Hindawi Publishing Corporation

Advances in Mechanical Engineering

Volume 2014, Article ID 260428, 6 pages
http://dx.doi.org/10.1155/2014/260428

Research Article
Characteristics of a Tire Friction and Performances of
a Braking in a High Speed Driving

Yumrak Oh1 and Hoguen Lee2

1
Research and Development Center, Hankook Tire, Daejeon 305-725, Republic of Korea
2
Department of Automotive Engineering, Daeduk University, Daejeon 305-715, Republic of Korea

Correspondence should be addressed to Hoguen Lee; leehg@ddc.ac.kr

Received 28 May 2014; Revised 28 July 2014; Accepted 29 July 2014; Published 14 August 2014

Academic Editor: Seung-Bok Choi

Copyright © 2014 Y. Oh and H. Lee. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The goal of pavement is to deliver the fine roughness and the safe road surface to traffic. It requires a secured and comfortable surface
using the controlled speed of road. Through adjusting driving speed, skid resistance can be altered in one of the performances of the
pavement surface. In high speed driving, there might be a certain level of risk, not in the same level as the proposed roads. Hence,
this study first analyzes the speed equation under a consideration of a braking distance and then suggests the friction coefficient in
high speed driving with the principle of conservation of energy. If we accept simply that the coefficient of friction is independent
of speed, the difference between analysis and test value for braking distance is greatly generated. Therefore we have to analyze the
coefficient of friction as an exponential function of braking speed of a vehicle.

1. Introduction (100 km/h or faster). Thus high speed driving of the vehicle
becomes more important to the safety of driver [1]. The pur-
A car and a tire require such diverse performances: handling, pose of this paper is to prevent vehicle accidents with correct
braking, durability, wear-resistance, NVH performance, fuel- prediction for the braking distance at high speed driving.
efficiency, and so forth. Among them, a driver’s stability is Driver’s safety and specifically braking performances are to be
mainly related with the performances of handling and brak- commonly considered under a higher speed. Recently under
ing. Technology has put a greater emphasis on a customer’s the management of the Ministry of Land, Transport and
stability through the installation of ABS system of airbags. Maritime Affairs, a verifying and announcing system about
There are three elements deciding performances of ABS: first, collision durability and ABS braking performances directly
ABS system of the car second, braking characteristics, and linked to the driver’s life has been introduced in Korea
third, friction characteristics of the brake pad. In 2001, NCAP with limitation to new cars for a domestic consumption.
(New Car Assessment Program) was introduced in Korea, While collision tests of cars have already been performed, a
and it has influenced the local car manufacturers to take a system with ABS notifying brake performances to consumers
braking performance of the car more seriously. Therefore, the under dry and wet conditions was introduced in 2001 to
expectation of automobile manufacturers on braking perfor- protect consumer’s benefit. This system referred to as New
mances of a tire has risen. Consequently, this has produced Car Assessment Program (NCAP) has been implemented in
an external atmosphere which spurs tire manufactures to advanced countries such as the USA and Japan.
develop technology improving performances of ABS braking.
In this regard, this study is to suggest experimental results 2. Friction Mechanism with respect to
of brake performances of the tire. The current speed limit is Characteristics of Road Surface
restricted to 100 km/h not only by NCAP tests but also under
most of the local road conditions. Nevertheless, nowadays According to the Coulomb Law, a friction coefficient of a
road conditions have been improved to allow higher speed perfectly elastic body such as steel is determined by the load
2 Advances in Mechanical Engineering

Tread rubber
Tread rubber Tread rubber

Road

(a) Smooth surface (b) Rough surface (c) Sharpened surface

Figure 1: Friction mechanism on texture of road surface.

and the friction force of the body, and the value of a friction Table 1: Friction mechanism with respect to characteristics of road
coefficient cannot exceed 1 [2, 3]. However, an object such surface.
as elastomer becomes deformed when an external force is Adhesion Hysteresis Cohesion
applied. Thus, to describe the mechanism of this process is
Molecular
far more complicated. The mechanism needs to be analyzed Mechanism Deformation Wear and tear
interaction
in a totally different way on the texture of the road surface
with which elastomer contacts. As shown in (1), the friction Road surface Smooth Rough Sharp
coefficient of elastomer is determined by adding three coeffi- High High wear
Comp’d factor Soft
cients such as an adhesion friction coefficient of a molecular hysteresis resistance.
interaction between the road surface and elastomer, a friction
coefficient of a hysteresis on deformations of elastomer [4–6],
and a friction coefficient of the cohesion due to wear or tear friction loss. On the other hand when the road surface is
wet, adhesion decreases generally. So, friction loss increases
𝜇overall = 𝜇Adhesion + 𝜇Hysteresis + 𝜇Cohesion . (1) on the wet road. The hysteresis mechanism means an energy
loss due to deformations of rubber produced by the sliding of
Here, the adhesion which means a friction mechanism rubber on the road compound. Table 1 summarizes a friction
of polymer interactions between surfaces of the tread rubber mechanism with respect to characteristics of road surface as
and the road surface determines friction characteristics on mentioned above.
the smooth and dry road surface as shown in Figure 1(a). The The result of a wet friction coefficient obtained from
grip especially on the icy or snowy road surfaces depends on Dynamic Friction Tester (DFT) on diverse types of road
the friction mechanism. surfaces is described below. As shown in Figure 2, four types
Hysteresis is a frictional characteristic by the loss of of road surface consisting of asphalt, cement, basalt, and
hysteretic energy which occurs due to the repeated defor- epoxy are suggested for this test in the laboratory. Asphalt
mation of the tread. As the hysteresis acts as the major
surface that was tested was made of the same asphalt that was
factor on the wet road surface, hysteresis characteristics of the
used on the highway. Concrete surface consisted of mixture
compound are very important for a wet brake performance.
Since the friction coefficient of cohesion applied to both with the same rate as the sand and cement. Basalt surface was
wear and tear is relevant to abrasion characteristics of the generated by basalt rock polishing. Also epoxy surface has
tread rubber, it is significant for very rough road surface. the same level coefficient of friction as ice. And then DFT
However, the influence of the friction coefficient by cohesion with a rotating disk plate is employed to measure a friction
over the total friction coefficient is generally as slight as coefficient.
negligible compared to adhesion or hysteresis [7–9] terms. Figure 3 explains how DFT measures the friction coeffi-
Grip characteristics with respect to the road surface are to cient. When the disk plate attached to three rubber samples
be summarized as follows. As for the characteristics of a rotates, there exists a friction between the rubber samples and
compound, a superior adhesion feature is favorable to a the wet ground surface. DFT measures friction forces until
smooth road surface, a high hysteresis is good to a rough road the disk plate stops due to the friction. After measuring torque
surface, and superior wear-resistance and high tear energy are applied to three rubber specimen attached flat plates, the
advantageous to a sharpened road surface. In case of snow frictional force and coefficient of friction can be measured.
or ice grip relevant to a smooth road surface, a compound is This test method is used to determine the relative effects
required to be softer. So, a compound with a low hardness is of various polishing techniques on materials or material
widely to be employed. Since a rubber tends to be hardened combination and is provided in ASTM in detail.
as the temperature drops, grip of rubber is deteriorated on icy
Dimension and shape of rubber sample attached disk
road surface. Thus, in order to prevent this, it is desirable to
use a silica compound with a low temperature-dependency plate in Figure 3 are well expressed in Figure 4.
against hardness. The adhesion mechanism results in molec- According to test results in Table 2, wet friction coeffi-
ular interactions between the rubber and the compound of cients for asphalt and concrete are 0.73 and 0.46 respectively,
road surfaces. There exists a higher adhesion element of whereas that for epoxy similar to icy road surface is less than
them on the dry road condition. The more adhesion, the less 0.1.
Advances in Mechanical Engineering 3

Asphalt Concrete Basalt Epoxy

Figure 2: Road surface textures.

Disk plate 𝜇p
Disk plate

Friction coefficient
𝜇s
Rubber
sample

Wet ground Rubber sample

surface

Figure 3: Configuration of dynamic friction tester.

Initial slope (Cs ): braking stiffness

Slip ratio (%)

5 𝜇p : peak friction coefficient

4 3 𝜇s : sliding friction coefficient

Figure 5: Schematic diagram on friction coefficient and slip ratio

7 3 10 curve.

16 Slip ratio on the axis of abscissa is defined as speed ratio

(Unit: mm)
between the car and the wheel as indicated in (2). Peak Fric-
tion Coefficient (𝜇𝑝 ) means the highest friction coefficient
obtained with respect to the change of slip ratio. Sliding
20 Friction Coefficient (𝜇𝑠 ) denotes the friction coefficient as the
wheel under a locked state slides. Braking stiffness relevant to
Figure 4: Dimension and shape of rubber sample attached disk
plate. stiffness, foot length, and foot width of the tire is the gradient
of friction coefficient on the initial slip ratio. Consider

Table 2: Friction coefficient with respect to road surface texture. 𝑉vehicle − 𝑉wheel
Slip ratio = × 100. (2)
𝑉vehicle
Surface (wet) Asphalt Concrete Basalt Epoxy
Test speed 80 KPH 80 KPH 80 KPH 40 KPH Slip ratio is the definition to express the degree of the slip
Friction arising from the difference between the vehicle speed and the
0.73 0.46 0.40 0.08 rotational speed of the tire. In case of braking it cannot exceed
coefficient
a value of 1 and generally has a value of approximately 10–20%
for ABS vehicles.
3. Relationship between the Speed of a Car and Friction tests were performed for 205/60R15 tire using the
the Friction Coefficient DFT with the focus on the change of friction characteristics
with respect to the speed of a car [12, 13].
In general, traction performances of the tire are represented Dynamic friction behavior of the tire with the change of
as a braking distance and a friction coefficient, which is speed from 50 Km/h to 110 km/h is expressed in Figure 6.
expressed as 𝜇-slip ratio curve. Firstly, the relationship Figure 6 presents a dynamic friction behavior of the
between the friction coefficient and the change of speed will tire with respect to the change of speed from 50 Km/h to
be suggested. As shown in Figure 5, major characteristic 110 km/h. From Figure 6, it can be well known that Peak
values relevant to friction need to be understood [6, 10, 11]. Friction Coefficient (𝜇𝑝 ) and Sliding Friction Coefficient (𝜇𝑠 )
4 Advances in Mechanical Engineering

2.0 the friction coefficient is the function of speed, the braking

∙ 205/60R15 distance can be depicted in

1.5 V
𝐿=∫ 𝑑V. (9)
Friction coefficient

𝜇 (V) 𝑔

1.0 Firstly, if the friction coefficient is a linear function

of speed, the braking distance can be obtained as (9) by
substituting (7) into (9). This can be also expressed in (11) by
0.5 developing (10) in Taylor series,
V 1 1 1
𝐿=∫ 𝑑V = [ ln ( ) − V] .
0.0 𝜇𝑜 (1 − 𝐴V) 𝑔 𝐴𝜇𝑜 𝑔 𝐴 1 − 𝐴V
0.0 0.1 0.2 0.3 0.4 (10)
Slip ratio
In order to change (10) into (11),
Velocity 50 KPH Velocity 90 KPH
Velocity 60 KPH Velocity 100 KPH
1 𝐴V
Velocity 80 KPH Velocity 110 KPH 𝐿=( + ) V2 . (11)
2𝜇𝑜 𝑔 3𝜇𝑜 𝑔
Figure 6: Friction characteristic with respect to speed change.
To change (11) into (12),
𝐿 1 𝐴V
= + . (12)
V2 2𝜇𝑜 𝑔 3𝜇𝑜 𝑔
decrease as the speed increases when a car brakes and that the
region of slip ratio with a peak friction also decreases [14–16]. Parameter 𝜇𝑜 and constant 𝐴 can be determined from the
gradient and the intercept. If the friction coefficient is an
4. Theoretical Background exponential function like (8), braking distance, 𝐿, can be
developed as follows:
Energy balance (4), kinematic energy of the car (3), and
V 1 1
friction energy between the road surface and the car are 𝐿=∫ −𝐵V
𝑑V = [ (1 − 𝑒𝐵V ) + V𝑒𝐵V ] . (13)
used to convert the braking distance of the car into friction 𝜇𝑜 𝑔𝑒 𝐵𝜇𝑜 𝑔 𝐵
coefficient. In (3), 𝑚 and V represent load and speed of the
If it is assumed that the value 𝐵V is small fully, (13) can be
car, respectively. In (4), 𝜇 and 𝐿 denote friction coefficient and
developed into
braking distance. Consider
1 𝐵V
1 𝐿=( + ) V2 . (14)
𝐸kinetic = 𝑚V2 , (3) 2𝜇𝑜 𝑔 2𝜇𝑜 𝑔
2
From the gradient and the intercept of (15),
𝐸friction = 𝜇𝑚𝑔𝐿, (4)
𝐿 1 𝐵V
𝐸kinetic = 𝐸friction . (5) = + . (15)
V2 2𝜇𝑜 𝑔 2𝜇𝑜 𝑔
Under the assumption that the friction coefficient has a The parameter, 𝜇𝑜 , and constant 𝐵 are to be determined.
constant value irrespective of the speed, it can be expressed Both a coefficient from a traction trailer and a braking
as distance from NF Sonata are presented in Tables 3 and 4. By
V2 employing the tire of 195/65R14, tests were performed on the
𝐿= . (6) wet asphalt road surface with water depth of 1.5 mm.
(2𝜇𝑔) As expected, braking performances of tires 1, 2, 3, and 4
If the friction coefficient is the function of speed, two are different from each other.
cases will be considered. One is decrement of the friction From the test results, it is well observed that mp and ms
coefficient in proportion to speed as shown in (7) and the decrease greatly as the speed increases during braking. This
other is decrement of the friction coefficient in exponential means that a friction coefficient is the function of speed of a
function as indicated in (8). Consider car. Table 4 shows changes of braking distances with respect
to the speed.
𝜇 = 𝜇𝑜 (1 − 𝐴V) , (7) Table 5 provides intercept, gradient, and 𝜇𝑜 , values calcu-
lated from 𝐿/V2 and V plot relevant to (15).
𝜇 = 𝜇𝑜 exp−𝐵V . (8) From the results, a braking distance of tire 5 can be
expressed as a function of speed as follows:
Here 𝜇𝑜 is intrinsic parameter which is irrelevant to the
speed. 𝐴 and 𝐵 are constants. Under the assumption that 𝐿 (𝑚) = (0.00467 + 5.275 × 10−5 × V) V2 . (16)
Advances in Mechanical Engineering 5

Table 3: Change of friction coefficient depending on speed change.

Tire 1 Tire 2 Tire 3 Tire 4

Speed (KPH) 40 60 80 40 60 80 40 60 80 40 60 80
𝜇𝑝 0.99 0.98 0.93 0.90 0.86 0.81 0.95 0.93 0.91 0.98 0.94 0.91
𝜇𝑠 0.69 0.63 0.54 0.58 0.52 0.45 0.71 0.62 0.53 0.76 0.66 0.58
Braking
— 22.7 — 24.3 — — 22.1 — — 21.2 —
distance (m)

Table 4: Changes of braking distance with respect to the speed.

Tire 1 Tire 2 Tire 3 Tire 4 Tire 5 Tire 6

0 KPH 0 0 0 0 0 0
Braking distance (m) 50 KPH 16.9 17.2 17.1 17.6 18.3 17.2
80 KPH 56.4 58.5 55.3 58.8 56.9 54.6

Table 5: Intercept and gradient adopted in modeling.

Tire 1 Tire 2 Tire 3 Tire 4 Tire 5 Tire 6

Intercept (×E−3) 3.310 3.136 3.868 3.506 4.670 4.101
Gradient (×E−5) 6.876 7.496 5.967 7.092 5.275 5.534
𝜇𝑜 1.189 1.255 1.020 1.223 0.843 0.960

800 speed. This comes from the fact that the hydroplaning phe-
nomenon appears in a high speed on wet road surface. On the
80 wet road surface, the tire drifts away from the road surface in
Theoretical (variable)
600 Theoretical (constant) some degree due to hydroplaning which ultimately causes a
Braking distance (m)

Experimental result
60
loss of grip.
40
400
20 5. Conclusion
0
Tire 1 Tire 2 Tire 3 Tire 4 Tire 5 Tire 6
For this study, a braking distance as a function of the speed
200 is to be inferred in (16) from test results. Equations proposed
in the study are nearly identical to the actual test results.
However, equations should be used in limited conditions,
0 because parameters are calculated by adopting the test results
0 20 40 60 80 100 120 140 160 180 200
Braking speed (km/h)
under fixed conditions with the specific tire and road con-
ditions. As a result, under conditions with the fixed tire and
Variable Constant road conditions, the braking distance can be estimated as
Tire 1 Tire 4 Tire 1 Tire 4 a function of the speed of a car by measuring changes of
Tire 2 Tire 5 Tire 2 Tire 5
Tire 6 Tire 6
a friction coefficient according to speed change. Moreover,
Tire 3 Tire 3
even though the car runs in a high speed, it is still possible
Figure 7: Comparison between a theoretical braking distance and to forecast the braking distance.
one from the model formula with respect to speed change.

Conflict of Interests
In case of perfectly elastic body, the braking distance is The authors declare that there is no conflict of interests
in proportion to the squares of speed in general. However, regarding the publication of this paper.
the braking distance on the wet road surface becomes far
longer than the theoretical value, which is proportional to the
squares of the speed. Figure 7 compares the braking distance References
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