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DEVELOPMENT OF A GRIP AND THERMODYNAMICS SENSITIVE PROCEDURE FOR THE DETERMINATION OF TYRE/ROAD INTERACTION CURVES BASED ON OUTDOOR TEST SESSIONS

Authors:

Abstract

Designers and technicians involved in vehicle dynamics face during their daily activities with the need of reliable data regarding tyres and their physical behaviour. The solution is often provided by bench characterizations, rarely able to test tyres in real working conditions as concerns road surface and the consequential thermal and frictional phenomena. The aim of the developed procedure is the determination of the tyre/road interaction curves basing on the data acquired during experimental sessions performed employing the whole vehicle as a sort of moving lab, taking into account effects commonly neglected.
1
DEVELOPMENT OF A GRIP AND THERMODYNAMICS SENSITIVE
PROCEDURE FOR THE DETERMINATION OF TYRE/ROAD
INTERACTION CURVES BASED ON OUTDOOR TEST SESSIONS
Flavio Farroni, Aleksandr Sakhnevych, Francesco Timpone
D.I.I. - Department of Industrial Engineering, University of Naples "Federico II"
Via Claudio 21, 80125 Naples, Italy
email: flavio.farroni@unina.it
Designers and technicians involved in vehicle dynamics face during their daily activities
with the need of reliable data regarding tyres and their physical behaviour. The solution is
often provided by bench characterizations, rarely able to test tyres in real working
conditions as concerns road surface and the consequential thermal and frictional
phenomena. The aim of the developed procedure is the determination of the tyre/road
interaction curves basing on the data acquired during experimental sessions performed
employing the whole vehicle as a sort of moving lab, taking into account effects commonly
neglected.
INTRODUCTION
The target of the research activity described in the paper, fixed in collaboration with a
motorsport racing team, with a sport vehicles manufacturer and with a tyre research and development
technical centre, is the development of a procedure able to estimate tyre interaction characteristics,
reproducing them in simulation environments taking into account the fundamental friction and thermal
phenomena concerning with tyre/road interaction [1][2].
A first tool, called TRICK [3], has been developed with the aim to process data acquired from
experimental test sessions, estimating tyre interaction forces and slip indices. Once characterized the
vehicle, filtering and sensors output correction techniques have been employed on the available data,
creating a robust procedure able to generate as an output a "virtual telemetry" and, following a
specifically defined track driving routine, to provide tyre interaction experimental curves with the
further benefit to reproduce the real interactions with road and the phenomena involved with it,
commonly neglected in bench data [4].
Among such phenomena, one of the most important is surely the effect that temperature
induces on tyre performances, especially in racing applications [5]. For this reason a specific model,
called TRT [6], has been realised and characterized by means of proper thermodynamic test [7],
becoming a fundamental instrument for the simulation of a tyre behaviour as close to reality as
possible. One of the most useful features provided by the model is the prediction of the so called "bulk
temperature", recognized as directly linked with the tyre frictional performances [8].
With the aim to analyze and understand the complex phenomena concerning with local contact
between viscoelastic materials and rough surfaces [9], GrETA grip model has been developed [10].
The main advantage the employment of the grip model represents is the possibility to predict the
variations induced by different tread compounds or ground textures on vehicle dynamics, leading to
the definition of a setup able to optimize performances as a function of the tyre working conditions.
The described models and procedures can cooperate, generating a many-sided and powerful
instrument of analysis and simulation.
1. TRICK (TYRE/ROAD INTERACTION CHARACTERIZATION AND
KNOWLEDGE)
Complete and detailed studies of tyres in a wide range of working conditions are commonly
carried out by means of complex, bulky and expensive test benches [11]; the proposed procedure
allows to employ the vehicle as a moving lab, easily applying experimental and processing techniques.
2
TRICK tool basically comprises of an 8 DOF quadricycle vehicle model, able o take into
account roll and aerodynamics effects, which processes experimental signals acquired from vehicle
CAN bus and from devices estimating sideslip angle, represented by additional devices (Datron [12],
GPS [13] or virtual sensors [14]), providing force and slip estimations useful to generate experimental
tyre interaction curves (Fig. 1
1
).
Data useful to identify tyre interactions are acquired during dedicated track test sessions and
processed in order to filter the acquired signals and correct the errors due to sensors noise and
misalignment; the aim of a specifically developed test routine is to investigate tyre behaviour in the
widest possible range of working conditions. In particular, it is important to focus on manoeuvres
which highlight the different tyre/road pure interactions and, regarding combined interactions,
performing laps that keep tyre at high exertion levels.
The procedure has been validated by comparing the results to the measurements of the
interaction forces made using dynamometric wheel instrumentation (Fig. 2), showing good agreement,
in particular as concerns the evaluation of the steady state dynamic effects.
Fig. 1 - Tyre experimental interaction characteristics obtained by means of TRICK tool
for a rear wheel drive sport vehicle.
The colour of the markers varies from blue to red at increasing vertical load values.
Fig. 2 - Comparisons, for front (left) and rear (right) tyres, between forces estimated by TRICK
and dynamometric wheels measurements employed for validations.
1
In the paper, for industrial confidentiality agreements, plots, diagrams and data will be provided as normalized.
3
2. TRT (THERMO RACING TYRE)
TRT is a physical tyre thermal model, developed in collaboration between the Department of
Industrial Engineering of the University of Naples Federico II and a top ranking motorsport team,
which 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 (SEL) is evaluated [15].
The model inputs come out from telemetry data, while its thermodynamic parameters come
either from literature or from dedicated experimental tests [7]. Specific test aimed to characterize
contact patch under variable load and camber conditions are carried out [16]
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, allowing to carry out thermal analysis
in transient conditions involving tyre temperature effects on vehicle
dynamics. Born as a thermal tyre
model for racing vehicles, in addition to predict the temperature with a high degree of accuracy, TRT
is able to simulate the high-frequency dynamics characterizing this kind of systems, estimating the
temperature distribution even of the deepest tyre layers, usually not easily measurable on-line.
3. GRETA (GRIP ESTIMATION FOR TYRE ANALYSES)
GrETA is a tyre/road friction physical model, developed to respond to the needs of motorsport
racing teams and tyre manufacturing companies, able to provide an effective calculation of the power
dissipated for hysteresis by road asperities indented in tyre tread and taking into account the
phenomena involved with adhesive friction, expressed by means of an original formulation whose
parameters are identified thanks to dedicated experimental tests [17].
Asphalt is modelled as the sum of sinusoidal waves distributed in the space characterizing the
different roughness scales, tread elementary volume has been defined as a square-based parallelepiped.
Its height is equal to tyre tread thickness and the base side to road macro-roughness wavelength
λMACRO (Fig. 3a).
Wavelengths λ and roughness indices Ra [18] characterizing soil profile have been estimated
by means of proper algorithms employed to analyze data acquired experimentally by laser scan on
different dry tracks and to reproduce the best-fitting sinusoidal waves corresponding to macro and
micro profiles.
Experimental tests have been carried out on tyre rubber compounds with the aim to acquire
data useful to properly model the behaviour of SBR copolymers constituting tread: rubber specimens,
properly cut and prepared, have been dynamically tested following DMA procedures [19] in a three
point bending proof, in order to acquire storage modulus E' and tan(δ) data (Fig. 3a). Test has been
carried out at fixed frequency and displacement (1Hz, 1%), making temperature increase at 1°C per
minute from -50°C up to 100°C.
When both the frequency and the temperature vary, it is possible to make use of the property
whereby an appropriate shift operation is capable of combining the effect of them: the main element
on which the temperature - frequency equivalence principle is based is that the components of the
stiffness dynamic modulus at any reference frequency and temperature (f1, T1) are identical to the
ones observable at any other frequency f2 at a properly shifted value of temperature α(T1):
(
)
(
)
1 1 2 1
, ,
E f T E f T
α
 
=
 
(1)
The most widely relationship used to describe the equivalence principle is the Williams-Landel-Ferry
(WLF) transform [20]. For tyre rubber it can be employed in a simplified way in order to determine
the unknown equivalent temperature T*= α(T1):
*
2 1
1
f T T
log
 
=
 
 
(2)
in
which a common ΔT value, identifiable by means of DMA tests at different frequencies, is about
8°C.
Once characterized road and tread polymers, an
innovative conditions thanks to the estimation of 3D stress/strain sta
Kuznetsov equations [21
], has been adopted. The friction maps generated as GrETA output and shown
in figure 3
b, are in good agreement with data available in literature and with the ones provided by
specific experimental activities [
22
Fig. 3a -
Fig. 3b -
3D plot reporting friction coefficient for a GT tyre as a function of sliding velocity Vs
and contact pressure p, at a tread average temperature of 25°C
4. RESULTS
Models, procedures and methodologies discussed in the previous paragraphs are able to
describe and analyze different aspects of the phenomena concerning with tyre/road interaction, but
their cooperation can constitute an even more powerful instrument to ex
such complex theme.
In the following different possibilities to make the models cooperate will be described,
highlighting the main features of each combination and discussing its results in detail. A general
overview of the devel
oped models and procedures is reported in figure
observe the connections that link the models, providing different solutions of employment.
Fig. 4 -
Integration solutions offered by TRICK tool in cooperation with physical m
4
T value, identifiable by means of DMA tests at different frequencies, is about
Once characterized road and tread polymers, an
Hysteretic friction model, applied in
innovative conditions thanks to the estimation of 3D stress/strain sta
tes by means of properly adapted
], has been adopted. The friction maps generated as GrETA output and shown
b, are in good agreement with data available in literature and with the ones provided by
22
]
Elementary tread volume and coordinates system.
3D plot reporting friction coefficient for a GT tyre as a function of sliding velocity Vs
and contact pressure p, at a tread average temperature of 25°C
Models, procedures and methodologies discussed in the previous paragraphs are able to
describe and analyze different aspects of the phenomena concerning with tyre/road interaction, but
their cooperation can constitute an even more powerful instrument to ex
tend the comprehension of
In the following different possibilities to make the models cooperate will be described,
highlighting the main features of each combination and discussing its results in detail. A general
oped models and procedures is reported in figure
4
, in which it is possible to
observe the connections that link the models, providing different solutions of employment.
Integration solutions offered by TRICK tool in cooperation with physical m
T value, identifiable by means of DMA tests at different frequencies, is about
Hysteretic friction model, applied in
tes by means of properly adapted
], has been adopted. The friction maps generated as GrETA output and shown
b, are in good agreement with data available in literature and with the ones provided by
3D plot reporting friction coefficient for a GT tyre as a function of sliding velocity Vs
Models, procedures and methodologies discussed in the previous paragraphs are able to
describe and analyze different aspects of the phenomena concerning with tyre/road interaction, but
tend the comprehension of
In the following different possibilities to make the models cooperate will be described,
highlighting the main features of each combination and discussing its results in detail. A general
, in which it is possible to
observe the connections that link the models, providing different solutions of employment.
Integration solutions offered by TRICK tool in cooperation with physical m
odels.
5
4.1. TRICK & TRT
TRICK and TRT have been successfully employed together, constituting an instrument able to
provide tyre thermal analysis, useful to identify the range of temperature in which grip performances
are maximized, allowing to define optimal tyres and vehicle setup. Results reported in the following
are referred to a GT sports car.
The test procedures adopted to characterize tyres, obtaining data useful to initialize properly
the models, can be schematically divided in two main subcategories: destructive, that imply the
removal of specimens or the final degradation of tyres and non-destructive, performed on the whole
tyre, that can be still employed after them; to the first one belong:
• DMA viscoelastic characterization
DMA has been described in paragraph 3.
Tests carried out on GT sports car have highlighted interesting aspects, in particular
comparing results with the ones obtained with common passenger tyres. Figure 5a shows that,
as expected, sport tyres are characterized by lower storage modulus values in their optimal
thermal working range (35 °C and over), that mean higher attitude to adhesion and to adapt to
road asperities, optimising contact area, at the price of a lower wear resistance; passenger tyres
are more stable and able to offer good adhesion levels also at very low temperatures, being
adapt to the widest possible range of working conditions. Figure 5b reports in a clear plot the
plausible reason of the so called "feeling the grip" phenomenon; GT tyres, differently from
passenger ones, are characterized by a well distinct relative maximum at about 42 °C and by
higher values of tan(δ) at the usual employment temperatures.
Remembering that DMA test has been carried out at 1Hz frequency, definitely different from
common tread stress frequencies, a quick calculation, hypothesizing an average road macro-
roughness wavelength equal to 0.01 m and an average sliding speed of 5m/s, allows to
estimate the real tyre temperature at which the tan(δ) maximum can be experienced by the
driver. Re-applying equation 2, considering f
1
as equal to 1 and f
2
as the ratio between the
sliding speed Vs and road macro-asperities wavelength λ, it is possible to obtain:
8 (log ( / )) 8 (log (5 / 0.01)) 21.6
10 10
T Vs C
λ
∆ = = °
(3)
that, added to the starting 42 °C, gives a temperature of 63.6 °C, in accordance with the
experimental value shown in the further analyses presented in the following (Fig. 8).
Fig. 5a - A comparison of storage modulus (E') between a common passenger tyre and a GT sport one.
Fig. 5b - A comparison of tan(δ) between a common passenger tyre and a GT sport one.
• track thermal tests
Thermal test session has been carried out following a specific procedure, developed with the
aim to collect tyre data at different thermal conditions. In order to acquire tyre temperature,
vehicle has been equipped with infrared sensors installed in the wheelhouses and pointing on
tread surface, whose signals have been acquired by Dewesoft hardware. Each tyre tread has
been interested by two different measur
steering manoeuvres
could be characterized by discontinuous temperature profiles.
After having carried out the
by TRICK procedure, a
forces and consequently grip estimation has been provided
Speed, slip, camber and force channels have been used as an input for TRT, whose results
have been compared with measured
available data and
an estimation of tyre bulk temperature
in the following.
Fig. 6 -
TRT results evaluation for front
Common analysi
s concerning the relatio
temperature are based on the only thermal data experimentally available, id est tyre external (and in
few cases, internal) surface temperature, measured with a great variety of methodologies. A typical
correlatio
n between lateral grip and measured temperature appears like the one shown in figure
from which very few information can be deducted.
Fig. 7 -
Front
as a function of tyre measured surface temperature.
6
been interested by two different measur
ements, particularly useful for front tyre
could be characterized by discontinuous temperature profiles.
After having carried out the
track experimental session,
acquiring data useful to be processed
forces and consequently grip estimation has been provided
Speed, slip, camber and force channels have been used as an input for TRT, whose results
have been compared with measured
surface temperatures (figure 6
), obtaining good
an estimation of tyre bulk temperature
, very usefully for the grip analysis discussed
TRT results evaluation for front
(left) and rear (right)
tyres.
s concerning the relatio
nship between tyre friction coefficient and
temperature are based on the only thermal data experimentally available, id est tyre external (and in
few cases, internal) surface temperature, measured with a great variety of methodologies. A typical
n between lateral grip and measured temperature appears like the one shown in figure
from which very few information can be deducted.
Front
(top) and rear (bottom) lateral grip reported
as a function of tyre measured surface temperature.
ements, particularly useful for front tyre
s, that during
could be characterized by discontinuous temperature profiles.
acquiring data useful to be processed
forces and consequently grip estimation has been provided
.
Speed, slip, camber and force channels have been used as an input for TRT, whose results
), obtaining good
agreement with
, very usefully for the grip analysis discussed
tyres.
nship between tyre friction coefficient and
temperature are based on the only thermal data experimentally available, id est tyre external (and in
few cases, internal) surface temperature, measured with a great variety of methodologies. A typical
n between lateral grip and measured temperature appears like the one shown in figure
7,
7
Fig. 8 - Front (top) and rear (bottom) grip as a function of tyre bulk temperature estimated by means of TRT.
Bell shape symmetrical envelope curves have been identified to highlight the trends.
Thanks to the availability of bulk temperature, it is possible to provide much more useful
correlations, as the ones reported in figure 8, from which optimal thermal range can be identified. The
reason for which bulk temperature offers better results can be attributed to the fact that surface
temperature varies with very fast dynamics, not able to modify in a so short time polymers
characteristics in order to have a response on the whole tyre frictional behaviour. Bulk temperature, on
the other side, can be considered as the tread core temperature, more reluctant to fest variations and
directly connected with rubber viscoelastic states. As a further validation of the described procedure, it
can be noticed that temperature optimal value is in good agreement with the theoretical result provided
in equation 3, confirming that thermal model can be employed as a predictive instrument to investigate
performance optimization and that, on the other side, a proper knowledge of polymer characteristics
can be a useful starting point to a better comprehension of tyre interaction dynamics.
4.2. TRT - GrETA - MF Model
Thermal and grip model can usefully cooperate, employing TRT output as an input for
GrETA, that can be used to introduce in MF interaction model the dependence from temperature, tyre
working variables, road roughness and compound characteristics.
The advantages coming from the interaction of these models, to be employed in vehicle
dynamics simulation environments, can be summarized in the following three points, but further
application possibilities are clearly available:
Prediction of tyre behaviour on different tracks of a racing championship, each one
characterized by different road roughness (earlier measured) and weather conditions.
8
Performance evaluation at compound characteristics variation, that allows to establish a dialog
channel with tyremakers, leading tyre construction and compound development to the
achievement of a common aim.
Definition of optimal vehicle setup, in terms of wheel characteristic angles, load balance and
tyre inflating pressure, and of driving strategies able to reach optimal grip/thermodynamic
conditions.
Being not available local velocity and pressure distributions, GrETA is supposed to work in
this case basing on global variables, measured on track or calculated in simulation; longitudinal and
lateral friction estimated values are considered as sort of normalized scaling factors for longitudinal
and lateral interaction forces coming as an output from Pacejka formulation.
Figures 9 and 10 show the differences between forces data from telemetry and from Pacejka
model, whose input are measured slip, load and camber values. In a first case the calculated forces are
reported as scaled by a coulomb friction model, always constantly equal to one except for static value
(it means considering standard Pacejka output, with no further processing); in a second case the same
Pacejka model is processed with GrETA friction scaling factors, taking into account phenomena
neglected in the first case. It can be noticed that grip model employment produces better results, in
particular as concerns longitudinal interaction in traction phase, thermally stressful for high
performance tyres and able to generate heat for friction power mechanism that induces not negligible
effects in tyre/road interaction modelling.
Fig. 9 - Longitudinal rear tyre forces modelled by MF with a coulomb friction law (left)
and with GrETA friction model (right), both compared with telemetry track data (in red).
Fig. 10 - Lateral rear tyre forces modelled by MF with a coulomb friction law (left)
and with GrETA friction model (right), both compared with telemetry track data (in red).
CONCLUSIONS AND FURTHER DEVELOPMENTS
As clear from previous paragraph, and as well known from vehicle dynamics experience, MF
model is not the most flexible and physical method to describe tyre/road interaction local phenomena,
9
but represents a very robust and intuitive solution to obtain the hardly achievable aim to model tyre
tangential forces.
For this reason, further developments of the activities discussed in the present work will focus
on the integration with a physical interaction model [23] which, starting from the knowledge acquired
about the topic by the vehicle dynamics research group, will be able to deeply cooperate with the other
developed models, creating an analytic and predictive instrument employed in a wide range of
automotive applications.
The main features that the integration of the models can provide is summarised as follows:
full geometric, thermodynamic, viscoelastic and structural characterization of tyres on which
the analysis is focused;
estimation of the tyre interaction curves from experimental outdoor test data (TRICK);
definition of a standard track driving procedure that employs tyres in multiple dynamic and
thermal conditions;
estimation of surface, bulk and inner liner tyre temperatures for variable working conditions
and real-time reproduction of tyre thermodynamic behaviour in simulation applications
(TRT);
correlation of tyre thermal conditions with friction phenomena observable at the interface with
road;
prediction of tyre frictional behaviour at tread compound and ground roughness variations
(GrETA);
modelling of tyre interaction by means of MF innovative formulations able to take into
account grip and thermodynamic effects on vehicle dynamics;
definition of the optimal wheels and vehicle setup in order to provide the maximum possible
performance improvement.
A further step in the field of tyre/road interaction modelling and analysis could be represented
by the development of a global wheel model [24], able to cooperate with the presented ones,
constituting an ideal instrument for the prediction and the simulation of the real tyre dynamics.
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... The tire structure was lacking of sidewalls and so the model was not able to reproduce the temperature distribution in all the parts of the system, losing important elements influencing the tire behavior. In any case, the availability of the bulk temperature in the TRT allowed to identify the compound optimal thermal range [11], starting from the polymer thermal characteristics, appropriately evaluated by means of indoor test procedures and a specifically developed version of the model for laboratory activities (TRT LAB) [12][13]. ...
... If improperly canalized, the additional thermal sources risk to damage the tire because of too high thermal stress levels induced. So, each adopted solution has to be studied in detail in order to properly handle the supplementary heat flow, whose correct employment may represent a key factor for the management of the tires in terms of optimization of the grip/temperature relationship during particular operating phases [11][12] [13]. Figure 6. ...
... These temperature differences may result in diversification of response in terms of tire performance regarding both the compound viscoelastic characteristics and the carcass thermo-mechanical behavior. The first one is connected to the tread temperature and thus to the friction level arising at the tire-road interface, meanwhile the second one is linked to the temperatures of tire bulk and sidewalls [11]. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 F o r P e e r R e v i e w 25 To examine the described issue in depth and to carry out more accurate estimations of exhaust gas heating at the rear axle, TRT EVO model is able to take also into account: ...
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The handling behavior of a vehicle is one of its most important properties because of its relation to performance and safety and to its deep link with concepts such as “over-steer” or “under-steer”. Tire-road interaction models play a fundamental role in the vehicle system modelling, since tires are responsible for the generation of forces arising within contact patches, fundamental for both handling and ride/comfort. Among the models used to reproduce such forces, Pacejka’s Magic Formula (MF) is undoubtedly one of the most used ones in real-time automotive simulation environments because of its ability to fit quite easily a large amount of experimental data, but its original formulation did not take into account of the tire thermodynamics and wear conditions, which clearly affect tire and vehicle dynamics and are not negligible, especially for high level applications, such as motorsport competitions. Exploiting a multiphysical tire model, which consists in an evolved version of the standard MF model (MF-evo), and a vehicle model properly validated throughout experimental data acquired in outdoor testing sessions carried out with an industrial partner, the current work presents a study on vehicle behavior variation induced by thermodynamic and wear parameters, defining a series of metrics to analyze and show results. One of the elements of interest on which the focus is placed is the possibility to highlight how under-over-steering behavior of a car changes according to different thermodynamic states of tires; to do this, a commercial software VI CarRealTime has been used to perform a series of objective steady-state maneuvers and long runs, exploiting the logic of a lap time optimizer.
... The adoption of the simplest possible tire structure configuration within the TRTLab model, reproducing the simplest version of the TRT one, provides the optimum tradeoff between two clear needs: a detailed and physical representation of the entire tire composite structure and a simplified performance oriented model. The two zoned TRTLab version model is therefore able to reproduce the principle thermal phenomena and to provide a suitable set of thermal parameters for the Thermo Racing Tire model [11]. ...
Conference Paper
The TRT model, developed to accurately reproduce the tire thermal dynamics in all the vehicle working conditions, has to be physically characterized [1][2]. An appropriate non-destructive procedure, that allows to obtain the thermal diffusivity of completely different tire layers, is described. The heat is directly supplied on the tire tread surface trough a specifically powered laser, while two thermal cameras acquire temperatures reached on both the outer and the inner layers. Using the above instrumentation layout to acquire the tire radial and circumferential temperature gradients and a specifically developed mathematical TRTLab model based on the use of Fourier's equation of diffusion applied to a three dimensional domain, allows to estimate the tire thermal diffusivity.
... Motorsport racing teams use to face with the restrictions linked to the employment of confidential tires, provided by tiremakers and not available to invasive testing. The development of procedures for the acquisition of data concerning the tire thermal working conditions represents an innovation able to make the difference in the definition of the optimal vehicle setup and of the realization of strategic vehicle simulation tools [9][10] [11]. ...
Conference Paper
The evaluation of the tire tread viscoelastic characteristics, especially by means of non-destructive procedures, is a particularly interesting topic for motorsport teams and companies, used to work with unknown and confidential compounds. The availability of such information would define new scenarios in vehicle analysis field, as the possibility to provide physical inputs to tire grip models or the study of the suspensions setup able to make tires work inside their optimal thermal working range. The employment of commercial devices allows to select by means of specific indices the optimal combination of tires to be installed on a vehicle, but it does not provide any information physically correlated with the tread polymers characteristics. The aim of the presented activity is the modelling of one of the cited devices, a dynamic dial indicator, interacting with a viscoelastic half-space. The obtained results allow, analyzing the signals acquired by the device, to identify the tread equivalent stiffness and damping as a function of tire working temperature, providing the basic guidelines for the development of an innovative procedure for a full non-destructive viscoelastic characterization of the tire compounds. Index Terms-Material non-destructive characterization, temperature effect, tire tread compound behavior, TSD, viscoelastic characteristics.
... Also in this case a "mean function" has been adopted, different from the previous one for a preliminary selection criteria that allows to arrange points inside ortho-slip ranges, providing the results highlighted in figure 6 by different colours. Points selected for G function identification show a friction and generalized stiffness trend ( Fig. 8 and 9) in good agreement with the expected theoretical ones [15] [16]. ...
Chapter
One of the most diffused tire/road interaction models, widely employed in simulation applications, is the Pacejka’s Magic Formula (MF) [1, 2]. It is a semi-empirical model able to fit full scale test data, characterized by a large number of coefficients, often called micro-parameters, grouped basing on physical considerations in order to create specific functions, called macro-parameters. MF model coefficients provided by tire manufacturers are generally not fully representative of the behaviour of tires in contact with road. This is due to the testing conditions employed to identify model coefficients: tests are usually performed on a specific rolling bench or on a flat-trac (Tire testing system, commercialised by MTS Systems Corporation. It applies forces and motions to a tire running on a continuous flat belt.), that keep the tire in contact with a steel or an abrasive paper covered belt. The impossibility to test the tires under real working conditions causes unavoidable approximation errors, mainly due to differences in thermal exchanges and wear phenomena [3] between tire/belt and real tire/road contact. Therefore it is commonly necessary to modify the MF coefficients in order to improve the bench data correlation and to be able to validate vehicle models with data coming from experimental tests. The aim of the developed tool, called TRIP-ID (Tire/Road Interaction Parameters IDentification), is to provide an innovative procedure to identify the Pacejka coefficients basing on the experimental tests carried out measuring global vehicle data during outdoor track sessions. In the presented application, the procedure collects and processes the data provided by TRICK tool [4], allowing to eliminate the outlier points, to discriminate wear and thermal phenomena, taking into account the combined slip condition and the effects of vertical load and camber angle on the global grip. The innovative approach proposed can be useful to reproduce in real time simulation applications the feedback that high performances tires give to sport vehicle drivers, whose interest and skills are focused on keeping them in the optimal thermal range. The coupling of a properly modified MF model with a thermal and with a friction model can provide a reliable simulation and analysis instrument for drivers, carmakers and tire producers.
... Since the motion of a ground vehicle is primarily determined by the friction forces transferred from roads via tyres, information about the tyre/road interaction is critical to many active vehicle safety control systems, including longitudinal control, yaw stability control and rollover prevention control systems. In particular friction formation is crucial tool for Brake Assist Systems (BAS), Electronic Stability Control (ESC-ESP) and Adaptive Cruise Control (ACC) systems that have recently become essential for active safety systems, as shown in [1][2][3][4][5]. For instance, in the case of adaptive cruise control, estimation of friction force enables the braking distances to be adjusted in real time. ...
... The adoption of the simplest possible tire structure configuration within the TRTLab model, reproducing the simplest version of the TRT one, provides the optimum tradeoff between two clear needs: a detailed and physical representation of the entire tire composite structure and a simplified performance oriented model. The two zoned TRTLab version model is therefore able to reproduce the principle thermal phenomena and to provide a suitable set of thermal parameters for the Thermo Racing Tire model [11]. ...
... Creation of virtual tyres obtained varying as desired the shape of the pure and combined interaction curves, useful to simulate the effect of tyre compound and structural variations on vehicle behaviour. Physical simulation of tyre/road interaction phenomena [35] by means of MF model integration with a physical grip model [13] and with a real-time tyre thermal model [10,33], able to reproduce local temperature distributions and their effect on tyre and vehicle performance. ...
Article
Tyres play a key role in ground vehicles' dynamics because they are responsible for traction, braking and cornering. A proper tyre-road interaction model is essential for a useful and reliable vehicle dynamics model. In the last two decades Pacejka's Magic Formula (MF) has become a standard in simulation field. This paper presents a Tool, called TRIP-ID (Tyre Road Interaction Parameters IDentification), developed to characterize and to identify with a high grade of accuracy and reliability MF micro-parameters from experimental data deriving from telemetry or from test rig. The tool guides interactively the user through the identification process on the basis of strong diagnostic considerations about the experimental data made evident by the tool itself. A motorsport application of the tool is shown as a case study.
... The Quarter Car Model is a known and widely used model ( Fig. 1) for the simulation of one-dimensional behavior of a vehicle suspension, [1,2] and for the preliminary development of new solutions and innovative architectures and devices for the vehicle stability enhancement [3]. In its simplified form, the suspension consists of a spring with stiffness K and a damper with damping coefficient C. [4][5][6][7] and road roughness. For a passive system with a highly irregular entry, there is an intrinsic tradeoff between the system stability and passenger comfort. ...
Article
One of the most challenge task in tire road interaction is the study of the behavior of the suspension when the wheel meets an obstacle. The suspension system of a vehicle has to absorb the effects of a bumpy road surface or of an obstacle that could influence the guide. It is also important to preserve the integrity of the internal components that can face premature aging because of the constant stress and vibration. In this paper a preliminary study concerning the suspension behavior meeting an obstacle conducted using a Quarter Car Model is presented. The methodology used will be described in detail starting from the modeling of a Quarter Car Model, then analyzing the structure of the suspension and simulating them in different conditions using Matlab Simulink software through SimMechanics and SimDriveline libraries.
... In the present paper, an innovative approach is proposed, not considering tire wear as a consequence of working dynamics, 14 or as a phenomenon to be studied as influenced by external factors 15 anymore, but as a starting unavoidable condition whose effect on tire thermal behaviour and on the overall tire and vehicle frictional performance can be analysed with an innovative approach, if compared to the previous authors' activities focused on temperature-grip relationship in the absence of tread wear. 16 Thermo racing tyre model Thermo racing tyre (TRT) model 17,18 is a physicalanalytical tire thermal model developed by Vehicle Dynamics UniNa research group, currently employed by motorsport and carmaking companies with the aim to predict and simulate in real-time the temperature of the different tire layers, based on telemetry data processing techniques. ...
Article
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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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 the results of an experimental activity carried out with the aim to investigate on the frictional behaviour of visco-elastic materials in sliding contact with road asperities is presented. Experiments are carried out using a prototype of pin on disk machine whose pin is constituted by a specimen of rubber coming from a commercial tyre while the disk may be in glass, marble or abrasive paper. Tests are performed both in dry and wet conditions. Roughness of the disk materials is evaluated by a tester and by a laser scan device. Temperature in proximity of the contact patch is measured by pyrometer pointed on the disk surface in the pin trailing edge, while room temperature is measured by a thermocouple. Sliding velocity is imposed by an inverter controlled motor driving the disk and measured by an incremental encoder. Vertical load is imposed applying calibrated weights on the pin and friction coefficients are measured acquiring the longitudinal forces signal by means of a load cell. As regards to the road roughness, the experimental results show a marked dependence with road Ra index. Dry and wet tests performed on different micro-roughness profiles (i.e. glass and marble) highlighted that friction coefficient in dry conditions is greater on smoother surfaces, while an opposite tendency is shown in wet conditions. Although affected by uncertainties the results confirm the dependence of friction on temperature, vertical load and track conditions.
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Knowledge about phenomena concerning with adherence is a key factor in the automotive field and in particular in the braking/traction and stability control systems design. Moreover, the continuous drivers’ seeking of the optimal grip conditions, makes the development of a physical friction model an essential instrument for the investigation of the factors acting on indentation and adhesion mechanisms on which tyre/road interaction is based. Rubber/asphalt friction, in fact, is influenced by a great number of variables and parameters, often hard to be controlled and measured: macro and micro roughness of the bodies in contact, pressure arising at their interface, materials stiffness characteristics and their frequency and temperature dependence, relative motion direction and speed. The possibility offered by a physical model to provide a better comprehension of the cited factors allows to act on them with a wide range of aims: studying soil textures structured in order to increase drivers' safety both in dry and in wet conditions, producing more performing rubber compounds, able to optimize frictional behaviour under certain temperatures or frequencies and, in particular in race applications - for which the presented studies have been originally carried out - in order to configure optimal vehicle setup and driving strategies. A deep knowledge of the mechanisms involved with tyre/road friction is a key factor in the design of the suspension system: an optimal setting of tyre working angles, operated in order to optimize temperature, contact pressure and sliding velocity distributions, can be efficiently provided by a physical grip model able to indicate the best wheel configuration at the boundary conditions changes.
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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.
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Surface roughness evaluation is very important for many fundamental problems such as friction, contact deformation, heat and electric current conduction, tightness of contact joints and positional accuracy. For this reason surface roughness has been the subject of experimental and theoretical investigations for many decades. The real surface geometry is so complicated that a finite number of parameters cannot provide a full description. If the number of parameters used is increased, a more accurate description can be obtained. This is one of the reasons for introducing new parameters for surface evaluation. Surface roughness parameters are normally categorised into three groups according to its functionality. These groups are defined as amplitude parameters, spacing parameters, and hybrid parameters. This paper illustrates the definitions and the mathematical formulae for about 59 of the roughness parameters. This collection of surface roughness parameter was used in a new software computer vision package called SurfVision developed by the authors. In the package, these definitions were extended to calculate the 3D surface topography of different specimens.
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The most powerful engine, the most sophisticated aerodynamic devices or the most complex control systems will not improve vehicle performances if the forces exchanged with the road are not optimized by proper employment and knowledge of tires. The vehicle interface with the ground is constituted by the sum of small surfaces, wide about as one of our palms, in which tire/road interaction forces are exchanged. From this it is clear to see how the optimization of tire behavior represents a key-factor in the definition of the best setup of the whole vehicle.Nowadays, people and companies playing a role in automotive sector are looking for the optimal solution to model and understand tire's behavior both in experimental and simulation environments. The studies carried out and the tool developed herein demonstrate a new approach in tire characterization and in vehicle simulation procedures. This enables the reproduction of the dynamic response of a tire through the use of specific track sessions, carried out with the aim to employ the vehicle as a moving lab.The final product, named TRICK tool (Tire/Road Interaction Characterization and Knowledge), comprises of a vehicle model which processes experimental signals acquired from vehicle CAN bus and from sideslip angle estimation additional instrumentation. The output of the tool is several extra "virtual telemetry" channels, based on the time history of the acquired signals and containing force and slip estimations, useful to provide tire interaction characteristics. TRICK results can be integrated with the physical models developed by the Vehicle Dynamics UniNa research group, providing a multitude of working solutions and constituting an ideal instrument for the prediction and the simulation of the real tire dynamics.
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