1 Copyright © 2012 by ASME
Proceedings of the ASME 2012 11th Biennial Conference On Engineering Systems Design And Analysis
July 2-4, 2012, Nantes, France
TYRE - ROAD INTERACTION: EXPERIMENTAL INVESTIGATIONS ABOUT THE
FRICTION COEFFICIENT DEPENDENCE ON CONTACT PRESSURE, ROAD
ROUGHNESS, SLIDE VELOCITY AND TEMPERATURE
Flavio Farroni1, Michele Russo, Riccardo Russo, Francesco Timpone
University of Naples “Federico II”
Department of Mechanics and Energetics
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
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
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
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
Friction is a dissipative phenomenon occurring between
surfaces in contact, opposing to their relative motion. In many
cases it is an undesired phenomenon, limiting movements,
generating heat and wear on the contact surfaces.
Despite that, it is hard to imagine a physical reality without
friction; performing traction forces that allow locomotion,
braking and acceleration of the bodies respect to the ground
would not be possible.
Friction phenomenon for elastomeric materials has been
widely studied: experiments show that friction coefficient is
function of several parameters, such as sliding velocity, local
pressure, contact surfaces roughness, material characteristics
The earlier studies about rubber friction, for which the laws
developed by Amontons and Coulomb for metal surfaces  
did not result valid, were carried out by Bowden and Tabor 
. The phenomena connected with friction of polymeric
materials are different from the ones concerning metals, mainly
for the strong dependence on loads, temperature and relative
velocity; Kummer  formulated an effective generalized
friction model, taking into account all these aspects developed
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in the field of a test program about tyre-road interaction. This
model hypothesized for the first time the resistant forces as
constituted by three components: adhesion, deforming
hysteresis and wear (Fig.1).
FIGURE 1 - FRICTION MECHANISMS
The hysteretic component results from the internal friction
of the rubber: during sliding the asperities of the rough
substrate exert oscillating forces on the rubber surface, leading
to cyclic deformations of the rubber, and to energy "dissipation"
via the internal damping of the rubber.
Adhesive friction, regarded as being the primary
contributor when a rubber block slides over a smooth
unlubricated surface, is usually pictured as being due to
molecular bonding between the rubber chains and the
molecules of the track. Both adhesive and hysteretic
component of rubber friction, are related to the material
properties. Of course, this is perhaps not so surprising in view
of the cross-linked macromolecular structure of the rubber.
Kummer postulated that adhesive and hysteretic forces are
not independent because adhesion is able to increment
extension of the contact area and with it the zone in which
hysteretic deformations occur.
Friction is also performed by rubbery material removal due
to road asperities, but entity of wear component is estimated to
be less than 2% on rough surfaces and, consequently,
Thanks to the work of Kummer and Savkoor , Moore
 hypothesized that the different components were
predominant at different roughness scales: the macro asperities
affect deformation connected with hysteresis and micro
asperities affect intermolecular bonds characterizing adhesion.
For this reason, the two aspects can be conceptually split and
treated by applying a sort of superposition principle.
In  Persson models road as a self affine fractal profile,
taking into account two different roughness scales (macro and
micro). Road surfaces macro-wavelength is of order of a few
mm, corresponding to the size of the largest sand particles in
the asphalt; less is known about the micro-wavelength, but the
author hypothesizes that in the context of rubber friction it may
be taken to be of order a few µm, so that the length scale region
over which the road surface may be assumed to be fractal may
extend over 3 orders of magnitude.
Wavelength parameters are connected with amplitude
parameters : the most useful to characterize surface
topography; as a consequence, also the vertical characteristics
of the surface will be described by macro and micro scale
The arithmetic average height parameter (Ra), also known
as the centre line average, is the most used roughness parameter
for general quality control. It is defined as the average absolute
deviation of the roughness irregularities from the mean line
over one sampling length. This parameter is easy to define, easy
to measure and gives a good general description of height
variations. The mathematical definition and the numerical
implementation of the arithmetic average height parameter are,
Road surface is often modelled as a sinusoidal wave
characterized to be perfectly rigid; rubber in contact with it is
an elastic, soft and virtually incompressible material, but it can
usually be stretched more than 500%. Its molecular structure
consists of long, linear flexible molecules forming random
coils. The molecular segments are mobile and the molecules are
interlinked into a 3D network.
Chemical crosslinks are usually made by sulphur linkages
coming out after a technological process, known as
vulcanization. The rubbery state of a polymer is determined by
the so-called glass transition temperature Tg. If the temperature
is above Tg the polymer shows a rubbery behaviour, below Tg a
Since rubbers do not follow reversible stress-strain
behaviour, the constitutive laws for large strains cannot be used
to fully describe the stress-strain relation. When rubber is
dynamically stretched and released the returned energy is less
than the energy put into the rubber. This visco-elastic effect
cannot be described by the perfect elastic dynamic modulus E;
it is necessary to introduce a dynamic storage modulus E' and a
dynamic loss modulus E'' to describe this hysteresis. Another
term frequently used is the loss angle, defined as tan(δ) = E''/E'.
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For an elastic solid the strain is in phase with the stress,
while for a visco-elastic solid the strain lags behind the stress
with a delay of δ/ω , where ω is the frequency (rad/sec).
The universal Williams, Landel and Ferry relation, named
after WLF , describes the equivalent behaviour of rubber
materials at exciting frequency and temperature variations; the
dependence on frequency is shown schematically in Fig. 2.
FIGURE 2 - RUBBER DYNAMIC CHARACTERISTICS
At low frequencies the storage modulus is low and rather
constant but as the frequency raises the compound becomes
increasingly stiff until at high frequencies it is hard and
The tan(δ), representing a direct measure of viscous
resistance to motion, increases with frequency during transition
phase, with a more marked slope than E'.
It is possible to see experimentally that if the frequency of
the test is increased, the temperature at which it is possible to
observe the glassy transition shifts towards higher values. In the
same way if the frequency is reduced, the temperature of the
This means that exciting the material at higher frequencies
is equivalent to excite it at lower temperatures and vice-versa.
This equivalence (known as WLF law) can be written in
the following way:
The equation can be used to relate the dynamic behaviour
in a physical condition, characterized by a temperature T1 and
by a frequency f1 to an equivalent one, characterized by a
temperature T2, and a consequent frequency f2.
E (f1,T1) = E (f2,T2)
Storage modulus E' and loss modulus E'' are found to
depend on the frequency of vibration as previously shown.
When the temperature raises to T2, the curves are displaced
laterally by a fixed distance, log(aT), on the logarithmic
frequency axis, where log(aT) reflects the change in
characteristic response frequency of molecular segments when
the temperature is changed from T1 to T2.
As an approximate guide, valid at temperatures about 50°C
above Tg, a temperature rise of about 8°C is equivalent to a
factor of 0.1 change in frequency.
Thus WLF law provides a powerful frequency-temperature
equivalence principle enabling to correlate mechanical
behaviour over wide ranges of frequency with temperature.
The aim of the present work is to provide an experimental
investigation above the above friction phenomena on surfaces
characterized only by a micro-roughness profile.
Thanks to a tribological testing machine friction relation
with some typical parameters such as vertical load, sliding
velocity and temperature, are investigated both in dry and in
Three different kinds of surface have been used: one made
up of glass, an other made of marble and a last one covered
with abrasive paper.
The rubber specimens have been extracted from a
passenger automotive pneumatic tyre.
The test results allow some considerations about the
phenomena occurring at the contact interface between rigid and
THE TEST MACHINE
Experiments were performed using a pin on disk machine
(Fig. 3) realized at the Department. This kind of tester is often
employed to measure friction and sliding wear properties of dry
or lubricated surfaces of a variety of bulk materials and
coatings. The elements of the machine are:
an electric motor, driven by an inverter;
a metal disk, moved by the motor through a belt, that can be
covered with another disk of different material;
an arm on which a rubber specimen is housed;
a load cell, interposed between the specimen and the arm,
that allows the tangential force measurement;
an incremental encoder, installed on the disk axis in order to
measure its angular position and velocity;
an optical pyrometer pointed on the disk surface in
proximity of the contact exit edge, that provides an estimation
of the temperature at the interface;
a thermocouple located in the neighborhood of the
specimen, used to measure ambient temperature.
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FIGURE 3 - TEST MACHINE
The arm is vertically approached to the rotating disk
surface and through the application of calibrated weights on the
arm, the normal force between specimen and disk can be
In these first experiments, mainly aimed to investigate the
adhesive contribution to friction, the used disk materials are:
glass (Ra < 0.03 m), marble (Ra = 0.1 m) and abrasive paper
(Ra = 25 m), chosen in order to simulate contact between
rubber and different surfaces. Tests were performed both in dry
and wet conditions.
As previously introduced, adhesion contribution to friction
is strictly connected with micro-roughness surfaces profile;
adopting test surfaces characterized by low macro-roughness
gives the possibility to neglect the macroscopic hysteresis
friction contribution, pointing attention on the adhesive
mechanisms and, eventually, on so called "micro-hysteresis"
The results provided by the performed tests are
characterized by a high level of scattering, so a great attention
should be posed in their interpretation.
Scattering is mainly due to:
Local temperature: although temperature in the specimen
neighborhood is continuously monitored during the test, actual
temperature in the contact zone can’t be measured.
Wear: life of a specimen exhibits three characteristic stages.
A new specimen presents a very smooth and hard surface
providing low friction values on all partner surfaces. In a
second stage the specimen surface is soft and “sticky”, friction
is higher, so this phase can be considered as the “useful life” of
the specimen. In a third stage, the specimen surface either
becomes hard again, or tends to break up; in both cases friction
falls to very low values and the specimen must be replaced.
Extension of the contact patch (Fig. 4): during the “useful
life”, wear continuously modifies the specimen surface, altering
contact patch extension. To monitor this phenomenon, in
several cases during the tests, the specimens have been marked
with ink, so to be able to print their contact patch on graph
paper. Under the three different known loads the specimens
show, as expected, an increasing contact area with increasing
load, with a clear tendency to saturation.
Under the 5N load the contact area has been estimated to be
equal to 70mm2 (pressure = 0.71bar), employing the 45.5% of
the available nominal area, equal to 154mm2. Under the 10N
load the contact area has an extension of 100mm2 (pressure =
1bar), that is the 65% of the available nominal area and,
concerning with the 50N load, real area is equal to 140mm2
(pressure = 3.5bar), that is the 91% of the nominal one. Even
under the same vertical load, local pressure and friction can
vary dramatically: in general the greater the pressure the lower
the friction .
FIGURE 4 - SPECIMEN CONTACT CONDITIONS
Track conditions: clean or rubbery; in dependence of the
track state friction may vary because of Ra variations; in
particular, glass surface increases its micro-roughness from a
starting value minor than 0.03µm to a value of about 0.6 µm; as
concerns marble, its micro-roughness moves from an initial 0.1
µm up to about 1 µm; paper roughness changes with an
opposite tendency, showing a passivation phenomenon due to
the filling of the valleys produced by rubber debris.
Water film thickness: during wet tests water film thickness
can vary because of the difficulty to assure a constant fluid feed
and for centrifugation effect occurring at high rotation speeds.
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For the reasons said, the following comparisons refer to
test conditions in which the above causes of scattering are
reasonably constant. Comparisons cannot be made among
results relative to different test conditions.
A first kind of test has been performed imposing to the disk
a linear ramp in velocity. Both velocity and tangential force
time histories were recorded (Fig. 5) in order to plot the
classical friction vs. velocity curve in which both static and
kinetic friction coefficients may be estimated.
During the ramp tests a temperature raising has been often
observed in correspondence of the exit edge of the contact zone
and these temperature variations were supposed to be
connected with adhesion coefficient variations.
FIGURE 5 - VARIABLE SPEED TEST ON DRY GLASS
A second series of experiments has been conducted at
constant speed. The disk speed was regulated in order to realize
in the contact zone the desired relative velocity in the range 0.1
- 2 m/s. Once the disk steady state velocity was reached the
loaded arm was slowly approached to the disk and the
tangential force time history was recorded (Fig. 6). In some
cases the specimen has been heated in order to investigate
rubber temperature effects on friction.
The kinetic friction coefficient was evaluated as the mean
value of the ratio between tangential and vertical force in the
time history steady state region. For each load and speed
condition, tests were repeated several times in order to verify
FIGURE 6 - CONSTANT SPEED TEST ON DRY GLASS
Since the measured temperature is only an index of the
contact temperature and not the actual one, a complete series of
tests has been performed only at constant velocity with a
temperature monitoring in order to verify its substantial
constant value during the proof.
Anyway ramp tests have been useful to validate the results
of the constant speed tests: the adhesion values measured
thanks to the first ones are, in fact, in good agreement with the
values obtained with the second ones; moreover, as expected,
ramp tests reproduce the classical decreasing trend for
increasing values of sliding velocity.
In the following only constant speed test results will be
In Fig. 7 a first comparison between results of tests carried
out at 10N of normal load over different micro-surfaces are
FIGURE 7 - ADHESION TESTS 10N DRY
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It is possible to notice that, thanks to its flatter surface,
glass offers greater adhesion than marble. Almost perfectly
smooth surface of glass gives the possibility to maximize the
contact area between the rubber specimen and the test surface.
On the other hand, marble presents a lightly waved surface
(from a micro-scale point of view) that does not allow a perfect
contact with rubber, making decrease adhesive friction
If abrasive paper was considered from the same point of
view it would be expected to show an even lower value of
adhesive friction coefficient. Experimental data underline an
opposite tendency, explainable with an occurring hysteretic
effect, often discussed in literature and called "micro-
This phenomenon is responsible, moreover of the good
performances offered in terms of friction by abrasive paper in
wet conditions, especially if compared with the results given by
glass and marble in the same conditions (Fig. 8).
FIGURE 8 - ADHESION TESTS 10N WET
Wet surfaces analysis allows to investigate the saturation of
the micro-asperities operated by water on different surfaces.
While in dry conditions glass maximizes available contact area,
in wet conditions it results easily covered by the water film,
carrying consequently adhesion coefficient to a deep decrease.
In these conditions, for low values of sliding velocity marble
surface is able to brake water film, thanks to its wavy profile. It
explains the higher values of marble wet adhesion showed in
figure respect to glass ones. At increasing sliding velocity the
specimens seem to float over water film and marble asperities
lose their film-braking characteristics.
Tests performed in wet conditions at normal loads of 5N
(Fig. 9) and of 50N (Fig. 10) show the same results.
FIGURE 9 - ADHESION TESTS 5N WET
FIGURE 10 - ADHESION TESTS 50N WET
Interesting considerations can be made about the
phenomenon of the saturation of the available contact area
observing Fig. 11 and 12; both of them show a decreasing trend
of adhesive friction with vertical load, in good accordance with
the well known theoretical hypothesis available in literature;
contact between rubber and paper, thanks to this last's rough
surface, is characterized by a less-than-proportional increase of
the contact area respect to vertical load increase; it can be
noticed observing the large distance that plots show in Fig. 11
between data obtained in different load conditions. Fig. 12,
relative to glass surface and to the same load conditions, shows
small changes between 10N and 50N data, explainable taking
into account the low glass roughness, that at these load
conditions already reached contact area saturation.
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FIGURE 11 - ADHESION TESTS DRY PAPER
FIGURE 12 - ADHESION TESTS DRY GLASS
With reference to rubber behaviour on paper and glass in
wet conditions (Fig. 13 and 14), it can be noticed an expected
deep friction coefficient reduction and, moreover, that wet glass
shows the already observed adhesion decreasing tendency with
load increasing (Fig. 13); an opposite trend is shown by wet
paper results (Fig. 14). In the first case water presence does not
change the flat profile that surface offers to the specimen, while
the opposite tendency, shown by paper, might be attributed to
the better squeezing effect assured by the higher load.
FIGURE 13 - ADHESION TESTS WET GLASS
This squeezing phenomenon hypothesis seems also
confirmed by Fig. 15 and 16, in which a comparison between
dry and wet conditions under the same load is proposed; in
particular, at low loads (Fig. 15) a typical drastic reduction
between dry and wet conditions can be observed, whereas at
high loads (Fig. 16) this reduction is less evident, confirming
that, even in wet conditions, paper is almost dry, probably
thanks to squeezing effect and, at higher velocities, to water
FIGURE 14 - ADHESION TESTS WET PAPER
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FIGURE 15 - ADHESION TESTS DRY/WET PAPER 10N
FIGURE 16 - ADHESION TESTS DRY/WET PAPER 50N
As a regard to glass, the above phenomena, because of the
small glass micro-roughness do not produce appreciable effects
(Fig. 17 and 18); in this case, in fact, even a small amount of
fluid interposed between the specimen and the track is enough
to establish a boundary lubrication regime.
FIGURE 17 - ADHESION TESTS DRY/WET PAPER 50N
FIGURE 18 - ADHESION TESTS DRY/WET GLASS 50N
To investigate on rubber temperature effects on friction, a
series of experiments has been conducted at constant speed on
dry paper, heating by an external source the surface specimen
until to a temperature of 120° and applying a 5 N vertical load.
The results (Fig. 19) show an expected increase of friction
coefficient with temperature, which is more evident at low
sliding velocities. This could be explained assuming that at high
sliding velocities the cold rubber specimen increases his
temperature because of friction and so it works in conditions
closer to the hot specimen ones.
At low sliding velocities, on the other hand, the cold
specimen is not warmed by the friction heat generation enough
to approach the performances of the hot one.
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FIGURE 19 - ADHESION TESTS 5N DRY
The experimental investigation conducted on friction
between pneumatic tyre rubber specimens and several micro-
rough surfaces in dry and wet conditions allows the following
The experimentation in this field is affected by a high level
of uncertainty related to the great number of parameters
involved in this kind of phenomenon. The main parameters
such as temperature, wear, contact area, have been monitored
with the aim to keep them constant during the test.
Of course, some other parameters, such as ambient
humidity, track rubberising and uniformity of the specimens
visco-elastic properties would merit deeper analyses.
Despite the above uncertainty causes, the study underlines
a deep friction dependence on surface roughness. In the case of
rough surfaces friction in higher, probably due to micro-
hysteresis phenomena, while in the case of smooth surfaces, the
glass almost perfectly smooth surface maximizes the actual
contact patch, providing higher adhesion respect to marble.
Friction vs. sliding velocity trend exhibits a maximum at
low velocities and then decreases as expected.
Moreover, the analysis has shown a strong dependence of
adhesion friction coefficient on vertical load on dry surfaces,
while in the case of wet surfaces, this dependence is barely
In particular, on dry surfaces, friction decreases as load
increases, in accordance with theoretical results available in
literature, while on wet surfaces two different behaviours can
be observed: on smooth surfaces the tendency is confirmed, on
the rough ones friction increases with increasing load.
The dependence on specimen initial temperature is evident
at low slide velocities and becomes lower as slide velocity
 Amontons, G., Histoire de l'Academie Royale del
Sciences avec les Mémories de Mathematique et de Physique,
 Coulomb, C. A., Histoire de l'Academie des Sciences.
 Bowden, F. P. and Tabor, D., The Friction and
Lubrication of Solids, 2nd ed., Clarendon Press, Oxford, 2001.
 Bowden, F. P. and Tabor, D., The Adhesion of Solids
in the Structure and Properties of Solid Surfaces, The
University of Chicago Press, Chicago, 1953.
 Kummer, H. W., Unified theory of rubber and tire
friction, Engineering Research Bulletin B-94, Pennsylvania
State University, 1966.
 Savkoor, A. R., On the friction of rubber, Wear, 8, Pag.
 Moore, D. F., The friction and lubrication of
elastomers, Pergamon Press, Oxford, 1972.
 Persson, B. N. J., Theory of rubber friction and contact
mechanics, Journal of chemical physics volume 115, number 8,
Pag. 3840, 2001.
 Gadelmawla, E. S., Koura, M. M., Roughness
Parameters, Journal of Material Processing Technology, 123
Elsevier, Pag. 133, 2002.
 Ferry, J. D., Viscoelastic properties of materials,
 Persson B. N. J., Albohr O., On the nature of surface
roughness with application to contact mechanics, sealing,
rubber friction and adhesion, J. Phys.: Condens., Matter 17, R1
- R62, 2005.
 Horigam Smith R., Analyzing Friction in the Design
of Rubber Products, CRC Press, Boca Raton, 2008
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