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Analysis of the results provided by a grip and thermodynamics-sensitive tire/road interaction force characterization procedure

Abstract and Figures

The automotive sector is looking for the optimal solution in modeling and understanding tire behavior in experimental and simulation environments.1,2,3 !e studies and tools described here represent a new approach in tire characterization and vehicle simulation procedures, leading to the complete reproduction of the dynamic response of a tire and of its frictional and thermodynamic behavior simply by means of specific track sessions and a few laboratory measurements. !is represents a bridge between a robust and widespread approach, like Pacejka’s, and purely physical modeling, that satis"es predictive requests and the need for deeper knowledge about complex phenomena.
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The Annual Review of Tire Materials and Tire Manufacturing Technology
฀฀฀ ฀฀
5 Foreword
Roger Williams, associate editor and former head of research, Dunlop, UK
10 Rolling resistance sensing
Yi Xiong and Ari J Tuononen, Aalto University, Finland
An optical tire sensor system for measuring tire tread deformation
14 Carbon black behavior
Menglong Huang and James Busfield, Soft Matter Group, School of Engineering
and Materials Science, Queen Mary University of London, UK
Impedance characterization of carbon black network structures in elastomer composites
18 Tire filler experiment
A S Deuri and D M Vaidya, Balkrishna Industries, India
The results of a study have shown that bagasse could be used as an environmentally friendly tire filler
22 Beyond the plunger test
Jorge Kuster, Leandro F Jaureguizahar and Tomás Arechaga, FATE Tires, Argentina
Proposing an innovative add-on to a tire plunger energy test starting from FEA
30 Tire design framework
Masataka Koishi, associate corporate ocer, Yokohama Rubber Co., Japan
Design knowledge exploration for the conceptual design of tires
34 Tire/road interaction models
Flavio Farroni, Department of Industrial Engineering, University of Naples, Italy
Analysis of the results provided by a grip and thermodynamics-sensitive tire/road interaction
force characterization procedure
40 Next-generation tire
Kozaburo Nakaseko, head of research and development, Sumitomo Rubber Industries, Japan
SRI’s new Enasave Next features new materials technology developed through
a design concept called 4D Nano Design
42 Road obstacle eects
Chongfeng Wei and Oluremi Ayotunde Olatunbosun, School of
Mechanical Engineering, University of Birmingham, UK
Explicit dynamic analysis for tires rolling over dierent road obstacles
48 Advanced tire CAE
Gregory Smith, Jaguar Land Rover, UK
Using improved tire models to support virtual vehicle development
52 FE analysis reliability
Mir Hamid Reza Ghoreishy and Ghasem Naderi, Department of Processing, Iran Polymer
& Petrochemical Institute, and Khatereh Azarandaz, Barez Industrial Group, Iran
Experimental verification of the predicted stinesses for a statically loaded tire in FEA
58 Tire tread abrasion
R Stoček, PRL Polymer Research Lab, Zlín, Czech Republic; R Kipscholl, Coesfeld, Dortmund,
Germany; G Heinrich, Leibniz Institute of Polymer Research Dresden, Germany
Predictive lab testing of chip and cut failure of tires
62 Motorsport tire wear
Henning Olsson, Optimum G, Colorado, USA
Predicting tire wear in motorsport using vehicle and tire simulation
68 Natural rubber strength
K Brüning, K Schneider and G Heinrich, Leibniz-Institut für Polymerforschung
Dresden, Institut für Werkstowissenschaft, TU Dresden, Germany
Self-reinforcement of natural rubber in truck tires
72 Tear fatigue analysis
G Heinrich and S Gorelova, Leibniz-Institut für Polymerforschung Dresden eV and Technische Universität
Dresden, Germany; K Schneider, Leibniz-Institut für Polymerforschung Dresden eV; R Calabrò, Politecnico
di Milano, Italy; R Lombardi, Università degli Studi di Napoli Federico II, Italy; C Kipscholl, Coesfeld GmbH
& Co. KG, Dortmund, Germany; T Horst, Westsächsische Hochschule Zwickau, Germany; A Schulze,
Leibniz-Institut für Polymerforschung Dresden eV and Technische Universität Chemnitz, Germany
Fracture behavior of elastomers under dynamic biaxial loading conditions
76 Tire property measurement
Hugues Baurier, Metravib, ACOEM Group, France
A new advanced flexometer for better prediction of tire service life and performance
Tire/road interaction models
Analysis of the results provided by a grip and thermodynamics-sensitive tire/road
interaction force characterization procedure
by Flavio Farroni, Department of Industrial Engineering, University of Naples, Italy
The automotive sector
is looking for the
optimal solution
in modeling and
tire behavior in
experimental and simulation
environments.1,2,3 e studies and
tools described here represent a new
approach in tire characterization
and vehicle simulation procedures,
leading to the complete reproduction
of the dynamic response of a tire and
of its frictional and thermodynamic
behavior simply by means of specic
track sessions and a few laboratory
measurements. is represents
a bridge between a robust and
widespread approach, like Pacejka’s,
and purely physical modeling, that
satises predictive requests and
the need for deeper knowledge
about complex phenomena.
The tools
e nal product is composed
of the following four tools,
which can cooperate to form
a multitude of solutions.
TRICK (Tyre/Road Interaction
Characterization & Knowledge)4
is basically composed of a vehicle
model able to process experimental
signals acquired from the vehicle’s
CANbus and from additional
instrumentation (DATRON5) to
estimate sideslip angle, providing
a sort of virtual telemetry, based
on the acquired signals’ time
history and containing force and
slip estimations useful to provide
tire interaction characteristics.
Complete and detailed studies
of tires in a wide range of working
conditions are commonly carried
out by means of complex, bulky
and expensive test benches.6 e
proposed procedure means the
vehicle can be employed as a moving
lab, easily applying experimental
and processing techniques.
TRIP-ID (Tyre/Road Interaction
Parameters Identication) provides
an innovative procedure to identify
the Pacejka coecients, starting
from the experimental tests carried
out to measure global vehicle data
during outdoor track sessions. e
procedure collects and processes the
data provided by TRICK, eliminating
the outlier points, discriminating
between the various tire wear and
thermal phenomena, and taking into
account the combined slip condition
and the eects of vertical load and
camber angle on the overall grip.
TRT (ermo Racing Tyre)7 is an
analytical-physical thermal tire model
developed with the aim of predicting
temperature with a high degree of
accuracy and able to simulate the
high-frequency thermal dynamics
characterizing high-performance
systems. e model can estimate
the temperature distribution of even
the deepest tire layers, usually not
easily measurable online, to predict
the eects that fast temperature
variations induce in the behavior of
viscoelastic materials, and to take into
account the dissipative phenomena
related to tire deformations.
GrETA (Grip Estimation for
Tyre Analyses)8 is a tire/road friction
physical model, developed to respond
to the needs of race teams and tire
manufacturers, able to provide an
eective calculation of the power
dissipated by road asperities indented
in the tire tread, taking into account
the phenomena involved with
adhesive friction, expressed by means
of an original formulation whose
parameters are identied thanks
to dedicated experimental tests.
ese tools are able to describe
and analyze aspects of phenomena
concerned with tire/road interaction,
but their cooperation can constitute
an even more powerful instrument
to extend the comprehension
of such a complex theme.
Figure 1: Model
integration solutions
Figure 2: G-G
diagram realized both
with experimental data
and with results of a
simulation performed
with starting MF-Tyre
parameters set
Figure 3: Detail of
the front (left) and
rear (right) tire slip
angles, both from
experimental data
and from outputs of a
simulation performed
with starting MF-Tyre
parameters set
A general overview of the
developed models and procedures
is shown in Figure 1, in which it is
possible to observe the connections
that link the models, providing
dierent solutions for employment.
TRICK and TRIP-ID were developed
with the initial aim of increasing
the condence of car makers in
adopting the Magic Formula in
virtual drive modeling and vehicle
dynamics models employed for
predictive performance analyses.
One of the main advantages of
the tool is the ability to validate
Pacejka coecients provided by tire
makers, or even do without their
contribution, identifying coecients
aer a proper vehicle characterization
and a specic track session.
e weak points of the initial
MF-Tyre parameter set identied
by tire companies via bench
procedures, and highlighted by
data analysis, are as follows:
First, there is too much grip
in the longitudinal and lateral
interaction, due to the dierences
between real roads and the belts
employed for testing. Next, there is
a lower likelihood than in reality for
the driver to be able to stabilize the
vehicle aer the limit of adhesion
has been crossed. Finally, there is
an absence of grip and stiness
variations due to thermal eects.
In Figure 2, a G-G diagram,
a classic and simple instrument
employed to evaluate global
vehicle performance,9 is plotted
(in nondimensional form, as are
all the following ones, for reasons
of industrial condentiality),
comparing on a reference track lap
the measured vehicle accelerations
with accelerations exported as output
from a commercial, highly validated
vehicle simulation model employed
in a virtual driving simulation
environment that has been adopted
for the specic MF-Tyre parameter
set provided by the tire maker.
High grip levels reached by bench
tested tires are oen due to the
fact that the testing countersurface
is abrasive paper (or a rough
material surface characterized by
low macro-roughness), that is able
to maximize the contact patchs
eective area, providing an interface
better than that on a real road.
e employment of abrasive paper
and severe testing cycles causes,
in addition to grip overestimation
(and consequent to it), a continuous
and massive heat generation at the
contact interface, which increases tire
temperature. As is well known, one
of the main eects of temperature
on tires is stiness variation2
(increasing temperature causes
decreasing stiness), particularly
evident in the front tires, which
in high-performance applications
are typically narrower and less
thermally inert than the rears. Figure
3 focuses on these considerations,
highlighting the unsatisfactory
results obtained with respect to front
slip angles employing the starting
tires’ parameter set; the imbalances
caused by poor estimation of slip
angles act on the whole vehicle’s
tendency to understeer or oversteer.10
e identication of the optimal
parameter set by means of the TRIP-
ID procedure also enables us to solve
the simulated vehicle driveability
problems linked to the shape of the
tires’ starting set. e mentioned
lower-than-reality likelihood of the
driver returning the vehicle to a stable
condition aer the limit of adhesion
has been crossed is due to two
factors: an excessively peaky trend of
lateral interaction curves and a too-
sharp decrease of cornering force in
a combined interaction at increasing
values of slip ratio. e improvement
that the characterized tires have
represented with respect to the cited
eects can be observed in Figure 4,
which compares the starting set’s pure
lateral interaction curves (on the le,
in black) with those of the optimal
identied set (on the right, colored).
It can be seen that data collected
during an experimental session and
processed by the TRICK tool is able
to provide information useful in
properly modifying the starting set,
obtaining an identied set that results
in good agreement with the drivers’
requests and with the objective
data already acquired by equipping
the real vehicle with measurement
instruments. Figure 5 shows the
results of the simulations performed
with the identied tire set, comparing
them with the ones relative to the
starting set, shown on the le.
TRICK and TRT can be successfully
employed together, providing an
Figure 4: Plot F left:
Starting set, front
tire, pure lateral
interaction. Plot F
right: Identified final
set, front tire, pure
lateral interaction. Plot
H left: Starting set,
rear tire, pure lateral
interaction. Plot H
right: Identified final
set, rear tire, pure
lateral interaction
Figure 5: (Right) G-G
diagram realized both
with experimental data
and with results of a
simulation performed
with the final identified
MF-Tyre parameter
set. (Left) Figure 2 for
instrument able to provide tire
thermal analyses, useful to identify
the range of temperature in which
grip performances are maximized
and enabling the optimal tires
and vehicle setup to be dened.
e test procedures adopted to
characterize the tires, obtaining
data useful to initialize the models
properly, can be schematically
divided into two main subcategories
– destructive and non-destructive.
To the rst belongs meridian
plane section analysis. is kind
of test consists of the observation
and measurement of the thickness
of the layers constituting the
meridian section. In Figure 6, it is
possible to distinguish the tread
layer, characterized by an evident
and deep pattern, the bulk layer,
in which steel cord plies are clearly
observable, and the innerliner, which
is very thin and impermeable.
e second component of the
destructive subcategory is thermal
conductivity and specic heat
measurements. Tire layers need to be
characterized from a thermodynamic
point of view, focusing in particular
on conductivity and specic heat
measurements. A standard test
procedure is carried out employing
a Stabilite 2017 argon-krypton laser
(Figure 7a) pointed at the whole tire
or on specimens of each layer and
emitting a beam of given power.
Knowing the specimen thickness
and measuring temperature of
the two surfaces by means of two
thermographic cameras (a Flir
Phoenix, Figure 7b and a Fluke
Ti-45, Figure 7c), it is possible to
provide an eective estimate of
the desired parameters, validated
thanks to comparison with tests
carried out with a COND1 device,
following certied procedures.11
e third component is DMA
viscoelastic characterization. Tests
carried out on sport tires have
highlighted interesting aspects, in
particular comparing results with
common passenger tire ones. Figure
8 shows that, as expected, sport
tires are characterized by lower
storage modulus values in their
optimal thermal working range
(35°C and over) that enable them to
oer better adhesion and to adapt
better to road asperities, optimizing
contact area at the price of a lower
wear resistance. Passenger tires are
more stable and able to oer good
adhesion levels even at very low
temperatures, being adapted to the
widest possible range of working
conditions. Figure 9 shows in a clear
plot the possible reason for the so-
called ‘feeling the grip’ phenomenon.
Sport tires, as distinct from passenger
ones, are characterized by a clear
relative maximum at about 42°C
and by higher values of tan δ at
the usual usage temperatures.
Specifying that the DMA test has
been carried out at a frequency of
1Hz, notably dierent from common
tread stress frequencies, a quick
calculation, hypothesizing an average
road macro-roughness wavelength λ
equal to 0.01m and an average sliding
speed Vs of 5m/sec, enables the real
tire temperature at which the tan δ
maximum can be experienced by
the driver to be estimated. Applying
a simplied version of the WLF
equation,8 it is possible to obtain
which, added to the starting
42°C, gives a temperature of
63.6°C, in accordance with the
experimental value shown in the
analyses already presented.
testing procedures
e rst of these to be applied is
contact patch analysis. A specic
test bench12 is used to apply a static
vertical load to the tested tires,
analyzing contact patch extension
and pressure distribution. It is
possible to interpose pressure-
sensitive Prescale sheets between the
tire and the at steel countersurface,
and to plan tests at dierent loads,
ination pressures and camber
angles. In Figure 10 the results
of a zero-camber testing session
on a front tire are reported.
Figure 6: Detail of tire
sections cut along the
meridian plane
Figure 7:
(a) The Stabilite 2017
argon-krypton laser
(b) The Phoenix
thermographic camera
(c) The Ti-45
thermographic camera
(d) The laser spot
on the tire external
(e) A thermographic
camera image of the
laser spot on the tire
external surface
(f) A thermographic
camera image of the
laser spot on the tire
internal surface
Figure 8: Comparison
of storage modulus
(E’) between a
common passenger
tire and a GT sport tire
Figure 9: Comparison
of tan bbetween a
common passenger
tire and a GT sport tire
Figure 10: Scans
of a GT tire contact
patch under different
testing conditions at
zero camber angle.
It is noticeable
that at increasing
load the contact
area increases,
progressively inserting
shoulders in the
interaction zone. At
high inflation pressure
the central rib is more
extended, while lower
pressure tends to
overload the shoulders
Figure 11: Installation
of infrared thermal
sensors and
localization inside
vehicle wheelhouses
Figure 12: TRT
results evaluation for
front and rear tires
e second is track thermal tests.
ese sessions are carried out to a
specically developed procedure,
with the aim of collecting tire data
under various thermal conditions.
In order to acquire tire temperature,
the vehicle is equipped with infrared
sensors installed in the wheelhouses
(Figure 11) and directed on the
tread surface. e signals are
acquired by Deweso hardware.
Each tire tread is interrogated by two
dierent measurements, particularly
useful for front tires, which when
steering could be characterized by
discontinuous temperature proles.
Aer carrying out the track
experimental session and
acquiring data to be processed
by the TRICK procedure, a
‘virtual telemetry’ is generated.
Speed, slip, camber and force
channels are used as input for TRT,
whose results are compared with
the measured surface temperatures
(Figure 12), delivering good
correspondence with available
data and, very usefully for the grip
analysis discussed in the following, an
estimation of tire-bulk temperature.
Common analyses concerning
the relationship between the tire
friction coecient and temperature
are based on the only thermal
data experimentally available,
i.e. the tire’s external (and in a
few cases, internal) temperature,
measured using a great variety of
techniques. A typical correlation
between lateral grip and measured
temperature appears like that shown
in Figure 13, from which very little
information can be deduced.
anks to the availability of
the bulk temperature, it is possible
to provide much more useful
correlations, such as the ones
shown in Figure 14, from which
an optimal thermal range can be
identied. e reason why the bulk
temperature oers better results
can be attributed to the fact that the
surface temperature varies with very
fast dynamics but it is not possible to
modify the polymers’ characteristics
quickly enough to see the response
of the whole tire’s frictional behavior.
Bulk temperature, on the other hand,
can be considered to be the tread’s
core temperature, more resistant to
fast variations and directly connected
to the rubber’s viscoelastic state.
As a further validation of the
described procedure, it can be
seen that the optimal temperature
value is in good agreement with
the theoretical result provided in
Equation 1, conrming that the
thermal model can be employed as a
predictive instrument to investigate
performance optimization strategies
and that a proper knowledge of
polymer characteristics can be a
useful starting point to a better
understanding of the dynamics
of tire-surface interaction.
e thermal and grip models can
usefully cooperate, employing the
TRT output as an input for GrETA,
which can be used to introduce into
the Pacejka interaction model the
dependencies on temperature, tire
working variables, road roughness
and compound characteristics.
e advantages coming from
the cooperation of these models
can be summarized in the following
three points, which have already
been exploited (further application
possibilities are clearly available).
e rst is the prediction
of tire behavior on the various
tracks of a racing championship,
each characterized by dierent
roughness (previously measured)
and weather conditions.
e next is a performance
evaluation of the characteristics
of various compounds, which
enables a dialog with the tire
makers to be established,
directing tire construction and
compound development to the
achievement of a common aim.
e third is the denition of an
optimal vehicle setup in terms of
wheel angles, load balance and tire
ination, and of driving strategies
that are able to reach optimal grip/
thermodynamic conditions.
Figures 15 and 16 show the
dierences between force data from
telemetry and from the Pacejka
model, whose inputs are the
measured slip, load and camber. In
the rst case the calculated forces
are reported as scaled by a Coulomb
friction model, always equal to one
except for the static value (which
means using a standard Pacejka
output, with no further processing).
In the second case the forces
are processed with GrETA friction
scaling factors, taking into account
phenomena neglected in the rst
case. It can be noticed that employing
the grip model produces better
results, particularly with respect
to longitudinal interaction in the
traction phase, which is thermally
stressful for high-performance
tires and able to generate heat for
the friction power mechanism,
10 12
which induces noticeable eects in
tire/road interaction modeling.
Physical interaction model
and further developments
It is clear that the Pacejka model is
not the most exible and detailed
method to describe local phenomena
of the tire/road interaction, but
represents a very robust and
intuitive solution to obtain the
barely achievable aim of modeling
the tire’s tangential forces.
For this reason, further
developments of the activities
discussed in the present work
will focus on the realization of a
fully physical interaction model
that, starting from the knowledge
acquired about the topic by the
vehicle dynamics research group,13,14
will be able to interact deeply
with the other models, creating an
analytical and predictive instrument
that can be employed in a wide
range of automotive applications.
e author wishes to acknowledge
the skilled and stimulating academic
environment of the Industrial
Engineering Department of the
University of Naples Federico
II and the support of several
companies, motorsport teams
and research institutes who are
all experts in their eld. tire
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Heinemann (2006)
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F, A physical-analytical model for
a real-time local grip estimation of
tire rubber in sliding contact with
road asperities, Proceedings of the
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Figure 13: Front
and rear lateral grip
reported as a function
of measured tire
surface temperature
Figure 14: Front and
rear grip reported as
a function of tire bulk
temperature estimated
by means of TRT.
Bell-shape curves
have been drawn to
highlight the trends
Figure 15:
Comparison between
longitudinal tire forces
modeled by MF with a
Coulomb friction law
and with GrETA friction
Figure 16:
Comparison between
lateral tire forces
modeled by MF with a
Coulomb friction law
and with GrETA friction
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Full-text available
In the paper a new physical tyre thermal model is presented. The model, called Thermo Racing Tyre (TRT) was developed in collaboration between the Department of Industrial Engineering of the University of Naples Federico II and a top ranking motorsport team. The model is three-dimensional and takes into account all the heat flows and the generative terms occurring in a tyre. The cooling to the track and to external air and the heat flows inside the system are modelled. Regarding the generative terms, in addition to the friction energy developed in the contact patch, the strain energy loss is evaluated. The model inputs come out from telemetry data, while its thermodynamic parameters come either from literature or from dedicated experimental tests. The model gives in output the temperature circumferential distribution in the different tyre layers (surface, bulk, inner liner), as well as all the heat flows. These information have been used also in interaction models in order to estimate local grip value.
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In this paper an experimental test rig aimed to characterize mechanical properties of a pneumatic tyre, together with some results, is presented. The objective is to determine tyre mechanical characteristics useful to physically model its behaviour; in particular: the normal interaction characteristic, the radial stiffness, the total stiffness and the longitudinal hysteretic cycles. To this aim two different kind of tests have been executed: radial and longitudinal. In the radial test the load is statically applied to the tyre, along the vertical direction, by means of an hydraulic press and it is measured together with the consequent radial deformation, so allowing the estimation of the tyre normal interaction characteristic and of its radial stiffness. Different radial tests can be conducted for an assigned tyre varying the inflation pressure. The longitudinal tests are conducted applying, under an assigned constant vertical load, a variable horizontal strain to the tyre by means of a linear actuator, two profile rail guides and a system to transfer the horizontal motion to the contact patch of the tyre, opportunely placed on a moving steel plate placed on the two linear guide rails. During the tests the horizontal load and the resulting deformations are measured and acquired so allowing the estimation of tyre total stiffness and of its longitudinal hysteretic cycles. Longitudinal tests can be conducted varying the assigned vertical load, the horizontal displacement law in terms of frequency and amplitude, the tyre inflation pressure. All the different types of rim can be mounted on the test rig thanks to a universal quick flange.
This paper deals with the frictional behaviour of a tyre tread elementary volume in sliding contact with road asperities. Friction is supposed as composed by two main components: adhesion and deforming hysteresis. The target, fixed in collaboration with a motorsport racing team and with a tyre manufacturing company, is to provide an estimation of local grip for on-line analyses and real time simulations and to evaluate and predict adhesive and hysteretic frictional contributions arising at the interface between tyre tread and road. A way to approximate asperities, based on rugosimetric analyses on macro and micro scale, has been introduced. The adhesive component of friction has been estimated by means of a new approach based on two different models found in literature, whose parameters have been identified thanks to a wide experimental campaign previously carried out. The hysteretic component of friction has been estimated by means of an energy balance taking into account rubber viscoelastic behaviour, characterized by means of proper DMA tests, and internal stress / strain distribution due to indentation with road. Model results are finally shown and discussed and the validation experimental procedure is described. The correct reproduction of friction phenomenology and the model prediction capabilities are highlighted making particular reference to grip variability due to changes in working conditions.
A Numerical–physical tyre model was developed . The whole model allows to obtain the road–tyre interactions so it can be used in vehicle dynamic simulations. In this article are presented its capabilities in normal interaction analysis. The normal interaction, i.e. the relationship between the normal load and the normal deflection, influences the tangential (longitudinal plus lateral) one, which determines the vehicle handling behaviour. The parameters used in this model depend on the structure of the tyre and they can be measured on the real tyre. The tyre has been schematized as composed by a flexible belt , the sidewalls and a rigid ring (Rim). The flexible belt is composed by a number of lumped masses linked by extensional and bending stiffnesses and dampers. The tyre model has been developed using the finite segment method. Using these method could be possible to include in the tyre simulations various non-linear structural effects due to large displacements and rotations. The model allows to simulate both steady state and transient conditions.
This paper deals with in curve vehicle lateral behaviour and is aimed to find out which vehicle physical characteristics affect significantly its stability. Two different analytical methods, one numerical (phase plane) and the other graphical (handling diagram) are discussed. The numerical model refers to the complete quadricycle, while the graphical one refers to a bicycle model. Both models take into account lateral load transfers and nonlinear Pacejka tyre road interactions. The influence of centre of mass longitudinal position, tyre cornering stiffness and front/rear roll stiffness ratio on vehicle stability are analyzed. The presented results are in good agreement with theoretical expectations about the above parameters influence, and show how some physical characteristics behave as saddle node bifurcation parameters.
The upper and lower bounds of the effective thermal conductivity of packed beds of rough spheres are evaluated using the theoretical approach of the elementary cell for two-phase systems. The solid mechanics and thermal problems are solved and the effects of roughness and packed bed structures are also examined. The numerical solution of the thermal conduction problem through the periodic regular arrangement of steel spheroids in air is determined using the Finite Element Method. The numerical results are compared with those obtained from an experimental apparatus designed and built for this purpose.
This paper investigates the use of GPS to estimate vehicle sideslip and tire information. Both a one antenna GPS antenna/receiver and dual GPS antenna method are studied. Analysis of the accuracy that can be achieved using the two different GPS solutions is provided. The algorithms are then validated on a fully instrumented Infiniti G35 sedan. Experimental data is given showing the performance of the GPS based sideslip estimates compared against a simple bicycle model and a DatronTM velocity sensor. NOMENCLATURE r Vehicle yaw rate
  • M Guiggiani
Guiggiani M, e Science of Vehicle Dynamics, Springer (2014)
A.: a Physical Analytical Tire Model for Handling Analysis -the Normal Interaction
Ty.M.H.A.: a Physical Analytical Tire Model for Handling Analysis -the Normal Interaction, Vehicle System Dynamics, Vol. 47, N. 1, pp15-27 (2009)