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Abstract—In the paper new structure elements have been
developed and implemented in the alreadyexisting TRT
thermodynamic tyre model. The updated model aims to
provide a complete tool to study and understand all the
phenomena concerning the tyre in thermal transient
conditions, since all the elements constituting its structure are
finally modelled. The computational cost, connected to a more
complex model to manage, was decreased by simplifying the
mesh of the previous version of the model and, thus, by
reducing the state vector length.
Index Terms—Tyre structure implementations, tyre
thermodynamics modelling, tyre temperature realtime
estimation
I. I
NTRODUCTION
he characterization of the tyres is an essential issue for
the formulation of vehicle dynamics models, since the
tyres allow the interaction with the road and are interested
by the fundamental slip related phenomena [1][2].
Nowadays everyone playing a role in automotive sector is
looking for the optimal solution in order to model and to
understand the tyres behaviour in both experimental and
simulation environments. The ability to predict the interior
temperature distribution, and thus the grip behaviour of the
tyre [3], is fundamental in terms of the vehicle handling
improvement and of the asset optimization according to
highly variable outdoor testing conditions [4].
The new implementations to the already existing TRT
thermodynamic model have a key purpose: to add new
structure elements and, thus, to enhance and optimize the
physical response, but not at the expense of the realtime
simulation.
II. TRT

T
HERMO
R
ACING
T
YRE MODEL
The model, called Thermo Racing Tyre (TRT) [5] was
developed in collaboration between the Department of
Manuscript received March 21, 2015
Flavio Farroni is with Dipartimento di Ingegneria Industriale, Università
degli Studi di Napoli Federico II, via Claudio n. 21 80125 Napoli Italy (e
mail: flavio.farroni@unina.it).
Aleksandr Sakhnevych is with Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II, via Claudio n. 21 80125
Napoli Italy (email: ale.sak@unina.it).
Francesco Timpone is with Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II, via Claudio n. 21 80125
Napoli Italy (corresponding author: phone: +39 081 76 83263; fax: +39 081
2394165; email: francesco.timpone@unina.it)
Industrial Engineering of the University of Naples Federico
II and a top ranking motorsport team.
The model is threedimensional and takes into account of
the following thermodynamic phenomena:
heat generation due to:
•
tireroad tangential interaction, known as “Friction
Power”;
•
effect of tyre cyclic deformation during the rolling,
known as “SEL” (strain energy loss);
heat exchange with the external environment due to:
•
thermal conduction between the tread and the road;
•
forced convection of the surface layer with the
outside air;
•
natural convection of the inner liner with the inner
air;
heat conduction between the tyre layers due to the
temperature gradient.
A. Tyre modelling
As in the original version, the tyre, modelled as slick, is
considered as unrolled in the circumferential direction along
xaxis, lacking of sidewalls and grooves (Fig. 1). Its
parallelepiped shape is constituted by three layers in the
radial direction z, indicated as surface (outer surface of the
tyre structure), bulk (intermediate layer), and inner liner
(inner coating).
Each layer is discretized by means of a grid, whose nodes
represent the points in which the temperature can be
determined in real time. To the generic ith node a
parallelepiped volume V
i
is associated, equal to
An Evolved Version of Thermo Racing Tyre
for Real Time Applications
T
Flavio Farroni, Aleksandr Sakhnevych, Francesco Timpone
University of Naples “Federico II” – Department of Industrial Engineering
Fig. 1. Discretization of the tyre. Each layer is subdivided in 15 elements in
longitudinal direction x and in 4 elements in transversal direction y. Thus,
the
entire tyre results discretized in 180 elements (but nevertheless the
discretization could be easily modified).
(1)
in which Δx and Δy are respectively the dimensions along
the longitudinalcircumferential and the transversalwide
directions, while the quantity ΔZ
m,i
represents the thickness
of a node’s mass associated to ith layer along the radial
one.
With special regard to the tyre’s structure, in which visco
elastic vulcanized polymers and fillers mainly constitute the
tread and the carcass includes also reinforcements, two
zones of homogeneous material have been identified and
characterized by the following physical parameters along the
radial direction:
•
density ρ
•
specific heat c
v
•
thermal conductivity K
where, in particular, the variability of the last two terms with
temperature is taken into account. Thus, each node has a
mass expressed as follows:
(2)
where the dimensionless C coefficient depends on its
position in the grid.
B. Base hypotheses
With the aim of modelling heat dynamics and tyre layers
temperature distribution, the following assumptions have
been adopted:
•
road: schematized as a geometric plane without
irregularities, isotropic and homogeneous in all its
characteristics, whose surface temperature is equal
to T
r
•
contact area: assumed to be rectangular, whose
dimensions are the width W of the tread and the
length L
a
depending on the tyre radial stiffness and
on the normal load applied
•
camber angle: assumed equal to zero
•
linear variation of the contact patch extension
related to the value reached under the application
of the static load by means of an appropriate set of
coefficients
•
motionless tyre with variable boundary conditions
•
neglection of the radiation heat transfer mechanism
C. Thermodynamic model
The developed thermodynamic tyre model is based on the
use of the diffusion equation of Fourier applied to a three
dimensional domain.
The complexity of the transient thermodynamical
phenomena under study and the degree of accuracy required
implies the dependence of the thermodynamic quantities,
and in particular of the thermal conductivity, on the
temperature. Furthermore, the nonhomogeneity of the tyre
has made it necessary to consider the variation of the above
parameters also along the thickness.
Therefore, the Fourier equation takes the following
formulation [6]:
(3)
Writing the balance equations for each generic node needs
the modelling of heat generation and of heat exchanges with
the external environment.
D. Heat exchange
The heat exchange between the tyre and the external
environment, remembering that the radiation mechanism is
neglected by hypothesis, it can be classified as follows:
Heat exchange with the road
The thermal exchange between the tread and the
asphalt has been modelled through Newton's formula
[7], schematizing the whole phenomenon by means of
an appropriate coefficient of heat exchange. The term
for such exchanges, for the generic th node will be
equal to:
(4)
where:
•
is the convective heat transfer coefficient,
estimated for the track testing conditions
;
•
is the track temperature .
Heat exchange with the outside/inside air
The whole mechanism of the heat transfer between a
generic surface and a moving fluid at different
temperatures is described by natural and forced
convection equations. The convection heat transfer is
expressed by Newton’s law of cooling, as before:
(5)
Therefore, the heat exchange with the outside air is
modelled by the mechanism of forced convection,
occurring when there is relative motion between the
car and the air, and by natural convection, when such
motion is absent.
Natural convection is also employed to characterize
the heat transfer of the inner liner with the inflating
gas. The determination of the convection coefficient ,
both forced
and natural
, is based on the
classical approach of the dimensionless analysis [7, 8].
Supposing the tyre invested by the air similarly to a
cylinder invested transversely from an air flux, the
forced convection coefficient is provided by the
following formulation [8, 9]:
(6)
in which:
•
is air conductivity, evaluated at an
average temperature between the effective air one
and outer tyre surface one;
•
is considered to be equal to the forward
speed of the vehicle (air speed is supposed to be
zero);
•
is the kinematic viscosity of air,
empirically obtained as:
(7)
•
is the characteristic length of the heat
transfer surface;
•
is the arithmetic mean between the
temperatures of the tyre outer surface and the
external air in relative motion.
The values of
evaluated with the above approach
are close to those obtained by means of CFD
simulations [10].
The natural convection coefficient
, however,
can be expressed as:
(8)
in which, for this case:
(9)
E. Heat generation
As concerns the tyre, the heat is generated in two different
ways: for friction phenomena arising at the interface with
the asphalt and because of stressdeformation cycles to
which the entire mass is subjected during the exercise
(SEL).
Friction power
The first heat generation is connected with the
thermal power produced at tyreroad interface because
of interaction; in particular, it is due to the tangential
stresses that, in the sliding zone of the contact patch,
do work dissipated in heat. Friction power can be
associated directly to the nodes involved in the contact
with the ground, and it is calculated as referred to
global values of force and sliding velocity, assumed to
be equal in the whole contact patch:
(10)
where a part of this thermal power is transferred to the
tyre and the remaining to the asphalt.
Since F
x
and F
y
are global forces between tyre and
road, and it is not known the contribution of each node
to these interaction forces, heat generated by means of
friction power mechanism transferred to the tyre has
been equally distributed to all the nodes in contact with
the ground. The model allows uneven local heat
distributions as soon as local stresses and velocities
distributions are known.
Strain Energy Loss
The energy dissipated by the tyre Q
SEL
because of
cyclic deformations is due to a superposition of several
phenomena: intraplies friction, friction inside singular
plies, nonlinear viscoelastic behaviour of all rubbery
components, etc.
During the rolling, the entire tyre is subjected to the
cyclic deformations with a frequency corresponding to
the tyre rotational speed. During the motion, portions
of tyre, entering in sequence in the contact area, are
subjected to deformations, which cause energy loss and
then heat dissipation.
In the model, the amount of heat generated by
deformation (SEL) is estimated through experimental
tests carried out deforming cyclically the tyre in three
directions (radial, longitudinal and lateral) [11].
Estimated energies do not exactly coincide with the
ones dissipated in the actual operative conditions, as
the deformation mechanism is different; it is however
possible to identify a correlation between them on the
basis of coefficients estimated from real data telemetry.
F. Contact area calculation
The size and the shape of the contact area are function of
the vertical load
, of the inner pressure
and of the
camber
and toe
angles.
The contact area is assumed to be rectangular in shape
with constant width W, equal to the tread’s one, and length
L
a
, variable with the above mentioned parameters, except
the toe angle. The number of nodes in contact is then
calculated from the effective area of contact, which is
obtained, taking into account actual vertical load and
inflating pressure, on the basis of the results provided by
FEM simulations and pressure sensitive films [12].
G. Constitutive equations
The power balance equations, on heat transfers, are written
for each elementary mass associated to each node, and differ
in relation to their position inside the grid.
The heat conductivity between the surface and the bulk
layers is indicated with k
1
, while with k
2
is indicated the heat
conductivity associated to the exchange between the bulk
and the inner liner layer.
In the model, the tyre is considered motionless and the
boundary conditions rotating around it to take into account
the fact that elements belonging to the surface layer will be
affected alternatively by the boundary conditions
Fig. 3. Thermal powers exchanged in all directions for the control volume
associated with node 2, assumed in contact with the external air. Note the
absence of the generative term and the presence of the term identifying the
exchange with the outside air, characterized by h
forc
coefficient.
Fig. 2. Thermal powers exchanged in all directions for the control volume
associated with node 2, assumed in contact with the road. It is possible to
notice the term identifying the cooling with the road, characterized by the
presence of the H
c
coefficient, and the one connected to the tyreroad
interaction.
corresponding to the contact with the road and to the forced
convective exchange with the external air.
As an example, heat balance equation
node are graphically reported in figure
s 2 and 3
that,
for the performed discretization, the nodes adjacent to
node are and along the
direction, 1 and 3 along the
y direction and 62 along the z direction.
The previous
images show the thermal powers, exchanged
in all directions respectively for the
two cases, only for node
2: road contact (Fig. 2) and contact with the external air
(Fig. 3).
Finally, the matrix equation at the basis
of the model
in which
is the generic coefficient, relative to the energy
balance equation of the node
, that multiplies the
temperature, while
is the generic coefficient not
multiplying nodes temperatures.
Generally, to properly
operate in order to provide the
tyre temperature distribution, the model requires the
following input data: normal, longitudinal and lateral
road
interaction forces, longitudinal and lateral sli
speeds, forward speed at the wheel centre, air and
temperature. The structural characteristics and
properties of the tyre and the thermal conductivity of the
track are also required.
Some of these data result from the
measurement
s available for different
preliminarily
analysed in order to check their reliability;
others, such as in particular the ones related to structural and
thermal characteristics of the tyre, are estimated on the basis
of measurements and tests conducted on the tyres [
In addition
to surface, bulk and inner liner temperature
distributions, the model also provides
the thermal flows
involving
the tyre, such as the flow due to the external air
cooling, the one due to the cooling with the road, the one
with the inflation air as well as
the flows due to friction,
hysteresis and exchanges between the different layers.
III. NEW
TRT
I
MPLEMENTATIONS
In the latest versions,
Thermo Racing Tyre
simplified in order to reduce the number of equations to
solve and so to decrease the computati
changes concerned the substitution of the node grid on the
internal layers (bulk and inner liner)
with a singular node
configuration.
The performance gain, obtained with the above
simplification, has been employed
to run
concerning the sidewalls nodes.
These
constituting
the tyre structure, have been
model to estimate more accurately the temperature of the
inner liner, since the latter is
actively involved in the
convective heat exchange with the external and the
corresponding to the contact with the road and to the forced
convective exchange with the external air.
As an example, heat balance equation
s for the surface
s 2 and 3
, recalling
for the performed discretization, the nodes adjacent to
direction, 1 and 3 along the
images show the thermal powers, exchanged
two cases, only for node
2: road contact (Fig. 2) and contact with the external air
of the model
is:
(11)
is the generic coefficient, relative to the energy
, that multiplies the
th node
is the generic coefficient not
operate in order to provide the
tyre temperature distribution, the model requires the
following input data: normal, longitudinal and lateral
tyre
interaction forces, longitudinal and lateral sli
ding
speeds, forward speed at the wheel centre, air and
road
temperature. The structural characteristics and
the thermal
properties of the tyre and the thermal conductivity of the
Some of these data result from the
telemetry
s available for different
tracks and are
analysed in order to check their reliability;
others, such as in particular the ones related to structural and
thermal characteristics of the tyre, are estimated on the basis
of measurements and tests conducted on the tyres [
13].
to surface, bulk and inner liner temperature
the thermal flows
the tyre, such as the flow due to the external air
cooling, the one due to the cooling with the road, the one
the flows due to friction,
hysteresis and exchanges between the different layers.
MPLEMENTATIONS
Thermo Racing Tyre
has been
simplified in order to reduce the number of equations to
solve and so to decrease the computati
on burden. The
changes concerned the substitution of the node grid on the
with a singular node
The performance gain, obtained with the above
mentioned
to run
the iterations
These
new elements,
the tyre structure, have been
introduced in the
model to estimate more accurately the temperature of the
actively involved in the
convective heat exchange with the external and the
internal
airflow [14].
A. TRT – Simplified mesh
The classic
TRT was a discrete three
discretized by means of a grid, whose nodes represented the
points in which the
temperature was determined instant by
instant, as shown in figure 1.
The number of nodes of the grid was given by the product
(∙∙) where
of nodes along the
direction,
along the direction and
along the
direction. Nodes enumeration had been carried
out starting from the first layer in contact with the road,
proceeding transversely.
Over time, TRT’s threelayer
as following (Fig. 4):
• Surface
(grid of nodes in blue)
tyre, made up of a
grid
given by the product (
•
Bulk
(parallelepiped in black)
modelled as a singular
node;
•
Inner liner
(parallelepipe
modelled as a singular node
Considering the model within a thermo
regarding respectively
the bulk and inner layers
temperature distribution of these zones is
anymore
because of their thermal inertia
consideration allowed to simplify the discretization,
reducing respectively the bulk and the inner layers to single
nodes. With this,
the computational burden
consequently TRT can be used
without any difficulties.
In fact, the number of
state variables and therefore of
equations
(11) has been reduced
above simplification was made preserving the heat transfers
between the layers, whose
inertial and thermal material
properties, as density, conductivity and specific heat, were
respectively
attributed to singular nodes.
To take into account the simplification adopted, the bulk
and inner liner nodes
only allow
radial direction of the tyre;
therefore
transfers inside the single
interior tiers have been supposed
absent. In particular, since the bulk and the inner nodes are
assumed to have the heat exchange area along the radial
direction equal to
the rectangle, whose dimensions coincide
with tyre
circumferential length
equations can be respectively written as:
Fig. 4. Simplified mesh, adopted for tyre structure. While the surface layer
is still modelled as a grid of nodes (in blue), the bulk (in black) and the
inner (in magenta) ones have as singular node
TRT was a discrete three
dimensional model,
discretized by means of a grid, whose nodes represented the
temperature was determined instant by
The number of nodes of the grid was given by the product
represented the number
direction,
the number of nodes
was the number of nodes
direction. Nodes enumeration had been carried
out starting from the first layer in contact with the road,
configuration was simplified
(grid of nodes in blue)
: outer surface of the
grid
of nodes, whose number is
)
(parallelepiped in black)
: intermediate layer
node;
(parallelepipe
d in magenta): inner layer
modelled as a singular node
.
Considering the model within a thermo
mechanical chain,
the bulk and inner layers
, a detailed
temperature distribution of these zones is
unnecessary
because of their thermal inertia
s. This
consideration allowed to simplify the discretization,
reducing respectively the bulk and the inner layers to single
the computational burden
is decreased and
in real time applications [15]
state variables and therefore of
(11) has been reduced
from n to (n/3+2). The
above simplification was made preserving the heat transfers
inertial and thermal material
properties, as density, conductivity and specific heat, were
attributed to singular nodes.
To take into account the simplification adopted, the bulk
only allow
the heat exchange along the
therefore
the tangential heat
interior tiers have been supposed
absent. In particular, since the bulk and the inner nodes are
assumed to have the heat exchange area along the radial
the rectangle, whose dimensions coincide
circumferential length
and width, the heat balance
equations can be respectively written as:
Fig. 4. Simplified mesh, adopted for tyre structure. While the surface layer
is still modelled as a grid of nodes (in blue), the bulk (in black) and the
inner (in magenta) ones have as singular node
configuration.
where T
surf,avg
is the mean temperature value of the entire
surface layer. The abovementioned
equations are therefore
developed in order to write a complete set of normal
equations (11), as follows:
B. TRT – Sidewalls implementation
To estimate more accurately the temperature distribution
even of the deepest tyre layers, usually not easily
measurable on
line, an innovative structure configuration
was adopted. The evolved tyre structure includes the
p
resence of the sidewalls, actively involved in
convective heat exchanges
with the external airflow and the
inner gas fluid threads inside the wheel.
Inside the chamber,
the tyre sidewalls thermally interact with the inner gas, that
is in its turn invol
ved in the heat convective exchange with
the inner liner.
As shown in figure 5, the TRT
tyre structure
sidewalls implementation
is still considered
sidewalls have been discretised as
two parallelepiped shaped
single node layers
. In this way their nodes, called
green) and bulk (in yellow), for a r
ight tyre, are respectively
in contact with the external air flux
and
contained inside the wheel chamber.
It is
Fig. 5. Particular diversification between the
in_board
nodes for a Right tyre is obtained regarding their position towards the
vertical longitudinal plane xz
of the vehicle reference system.
(
12
)
(
13
)
is the mean temperature value of the entire
equations are therefore
developed in order to write a complete set of normal
form
(
14
)
(15)
To estimate more accurately the temperature distribution
even of the deepest tyre layers, usually not easily
line, an innovative structure configuration
was adopted. The evolved tyre structure includes the
resence of the sidewalls, actively involved in
the
with the external airflow and the
Inside the chamber,
the tyre sidewalls thermally interact with the inner gas, that
ved in the heat convective exchange with
tyre structure
with
is still considered
unrolled. The
two parallelepiped shaped
. In this way their nodes, called
surface (in
ight tyre, are respectively
and
with the inner gas
It is
also necessary to
highlight that the same s
idewall
in_board and out_board
, regarding their position towards
the vertical longitudinal plane of
(in_board and out_board
sidewalls
nearest and the farthest
ones
convective powers, respectively investing the sides of the
tyre, will be different.
The sidewalls take in account
convective heat exchanges. In partic
external
sidewall nodes, the convective exchange
the external airflow is obtained from the heat transfer area
A
Side
, calculated knowing
the CAD
the internal
sidewall nodes are involved in the convective
heat exchange with the inner gas fluid threads.
balance equations related to
respectively
external and internal nodes are:
The (16) and (17) are further developed as follow
IV. R
ESULTS
First of all, a comparison between the fully discretized
version of TRT and the mononodes one is illustrated. Other
things being equal, the above models have negligible
differences between temperature trends for all the tyre
layers,
as shown in figure 6.
In figure 7
, the temperature trends of all the tyre layers of
the new
modelled TRT with the sidewalls implementation
for all
the four wheels, are illustrated
that in the above
figures the temperature values are
dimensionless
because of confidentiality
agreements)
As expected, the
mean temperature values of respectively
the internal (tread bulk/inner and sidewall bulk) and the
external (tread surface and sidewall surface) tyre layers are
fairly close.
The difference in the ther
external layers is due to
their position inside the tyre
structure: t
he tread layers, especially the surface one, are
in_board
and out_board
nodes for a Right tyre is obtained regarding their position towards the
of the vehicle reference system.
idewall
nodes are diversified in
, regarding their position towards
the vertical longitudinal plane of
symmetry of the vehicle
sidewalls
are correspondingly the
ones
); therefore the thermal
convective powers, respectively investing the sides of the
The sidewalls take in account
both the conductive and the
convective heat exchanges. In partic
ular, as regards the
sidewall nodes, the convective exchange
rate with
the external airflow is obtained from the heat transfer area
the CAD
of the tyre; meanwhile,
sidewall nodes are involved in the convective
heat exchange with the inner gas fluid threads.
The heat
respectively
the sidewall layer’s
(16)
(17)
The (16) and (17) are further developed as follow
s:
(18)
(19)
ESULTS
First of all, a comparison between the fully discretized
version of TRT and the mononodes one is illustrated. Other
things being equal, the above models have negligible
differences between temperature trends for all the tyre
, the temperature trends of all the tyre layers of
modelled TRT with the sidewalls implementation
the four wheels, are illustrated
(it must be highlighted
figures the temperature values are
agreements)
.
mean temperature values of respectively
the internal (tread bulk/inner and sidewall bulk) and the
external (tread surface and sidewall surface) tyre layers are
The difference in the ther
mal shapes of the
their position inside the tyre
he tread layers, especially the surface one, are
subjected to the instant thermal powers generated
tyre/road interaction
; meanwhile a slow temperature trend
induc
ed concurrently by the rolling fatigue effect and by the
convective heat exchanges characterizes the sidewalls
dynamics. That is why,
the internal tyre strata seem to have
Fig. 7. The
temperatures of both the external layers, the tread and the
sidewall surfaces, and the internal ones, the bulk/inner and sidewall plies,
are close concerning the mean values, while the thermal dynamics is
different due to the different physical phenomena t
hey are involved with.
Fig. 6. The comparison between the TRT model and the simplified
singular node configuration version shows negligible differences between
the temperature trends of all threetyre layers.
subjected to the instant thermal powers generated
by the
; meanwhile a slow temperature trend
ed concurrently by the rolling fatigue effect and by the
convective heat exchanges characterizes the sidewalls
the internal tyre strata seem to have
a slow temperature ascent during the rolling motion of the
wheel, while the tread su
rface layer
oscillating profile.
V. C
ONCLUSION
The adoption of a
new simplified
the implementation of
an opportune mesh
a complete tyre temperature distribution
working conditions,
being able
model to the telemetry data,
computer resources expended
model aims to provide a tool
useful
all the thermal phenomena concerning the tyre during its
interaction with both the
external environment and the
internal chamber. In fact,
the factors like the inflating gas
pressure, since its influence on the tyre rolling fatigue
be optimized with the above instrument.
It has to be highlighted that, t
manner, the model needs an initial tuning phase to be carried
out only once for each season, because of changes in car
setup and tyres construction. Onc
operation, known all inputs, the results obtained
agreement with the telemetry data, with reference to the
various operating conditions of the different
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nical Engineering (I.RE.M.E.), v
841847, 2013.
[14] F. Calabrese, M. Baecker,
C. Galbally
thermome
chanical tire model for advanced handling applications”
SAE 2015 World Congress
, Detroit, USA, 2015.
[15]
M. Frantzen, A. H. C. Ng, P. Moore,
system for real
time optimization and decision making support”
Robotics and Computer
Integrated Manufacturing, vol. 27, issue 4,
pp. 696705, August 2011.
temperatures of both the external layers, the tread and the
sidewall surfaces, and the internal ones, the bulk/inner and sidewall plies,
are close concerning the mean values, while the thermal dynamics is
hey are involved with.
Fig. 6. The comparison between the TRT model and the simplified
singular node configuration version shows negligible differences between
a slow temperature ascent during the rolling motion of the
rface layer
is characterized by an
ONCLUSION
new simplified
tyre configuration and
an opportune mesh
allowed to obtain
a complete tyre temperature distribution
in all the tyre
being able
to fit the response of the
model to the telemetry data,
minimizing moreover the
computer resources expended
. In this way, the updated
useful
to study and understand
all the thermal phenomena concerning the tyre during its
external environment and the
the factors like the inflating gas
pressure, since its influence on the tyre rolling fatigue
, can
be optimized with the above instrument.
It has to be highlighted that, t
o be used in a predictive
manner, the model needs an initial tuning phase to be carried
out only once for each season, because of changes in car
setup and tyres construction. Onc
e developed through this
operation, known all inputs, the results obtained
are in good
agreement with the telemetry data, with reference to the
various operating conditions of the different
tracks.
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