Thesis presentation

1. +
Master of Engineering in Mechanical Engineering
By: Kirsten Braun
Supervisors: Dr. Theunis R. Botha, Prof. Pieter Schalk Els
The Effect of Wear on the Stiffness of an
Agricultural Tyre

2. Introduction (1/2)
• As commercial farms are ever increasing in size, due to the acquisition of non-
contiguous land, as well as due to the urbanization of areas which have
traditionally been used for agricultural production, a substantial increase in the
operation of low speed rated agricultural equipment on public roads has been
seen
• Agricultural vehicles are therefore being operated on terrains which are more abrasive than
what they are designed for, which is leading to significantly faster wear rates, ultimately
compromising the life cycle and safety of the vehicle
• With operational costs of agricultural vehicles regularly being forced to a
minimum, more agricultural vehicles are found operating with tyres ranging from
new tyres with fully intact tread to fully worn tyres with no remaining tread
• This is often not considered by original equipment manufacturers (OEM’s), as the
manufacturer designs tyres with the expectation that the user replaces the tyre
once a specified wear threshold is reached

3. Introduction (2/2)
• Tyre stiffness is commonly known to directly influence the handling,
ride comfort and other performance aspects of the vehicle
• With the characteristics of a tyre changing over its operational life due to
wear and tyres being used beyond their designed usage, agricultural tyres
are being driven to their limit
• However, the affect that tyre wear has on the overall stiffness of a tyre is not
very well understood

4. Scope
• This study develops a 3D finite element (FE) model to capture the behavior of an
typical large lugged agricultural tyre.
• Based on availability, selected is the TM700 Trelleborg 280/70R16 orchards/vineyards tyre
• FEA model is validated at an unworn state (zero wear) against historical
longitudinal, lateral and vertical stiffness data
• Succeeding model validation, the geometry of the tyre model is adjusted to
replicate the tread of a worn tyre at the wear states of 50% and 100%
• Through maintaining the test conditions of the historian data, such as applied force,
inflation pressure, coefficient of friction and camber, a direct but relative comparison
between the respective result sets is made

5. Objectives
• This study aims to determine whether tyre wear affects the stiffness of an
agricultural tyre
• A validated model is used to predict the relationship between the percentage of wear (0%,
50%, 100%) and the tyre’s vertical, longitudinal and lateral stiffness
• Should the stiffness be affected significantly, it may require OEM to consider both new and
worn tyres during the design phase of tyre development.

6. Pneumatic Tyre and
Tyre Stiffness
• Before developing a representative model,
one of the first steps was to determine its
complexity
• This was done through researching the
respective regions of a typical agricultural
tyre, and identifying their individual
characteristics and the effect that they have
on the overall tyre behaviour
• Literature1, 2, 3, identifies tyre stiffness as a
highly important characteristic of a tyre
that influences the performance of the tyre
during both static and dynamic maneuvers
• It is deduced that any influence that wear
has on the tyre stiffness will lead to possible
changes in performance
1 Lines and Murphy (1991); 2 Zegelaar (1998); 3 Gipser (2005)
Tyre assembly/construction of a Radial tyre (Quintarelli, 2018)
Modified flexible ring model incorporating the tyre-road interaction
(Zeglaar, 1998)

7. Investigative
Approaches (1/2)
• In order to gain a better understanding of
how specific variables influence a tyre's
performance attributes, numerous tyre
characteristics such as side-force versus
slip-angle curves or force versus deflection
curves are required1
• However, these characteristics are generally
not available for large agricultural tyres as tyre
manufacturers either do not have these
characteristics or do not choose to publish
them
• Therefore, in the effort to parameterize a tyre,
extensive experimental work is required (often
requiring static/dynamic tyre test rigs)
1 Babulal (2016);
Static Tyre Test Rig in Position for Vertical and Longitudinal Tyre Testing
(Wright, 2016)
Dynamic Tyre Test Rig in Position for Vertical and Longitudinal Tyre
Testing

8. Investigative Approaches (2/2)
• In an era of simulation-driven development, the use of tyre modelling enables the
acceleration of the tyre development process
• The non-linear behavior of tyres makes them a complex vehicle component to
accurately model
• The inherent viscoelasticity of tyres and their sensitivity to loading speed, temperature and
their environmental surroundings all contribute to the complexity of precisely predicting
tyre behavior1
• The use of modelling and virtual testing allows some of the difficulties and issues
which arise from experimental work to be avoided
• This however requires that the model accurately predicts the intended properties and can
be used to test the desired phenomena
1 Veen (2007);

9. Tyre Model
• As an investigation adapts from studying simple
static tyre behavior to exploring dynamic
maneuvers, more complex multi-body models
are required1, 2
• As empirical models do not consider the
geometric shape of the tyre, this particular
approach cannot be used to determine the effect
that a geometric change has on a tyre's
characteristics
• Due to the low frequency of static tests, and the
complex geometrical and irregular shape of tyres,
the mathematical modelling of FEA would allow
for the physics and tyre behavior to be captured.
• Research1,2,3,4,5 demonstrates the ability FE
models have to accurately predict the force-
displacement relation
1 Conradie (2014); 2 Stallmann and Els (2013); 4 Stallmann and Els (2014); 4 Zegelaar (1998); 5 Stallmann (2018)
Classifications of Tyre Models (Conradie, 2014)
Empirical, Semi-Empirical and Theoretical Tyre Models (Zegelaar,
1998)

10. External Tyre Geometry
• Optical measuring techniques presented in
1, 2, 3 have shown good accuracy when it
comes to the developed geometric tyre
representative
• Due to the availability and efficiency, the
geometry of the tyre was obtained through
using a calibrated 3D portable laser scanner
• This device is a highly accurate device that
uses computer software to process the
collected data
• By sweeping the portable scanner over the
tyres surface the emitted laser light is able
to create a 3D point cloud
• During post-processing, the incorrectly
documented data points, as well as external
points from the surroundings picked up by
the laser are removed
3D portable scanner tyre and calibration setup
Post-processed of 0Bar case in CloudCompare (a) point cloud and (b) meshed
surface
1 Conradie (2014); 2 Stallmann (2018); 3 Ghoreishy (2008);

11. Pneumatic Tyre
• Before developing a representative
model, one of the first steps was to
determine the complexity of the
internal geometry
• This was done through researching the
respective regions of a typical agricultural
tyre, and identifying their individual
characteristics and the effect that they
have on the overall tyre behaviour
Tyre assembly/construction of a Radial tyre (Quintarelli, 2018)

12. Internal Tyre Geometry
Internal design of the 3D geometry for selected tyre
• As optical measuring techniques are only
able to scan the surface of an object, the
interior tyre construction is determined
by bisecting the tyre and determining the
respective layers of the tyre.
• However, due to limitations to equipment,
the internal construction, specifically of the
number of belt layers, needed to be
estimated
• Despite this estimation, the basic design of
two belt layers is not uncommon for
agricultural tyres, confirmed by the design
implementation for the large off-road tyre
studied in 1
1 Stallmann (2018);

13. Material Properties (1/2)
• Hyperelasticity is a reversible process in which
the energy, or work dissipated within a
material during loading process is completely
removed when the load is removed1
• Common formulations used to model
hyperelastic nature of rubber in FEA is the
Mooney-Rivlin (first and second-order) and the
Ogden model, as these models offer stable
solutions2,3,4
• Due to the proven accuracy of Mooney-Rivlin
model, the simplicity of its formulation, this
hyperplastic material model was used to
represent the tread and sidewall of the tyre
Mean Percentage Error [%]
Material Model
Sidewall
Tread
5.31
8.41
Neo-Hookean
1.62
4.02
Mooney-Rivlin
5.33
7.63
Yeoh
1.43
2.94
Ogden
Mean Percentage Error Compassion between Hyperelastic Model
Material Properties and Experimentally Obtained Properties of
Rubber for a Large Off-Road Tyre (Stallmann, 2018)
1 Melly (2021); 2 Conradie (2014); 3 Ghoreishy (2008); 4 Stallmann (2018);

14. Material Properties (2/2)
• As the particular construction of the
TM700 tyre as well as the material
properties of the selected subject tyre is
unknown, this study uses a
combination of properties found in 1, 2
as an estimate to what the material
properties of the subject tyre may be
• Fine-tuning of the properties is performed
to better fit historian data on an unworn
tyre
Material Models
Material
Model
This Thesis
Baranowski et. Al.
(2012)
Conradie (2014)
Mooney-Rivlin
Mooney-Rivlin
Neo-Hookean and
Orthotropic
Tread
Mooney-Rivlin
Mooney-Rivlin
Ogden and
Orthotropic
Sidewall
Isotropic
Mooney-Rivlin and
Isotropic
Isotropic
Bead
Isotropic*
Orthotropic
Orthotropic
Belt
Material types used for the respective tyre segments in Conradie (2014) and
Baranowski et al. (2012).
1 Stallmann (2018); 2 Ghoreishy (2008);
* Successfully modelled as isotropic material by Stallmann (2018)

15. Developed Tyre Model
• Tyre model is developed in ANSYS
Mechanical
• “Large deflection" : Accounts for the
nonlinear changes in stiffness as a
result of the transforming shape of the
parts that are simulated.
• Required for accurately representing
rubber deformation
• Stiffness matrix is reiteratively calculated
as the tyre deforms
Developed Tyre Model
External design of the 3D geometry for selected tyre

16. Contacts
Visual representation of the simulated connections/contacts
between the respective tyre parts
• Bonded contacts used for contacts where motion
between two parts is negligible,
as this contact suppresses all relative motion
between the bodies in contact1
• Where relative motion between two bodies is
anticipated to be large, i.e. between the tread and
the contact surface, frictional contacts are used
• 1 presents a static frictional coefficient of 0.7 for an
all-terain off-road tyre
• 2 states that truck tyres generally exhibit lower
coefficients due to their difference in tread
construction and higher loading within the contact
patch.
• Thus, warranting a lower coefficient than
presented in 1, therefore, coefficient of 0.64 is used
1 Stallmann (2018); 2 Gillespie(1992)
Contact Type
Contact Name
Bonded
B1, B2, B3, B4
Frictional (0.64)
F1
Simulated connections/contacts between the respective tyre
parts

17. Boundary Conditions
1 Stallmann (2018);
• FE model aims to replicate a STTR test set up
• Neumann boundary condition is applied
onto the tyre structure steadily
Loading’s applied to the three-dimensional ANSYS tyre model
Dirichlet Boundary
Condition
Standard Earth Gravity
Internal
Pressure
Vertical Vertical + Longitudinal Vertical +
Lateral
Time = 0
Tyre Constrained
Gravity Applied
Time = 1
Tyre is Pressurized
Time = 2
Directional Displacement
Applied

18. Element Types
• Bodies modelled as solids (carcass, sidewall, belt) were automatically assigned element
types SOLID186, SOLID187
• Assignment of these element types is dependent on the shape of the body as well as the
selected mesh method
• With the goal of reducing computational times, bodies with one significantly larger
dimension (bead), BEAM 188 elements are used
• Convert a 3D structure or body into an idealized one-dimensional set of line element
• In this instance the stress along the length of the beam is often significantly higher than the
other directions, making then relatively negligible
Behaviour
Node Structure
Element Type
Exhibits quadratic
displacement behavior
10-noded element tetrahedral structural solid
SOLID186
20-noded structural solid
SOLID187
–
2-noded beam element
BEAM188
Element Types and Characteristics (ANSYS Inc.,2021a).

19. Element Types
• Bodies modelled as solids (carcass, sidewall, belt) were
automatically assigned element types SOLID186,
SOLID187
• Assignment of these element types is dependent on the
shape of the body as well as the selected mesh method
• With the goal of reducing computational times, bodies
with one significantly larger dimension (bead), BEAM 188
elements are used
• Convert a 3D structure or body into an idealized one-
dimensional set of line element
• In this instance the stress along the length of the beam
is often significantly higher than the other directions,
making then relatively negligible
Behaviour
Node Structure
Element Type
Exhibits quadratic
displacement behavior
10-noded element tetrahedral structural solid
SOLID186
20-noded structural solid
SOLID187
2-noded beam element
BEAM188
Element Types and Characteristics (ANSYS Inc.,2021a).
BEAM188
SOLID186
SOLID187

20. Tyre Stiffness
• Literature1, 2, 3, identifies tyre stiffness as a highly important characteristic of a tyre
that influences the performance of the tyre during both static and dynamic
maneuvers
• It is deduced that any influence that wear has on the tyre stiffness will lead to possible
changes in performance
1 Lines and Murphy (1991); 2 Zegelaar (1998); 3 Gipser (2005)
Modified flexible ring model incorporating the tyre-road interaction
(Zeglaar, 1998)

21. Stiffness Measurement
• Gradient along the linear regions of both the historical and simulated
results was deemed an appropriate approach to compare the two
sets of data and sequentially validate the tyre model
• The sensitivity to the change in the response, or tyre stiffness, was
used to determine the range over which the linear region is take
• Coefficient of determination (R2) is extremely useful summary index as
it is able to objectively determine the fit of a model
• R2 is used to quantify the goodness of fit between the linear curve and the
predicted behavior

22. Model Validation (1/2)
• The method of validating a tyre model
using experimental data in 1 is an
appropriate technique for this study to
employ as inaccessibility of testing
equipment and the existence of historical
data or the Trelleborg tyre makes this the
only viable validation approach.
• Through capturing the correct model inputs
and verifying the tyre behavior using historian
data, the soundness of a model and its results
are verified
1 Stallmann (2018); 2 Schielzeth (2012)
Historical data set of the Trelleborg TM700 280/70R16 tyre
Load
(N)
Camber Angle
(˚)
Inflation Pressure
(Bar)
Stiffness
Experimental
0 and -5
0.8, 2.0
Vertical
5500
0
0.8, 2.0
Longitudinal
5500
0
0.8, 2.0
Lateral
* : Test dependent value that is measured off of the respective results

23. Model Validation (2/2)
• Validation indicated sufficient ability to predict
vertical and longitudinal tyre behavior
• Errors in lateral stiffness are assumed to be due to
a possible that:
• The phenomenon contributing to the lateral direction,
and is not as predominant in the vertical and
longitudinal directions
• Phenomenon is not being represented in the model
• Nonetheless, due to the error in lateral stiffness the
model is deemed unreliable with regard to predicting
lateral tyre behavior until further validation
Average stiffness differences for each direction
Average Stiffness Difference
Stiffness
5%
Vertical
7%
Longitudinal
27%
Lateral

24. Model Validation (2/2)
• Validation indicated sufficient ability to predict vertical and
longitudinal tyre behavior
• Errors in lateral stiffness are assumed to be due to a possible that:
• The phenomenon contributing to the lateral direction, and is not as
predominant in the vertical and longitudinal directions
• Phenomenon is not being represented in the model
• Nonetheless, due to the error in lateral stiffness the model is
deemed unreliable with regard to predicting lateral tyre behavior
until further validation
Average stiffness differences for each direction
Average Stiffness Difference
Stiffness
5%
Vertical
7%
Longitudinal
27%
Lateral
Longitudinal Stiffness
Lateral Stiffness
Vertical Stiffness

25. Tyre Wear (1/2)
• There are several reasons why tyre characteristics
change over its operational life
• Structure of rubber compounds differ between old
and new tyres, and
• Rubber ages through the exposure to oxygen and
ultraviolet light1
• As a result of repeated flexing as a product of
operation, tyre walls fatigue, and tyre tread reduces
as a result of wear
• Friction is regarded as a fundamental mechanism
through which energy is dissipated, leading to
surface degradation and tyre wear2
1 Lines (1991); 2 Moore (1980)
Schematic diagram breaking down the friction and wear
mechanisms that exists in rubber-like materials (Veen, 2007)

26. Tyre Wear (2/2)
• An experimental study completed by Wright (2016)
investigates the extent to which wear affects the
stiffness of an all-season Pirelli Scorpion Verde
235/55R19 (105V) passenger car (SUV) tyre with a tread
depth reaching around 10mm
• Wright adds to this by concluding that the effect of wear
on the stiffness of the SUV tyre reaches substantial
deviations of up to 11%, in some cases
• Wright is unable to determine a clear trend from the full
stiffness-wear data set and motivates this on the
premise that the wearing procedure employed in the
study introduces irregularities and unevenness across
the contact patch
• As the lugs of an agricultural tyre make up a significant
amount of the tyres volume compared to that of SUV
tyres, it is hypothesized that the effect of wear on tyre
stiffness is somewhat more pronounced in agricultural
tyres
Wright (2016) Argument
Trend
Stiffness
Expected tyre-stiffness behaviour.
Outlier accredited to experimental tests
conducted on a segment of the tyre with
a different tread profile, caused by
uneven wearing technique
Upward
Vertical
Due to independence between
longitudinal stiffness and the tread
profile at the contact patch
Declining
Longitudinal
N/A
N/A
Lateral
1 Wright (2016)
Wright (2016) results - Percentage change in stiffness

27. Effect of Tyre Wear (1/2)
• With agricultural tyres being
found operating with tyres
ranging from new to completely
worn, the effect of tyre wear at
50% and 100% worn is simulated
ANSYS simulated tyre profile at 50% (tread depth of 15mm) and 100%
(tread depth of 0mm) worn tyre worn
50% Wear State
100% Wear State

28. Effect of Tyre Wear (2/2)
• Decreasing stiffness with tyre wear is
noted for the vertical case which is in
line with 1 which found that carcass
stiffness increases as a tyre ages and
wears
• Increasing stiffness with tyre wear for
longitudinal and lateral loading was
found
• The average influence of wear between
an unworn and completely worn tyre on
the vertical, longitudinal and lateral tyre
stiffness is found to be -17%, 18% and
10% respectively (range presented in
table)
• Greater effect of wear on stiffness of
agricultural tyres found, compared to
SUV tyres
Effect of tyre wear on stiffness between SUV / passenger car tyre (Wright, 2016)
and agricultural tyre in this thesis
This Thesis (%)
SUV / Passenger Tyre Wright (2016) (%)
Stiffness
–13.9 to –21.8
– 5.0 to 2.2
Vertical
15.3 to 30.4
11.0
Longitudinal
6.1 to 13.9
–
Lateral
1 Lines and Murphy (1991);
This thesis results showing the percentage change in vertical, longitudinal and lateral
stiffness for the range of inflation pressures and camber angles with tyre wear

29. Effect on Cambered Tyres
• Narrowing of the contact patch of a
cambered tyre 1 states that tension
within the belt cords is released,
resulting in the slightly lowering of
the tyres vertical stiffness
• Reiterated by results found
• The initial non-linearity is backed
up by 1 which states that it can be
attributed to curvature of the
crown / carcass
• In addition, the formulation of a
"full" contact patch of a cambered
tyre requires more tyre deflection
compared to that of an upright
tyre
1 Gruber et al. (2008);
This thesis results showing the effect of camber on the percentage change in vertical
stiffness with tyre wear

30. Thank you