MANE 6960
A Tribological Approach
to Tire Traction
Research Paper
Andrew Wright
11/27/2012
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INTRODUCTION
The tribological concepts surrounding the friction and wear of elastomeric materials are
interesting as well as relevant in the modern society. Some applications include the shear
resistance of viscoelastic adhesives, the durability of windshield wipers, and elastomeric
prosthetic devices [11]. For this paper, I have focused the subject matter to the friction of
automobile tires on roads. This topic is especially relevant to the United States because cars are
the main source of transportation. Car crashes are a significant source of fatalities in the United
States, and many deaths are caused by drivers losing control on the road. The contributions to
friction in car tires can be very different depending on the conditions of the road, which increases
the danger when driving during inclement weather. If scientists and engineers can better
understand the contributions of friction in rubber car tires under all environmental conditions,
safer tire designs can be developed which will reduce the number of fatalities due to car crashes.
There are two topics that I will discuss in this paper. Firstly, I will present a summary of
the major contributors to friction in elastomeric materials. Plots and graphs are used to help
communicate the theory, and numerous technical papers are cited which solidify the statements.
The second part of the paper will be devoted to a phenomenon called the “Sealing Effect” and
how it relates to the frictional properties of rubber car tires on roads. The Sealing Effect is a
particular example of elastomeric friction which occurs when water (or another liquid) is present
in the contacting substrate. The presence of water changes the relevant friction factors, and can
have a big impact on the coefficient of friction and other statistical properties at the interface.
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FRICTION OF RUBBER
The friction of elastomeric materials, especially when the interface is a rough surface, is
an interesting phenomenon because it is not purely a function of the interface between the two
objects. The two biggest contributors that affect the friction between an elastomer and a surface
are adhesion and viscoelastic effects. According to Moore, the adhesion factor is caused by van
der Waals forces present between the rubber tire and the smooth surface [8]. In most cases this
contribution is rather small, but since elastomers have relatively low elastic modulii, these forces
can cause a large contact area at the interface of the tire [8]. When the car tire is in motion, this
enlarged contact area increases the frictional force on the tire. The viscoelastic properties of
elastomeric materials cause internal friction in the rubber when it is in contact with the substrate.
The internal friction of rubber is a function of the frequency of the external loading caused by the
rough asperities of the contacting surface. At certain frequencies, the internal friction of the
rubber becomes very high and results in a large amount of energy dissipation. This phenomenon
is called the “hysteretic contribution” to friction [5]. The amount of internal friction generated is
then directly related to the viscoelastic modulus of the rubber, which is a bulk material property.
Therefore while most frictional interactions between materials are purely influenced by
interfacial properties, elastomeric friction is also influenced by bulk material properties.
Temperature conditions play an important role in the friction and wear of car tires because
the viscoelastic bulk properties of elastomers are heavily temperature-dependant [1]. In general,
the friction in a rubber material will decrease as temperature increases. This is because as the
rubber gets hotter, the viscoelastic spectrum of the material shifts such that it takes higher load
frequencies to dissipate the same amount of energy [1]. If the roughness (and therefore load
frequency) of the road remains constant but the temperature increases, the energy dissipation will
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decrease which effectively results in a lower frictional force. This phenomenon is shown
graphically in Fig. 8, which graphs the quotient ImE/ReE at different frequencies of loading.
Figure 1 – Graphs of the shear stress as a function of velocity between the elastomers and the Si wafer (left) and the
theoretical shear stress distribution as predicted by the Chernyak-Leonov model for adhesive friction [11].
In theory,
if a rubber car tire is sliding against a perfectly smooth surface there will be no internal friction
effects. The reason for this is that the hysteresis effects in elastomeric materials are only present
when there is roughness in the substrate. When the substrate is an extremely smooth surface, the
largest contributor to friction is instead caused by elastic deformation of the rubber and adhesion
from the contact of the rubber and the substrate at the interface. In a paper by Vorvolakos and
Chaudhury, this theory is proven [11]. Vorvolakos and Chaudhury used an extremely smooth Si
wafer with a silicone elastomer to gather data on this subject. The frictional data they gathered is
shown in Fig. 1 above, along with the theoretical graph of the shear stress versus velocity for an
adhesion-driven elastomeric friction problem. The graph of the shear stress distribution (left in
Fig. 1) in the tested elastomer exhibits the same bell shape as the theoretical stress distribution
(right in Fig. 1). They concluded that because the trend in their data matched the graph of the
adhesion-driven shear stress distribution, that the smooth substrate effectively reduced the
internal friction in the rubber to zero. This paper shows that in ideal situations where the
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substrate is extremely smooth, adhesive friction can dominate over internal friction in
elastomeric materials.
Figure 2 – Resulting coefficients of friction in Mofidi’s paper, for various lubricating oils [6].
In reality, all surfaces have some roughness. Even polished and machined surfaces can
have rough nesses on a scale large enough to cause internal friction. A paper by
Mofidi illustrates this trend, and shows that for most realistic roughness scales the viscoelastic
friction is the dominate contributor [6]. In this paper, an experiment
is carried out by which a metallic cylinder (D = 1.5 cm) is rubbed
against a rubber block (thickness = 4 mm) with various types of
lubrication oils (see Fig. 3 for an illustration). The steel surface had
a calculated root-mean-square surface roughness of 0.08
micrometers. The load on the block was 100 N, with tests lasting 15
min. Longitudinal oscillations with a stroke of 1 mm and a
Figure 3 - Test setup in Mofidi’s paper [6].
frequency of 50 Hz were created using a rocating tribometer. Fig. 2
shows some of the coefficients of friction calculated in the paper for various lubrication oils that
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were tested. The results show that for varying lubrications of different viscosities, the calculated
coefficient of frictions were all roughly the same. This result is evidence that the adhesive and
molecular components of the friction that are most highly influenced by the interfacial
environment were negligible compared to the internal friction effects caused by viscoelastic
effects in the rubber.
Figure 4 – Calculated coefficients of friction in Mofidi’s experiment at two different temperatures.
Fig. 4 shows more data from Mofidi’s experiment: the coefficients of friction for various
lubrication oils at two temperatures (40 degrees C and 80 degrees C). As you can see by the
chart, the lower temperature results in much higher coefficients of friction for all oils tested. As
was stated earlier in the paper, the internal friction of an elastomer increases as temperature
decreases as a result of the viscoelastic temperature dependence of the elastomer. Since this
trend is also seen in Mofidi’s experiment for each oil, this is again more evidence that the
internal friction component is dominating the adhesive and molecular interfacial components.
The take home message is that these viscoelastic effects are the dominant factor in any realistic
application because all engineering materials have some roughness to them.
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THE SEALING EFFECT
Driving in your car can be more dangerous when there is precipitation because the liquids
that pool on the roads reduce the friction of your rubber tires. In fact, the traction of your rubber
tires on wet roads is actually about 20-30% smaller than for dry roads [1]. Persson explains that
the cause of this friction reduction is not due to any hydrodynamic effects that come into play,
but rather the “Sealing Effect”, which reduces the roughness of the surfaces in contact.
When roads get wet, such as when it rains, the roughness at the surface drops
substantially. Asperities in the substrate get filled in by the liquid, which result in a smoother
interface for tires. This event is illustrated in Fig. 6, from Persson [1]. When the water on the
roads fills these rough asperities, the interface is much smoother than when the road is dry.
Figure 5 – Kinetic friction coefficient for dry and wet roads as a
function of velocity [1].
Figure 6 - Illustration of a rubber tire in contact
with a a) dry and a b) wet surface. See Ref. 1.
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According to Persson, it is important to limit the speed of the moving object to around 20
MPH [1] when discussing the Sealing Effect. When this assumption is made, the hydrodynamic
build-up of water ahead of the tire is negligible and therefore the water seal creates a smooth
interface for the rubber tire. As I have discussed in the previous section of this paper, the science
behind the friction and wear of rubber on a smooth surface is much different than when the
rubber is in contact with a rough surface.
The hysteretic contribution to the
friction is present for both wet and dry
road conditions, however it is higher in
dry rubber friction. The reason that the
internal friction component drops off
significantly when water fills the
Figure 7 - A graph of the real part of the viscoelastic modulus as a
function of the frequency of external loading on the elastomer.
asperities is because the interface no
longer exerts the pulsating loads into the
rubber which induce the highest energy
dissipation. At reduced frequencies, and
even at zero loads for the case of a
completely smooth surface, the lower
frequency of loading reduces the value
of ImE/ReE (see Fig. 8) which results in a
lower amount of energy dissipation. Fig.
7, from Mofidi’s paper, displays this trend in a
Figure 8 – A graph that shows that as temperature is increased,
for the same external load frequency there is lower energy
dissipation in the elastomeric tires [7].
different way. It shows a graph of the real part of the viscoelastic modulus as a function of the
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frequency of the external loading. In reality, there are many different asperities in contact with
the car tire, on more than one length scale. The result of this is that there is often a range of
loading frequencies, such as the range from ω0 to ω1 shown in Fig. 8 [7]. In order to calculate
the net increase in friction, one would have to add up the contributions from asperities on all
length scales.
In theory, the adhesion factor grows in cases where the surface is smoother because there
is more contact area for the rubber to contact and slip against the interface. As Modifi shows in
his paper, however, and as I mentioned in the previous section, even for situations with nanoscale roughness, the viscoelastic contribution to rubber friction overpowers the adhesion factor.
Therefore even though the friction caused by adhesion between the rubber and the water-filled
road increases, it is negligible compared to the loss in viscoelastic friction.
CONCLUSION
Unlike other engineering materials, the friction of elastomeric materials is a function of
both the bulk properties of the elastomer and the interface between the contacting materials. The
two biggest contributors to friction in elastomeric materials are adhesion and internal friction
caused by hysteresis effects. For most real surfaces with non-zero roughness values, the internal
friction component dominates the behavior. As Modifi showed, this is even true for polished
materials with a roughness on the order of microns or smaller [6]. However, it can be shown, as
by Vorvolakos, that with extremely smooth surfaces it is possible for the adhesive component to
dominate the frictional behavior [11]. When rubber tires slide on surfaces containing water,
similar to the smooth surfaces that Vorvolakos examined, the internal friction component is
reduced. Persson has labeled this phenomenon the Sealing Effect, and claims that it is the reson
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for why the traction of rubber car tires is substantially lower in wet conditions than it is in dry
conditions [1].
By gaining a better understanding of the Sealing Effect as well as the effects of
elastomeric friction on the wear of car tires, scientists and engineers can make better tire and
road designs that could reduce the number of car accidents per year. There is some evidence
already that increased technological advances and research has made driving safer. The U.S.
census bureau compiles all kinds of automobile related crash data. Reports of this data are
released as pdf files, and can be accessed via Ref. 10. Fig. 9 shows data from one such report:
the percentage of licensed drivers in fatal car crashes over time. As you can see, there is a
significant downward trend in the data that starts around 2005. While it is unclear whether this
reduction in fatal crashes is due primarily to any advances in rubber tire or road design, it is
reasonable to assume that this reduction can be attributed to some kind of related technological
advancement.
Percentage of Licensed Drivers in Fatal Car
Crashes
0.04
Percentage
0.035
0.03
0.025
0.02
0.015
1990
1995
2000
2005
2010
Year
Figure 9 – The percentage of licensed drivers in the United States involved in fatal car crashes. See Ref. 10.
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REFERENCES
1. Persson, B., Tartaglino, U., Albohr, O., & Tosatti, E. (2005). Rubber friction on wet and dry
road surfaces: The sealing effect. Physical Review B, 71(3).
2. Persson, B. N. J., Albohr, O., Tartaglino, U., Volokitin, A. I., & Tosatti, E. (2005). On the
nature of surface roughness with application to contact mechanics, sealing, rubber friction and
adhesion. Journal of Physics: Condensed Matter, 17(1), R1–R62.
3. Liu, F., Sutcliffe, M. P. F., & Graham, W. R. (2012). Prediction of tread block forces for a
free-rolling tyre in contact with a rough road. Wear, 282-283, 1–11.
4. Meyer W E and Walter J D 1983 Frictional Interaction of Tire and Pavement STP 793
(Philadelphia, PA: American Society for Testing and Materials) p 85 (ISBN: 0803102313).
5. Kluppel, Manfred; Heinrich, Gert. Rubber Chemistry and Technology 73. 4 (Sep/Oct 2000):
578.
6. Mofidi, M., Prakash, B., Persson, B. N. J., & Albohr, O. (2008). Rubber friction on
(apparently) smooth lubricated surfaces. Journal of Physics: Condensed Matter, 20(8), 085223.
7.
Persson, B. N. J. (2010). Rubber friction and tire dynamics. Journal of Physics: Condensed
Matter, 23(1), 015003.
8. Moore, D. F. (1972). The friction and lubrication of elastomers. Pergamon Press (Oxford and
New York).
9. Meyer, W. E., & Walter, J. D. (Eds.). (1983). Frictional Interaction of Tire and Pavement: A
Symposium (Vol. 793). ASTM International.
10. Motor Vehicle Accidents and Fatalities - The 2012 Statistical Abstract - U.S. Census Bureau.
(n.d.). Retrieved November 18, 2012, from
http://www.census.gov/compendia/statab/cats/transportation/motor_vehicle_accidents_and_fat
alities.html.
11. Vorvolakos, K., & Chaudhury, M. K. (2003). The Effects of Molecular Weight and
Temperature on the Kinetic Friction of Silicone Rubbers. Langmuir, 19(17), 6778–6787.
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