Proceedings of the ASME 2012 11th Biennial Conference On Engineering Systems Design And Analysis ESDA2012
July 2-4, 2012, Nantes, France
ESDA2012-82160
DRAFT
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 Naples, Italy
1Contact Author
ABSTRACT 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.
INTRODUCTION 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 and temperature.
The earlier studies about rubber friction, for which the laws developed by Amontons and Coulomb for metal surfaces [1] [2] did not result valid, were carried out by Bowden and Tabor [3] [4].
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 [5] formulated an effective generalized friction model, taking into account all these aspects developed
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, negligible.
Thanks to the work of Kummer and Savkoor [6], Moore [7] 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.
ROUGHNESS In [8] 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 [9]: 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 parameters.
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, respectively:
Rୟ =1l න
|y(x)|୪
dx
Rୟ =1n|y୧|୬
୧ୀଵ
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 glassy one.
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'.
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 [10], 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 glasslike.
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 maximum decreases.
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 wet conditions.
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 deformable bodies.
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.
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 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" one.
DATA ANALYSIS 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 [11].
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.
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 their repeatability.
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 discussed.
In Fig. 7 a first comparison between results of tests carried out at 10N of normal load over different micro-surfaces are shown:
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 contribution.
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-hysteresis" [12].
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.
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 centrifugation.
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.
CONCLUSIONS The experimental investigation conducted on friction
between pneumatic tyre rubber specimens and several micro-rough surfaces in dry and wet conditions allows the following considerations.
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 remarkable.
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 increases.
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