Hohenheim
Tyre load and lateral forces at the
tractor rear axle, braking in a curve
Späth 2002

53. Agrartechnik
Hohenheim
Calculated relaxation lengths for different
measurement procedures
m
0 3 6 9 12
0,0
0,5
1,0
1,5
2,0
tyre 20.8 R38
FZ
= 20 kN; pi
= 0.8 bar
asphalt
km/h
calculation with amplitude ratio
calculation with phase shift
calculation with step function
relaxationlengthEL
driving speed v

54. Agrartechnik
Hohenheim
Lateral spring and damping parameters
tyre
20.8 R38
tyre
load
FZ
[kN]
inflation
pressure
pi
[bar]
driving
speed
v
[km/h]
lateral
stiffness
k
[kN/m]
lateral damping
coefficient
c
[kN·s/m]
20 0.5 5 128.5 81.5
0.8 145.7 117.1
1.2 175.0 95.2
Influence of
inflation
pressure
1.6 215.9 103.9
20 0.8 2 117.7 274.6
5 145.7 117.1
Influence of
driving speed
10 165.6 43.5

55. Agrartechnik
Hohenheim
Conclusions 1
Conclusions
The method of measuring and determining dynamic tyre
stiffness and damping may affect their values
There is some evidence to suggest that data collected
from a single wheel tester is likely to produce higher
values for vertical stiffness and lower values for the
damping coefficient when compared to that measured
on the target vehicle.
Conclusions
This may be accounted for by moment of inertia affects
in vehicles that are absent in single wheel testers

56. Agrartechnik
Hohenheim
Conclusions 2
Predicting damping behaviour is less reliable than
predicting the value of tyre stiffness.
Conclusions

57. Agrartechnik
Hohenheim
Conclusions 3
Unknown affect of variables:
Effect of tyre temperature
The effect of tyre deflection
The effect of tread band filtering
The effect of tyre run out
Safest to go and measure the tyre data required
Conclusions

58. Agrartechnik
Hohenheim
Conclusions 4
Most of the off road tyre data reported is only suitable
for low frequency simulation and analysis where the
tyre-ground contact length is relatively short compared
to the input frequency wave length.
This allows the use of point contact and rigid treadband
tyre models.
Accurate adaptive footprint models yet to be developed.
Conclusions

59. Agrartechnik
Hohenheim
9th European Conference of the ISTVS
Harper Adams , September 8 – 11, 2003
The dynamic characteristics of off road tyres
Volkmar Schlotter Alex Keen
Hohenheim University Harper Adams University