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EXPERIMENTAL INVESTIGATIONS ABOUT ADHESION
COMPONENT OF FRICTION COEFFICIENT DEPENDENCE ON ROAD
ROUGHNESS, CONTACT PRESSURE, SLIDE VELOCITY AND
DRY/WET CONDITIONS
Flavio FARRONI, Ernesto ROCCA, Riccardo RUSSO,
Sergio SAVINO, Francesco TIMPONE
DiME - Department of Mechanics and Energetics,
University of Naples "Federico II",
Via Claudio 21, 80125 Napoli, Italy
ABSTRACT
The results of an experimental activity carried out with the aim to investigate on the adhesive behaviour of
visco-elastic materials in sliding contact with road asperities are presented.
Experiments are carried out using a prototype of pin on disk machine in which pin is constituted by a
specimen of rubber coming from a commercial tire, while different disks are realized in glass, marble, steel and
in abrasive paper of different roughness. Tests are performed in both dry and wet conditions.
Roughness of the test surfaces is evaluated by a rugosimeter, while pressure is evaluated, off-line, analysing
the extension of the contact patch left by the pin on a sheet of graph paper under known applied loads. Slide
velocity is imposed by an inverter controlled motor driving the disk.
Basing on well known theoretical hypotheses, adhesive component of friction coefficient is estimated making
the specimens slide on surfaces characterized by low values of macro-roughness, in order to underline the
differences in rubber behaviour respect to micro-roughness surface variations.
The results confirmed adhesion dependence on pressure and sliding velocity in both cases of smooth
surfaces, where the main friction mechanism is the adhesive one, and of rough surfaces, where the main friction
mechanism is the hysteretic one.
Analysing various surfaces roughness it is possible to notice a maximized adhesive contribution on flat
surfaces; it reduces with increasing roughness, while hysteretic friction comes over instead of it because of
asperities penetration into rubber sliding surface.
Moreover in the case of rough surfaces the separation between static and dynamic friction coefficient is
evident and the static coefficient is greater than the dynamic one.
On the other hand in case of smooth surface the absence of indentation phenomena doesn’t allow to
recognize, in the measured force time history, the “classical” peak usually associated to the static friction
coefficient.
Dry and wet tests performed on different micro-roughness profiles highlighted that friction coefficient in dry
conditions is greater on smoother surfaces, while an opposite tendency is shown in wet condition, when
asperities are greater enough to break the thin water layer, providing a certain degree of indentation.
A proposal for a methodology able to estimate the only adhesive friction component, developed thanks to wet
contact tests, is expressed in the end of the paper.
Keywords: friction, adhesion, visco-elasticity, roughness, tyre/road interaction
1. INTRODUCTION
The complete knowledge about friction phenomenon for elastomeric materials
represents one of the hardest topics of modern science, probably because of the
complexity of the connected mechanisms and of the great number of variables
involved with it.
Friction coefficient, usually considered as a mere ratio between tangential and
vertical forces, needs to be decomposed among its physical different components to be
better investigated and understood.
With reference to the contact conditions between tyres and road (i.e. rubber and
asphalt) in literature are cited three main tangential force components [1].
1. The adhesive component, that is the force needed to break the intermolecular
bonds created at the interface between the two materials in contact.
2. The hysteretic component that is the difference between the force needed to
deform the rubber and the one returned by the rubber during its restoring. Such
difference is not zero because of the rubber's viscoelastic behaviour.
3. The wear component, that is the force needed to remove material from the
rubber. This last component is often neglected (at least in the case of passenger
tyres).
The adhesive component is closely linked to the real extent of the contact area. The
real contact area, in fact, is different from the nominal one because rubber (supposed
perfectly smooth) and asphalt (markedly rough) contact only in the zones where the
highest peaks of the asphalt are able to indent the rubber.
As long as the real area of contact increases linearly with the vertical force, also the
tangential force increases linearly and the adhesive contribution to friction remains
constant. Due to the rubber viscoelasticity, however, at the higher vertical forces the
contact area increases with a less-than-linear law, so the adhesive contribution to
friction tends to become less and less significant.
The hysteretic component is closely linked to the work of deformation of the rubber
performed by the peaks of the asphalt that crawl on it. Considering that the viscoelastic
characteristics of rubbers vary with the indentation degree and with the frequency of
the stresses imposed, it is realized that the contact pressure, the sliding speed and the
roughness of the asphalt have considerable influence of the hysteretic contribution to
friction.
On the other hand, the quality and amount of intermolecular bonds between two
surfaces in contact can be profoundly altered by the presence of an interposed third
body. Here then explained the influence exerted by the different wet / dry conditions
on the adhesive friction component.
Many studies evidenced that hysteretic and adhesive components manifest
themselves with different entity in relation to the asphalt roughness scale that is
considered: in the macro-roughness field the hysteretic effects results remarkable; in
micro-roughness field the adhesive effect due to Van Der Waals forces is predominant.
For this reason, the presence of water, or debris, that alter the asphalt macro-
roughness, can significantly worsen also the hysteretic contribution to friction.
In the present paper the influence of vertical force (i.e. contact pressure), sliding
velocity and dry/wet conditions on the friction between rubber and several material
(i.e. several “road” roughness) will be experimentally investigated.
The paper is organized as follows: in section 2 the viscoelastic behaviour of rubber
is described. In section 3 the most important parameters useful to characterize road
roughness are discussed. In section 4 the test rig and the adopted experimental
procedures are presented, the obtained results are discussed in section 5.
2. VISCO-ELASTIC MATERIALS CHARACTERIZATION
The study of the visco-elastic properties of the elastomeric materials is of
fundamental importance for understanding their mechanical behaviour in presence of
dynamic stresses and vibration.
The elastomers, classifiable as a subcategory of polymers, represent a class of
materials increasingly employed in industry; in particular, the most widespread types
are synthetic rubbers, including the copolymers of styrene and butadiene (SBR) and
copolymers of acrylonitrile and butadiene rubber (NBR).
Because of their low elastic modulus, elastomers are not used in engineering for
structural purposes; on the contrary, their attitude to achieve very high deformations
and their viscous behaviour open up a wide area of use in the absorption of shocks and
vibrations, as well as in the production of tyres for motor vehicles.
In all these applications it is essential to characterize the behaviour of the material
as a function of load, frequency of the stress cycles and temperature, in order to predict
phenomena of relaxation and creep in presence of stresses and consequential
deformations and to evaluate the response of the material at various frequencies.
The stress-deformation curve of a generic elastomer is typically non-linear, with the
breaking of the material that occurs at very high deformations.
However, since the deformations imposed on a tyre tread is often below 10%, it
allows to study the viscous properties of the material adopting visco-elastic linear
models; the most common are those based on the use of standard mechanical elements
such as springs (perfectly elastic elements) and dampers (purely viscous elements).
These elements can be combined in series or parallel configurations giving rise to a
wide range of models (Maxwell, Voigt-Kelvin, Zener, etc.).
The analysis of the response to deformation for a visco-elastic solid can be
conveniently conducted referring to sinusoidal loads [2] [3]: when an elastomeric
material is subjected to an harmonic deformation
where ε
1
is the amplitude of the applied deformation and ω is the pulsation, the
induced stress σ
1
is harmonic too
with the same frequency but out of phase respect to deformation.
The stress σ
1
can be expressed as the sum of two contributions, one in phase with
the imposed deformation and a second in quadrature phase
where:
E', said storage modulus, is the elastic modulus part relative to the in phase response
of the material
E'', said loss modulus, represents the elastic modulus of the part in quadrature phase.
The quantities E' and E'' are related to ε
1
0
, σ
1
0
and δ through the relationships
it follows then that
It is defined then the complex dynamic modulus, similar to the Young's modulus for
visco-elastic materials
E' and E'' values (or of their reciprocal G' = 1/E' and G'' = 1/E'') and tan δ are
strongly dependent on the temperature and on the frequency at which the rubber is
stressed, as schematically represented in Fig. 1.
Fig. 1 - G', G'' and tan(δ) temperature and frequency qualitative dependence
As regards the influence of temperature, the behaviour of polymers is strongly
dependent on it: typically, the dynamic modulus decreases with increasing
temperature, while the phase angle increases until it reaches a maximum
before decreasing again.
The temperature range in which E* and δ show high variations is said "glass
transition zone"; outside this range, modulus and phase result independent on
temperature. For weakly crosslinked polymers, such as those used for tires, it is
therefore possible to identify three areas: glass region (low temperature), transition
region, viscous region (high temperatures).
For the elastomers used for tyres, glass transition temperature is often below 0°C, so
that usual working conditions are characterized by optimal frictional performances.
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
frequency and temperature in a single variable called reduced frequency: the main
assumption on which the temperature-frequency equivalence principle is based, is that
the values of the complex modulus (and phase shift) at any selected frequency f
1
and at
any reference temperature T
1
are identical to those of any other frequency f
2
at an
equivalent temperature T
2
:
The most widely used relationship between shift factor α(T) and T is the Williams-
Landel-Ferry (WLF) transform:
where C
1
and C
2
are constants typical of the polymer type and T
0
is a reference
temperature. The relationship between WLF log (α (T)) and 1 / T is usually non-linear,
but the deviation from linearity is sensitive only at the highest and at the lowest
temperatures.
The physical meaning of the law is that rubber stressed at high frequency behaves
like if the stress is applied at lower frequency but at the same time, at a colder working
temperature. High frequency acts reducing the time between two consecutive stresses,
forbidding to the rubber to completely relax, in the same way as a low working
temperature would do.
3. ROAD ROUGHNESS CHARACTERIZATION
In nature, all surfaces are rough and wavy: they are described by peaks and valleys
whose size is sensibly lower than the one characterizing the extension of the bodies
themselves.
Assuming ideally smooth surfaces in contact, the contact area is defined nominal
area and the pressure generated by the normal load is said nominal pressure. Taking
into account of the actual geometry of surfaces in contact, i.e. of their roughness, it is
possible to speak about real area and "real pressure".
Roughness is usually represented as composed by asperities randomly distributed; a
simple model was presented by Greenwood and Williamson [4], who highlighted that
roughness of engineering surfaces shows a Gaussian distribution of peaks with a
standard deviation σ*. For simplicity the peaks are assumed spherical with a radius of
curvature β correlated with the average slope of the profile.
Road roughness is often modeled as characterized by three main roughness scales:
the biggest one, called mega-texture, mainly due to paving installation techniques; a
middle one, called macro-roughness, given by the dimensions and geometrical
configurations of the aggregates composing the bitumen conglomerate and the
smallest, the micro-roughness, given by the surface roughness of the aggregates. (Tab.
1).
Range Size
Horizontal Vertical
Mega-texture 50 – 500 mm 5 – 50 mm
Macro-texture 0.5 – 50 mm 0.2 – 5 mm
Micro-texture 0 – 0.5 mm 0 – 0.2 mm
Tab. 1
Each scale is usually modelled as a sinusoidal wave [5], characterized by
wavelength and amplitude values identified by means of statistical procedures [6]. The
most common index able to reproduce roughness profile is the arithmetic average
height parameter (R
a
), also known as the centre line average. 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, respectively:
The different friction components are 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;
studying friction on a very low macro-roughness, as explained in the following, could
allow to “isolate” the adhesion effects, depurating the global phenomenon from the
hysteretic component (Fig. 2).
Fig. 2 – Effects of indentation over different roughness scales
In wet contact mechanics, although the lubrication regime, the presence of macro
asperities provides indentation phenomena able to brake the water film observable at
tyre/road interface; the absence of this roughness scale manifests itself by the almost
total covering of the micro-asperities of the aggregates, with the consequential
disappearing of the inter-molecular bonds and the well noticeable loss of friction (Fig.
3).
Fig. 3 – Wet contact indentation and main variables effects
4. THE EXPERIMENTS
4.1 Test bench description
Experiments have been performed using a pin on disk machine (Fig. 4) 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 neighbourhood of the specimen, used to measure
ambient temperature.
Fig. 4 – The Pin on Disk experimental set-up
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 varied.
In these experiments the disk materials, chosen in order to simulate contact
between rubber and different surfaces, are: glass (R
a
< 0.03 µm), marble (R
a
= 0.16
µm), steel (R
a
= 0.7 µm) and two kinds of abrasive paper: paper 240 (R
a
= 14 µm) and
paper 40 (R
a
= 120 µm). 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" one.
4.2 Specimen characterization
Tyre tread specimen, properly cut and prepared, has been dynamically tested in a
three point bending proof, in order to acquire storage modulus and tan(δ) data.
Tests have been carried out at fixed frequency and maximum displacement (1Hz,
0.05), making to increase temperature at 1°C per minute from -50°C up to 100°C.
The results of the characterization are shown in Fig. 5 (E’) and in Fig. 6 (tan(δ)),
highlighting a clear glassy transition zone and the expected trends respect to
temperature [7].
Fig. 5 – E’ thermal characterization data and their detail in the [0 – 100] °C zone
Fig. 6 – tan(δ) thermal chatacterization data
Moreover, with the aim to identify properly the glassy transition temperature, the
specimen has been object of analysis performed with Differential Scanning
Calorimetry (DSC) technique [8]. The results are showed in Fig. 7, highlighting an
identified T
g
of -36.41°C.
Fig. 7 - T
g
identification
4.3 Testing procedure
Experiments have been conducted at constant speed, building friction vs. sliding
velocity curves point by point. For each point, disk speed has been set 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. 8). The dynamic
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 their repeatability.
Fig. 8 - 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.
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, wear phenomena, distortions of the contact patch and
track conditions [9].
5. RESULTS ANALYSIS
Interesting considerations can be made about the phenomenon of the saturation of
the available contact area observing Fig. 9 and Fig. 10; glass shows a clearly
decreasing trend of adhesive friction with vertical load, in good accordance with the
well known theoretical hypothesis available in literature [10]: contact between rubber
and glass, thanks to this last's flat surface, is characterized by a less-than-proportional
increase of the contact area respect to vertical load increase, it is explainable taking
into account the low glass roughness, that already at low load conditions already
reaches contact area saturation.
Paper, on the other hand, manifests a starting increasing trend with load, after which
saturation phenomenon comes out, making to decrease friction forces. It is due to the
particular shape of abrasive paper particles, that strongly indent rubber even from low
vertical loads, exhausting their gripping properties at the increasing of this last.
Fig. 9 - Adhesion test - Dry Glass
Fig. 10 - Adhesion test - Dry Paper (40)
In Fig. 11 a comparison between results of tests performed at 10N of normal load
over the five different micro-surfaces are shown: it is possible to confirm that, thanks
to its flatter surface, glass offers greater adhesion than marble and steel. Almost
perfectly smooth surface of glass allows to maximize the contact area between the
rubber specimen and the test surface.
On the other hand, marble and iron present a lightly waved surface (from a micro-
scale point of view) that does not allow a perfect contact with rubber, making decrease
adhesive friction contribution.
Fig. 11 - Adhesion test - dry conditions, normal load 10N
If abrasive papers were considered from the same point of view, they would be
expected to manifest an even lower value of adhesive friction coefficient, caused by
their sharp profile [11]. Experimental data underline an opposite tendency, explainable
by means of the WLF law and of an occurring hysteretic effect, often discussed in
literature and called "microhysteresis" [12]: from a microscopic observation, steel
surface is characterized, among the examined five, by the lowest micro-wavelength
value, with the consequence that rubber sliding on it behaves as “frozen”; at the same
time, it is possible to observe that at increasing values of wavelength characterizing the
different surfaces, the sliding velocity at which the maximum of the friction curve is
noticeable increases as expected by theoretical models.
If the “flight phase” between two consecutive asperities is long enough to allow to
rubber to restore its starting configuration, then equivalent temperature will not be
much different from actual working temperature.
Fig. 12 - Adhesion test - wet conditions, normal load 10N
The arise of hysteretic phenomena 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, marble and steel in the same
conditions (Fig. 12).
While in dry conditions glass maximizes available contact area, in wet conditions it
results easily covered by water, carrying consequently adhesion coefficient to a deep
decrease [12].
In these conditions, for low values of sliding velocity rough micro surfaces are able
to brake water film, as showed by marble and confirmed by steel. At low sliding
velocity it is moreover possible to witness a sort of squeezing effect, that makes
specimen able to throw water out from valleys and provide again small available
surfaces.
At increasing sliding velocity the specimens seem to float over water film and
micro-asperities lose their film-braking characteristics. Macro asperities composing
abrasive paper, provide instead water film braking also at high velocities, even if
showing friction coefficient values lower than in dry conditions.
Fig. 13, 14 and 15 allow a comparison among the different ways in which the
presence of water modifies the interaction between the sliding bodies: glass
dramatically losses its great adhesive attitude in presence of small amounts of water;
blue dotted curve shows friction levels mainly due to water shear forces and squeezing
effect, particularly present at low sliding velocities. The difference between red and
blue dots could provide an efficacious estimation of the pure adhesive component,
being not acting indentation effects and other friction causes like wear.
Fig. 13 - Adhesion test – glass surface, normal load 10N
Steel data analysis results in the same strongly decreasing trend previously
highlighted, characterizing low sliding velocity dependence a certain value on.
Dry adhesion, as expected, is lower than on glass, while the less flat surface
provides little higher adhesion in wet conditions. The pure adhesion, characterized
again as the difference between red and blue dots, results as lower than on glass,
reproducing theoretical predictions.
Fig. 14 - Adhesion test - steel surface, normal load 10N
Referring to Fig. 15, it is clear how the sharp paper profile manifests its low
adhesive attitude, because of the difficulty in recreating the optimal contact conditions
needed by inter-molecular chains to set up. Difference between the two curves are
small, even if in this case wet contact it concerns not only with hysteretic
phenomenon, but also with a certain amount of adhesion, due to an available area,
provided by water film braking, no more negligible.
Fig. 15 - Adhesion test – paper (40) surface, normal load 10N
6. CONCLUDING REMARKS
An experimental investigation carried out with the aim to investigate on the
adhesive component of friction coefficient for visco-elastic materials in sliding contact
with road asperities has been presented.
Tyre tread specimens have been characterized by means of DMA and DSC
machines and road profiles have been considered as a sum of two sinusoidal waves,
each characteristic of a roughness scale. Focusing on the micro-roughness scale, five
different test surfaces have been employed on a pin-on-disk tribometer, in order to
analyse the influence of the different micro-profiles on the adhesion phenomenon.
The study highlighted a deep adhesion dependence on surface roughness: in the
case of rough surfaces the microhysteresis effect is noticeable, while in the case of
smooth surfaces, the almost perfectly flat profile allows to maximize the contact patch,
providing a high attitude to molecular bonds formation.
Adhesive friction vs. sliding velocity trend exhibits a maximum at low velocities
and then decreases as expected; adhesion relationship with vertical load is strongly
influenced by roughness, probably because of the area saturation phenomena involved
with this kind of tests.
The presence of water makes to decrease drastically adhesive attitude of flat
surfaces, confirming the hypotheses made from a macroscopic point of view on the
intermolecular bonds formation.
Future works could focus on the behaviour of different rubber compounds sliding
over the same five micro-rough surfaces, paying particular attention to thermal effects.
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[8] Höhne, G., Differential Scanning Calorimetry, Springer, 2003.
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