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Tire Wear Modeling
By Chris Klobedanz
Dated 12/9/2013
Final Project
Tires seem like simple devices, but today’s tires are highly complex products that are
manufactured in an intricate process, bonding together numerous parts of rubber and steel.
These devices are an integral part of day-to-day life for most of the world and are expected to
perform up to a high level of standards in even the most extreme conditions. The evolution of
tire design has evolved tirelessly over time to compensate for factors that wear away tire
material, decreasing their safety and functionality; tire wear is an unavoidable result of use.
Ultimately, tire wear is the result of frictional work in the tire-pavement interface that is
generated when tread surface elements go through a frictional force-slip cycle during each
passage through the footprint [1]. Wear is caused and/or accelerated by a number of factors,
including the physical properties of rubber, a combination of unbalanced loading and incorrect
inflation of the tire, the mechanical systems of the automobile, terrain, and environmental
conditions [2,3].
Description of Problem:
This paper first examines the properties of a standard tire and a typical pavement surface
which have a bearing on the tire wear model. Then, the interaction of these two contacting
surfaces is discussed. Next, the influence of external factors on the system is explored. Finally,
we take a look at how current studies are used to contribute to tire tread design and selection for
certain applications.
Overview of Interfacing Bodies:
The tires of a vehicle support the steering, braking, load, traction, and help to absorb
shock caused by unsmooth road conditions. A typical radial pneumatic tire is made up of
synthetic rubber, natural rubber, fabric, metal wire, along with various chemical compounds.
Some of the typical features of a tire that increase wear resistance are the tread, sidewall, beads,
belts, ply, and inner liner [2,4]. These features are described more in depth below and illustrated
in Figure 1:
Figure 1: Tire Features
Tread – The tread is the thick rubber (or rubber-composite compound) part of the tire that comes
into contact with the surface of the road and provides the necessary level of traction. The tread
pattern is made up of blocks, grooves, ribs, sipes, and the shoulders as illustrated in Figure 2.
The blocks (lugs) are the areas that contact the road surface. The grooves run circumferentially
around the tire to help channel water away from the blocks; grooves can be classified into a more
general category called “voids”, which are defined as all of the spaces between blocks which
allow expansion of the blocks under compression, as well as create channels for water diversion.
The ribs are the raised areas between grooves that run circumferentially around the tire and
increase driving stability and prevent skidding. Sipes are shallower cuts across the tire that
direct water perpendicularly away from the tire to prevent hydroplaning. The shoulders are the
blocks at the edge of the tread which transition down to the sidewall. [4]
Figure 2: Tread Features
Sidewall – The sidewall is the transition area between the tread and the beads. It provides
flexibility and tensile strength to the tire, as well as containing air pressure. Sidewalls are
usually composed of rubber reinforced with fabric or steel cords. [4]
Beads – The beads are the tire interfaces that contact the wheel rim and ensure no air leakage or
circumferential shift occurs. The beads are usually composed of high strength, low flexibility
rubber. [4]
Belts – The belts are layers beneath the tread, usually made of steel, which provide puncture
resistance and reinforce the structure of the tire, helping the tire make better contact with the
road. [4]
Ply – Plies are layers of firm cords embedded in the rubber (like rebar in concrete) that prevent
the rubber from stretching and tearing due to tire slip and internal pressure. [4]
Inner Liner – The inner liner is a toroid rubber balloon that is inflated inside the tire to retain air
All of these features create a complex mechanism composed of numerous materials, each
providing an important function. All of these features need to be accounted for when
considering how tire wear takes place, where it occurs in the largest magnitude, and what its
consequences are.
Pavement Surface:
The primary method of classifying pavements is by the road surface texture. The two
recognized scales of texture classification are macrotexture and microtexture. Macrotexture is
defined by the geometrical configurations, the size, and the distribution of aggregate particles
and their surrounding voids. High macrotexture pavements are rougher surfaces that often
contain large, angular aggregate particles. Microtexture is defined by the basic surface
roughness of individual aggregate particles, and is often unnoticeable by the naked eye [1].
Figure 3 illustrates these classifications:
Figure 3: Surface Classifications
The composition of the road surface is also important when trying to define the state of
the road surface. The chemical nature can affect the hardness of the surface, the change in
texture over time, the change in texture based on varying weather conditions, and numerous
other factors. [1]
Without understanding the influence these characteristics have on tire materials, it is
impossible to create a realistic system to reflect the wear of tire materials.
The Tire-Road Interface:
The primary location of the abrasive action between tire and pavement during automobile
operation is on the thin layer (a fraction of a millimeter) of rubber in the tread of the tire
immediately in contact with the road, called the footprint [1]. This layer and the underlying belt
layers are cyclically compressed and uncompressed, creating shear stresses and strains. These
stresses and strains make up the frictional work between surfaces, which in turn causes wear of
the tread. The magnitude of the tread is a function of the intensity and duration of the frictional
work, the nature of the pavement, properties of the rubber, and other environmental factors [1].
System Modeling:
A quantifiable model is outlined in Reference (2) which builds a steady rolling tire model
taking into account the slip of the tire on the road. The resulting steady-state formula derived
from this model is shown below, along with an illustration of the model, Figure 4:
ܸሶ ൌ ‫ ܭ‬ு ߛሶ
Where: ܸሶ = ratio of volume wear
K = wear coefficient
P = normal pressure of contact surface
A = contact area
H = hardness of softer material
ߛ = slip ratio
Figure 4: Steady Rolling Tire Model
Wear equations:
There is no single accepted method for calculating tire wear based on all of the involved
factors. Some methods independently attempt to quantify tire wear by isolating all but a few
factors. Below equation (2) considers abrasion pattern, slippage, and temperature effects,
equation (3) considers fatigue theory and the geometry of the contact surface but does not
consider temperature, and equation (4) considers tire and road material properties [5]:
RW = θ2*p*f*r0(1 + α(ts-t0) + c*d)
RW = constant*(E/σ0)µδ-βδ-1(θ*a)2+βδ/(2+βδ)
RW = K*(P*θ2 + Q*θ3 5)
Where: RW = rate of wear
p = resilience of the wheel
α = temperature coefficient
t0 = reference temperature
E = Modulus of Elasticity
µ = coefficient of friction
β = track roughness parameter
P,Q = material constants
θ = slip angle
f = wheel stiffness
ts = tire surface temperature
c,d,K = constants
σ0 = ordinary tensile strength
δ = fatigue exponent
a = length of contact area
Other methods, such as Pacejka’s “Magic Formula” uses laboratory observed data to
determine constants that best fit tire wear models. Pacejka’s series of tire design models were
named “magic” because they are not formed on any physical basis, but fit a wide array of
construction and operating conditions. The general form of the magic formula is:
R(k) = d*sin(c*arctan(b(1-e)*k + e*arctan(bk)))
Where: R(k) = a force or moment
k = slip parameter
b,c,d,e = fitting constants
The simplest equation that relates treadwear and frictional work is:
Where: RW = rate of wear
A = rubber lost per unit frictional work
EF = frictional work per unit area
In equation (6), the variables A and EF are functions of the items shown in Figure 4, which add
to the complexity of the equation when looking at in further detail:
Figure 4: Simple Wear Equation
Finite Element Modeling:
Finite element modeling is commonly used to analyze the complex interface between a
tire and a road surface, but like the above equations, accuracy is only attained when all factors
are incorporated into the model. Experiments to see the effect of surface temperature of a tire
must account for the surrounding environmental conditions. Analysis of tire slip must take into
account the effect of cornering and skidding. Without a fully-developed scope of the system,
realistic predictions of performance are impossible.
Reference (1) has conducted several studies to help give credibility to building tire-wear models.
Several trends are depicted in Figures 5 and 6. Figure 5 shows, as expected, that tire
performance decreases in wetter conditions. Figure 6 shows that tire wear generally increases at
hotter temperatures.
Figure 5: Tire Performance in Rain
Figure 6: Tire Wear at Varying Surface Temperatures
Various design modifications are made based on the findings of an accurate tire wear
model. For example, professional auto racing scrutinizes the effect of tire materials on the
speed, acceleration, and duration of performance of a tire. A harder tire will last longer and
maintain speed well, but will not accelerate as fast as a softer tire. On a hot day, however, when
tire wear is already occurring at a fast rate, softer tires may not last as long as needed.
1. The Tire Pavement Interface, Pottinger and Yager, American Society for Testing and
Materials, 1986
2. Study on the Simulation of Radial Tire Wear Characteristics, Guang Tong and Xiaoxiong
Jin, Tongji University
3. Michelin – Fundamentals of Tire Wear: http://www. youtube. com/watch?v=UklcqWeaCc
4. Vehicle Dynamics: Theory and Applications, Reza Jazar, Springer, ISBN 978-0-38774243-4, dated March 2011
5. Tire Wear Model, Edward Saibel and Chenglang Tsai, Dept. of Mechanical Engineering
Carnegie-Mellon University
6. Tyre/Road Friction Modeling, R. Van Der Steen, Eindhoven University of Technology,
May 2007
7. Traction (engineering): http://en. wikipedia. org/wiki/Traction_%28engineering%29
8. Hans B. Pacejka: http://en. wikipedia. org/wiki/Hans_B. _Pacejka
9. J. R. Davis, Surface Engineering for Corrosion and Wear Resistance, ASM, London,
10. M. J. Neale, The Tribology Handbook 2nd Edition, Butterworth, London, 1995
11. K. L. Johnson, Contact Mechanics, CUP, Cambridge, 1987
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