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A Real-Time Thermal Model for the Analysis of Tire/Road Interaction in Motorcycle Applications

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While in the automotive field the relationship between road adherence and tire temperature is mainly investigated with the aim to enhance the vehicle performance in motorsport, the motorcycle sector is highly sensitive to such theme also from less extreme applications. The small extension of the footprint, along with the need to guarantee driver stability and safety in the widest possible range of riding conditions, requires that tires work as most as possible at a temperature able to let the viscoelastic compounds-constituting the tread and the composite materials of the whole carcass structure-provide the highest interaction force with road. Moreover, both for tire manufacturing companies and for single track vehicles designers and racing teams, a deep knowledge of the thermodynamic phenomena involved at the ground level is a key factor for the development of optimal solutions and setup. This paper proposes a physical model based on the application of the Fourier thermodynamic equations to a three-dimensional domain, accounting for all the sources of heating like friction power at the road interface and the cyclic generation of heat because of rolling and to asphalt indentation, and for the cooling effects because of the air forced convection, to road conduction and to turbulences in the inflation chamber. The complex heat exchanges in the system are fully described and modeled, with particular reference to the management of contact patch position, correlated to camber angle and requiring the adoption of an innovative multi-ribbed and multi-layered tire structure. The completely physical approach induces the need of a proper parameterization of the model, whose main stages are described, both from the experimental and identification points of view, with particular reference to non-destructive procedures for thermal parameters definition. One of the most peculiar and challenging features of the model is linked with its topological and analytical structure, allowing to run in real-time, usefully for the application in co-simulation vehicle dynamics platforms, for performance prediction and setup optimization applications.
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applied
sciences
Article
A Real-Time Thermal Model for the Analysis of
Tire/Road Interaction in Motorcycle Applications
Flavio Farroni 1, * , NicolòMancinelli 2and Francesco Timpone 1
1
Dipartimento di Ingegneria Industriale–Universit
à
degli Studi di Napoli Federico II, 80138 Napoli NA, Italy;
francesco.timpone@unina.it
2Vehicle Dynamics, Ducati Motor Holding spa-Ducati Corse Division, 40132 Bologna BO, Italy;
nicolo.mancinelli@ducati.com
*Correspondence: flavio.farroni@unina.it; Tel.: +39-33-3374-2646; Fax: +39-08-1239-4165
Received: 4 February 2020; Accepted: 23 February 2020; Published: 28 February 2020


Abstract:
While in the automotive field the relationship between road adherence and tire temperature
is mainly investigated with the aim to enhance the vehicle performance in motorsport, the motorcycle
sector is highly sensitive to such theme also from less extreme applications. The small extension
of the footprint, along with the need to guarantee driver stability and safety in the widest possible
range of riding conditions, requires that tires work as most as possible at a temperature able to let
the viscoelastic compounds-constituting the tread and the composite materials of the whole carcass
structure-provide the highest interaction force with road. Moreover, both for tire manufacturing
companies and for single track vehicles designers and racing teams, a deep knowledge of the
thermodynamic phenomena involved at the ground level is a key factor for the development of
optimal solutions and setup. This paper proposes a physical model based on the application of the
Fourier thermodynamic equations to a three-dimensional domain, accounting for all the sources of
heating like friction power at the road interface and the cyclic generation of heat because of rolling
and to asphalt indentation, and for the cooling eects because of the air forced convection, to road
conduction and to turbulences in the inflation chamber. The complex heat exchanges in the system are
fully described and modeled, with particular reference to the management of contact patch position,
correlated to camber angle and requiring the adoption of an innovative multi-ribbed and multi-layered
tire structure. The completely physical approach induces the need of a proper parameterization of
the model, whose main stages are described, both from the experimental and identification points
of view, with particular reference to non-destructive procedures for thermal parameters definition.
One of the most peculiar and challenging features of the model is linked with its topological and
analytical structure, allowing to run in real-time, usefully for the application in co-simulation vehicle
dynamics platforms, for performance prediction and setup optimization applications.
Keywords: motorcycle tires; thermal modeling; performance optimization; real-time simulations
1. Introduction
A four-wheeled vehicle, even if often exerting a hyper static equilibrium, requires that its stability
is guaranteed by an optimal adherence with road, allowing to satisfy safety, performance, and comfort
requirements. If such evidence is fundamental for cars vehicle dynamics, the optimization of tire/road
interaction becomes a key factor in motorcycles, and in particular considering racing ones, characterized
by working with high roll angles and speed [1].
In a deeper analysis of tire/road interaction in motorsport sector, the focus moves necessarily to the
optimization of the contact conditions in reference to the behavior of materials constituting tire tread
and inner layers [
2
,
3
]. In particular, the adhesive bonding [
4
] and the power dissipated in the local
Appl. Sci. 2020,10, 1604; doi:10.3390/app10051604 www.mdpi.com/journal/applsci
Appl. Sci. 2020,10, 1604 2 of 13
indentation of road asperities [
5
], are highly influenced by the viscoelastic properties of tire polymers;
such properties mainly vary with stress frequency [6], local displacement [7], and temperature [6,8].
The relationship between tire performance and temperature is a widely discussed topic [
9
11
],
and racing tires, with the aim to exhibit an extra-ordinary frictional attitude, are designed adopting
specific mixing of materials working at their best in a narrow thermal range. The challenge, for the
driver and for the team engineers, is getting information on such thermal range to make sure that the
tire spends the most of its time inside it, acting on proper vehicle setup, driving style and controls.
Moreover, several studies report that tire tread exhibits optimal grip depending on the temperature
reached in its core layer [
12
,
13
], not reachable by measurement instruments for thermal monitoring,
and that global tire stiness is highly influenced by the thermodynamic conditions of the carcass [
14
],
also not directly measurable. For this reason, and for the increasing request of tools able to reproduce
with high reliability the contact with road in a vehicle dynamics environment, the development of a
tire thermal model has become a necessity for the players requiring the predictivity in challenging
simulation scenarios.
In literature, the first approaches to such issue are related to the modeling of the Fourier equations
applied to a three-dimensional domain, in some cases coupled with a mechanical model of the
tire [
15
,
16
], in other with stand-alone tools able to work together with other interaction formulations,
like Pacejka’s MF [
17
], or with FEM [
18
]. During the past years the focus has moved to highly
discretized models able to work in real time [
19
], whose maximum level of complexity has been
requested by motorcycle applications, for which tire contact patch moves along lateral direction of the
tread, generating local stress [
20
] able to modify significantly the whole balance of energy with respect
to car tires [19].
The paper describes the main structure and the approach followed in the thermodynamic modeling
of a motorcycle racing tire, accounting for the parameterization of the diusivity of the dierent layers,
of the contact patch under variable working conditions, of the heat generation eects and of the
conductive/convective interactions with the external environment, leading to a physical formulation
for the real-time simulation of a virtual tire, conceived for a better knowledge of the mechanisms
responsible for its forces exchange and for the development of performance optimization strategies
linked to specific vehicle setup and boundary conditions management.
2. thermoRIDE–Tire Thermodynamic Model
thermoRIDE is a physical-analytical tire model, employable to study and understand all the
phenomena concerning the tire during its interaction with both the external environment and the inner
wheel chamber (inner air, rim, brakes, vehicle geometry, etc.,), as illustrated in Figure 1.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 13
local indentation of road asperities [5], are highly influenced by the viscoelastic properties of tire
polymers; such properties mainly vary with stress frequency [6], local displacement [7], and
temperature [6,8].
The relationship between tire performance and temperature is a widely discussed topic [9–11],
and racing tires, with the aim to exhibit an extra-ordinary frictional attitude, are designed adopting
specific mixing of materials working at their best in a narrow thermal range. The challenge, for the
driver and for the team engineers, is getting information on such thermal range to make sure that the
tire spends the most of its time inside it, acting on proper vehicle setup, driving style and controls.
Moreover, several studies report that tire tread exhibits optimal grip depending on the
temperature reached in its core layer [12,13], not reachable by measurement instruments for thermal
monitoring, and that global tire stiffness is highly influenced by the thermodynamic conditions of the
carcass [14], also not directly measurable. For this reason, and for the increasing request of tools able
to reproduce with high reliability the contact with road in a vehicle dynamics environment, the
development of a tire thermal model has become a necessity for the players requiring the predictivity
in challenging simulation scenarios.
In literature, the first approaches to such issue are related to the modeling of the Fourier
equations applied to a three-dimensional domain, in some cases coupled with a mechanical model of
the tire [15,16], in other with stand-alone tools able to work together with other interaction
formulations, like Pacejka’s MF [17], or with FEM [18]. During the past years the focus has moved to
highly discretized models able to work in real time [19], whose maximum level of complexity has
been requested by motorcycle applications, for which tire contact patch moves along lateral direction
of the tread, generating local stress [20] able to modify significantly the whole balance of energy with
respect to car tires [19].
The paper describes the main structure and the approach followed in the thermodynamic
modeling of a motorcycle racing tire, accounting for the parameterization of the diffusivity of the
different layers, of the contact patch under variable working conditions, of the heat generation effects
and of the conductive/convective interactions with the external environment, leading to a physical
formulation for the real-time simulation of a virtual tire, conceived for a better knowledge of the
mechanisms responsible for its forces exchange and for the development of performance
optimization strategies linked to specific vehicle setup and boundary conditions management.
2. thermoRIDE–Tire Thermodynamic Model
thermoRIDE is a physical-analytical tire model, employable to study and understand all the
phenomena concerning the tire during its interaction with both the external environment and the
inner wheel chamber (inner air, rim, brakes, vehicle geometry, etc.,), as illustrated in Figure 1.
Figure 1. thermoRIDE model scheme.
thermoRIDE model takes into account the following physical phenomena:
Figure 1. thermoRIDE model scheme.
Appl. Sci. 2020,10, 1604 3 of 13
thermoRIDE model takes into account the following physical phenomena:
Heat generation within the tire structure due to:
Tire/road tangential interaction, known as FP (friction power);
Eect of tire cyclic deformation during the tire rolling, known as SEL (strain energy loss).
Heat exchange with the external environment due to:
Thermal conduction between the tire tread and the road pavement;
Thermal convection of the tread surface with the external air;
Thermal convection of the inner liner surface with the inner air.
Heat conduction between the tire nodes due to the temperature gradient.
2.1. Mathematical Model
thermoRIDE thermodynamic model is based on the use of the Fourier’s diusion equation applied
to a three-dimensional domain.
It refers to energy contained within the system, excluding potential energy because of external
forces fields and kinetic energy of motion of the system as a whole, and it keeps account of the gains
and losses of energy of the system.
The law of heat conduction, also known as Fourier’s law, states that the time rate of heat transfer
through a material is proportional to the negative gradient in the temperature and to the area through
which the heat flows. The dierential form of Fourier’s law shows that the local heat flux density
q
is
equal to the product of thermal conductivity k and the negative local temperature gradient
T. The
heat flux density is the amount of energy that flows through a unit area per unit time:
q=k∗ ∇T(1)
where:
qis the local heat flux density, in [W/m2];
kis the material’s conductivity, in hW
mKi;
• ∇Tis the temperature gradient, in hK
mi.
It is possible to obtain a parabolic partial dierential equation from the Fourier’s law, especially
useful for the numerical integration problems in transient thermal conditions. An infinitesimal volume
element
dV =dx dy dz
is considered in order to derive the system of the diusion equations for each
part of the tire structure.
Since the change in the internal energy of a closed system is equal to the amount of heat supplied
to the system, minus the amount of work done by the system on its surroundings, and the control
volume is considered not deformable, the internal energy dU of the infinitesimal volume dV is given
by:
dU =dm cvT=ρdV cvT(2)
where the volume cannot do any work (dL=0), as assumed above. That is why the change in the
internal energy dU is considered only to the amount of heat dQ added to the system.
The quantity dQ stands for the heat supplied to the system by its surroundings and it takes into
account two dierent contributions:
Heat exchanged dQEX =dt HdS
q·
ndS through the outer surface of the volume dV;
Heat generated dQG=.
qGdV dt inside it.
Appl. Sci. 2020,10, 1604 4 of 13
Therefore, the equation leads to:
dQ =dQEX +dQG(3)
where:
.
qGis the heat amount generated per unit time and per unit volume, in W
m3s;
nis the normal unit vector respectively to the faces of the volume element.
For Gauss’s divergence theorem, which postulates the equality between the flux of a vector field
through a closed surface and the volume integral of the divergence over the region inside the surface,
an integral taken over a volume
HdV div
qdV
can replace the one taken over the surface bounding
that volume HdS
q·
ndS, as following:
dQEX =dt IdS
q·
ndS =dt IdV
div
qdV (4)
In addition, the integral symbol can be avoided without aecting the physical meaning of the
expression above, since the equation was carried out for an infinitesimal volume element dV:
dQEX =dt div
qdV (5)
Combining the Equations (4) and (5), it results:
dQEX =dt div (k∗ ∇T)dV (6)
In conclusion, summing up (2), (3), and (5), the energy balance equation is obtained for the
infinitesimal volume dV:
ρdV cvdT =.
qGdV dt +dt div(k∗ ∇T)dV (7)
which, divided both sides by the quantity
ρdV cvdt
, defines the diusion or heat equation of
Fourier:
T
t=
.
qG
ρcv
+div(k∗ ∇T)
ρcv(8)
Equation (8) allows to obtain the three-dimensional distribution of temperature T(x,y,z,t), once the
boundary condition are specified.
The Fourier’s heat equation governs the temperature variation in time in relation to a special
thermal gradient, and shows how the temperature will vary over time because of the generative eects
or because of the ones linked to the heat transport.
In general, the Fourier’s law allows studying only stationary thermal phenomena, whereas the
heat diusion equation also admits transient states. The complexity of the phenomena under study
and the degree of accuracy required have made it necessary to take into account the dependence
of the thermodynamic quantities and in particular of the thermal conductivity on the temperature.
Furthermore, the non-homogeneity of the tire has made it necessary to consider the variation of the
above parameters also along the thickness.
2.2. Physical Model
2.2.1. Tire Structural Model
Depending on the tire peculiar characteristics (dimensions, diusivity, and inertia), the tire
discretization can vary considerably with the main purpose to satisfy both the representation of all the
Appl. Sci. 2020,10, 1604 5 of 13
physical phenomena characterizing transient and steady-state tire thermal dynamic and the necessity
to preserve the hard real-time requirement in all the tire operating conditions.
The default tire discretization along the radial and lateral directions are respectively illustrated
in Figure 2on the left and right sides. However, the motorcycle tire discretization along the ISO y
direction can be freely modified up to 16 ribs (5 ribs default configuration is represented in the Figure 2)
once the pre-initialized boundary conditions maps for the specific mesh configuration are available for
the specific tire under analysis.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13
The default tire discretization along the radial and lateral directions are respectively illustrated
in Figure 2 on the left and right sides. However, the motorcycle tire discretization along the ISO y
direction can be freely modified up to 16 ribs (5 ribs default configuration is represented in the Figure
2) once the pre-initialized boundary conditions maps for the specific mesh configuration are available
for the specific tire under analysis.
Figure 2. Example of thermoRIDE tire mesh configuration.
The default six layers of the tire structure along the radial direction are the followings:
Tread surface, which is the most external part of the tread, the one which is in contact with the
tarmac and the external air;
Tread core is just below the surface and it is strictly connected with the grip level the tire is able
to provide but it affects also the tire stiffness;
Tread base is the deepest part of the tread, the last part before the belt; its temperature is more
linked to the tire stiffness rather than the grip level;
Belt is just below the Tread Base and it gives a big contribution to the SEL;
Plies which is the last layer of the tire structure, it is another important contributor to the SEL,
thanks to the energy dissipated by the friction among different plies and within the plies;
Inner liner is the layer in contact with the inner air, which is not contributing to SEL dissipation
neither linked to tire stiffness and grip.
2.2.2. Contact Patch Evaluation
The size and the shape of contact area are obtained by means of specifically developed test
procedures, based on the pressure sensitive films or employing more complex models like multibody
(MBD) or finished elements (FEA) ones.
Since the characterization procedures are linked to static application of vertical load in
different conditions of internal pressure and wheel alignment configuration expressed in terms
of camber γ, the contact patch configuration concerning its shape and extension refers to static load
conditions in case of the employment of the sensitive film characterization methodology.
Figure 2. Example of thermoRIDE tire mesh configuration.
The default six layers of the tire structure along the radial direction are the followings:
Tread surface, which is the most external part of the tread, the one which is in contact with the
tarmac and the external air;
Tread core is just below the surface and it is strictly connected with the grip level the tire is able to
provide but it aects also the tire stiness;
Tread base is the deepest part of the tread, the last part before the belt; its temperature is more
linked to the tire stiness rather than the grip level;
Belt is just below the Tread Base and it gives a big contribution to the SEL;
Plies which is the last layer of the tire structure, it is another important contributor to the SEL,
thanks to the energy dissipated by the friction among dierent plies and within the plies;
Inner liner is the layer in contact with the inner air, which is not contributing to SEL dissipation
neither linked to tire stiness and grip.
2.2.2. Contact Patch Evaluation
The size and the shape of contact area are obtained by means of specifically developed test
procedures, based on the pressure sensitive films or employing more complex models like multibody
(MBD) or finished elements (FEA) ones.
Since the characterization procedures are linked to static application of vertical load
Fz
in dierent
conditions of internal pressure
Pi
and wheel alignment configuration expressed in terms of camber
γ
,
the contact patch configuration concerning its shape and extension refers to static load conditions in
case of the employment of the sensitive film characterization methodology.
However, the instantaneous dynamic contact patch extension and shape can be rather dierent,
because of particular transient conditions of wheel loading, centrifugal eect on the rolling tire, and
viscoelastic tire intrinsic characteristics. The adoption of a MBD/FEA tire model able to fit both static
and dynamic experimental data, respectively represented by vertical rim lowering and contact patch
extension and shape in quasi-static conditions and strain energy loss cycle areas in dierent load
and frequency conditions because of viscous properties of the tire structure, can constitute a valid
Appl. Sci. 2020,10, 1604 6 of 13
instrument to implement the contact patch dynamic characteristics within the thermoRIDE model,
by means of discretized areas associated to the control volume, as illustrated in Figure 3. Moreover,
such models are capable to provide footprint areas depending on wheel travelling velocity or rolling
frequency, aecting tire shape because of centrifugal eects.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 13
Figure 3. Example of thermoRIDE contact patch geometry representation.
However, the instantaneous dynamic contact patch extension and shape can be rather different,
because of particular transient conditions of wheel loading, centrifugal effect on the rolling tire, and
viscoelastic tire intrinsic characteristics. The adoption of a MBD/FEA tire model able to fit both static
and dynamic experimental data, respectively represented by vertical rim lowering and contact patch
extension and shape in quasi-static conditions and strain energy loss cycle areas in different load and
frequency conditions because of viscous properties of the tire structure, can constitute a valid
instrument to implement the contact patch dynamic characteristics within the thermoRIDE model,
by means of discretized areas associated to the control volume, as illustrated in Figure 3. Moreover,
such models are capable to provide footprint areas depending on wheel travelling velocity or rolling
frequency, affecting tire shape because of centrifugal effects.
At the current stage, thermoRIDE is able to adopt real contact patch areas from both the
experimental activities (static, as said) or the MBD/FEM model outputs (static or dynamic, depending
on the model), expressing thanks to parameters identification algorithms the footprint extension as a
function of the main variables affecting its shape, as in the following:
 =
(,,) (9)
2.2.3. Heat Exchange with Road Surface
The thermal conductive exchange between the tread and the asphalt has been modeled through
Newtons formula, schematizing the whole phenomenon by means of an appropriate coefficient of
heat exchange. The term for such exchanges, for the generic i-th node will be equal to:
=
(−
)∙∆∙∆ (10)
where:
is the convective heat transfer coefficient, estimated for the track testing conditions, in
∙;
is the track temperature [K].
The heat generation at the tire-road interface is connected with the thermal power because of the
tangential stresses that, in the sliding zone of the contact patch, 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:
=∙+
∙
(11)
Figure 3. Example of thermoRIDE contact patch geometry representation.
At the current stage, thermoRIDE is able to adopt real contact patch areas from both the
experimental activities (static, as said) or the MBD/FEM model outputs (static or dynamic, depending
on the model), expressing thanks to parameters identification algorithms the footprint extension as a
function of the main variables aecting its shape, as in the following:
ACP =f(Fz,Pi,γ)(9)
2.2.3. Heat Exchange with Road Surface
The thermal conductive exchange between the tread and the asphalt has been modeled through
Newton
0
s formula, schematizing the whole phenomenon by means of an appropriate coecient of
heat exchange. The term for such exchanges, for the generic i-th node will be equal to:
QC=Hc·(TrTi)·X·Y(10)
where:
Hcis the convective heat transfer coecient, estimated for the track testing conditions, in W
m2·K;
Tris the track temperature [K].
The heat generation at the tire-road interface is connected with the thermal power because of the
tangential stresses that, in the sliding zone of the contact patch, 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:
FP =Fx·vx+Fy·vy
A(11)
Appl. Sci. 2020,10, 1604 7 of 13
2.2.4. Heat Exchange with External/Inside Air
The whole mechanism of the heat transfer between a generic surface and a moving fluid at
dierent temperatures is described by natural and forced convection equations. The convection heat
transfer is expressed by Newton’s law of cooling, as before:
hconv·Tf luid Ti·X·Y(12)
Therefore, the heat exchange with the outside air is modeled by the mechanism of forced
convection, occurring when there is relative motion between the motorcycle 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 coecient h, both forced
hf orc
and natural
hnat
, is
based on the classical approach of the dimensionless analysis.
Supposing the tire invested by the air similarly to a cylinder invested transversely from an air
flux, the forced convection coecient is provided by the following formulation [8,9]:
hf orc =Kair
L·
0.0239· Vx·L
νair !0.805
(13)
in which:
Kair
is air conductivity, evaluated at an average temperature between the eective air one and
outer tire surface one, in hW
m·Ki;
Vxis considered to be equal to the forward speed, in hm
si;
νair is the kinematic viscosity of air, in hm2
si;
Lis the characteristic length of the heat transfer surface, in [m];
Tm,air
is the arithmetic mean between the temperatures of the tire outer surface and the external
air in relative motion, in [K].
The values of
hf orc
evaluated with the above approach are close to those obtained by means of
CFD simulations for a motorcycle tire, represented in Figure 4.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 13
2.2.4. Heat Exchange with External/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:
 ∙
 −
∙∆∙∆ (12)
Therefore, the heat exchange with the outside air is modeled by the mechanism of forced
convection, occurring when there is relative motion between the motorcycle 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 h, both forced  and natural ,
is based on the classical approach of the dimensionless analysis.
Supposing the tire 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]:
 =
0.0239∙
 . (13)
in which:
 is air conductivity, evaluated at an average temperature between the effective air one and
outer tire surface one, in
∙;
Vx is considered to be equal to the forward speed, in
;
 is the kinematic viscosity of air, in
;
L is the characteristic length of the heat transfer surface, in [m];
, is the arithmetic mean between the temperatures of the tire outer surface and the external
air in relative motion, in [K].
The values of  evaluated with the above approach are close to those obtained by means of
CFD simulations for a motorcycle tire, represented in Figure 4.
Figure 4.
Example of motorcycle Computational Fluid Dynamics (CFD) simulations, useful for both
front and rear tires convection parameterization.
Appl. Sci. 2020,10, 1604 8 of 13
The natural convection coecient hnat, however, can be expressed as:
hnat =Nu·kair
L(14)
in which, for this case:
Nu =0.53·Gr0.25·Pr0.25 (15)
2.2.5. Hysteretic Generative Term
The energy generated by the tire because of cyclic deformations is due to a superposition of
several phenomena: intra-plies friction, friction inside singular plies, nonlinear viscoelastic behavior of
all rubbery components, etc.
During the rolling, the entire tire is subjected to the cyclic deformations with a frequency
corresponding to the tire rotational speed. During the motion, portions of tire, entering in sequence in
the contact area, are subjected to deformations, which cause kinetic energy loss and heat dissipation.
The amount of heat generated by deformation (SEL) is estimated through experimental tests
carried out deforming cyclically the tire in three directions (radial, longitudinal, and lateral).
Estimated energies do not exactly coincide with the ones dissipated in the actual operative
conditions, as the deformation mechanism is dierent; it is however possible to identify a correlation
between them on the basis of coecients estimated from real data telemetry and from the specifically
developed dynamic analysis involving MBD/FEA models.
At the current stage, the empirical SEL formulation is a function of the following parameters and
it deeply depends on the tire characteristics:
SEL =f(F,ω,γ,Pi)(16)
whose further details and trends are available in [21] and where:
Fis the average interaction force at the contact patch, in [N];
ωis the wheel rotation frequency, in [rad/s];
γis the wheel alignment camber angle, in [rad];
Piis the gauge pressure within the wheel internal chamber, in [bar].
2.2.6. Model Input/Output Interface
The input data required by the thermoRIDE model consists of the following telemetry channels,
as summarized in Table 1.
Table 1. thermoRIDE model inputs.
Physical Quantity Description
FzVertical interaction force
FxLongitudinal interaction force
FyLateral interaction force
vxWheel hub longitudinal velocity
srSlip ratio
saSlip angle
ωWheel angular velocity
γInclination angle
Tair Ambient air temperature
Troad Road pavement temperature
Some of these data result from the telemetry measurements available for dierent tracks and are
preliminarily analyzed in order to check their reliability; others, such as in particular the ones related
Appl. Sci. 2020,10, 1604 9 of 13
to structural and thermal characteristics of the tire, are estimated on the basis of measurements and
tests conducted on the tires.
In addition to tread and inner liner temperature distributions, as reported in Table 2, the model
also provides the thermal flows involving the tire, 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 dierent layers.
Table 2. thermoRIDE model outputs.
Physical Quantity Description
TtreadSurf Tread surface temperature
TtreadCore Tread core temperature
TtreadBase Tread base temperature
TinnerLiner Inner liner temperature
TinnerAir Internal air temperature
PinnerAir Internal air pressure
WextConvection Ambient air convection
WintConvection Chamber air convection
WextConduction Road pavement conduction
WlongFriction Longitudinal friction
WlatFriction Lateral friction
Wsel Strain Energy Loss
It has to be highlighted that, once per season, it is necessary to carry out an appropriate set of
tuning factors to use it in a predictive manner.
The above procedure is linked with the vehicle specific configuration, connected with motorcycle
setup and tires construction. Once the tuning phase is completed, known all vehicle data thermoRIDE
inputs, the results obtained are in good agreement with the experimental data, with reference to the
various operating conditions of the dierent tracks, allowing to adopt the model for analysis and
supporting vehicle design determination.
3. Results
In the Figures 5and 6, the temperature trends of all the tire layers of the thermodynamic model are
illustrated (it must be highlighted that in the above figures the temperature values are dimensionless
because of confidentiality agreements with industrial partners). It has to be clarified that the measured
data in Figure 5in red (acquired from external IR sensors) report the temperature of fixed points along
the lateral direction of the tire tread, while the simulated ones, in blue, are related to each one of the 15
ribs available, in any moment of the run.
Appl. Sci. 2020,10, 1604 10 of 13
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 13
Figure 5. Comparison between the tread external temperatures obtained by means of the 16-ribs’
configuration model (in blue) and the acquired ones (in red).
Figure 6. Tire temperatures of all the tire layers obtained by means of the thermoRIDE model: tread
surface (in blue), tread core (in red), tread base (in black) and innerliner (in green).
The difference in the thermal shapes of the external layers is due to their position inside the tire
structure: the tread layers, especially the surface one, are subjected to the instant thermal powers
generated by the tire/road interaction and convective flows; meanwhile a slow temperature trend
induced concurrently by the rolling fatigue effect and by the convective heat exchanges characterizes
the internal layers’ dynamics. That is why, the internal tire layers seem to have a slow temperature
ascent during the rolling motion of the wheel, while the tread surface is characterized by an
oscillating profile.
The ability to predict the interior temperature distribution, and thus the grip behavior of the tire,
is fundamental in terms of the vehicle handling improvement and of the asset optimization according
to highly variable outdoor testing conditions.
Vehicle optimal setup is deeply linked with the correct compound working conditions, as
highlighted in Figure 7 for a reference automotive tire, not directly linked to the described motorcycle
Figure 5.
Comparison between the tread external temperatures obtained by means of the 16-ribs’
configuration model (in blue) and the acquired ones (in red).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 13
Figure 5. Comparison between the tread external temperatures obtained by means of the 16-ribs’
configuration model (in blue) and the acquired ones (in red).
Figure 6. Tire temperatures of all the tire layers obtained by means of the thermoRIDE model: tread
surface (in blue), tread core (in red), tread base (in black) and innerliner (in green).
The difference in the thermal shapes of the external layers is due to their position inside the tire
structure: the tread layers, especially the surface one, are subjected to the instant thermal powers
generated by the tire/road interaction and convective flows; meanwhile a slow temperature trend
induced concurrently by the rolling fatigue effect and by the convective heat exchanges characterizes
the internal layers’ dynamics. That is why, the internal tire layers seem to have a slow temperature
ascent during the rolling motion of the wheel, while the tread surface is characterized by an
oscillating profile.
The ability to predict the interior temperature distribution, and thus the grip behavior of the tire,
is fundamental in terms of the vehicle handling improvement and of the asset optimization according
to highly variable outdoor testing conditions.
Vehicle optimal setup is deeply linked with the correct compound working conditions, as
highlighted in Figure 7 for a reference automotive tire, not directly linked to the described motorcycle
Figure 6.
Tire temperatures of all the tire layers obtained by means of the thermoRIDE model: tread
surface (in blue), tread core (in red), tread base (in black) and innerliner (in green).
The dierence in the thermal shapes of the external layers is due to their position inside the tire
structure: the tread layers, especially the surface one, are subjected to the instant thermal powers
generated by the tire/road interaction and convective flows; meanwhile a slow temperature trend
induced concurrently by the rolling fatigue eect and by the convective heat exchanges characterizes the
internal layers’ dynamics. That is why, the internal tire layers seem to have a slow temperature ascent
during the rolling motion of the wheel, while the tread surface is characterized by an oscillating profile.
The ability to predict the interior temperature distribution, and thus the grip behavior of the tire,
is fundamental in terms of the vehicle handling improvement and of the asset optimization according
to highly variable outdoor testing conditions.
Vehicle optimal setup is deeply linked with the correct compound working conditions, as
highlighted in Figure 7for a reference automotive tire, not directly linked to the described motorcycle
thermal model, but able to show expected physical trends. Such optimization is achievable with a
Appl. Sci. 2020,10, 1604 11 of 13
proper suspension layout in terms of stiness, compliance, and of suitable wheel alignment geometry.
In particular, owing to the availability of information on the time by time tread core temperature,
plotted on the x-axis, it becomes clear that the tire shows an optimal grip in a specific thermal range that
results to be the variable for each dierent compound, useful to be known in order to set an optimal
configuration of the vehicle in any condition.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 13
thermal model, but able to show expected physical trends. Such optimization is achievable with a
proper suspension layout in terms of stiffness, compliance, and of suitable wheel alignment
geometry. In particular, owing to the availability of information on the time by time tread core
temperature, plotted on the x-axis, it becomes clear that the tire shows an optimal grip in a specific
thermal range that results to be the variable for each different compound, useful to be known in order
to set an optimal configuration of the vehicle in any condition.
Figure 7. Tread core compound grip-temperature dependence.
Differences in terms of interaction characteristics (Figure 8), in which a considerable stiffness
decrease because of a higher tire temperature is clearly appreciable, are shown both for longitudinal
and lateral tire interaction curves.
Figure 8. Temperature influence on tire interaction characteristics curves (longitudinal interaction on
the left and lateral interaction on the right).
The influence of a large amount of parameters can be evaluated, such as, inclination angle,
inflation pressure, different track and weather conditions, and the influence of the manufacturer’s
vehicle settings. To exploit the entire amount of grip available on the tire-road interface in order to
preserve the highest level of handling performance preventing the tire from sliding, more and more
physical phenomena regarding the vehicle and its subcomponents have to be taken into account
within the integrated vehicle control systems.
4. Conclusions
The paper focuses on the development of a specific version of a tire thermal model for
motorcycle applications. The main differences from the common thermodynamic models are related
to the particular management of contact patch, responsible for the fundamental friction generation
phenomena and for conduction with road, and that in motorcycle tires is characterized by particular
elliptical and arched shape, in continuous motion along the lateral direction because of high
roll/camber angle.
Figure 7. Tread core compound grip-temperature dependence.
Dierences in terms of interaction characteristics (Figure 8), in which a considerable stiness
decrease because of a higher tire temperature is clearly appreciable, are shown both for longitudinal
and lateral tire interaction curves.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 13
thermal model, but able to show expected physical trends. Such optimization is achievable with a
proper suspension layout in terms of stiffness, compliance, and of suitable wheel alignment
geometry. In particular, owing to the availability of information on the time by time tread core
temperature, plotted on the x-axis, it becomes clear that the tire shows an optimal grip in a specific
thermal range that results to be the variable for each different compound, useful to be known in order
to set an optimal configuration of the vehicle in any condition.
Figure 7. Tread core compound grip-temperature dependence.
Differences in terms of interaction characteristics (Figure 8), in which a considerable stiffness
decrease because of a higher tire temperature is clearly appreciable, are shown both for longitudinal
and lateral tire interaction curves.
Figure 8. Temperature influence on tire interaction characteristics curves (longitudinal interaction on
the left and lateral interaction on the right).
The influence of a large amount of parameters can be evaluated, such as, inclination angle,
inflation pressure, different track and weather conditions, and the influence of the manufacturer’s
vehicle settings. To exploit the entire amount of grip available on the tire-road interface in order to
preserve the highest level of handling performance preventing the tire from sliding, more and more
physical phenomena regarding the vehicle and its subcomponents have to be taken into account
within the integrated vehicle control systems.
4. Conclusions
The paper focuses on the development of a specific version of a tire thermal model for
motorcycle applications. The main differences from the common thermodynamic models are related
to the particular management of contact patch, responsible for the fundamental friction generation
phenomena and for conduction with road, and that in motorcycle tires is characterized by particular
elliptical and arched shape, in continuous motion along the lateral direction because of high
roll/camber angle.
Figure 8.
Temperature influence on tire interaction characteristics curves (longitudinal interaction on
the left and lateral interaction on the right).
The influence of a large amount of parameters can be evaluated, such as, inclination angle, inflation
pressure, dierent track and weather conditions, and the influence of the manufacturer’s vehicle
settings. To exploit the entire amount of grip available on the tire-road interface in order to preserve
the highest level of handling performance preventing the tire from sliding, more and more physical
phenomena regarding the vehicle and its subcomponents have to be taken into account within the
integrated vehicle control systems.
4. Conclusions
The paper focuses on the development of a specific version of a tire thermal model for motorcycle
applications. The main dierences from the common thermodynamic models are related to the particular
management of contact patch, responsible for the fundamental friction generation phenomena and for
conduction with road, and that in motorcycle tires is characterized by particular elliptical and arched
shape, in continuous motion along the lateral direction because of high roll/camber angle.
Appl. Sci. 2020,10, 1604 12 of 13
Such peculiar behavior required a dedicated modeling approach, coupled with the possibility to
implement micro-hysteresis dierences in each single rib, referred to the possibility to adopt dierent
compounds in the same tire, very common in motorsport.
The results of simulations carried out by coupling the tire thermal model with a vehicle one
have been reported, showing a significant good agreement with the experimental results coming from
dedicated outdoor acquisitions on an instrumented testing motorcycle. Once validated the model
calibration, the main advantages of a predictive and reliable thermal model are the evaluation of the
thermal fluxes and temperature interesting the inner layers of the tire structure (deeply linked to grip
and stiness variations, highly influencing vehicle performances and ride/comfort dynamics) and the
possibility to study the vehicle setup and aerodynamics, owing to the estimation of the exact amount
of energy to be generated/subtracted to let the tire work in the optimal thermal range.
Further development stages are concerning the implementation of the tread wear mechanisms,
correlated with the energy provided to the tire lap by lap and deeply influencing the temperature
distribution during the race event. Moreover, the real-time availability of knowledge on local
temperature, coupled with reliable interaction forces estimation, is a key factor to the realization of
MiL (model in the loop), HiL (hardware in the loop), and DiL (driver in the loop) simulation scenarios.
Author Contributions:
For research articles with several authors, a short paragraph specifying their individual
contributions must be provided. The following statements should be used “conceptualization, F.F., N.M. and
F.T.; software, F.F., N.M.; validation, N.M.; data curation, N.M..; writing—original draft preparation, F.F.;
writing—review and editing, F.T. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare that they have no conflict of interest.
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©
2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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The tire and vehicle setup definition, able to optimise grip performance and thermal working conditions, can make the real difference as for motorsport racing teams, used to deal with relevant wear and degradation phenomena, as for tire makers, requesting for design solutions aimed to obtain enduring and stable tread characteristics, as finally for the development of safety systems, conceived in order to maximise road friction, both for worn and unworn tires. The activity discussed in the paper deals with the analysis of the effects that tire wear induces in vehicle performance, in particular as concerns the consequences that tread removal has on thermal and frictional tire behaviour. The physical modelling of complex tire–road interaction phenomena and the employment of specific simulation tools developed by the Vehicle Dynamics UniNa research group allow to predict the tire temperature local distribution by means of TRT model and the adhesive and hysteretic components of friction, thanks to GrETA model. The cooperation between the cited instruments enables the user to study the modifications that a reduced tread thickness, and consequently a decreased SEL (Strain Energy Loss) and dissipative tread volume, cause on the overall vehicle dynamic performance.
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Some general observations relating to tyre shear forces and road surfaces are followed by more specific considerations from circuit racing. The discussion then focuses on the mechanics of rubber friction. The classical experiments of Grosch are outlined and the interpretations that can be put on them are discussed. The interpretations involve rubber viscoelasticity, so that the vibration properties of rubber need to be considered. Adhesion and deformation mechanisms for energy dissipation at the interface between rubber and road and in the rubber itself are highlighted. The enquiry is concentrated on energy loss by deformation or hysteresis subsequently. Persson's deformation theory is outlined and the material properties necessary to apply the theory to Grosch's experiments are discussed. Predictions of the friction coefficient relating to one particular rubber compound and a rough surface are made using the theory and these are compared with the appropriate results from Grosch. Predictions from Persson's theory of the influence of nominal contact pressure on the friction coefficient are also examined. The extent of the agreement between theory and experiment is discussed. It is concluded that there is value in the theory but that it is far from complete. There is considerable scope for further research on the mechanics of rubber friction.
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The Nature of Viscoelastic Behavior. Illustrations of Viscoelastic Behavior of Polymeric Systems. Exact Interrelations among the Viscoelastic Functions. Approximate Interrelations among the Linear Viscoelastic Functions. Experimental Methods for Viscoelastic Liquids. Experimental Methods for Soft Viscoelastic Solids and Liquids of High Viscosity. Experimental Methods for Hard Viscoelastic Solids. Experimental Methods for Bulk Measurements. Dilute Solutions: Molecular Theory and Comparisons with Experiments. Molecular Theory for Undiluted Amorphous Polymers and Concentrated Solutions Networks and Entanglements. Dependence of Viscoelastic Behavior on Temperature and Pressure. The Transition Zone from Rubberlike to Glasslike Behavior. The Plateau and Terminal Zones in Uncross-Linked Polymers. Cross-Linked Polymers and Composite Systems. The Glassy State. Crystalline Polymers. Concentrated Solutions, Plasticized Polymers, and Gels. Viscoelastic Behavior in Bulk (Volume) Deformation. Applications to Practical Problems. Appendices. Author & Subject Indexes.