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Machine Dynamics Research
2015, Vol. 39, No 1, 135 - 142
Numerical Analysis of Stress Distribution in a Car
Tire Equipped with Snow Chains
Zbigniew Olszewski, Konrad Waluś, Piotr Krawiec, Łukasz Warguła
Poznan University of Technology
e-mail: [email protected]
Abstract
Car tire is made of a composite material, whose individual components have
significantly different mechanical properties. Its primary task is to transfer forces generated
by the vehicles drive system so that the driver maintains sufficient control over the vehicle,
as well as to preserve optimal performance characteristics. Presence of snow and slush,
especially on roads with significant inclination leads to a drastic deterioration of the
vehicles traction. In this case, in order to ensure sufficient control over the vehicle snow
chains are used, whose task is to change the nature of the interaction between the tire and
the surface through an increase in the radial forces operating in the area of contact, by
increasing the surface area, and the expansion of the wheels outer surface macrostructure.
Stress distribution in the tire, especially in the area of direct contact between the tire, the
chain and the surface is a result of the mechanical properties of tires composite constituents,
chain geometrical characteristics, tire pressure, hardness, and surface type, thickness and
density of the snow cover, and temperature of the system. Value of these stresses has a
direct and significant impact on the issue of safety, operating characteristics of the vehicle,
and the durability of road surface and tires. In order to evaluate the stresses in the tire
equipped with chains, authors' previous numerical model was further developed, which has
been earlier successfully used to estimate the value of the deflection, and the surface area of
the contact area as a function of load. Model takes into account all relevant geometric and
material features of actual tire-chain-surface as well as the loads acting on the wheel. In this
paper numerical model of the tire equipped with snow chains, and the results of the stress
distribution obtained by numerical simulation for pressure and load conditions
corresponding to a typical real were presented.
Key words: composite, energy dissipation, snow chains, failure, tire
1. Introduction
On surfaces with reduced coefficient of friction, in the presence of a large
amount of snow and slush and on roads with large inclination in order to improve
traction properties of the vehicle snow chains are used. Use of chains is changing
the nature of frictional-geometric cooperation between the tire and the surface
causing an increase in the radial forces operating in the area of contact to facilitate
acceleration, braking and improving overall vehicle handling. Stress distribution in
136
Z. Olszewski, K. Waluś, P. Krawiec, Ł. Warguła
the tire fitted with a traction improving device affects the value friction coefficent,
especially in the part immediately adjacent to the road and tire contact area, what is
an important issue for the sake of traffic safet, and operating characteristics of tires.
Cooperation between the tire and the road surface, is a process extremely complex,
depending on the interaction of many factors, such as the geometric features of the
tire defined by the air pressure, unit load on each wheel, micro and macrostructure
of road surface, and in the case of tires equipped with chains by mechanical
properties of individual cells and their spatial distribution [Bojar et al., 2011,
Drożyński et al., 2010, Olszewski, Waluś, 2012, Tokarczyk, Uścińska, 2012,
Uscińska et al., 2012, Waluś et al., 2009].
Pneumatic tire is composite element, composed of several materials with
different mechanical properties. Its primary task is to transfer forces generated by
the vehicle drivetrain system in a matter to ensure safety and maintain sufficient
vehicle control. Main component of a tire composite is rubber (nowdays synthetic
rubber - later natural rubber), with strongly outlined visco and hiperelastic
properties, in which steel wires are embedded, providing increased stiffness, and
improving the strength characteristics. [Marvalova, 2007, Parsons, 1987, Person ,
1998, Tarasiuk, 2008]. The carcass is made of radially arranged cord plies acting as
a thread stiffening element, and providing basic protection against puncture
[ABAQUS, 2011, Jurkowska, Jurkowski, 1975]. General construction of a car tire
is shown in Fig.1.
Fig. 1. Construction of typical pneumatic tire – [www.felgi-opony.com]
Snow chains (Fig.2), are an optional quipment of the vehicle consisting of
two sections covering the rim of the tire, connected by a series of chains or plates
overlapping crosswise the tread. Their primary function is to increase the traction
of the vehicle in contact with the snowy or icy road.
Numerical Analysis of Stress Distribution in a Car Tire Equipped with Snow Chains
137
Fig. 2. Photo of actual snow chains
2. Model characteristic
Subject of the analysis was a tire size 165/65 R14 which dimensions and
geometric properties has been obtained from the catalog of the European Tyre and
Rim Technical Organisation (ETRTO). During model development were taken into
account all the relevant components of the tire without tread as irrelevant to the
analysis. Model takes into account elastomers material viscosity and hyperelastic
properties by automatically creating a response curves using the defined function
potential strain energy, in the form of
1 el
( J  1) 2i
i 1 Di
N
N
U   Cij ( I1  3) i  ( I 2  3) j  
i  j 1
(1)
where U is the amount of Energy per reference unit, N – is a constant dependent on
the type of material, Cij and Di are temperaturę dependtant material parameteters;
I1 and I 2 are first and second deviators of stress invariants defined as
I1  12  22  32
i
I 2  12  22  32
(2)
Z. Olszewski, K. Waluś, P. Krawiec, Ł. Warguła
138
where the deviantor of normal stress is defined as
el
1
3
i  J i ; where J expresses
total volume; J elasticity of the total volume in main directions. And initials
shear modulus expressed as
o  2(C10  C01) ;
K0 
2
D1
(2)
for C10=1000000; C01=0; D1=0.
Some of the components such as bead and the rim had not been modeled
directly, but through selecting the adequate boundary conditions (geometry
immobilization). In order to reliably model the cord rebar layers function was used
allowing to simulate phenomena occurring in cord and carcass by adding a feature
characterizing the spatial layout of the cord, and its mechanical parameters. Used
parameter values are shown in Table 1.
In order to simplify, a uniform composition and the material properties of the
elastomer component of the composite were taken, assuming a negligible effect in
case a simulation conducted under static conditions
Tab. 1. Material parameters of cord and carcass
Poisson
Area per bar
Spacing
coefficient
[m]
[m]
Material
Young Modulus
[Pa]
Carcass
1*109
0,3
1,96E-6
0.002
Belts
1*109
0,3
7E-8
0.00015
Road surface was modeled as a rigid body (analitycal rygid), which was then
stripped of all degrees of freedom except for movement in a radial direction of the
tire. Snow chains, were modeled as an incompressible, elastic frame, the chain
segments arranged radially parallel to the axis of rotation of the wheel. Also
defines binding contact between the different elements of the model, taking into
account the coefficient of friction for each pair of friction [Unarski 2002, Waluś,
2013a, Waluś, 2013b, Waluś, 2013c, Waluś, 2013d, Waluś, 2013e, Waluś et al.,
2011]. At the end of the external load has been defined as the pressure applied to
the inner surface of the tire, force applied to the lower surface of the ground and
force of gravity. Contact properties between individual elements of the model have
been defined using an penalty algorithm with a defined coefficient of friction for
the tangential direction, and as "hard contact" in the normal direction [Talaśka et
al., 2012, Olszewski et al., 2014, ABAQUS, 2012]. General structure of the final
Numerical Analysis of Stress Distribution in a Car Tire Equipped with Snow Chains
139
simplified numerical model, together with the applied finite element mesh is shown
in Fig. 3.
Fig. 3. Geometrical model, and simplified numerical model of tire equiped with snow
chains.
3. Analysis results
Model has been analyzed for values of the load force equivalent to a
weight of 350 kg and the inflation pressure equal to 2 bar, which roughly
corresponds to a typical operational values for a compact car. The analysis results
as a map of the stresses in the axial and radial plane are shown in Fig. 4 and 5.
Fig. 4. Stress map in tyres radial plane
140
Z. Olszewski, K. Waluś, P. Krawiec, Ł. Warguła
Fig. 5. Stress map in tyres axial plane
4. Conclusions
Presented model of the tire equipped with snow chains constitutes a
development of the previous model, which been successfully been used to estimate
the value of deflection of the tire as a function of load, and to estimate the size of
the contact [Olszewski et al. 2014, Walus et al., 2009]. Is can suggest about the
suitability of the model for other uses associated with the use devices used on
surfaces with limited grip. Obtained results of simulation studies indicate a slight
impact of the use of anti-skid chains on the distribution of stress in the tire. It can
be concluded that the use of anti-skid chains leads to a slight increase in the value
of stresses in the material of the tire occurring directly over the end of the chain at
the time of contact with the ground and which is a direct consequence of its
bending.
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