Tribological Evaluation of Studded Tire Wear and the Effect of Stud
Approach Angle
by
Jeremiah Blair Jones
A Project Report
in Partial Fulfillment of the
Requirements for the class of
Friction, Wear and Lubrication of Materials
Rensselaer Polytechnic Institute
Hartford, Connecticut
May 2015
1
© Copyright 2015
by
Jeremiah Blair Jones
All Rights Reserved
CONTENTS
LIST OF TABLES ............................................................................................................. 4
LIST OF FIGURES ........................................................................................................... 5
1. Introduction.................................................................................................................. 6
1.1
Background ........................................................................................................ 6
1.2
Problem Statement ............................................................................................. 7
2. Evaluation of Materials Used ...................................................................................... 9
2.1
Stud .................................................................................................................... 9
2.2
Tire ................................................................................................................... 10
2.3
Road ................................................................................................................. 11
3. Simplified COMSOL Multiphysics Model ............................................................... 12
3.1
COMSOL Physics Modules ............................................................................. 12
3.2
Meshing ............................................................................................................ 13
4. Results and Discussion .............................................................................................. 14
5. Conclusion ................................................................................................................. 19
6. References.................................................................................................................. 21
APPENDIX A: Comparison of 0 Degree Model with and Without Tire Pressure
Boundary Condition................................................................................................... 23
APPENDIX B: COMSOL Model Output Figures........................................................... 25
LIST OF TABLES
Table 1: Tungsten Carbide Material Properties ............................................................... 10
Table 2: Rubber Tire Assumed Properties....................................................................... 11
Table 3: Assumed Road Material Properties ................................................................... 11
Table 4: Tabulated Resulting Stress Based on Approach Angle ..................................... 14
LIST OF FIGURES
Figure 1: S700 Racing Slick Tire [1] ................................................................................. 6
Figure 2: Tread Features for a Winter Tire [2] .................................................................. 7
Figure 3: Studded Snow Tire [3] ....................................................................................... 7
Figure 4: Car Tire Stud Assemblies [4] ............................................................................. 9
Figure 5: Tire, Stud, and Road Model Meshing .............................................................. 13
Figure 6: Von Mises Stress Based on Approach Angle .................................................. 14
Figure 7: -10 Degree Stress Case..................................................................................... 15
Figure 8: -6 Degree Stress Case....................................................................................... 16
Figure 9: -2 Degree Stress Case....................................................................................... 16
Figure 10: 0 Degree Stress Case ...................................................................................... 17
Figure 11: -6 Degree Stress Case..................................................................................... 18
Figure 12: -10 Degree Stress Case................................................................................... 18
1. Introduction
1.1 Background
When evaluating the performance of a car with respect to its handling, stability, traction,
and control, the tires are generally the first and the most important component to be
evaluated. If the tires are not aligned correctly, the steering system of the car will have a
difficult time accurately relaying the steering commands given by the driver at the
steering wheel and therefore control and stability of the car will be diminished. The
handling, traction and control can also be negatively affected if the tires are improperly
inflated, i.e. either under inflated or over-inflated. The conditions in which the tires are
being used are very significant factors with regards to tire performance. Although the
conditions are not directly related to the design and configuration of the tire itself, these
conditions tend to amplify (either positively or negatively) the performance of said
design characteristics as well as the wear and degradation of them. One example of
ambient condition negatively amplifying the performance of a tire is when a racing slick
tire, as shown in Figure 1, is used on an icy surface. When this type of tire is used a dry
surface, the tire performance very well with regards to traction and control. However
when introduced to a slick icy surface, the tire has a very difficult time trying to gain
traction and control. The reason for this negative amplification in performance is that
when the road is dry, the racing slick tire has a very large coefficient of friction with the
road as well as a large surface area (generally the entire width of the tire). This allows
the tire to maintain large amounts of traction in both acceleration and stopping. When
the same tire is put onto the icy surface, the coefficient of friction decreases significantly
and therefore decreases the ability of the tire to accelerate or decelerate the vehicle.
Figure 1: S700 Racing Slick Tire [1]
One method used to counter the decrease in the coefficient of friction is to introduce
treads in the tire. FIGURE 2 shows an example of tire treads and the features associated
with the tire tread. Additionally, if metal studs are introduced to the road contacting
surface area of tire tread, an increase in stability, traction and control can potentially be
obtained. FIGURE 3 shows an example of a tire with the metal studs protruding from
the surface of a tire.
Figure 2: Tread Features for a Winter Tire [2]
Figure 3: Studded Snow Tire [3]
1.2 Problem Statement
Although studded tires have the potential to provide an increase in stability and control
during winter months where temperatures fall below freezing, the studs also have the
potential to damage and cause unnecessary wear in the roads which they are employed
on. As a result, there have been and continue to be many tribological reports published
discussing at length the effects of studded tires on road wear. Due to the large quantity
of analysis and focus being put onto to the road wear, this project will not evaluate this
subject any further. Another tribological wear evaluation though can be performed on
the metal studs and how they wear. This project will evaluate the wear of the metal
studs themselves based on the approach angle1. To accomplish this evaluation, this
project will first compile all of the materials in the system and their dimensions (the
metal studs used in snow tires, the tires themselves, and the road). Then a simplified two
dimensional finite element model will be developed using COMSOL Multiphysics. This
2-D model will allow for the studs and their wear to be evaluated. Due to the limited
scope of this project, simplifications in the modeling and load analysis had to be taken.
These simplifications will be detailed further in their respective discussions.
1
The approach angle is the angle which the outer surface of the stud makes with the road as it comes
into contact with the road.
2. Evaluation of Materials Used
Each of the above mentioned sub-sections of the system being evaluated (tire, stud and
road) can be designed and manufactured using different materials or compositions of
materials. This project will chose a single material or material composition whose
material properties are either readily available or can be accurately assumed based on the
material composition.
2.1 Stud
The studs used in commercial snow tires are actually comprised of two parts. Figure 4
shows five different sized stud assemblies. The flanged lower portion of the stud
assembly is a cylindrical outer body which serves to hold the stud in place within the tire
[4]. This is accomplished by the flanged bottom which, when installed correctly, will
maintain the tip of the stud assembly protruding through the rubber part of the tire and in
contact with the ground. The top part of the stud assembly which can be seen by looking
at the exterior of a tire, commonly referred to as the stud, is a metal pin.
Figure 4: Car Tire Stud Assemblies [4]
If it is assumed that the cylindrical outer body of the stud assembly performs as
designed, then it should have minimal effect on the wear of the stud. Since the focus of
this project is to evaluate the effect of the approach angle between the stud and the road,
it is a valid simplification to assume the studs are all installed correctly. For this reason,
the lower outer body was not included in the 2-D model associated with this project and
therefore the material of this portion of the stud assembly can be neglected. The pin, or
stud, of the assembly is commonly tungsten carbide [4].
The applicable material
properties of tungsten carbide are shown in Table 1. The dimensions of the pin can vary
depending on the manufacturer and intended use. For this project, the following stud
dimensions were assumed: pin diameter of 2.6 mm and a pin prominence (distance the
pin protrudes through the tire tread) of 1.9 mm [5].
Table 1: Tungsten Carbide Material Properties
Parameter
Value (units)
Density
14500 (kg/m^3) [6]
Poisson’s Ratio
0.25 [7]
Elastic Modulus
614e9 (Pa) [7]
Strength
2330e6 (Pa) [7]
Hardness (Rockwell)
91 (Rockwell A) [7]
2.2 Tire
The main raw component of commercial car tires is natural rubber, although synthetic
rubber is also used. However, in order to achieve the desired material properties most
commonly associated with tires (flexible but strong and wear resistant) the rubber must
be treated through various processes. In addition to the rubber treatment process which
could vary from tire to tire, the dimensions and surface characteristics (treads) of one tire
can vastly differ from another tire. Since this project is focusing on the wear of the
metal studs protruding through the surface of the treads, the tread pattern is neglected.
Table 2 shows the tire material properties which will be assumed in this project. The
overall tire dimensions which will be used for this project are: a tire width of 215 mm,
tire diameter of 17 inches, a tire thickness of 15/32 inches, and a tire contact depth of
0.02 m. The width and diameter were derived from TireRack.com using the standard
size tire for a 2012 Kia Forte Koup SX [8]. The tire thickness is derived from using a
standard tread depth on a new tire [9] plus a few additional 1/32 of an inch to account for
the rubber beneath the tread itself. This allows the thickness of the tire to be more than
10 times greater than the thickness of metal stud being used in this project.
Table 2: Rubber Tire Assumed Properties
Parameter
Value (units)
Density
1013.5 (kg/m^3) [10]
Poisson’s Ratio
0.5 [11]
Elastic Modulus
750 (psi) [11]
Strength
N/A
Hardness (Rockwell)
N/A
2.3 Road
There are many different materials which roads can be made with/comprised of.
Examples are asphalt, concrete, dirt, and sand. Along with the road being comprised of
almost all of the aforementioned example materials, they roads can also be made up of
various combinations of these materials. Also, roads can become covered with such
things like water or ice which would change the interactions and material properties in
contact with car tires and studs. For this project the road material was assumed to be an
asphalt mixture to ease the research for material properties. Table 3 shows the material
properties that will be assumed for this project. The thickness of asphalt that will be
used for this project is 50 mm. The width and depth used was chosen to match the
respective tire dimensions for model simplicity.
Table 3: Assumed Road Material Properties
Parameter
Value (units)
Density
2000 (kg/m^3) [12]
Poisson’s Ratio
0.35 [13]
Elastic Modulus
5000e6 (Pa) [13]
Strength
320e3 (Pa) [14]
Hardness (Rockwell)
1.3 Mohs [15]
3. Simplified COMSOL Multiphysics Model
COMSOL Multiphysics is a computer program which utilizes finite element analysis to
solve a wide range of problems which could be labor intensive to solve analytically. In
order to utilize COMSOL Multiphysics, first the physics and finite element models need
to be created. For this project, a simplified two-dimensional model is created of a single
stud.
3.1 COMSOL Physics Modules
In order to model the stresses associated with the tire, stud and road interaction, the Solid
Mechanics physics module was used. This physics module is used to model various
loading conditions of finite element models and utilizes Equation 1 to solve the models.
−∇ ∗ 𝜎 = 𝑭
After choosing the physics models in COMSOL Multiphysics, the geometry and initial
conditions were defined. For this model, the three domains (tire, stud, and road) were
defined as follows: tire domain was defined as a 0.02 m (x-dimension) by 0.01 m (ydimension) rectangle, the stud domain was defined as a 0.0026 m (x-dimension) by
0.0019 m (y-direction) rectangle, and the road domain was defined as a square with side
lengths of 0.02 m. In order to ensure that the contact surfaces were properly defined, an
initial offset between the tire/stud assembly and the road was set to 0.0005 m. This
allowed for the bottom surface of the stud to be set as the source contact surface and the
entire top road surface to be set as the destination contact surface.
Once the geometry was determined and coupled appropriately, the boundary conditions
and material properties were defined. The first boundary condition that had to be set
was that the bottom edge of the road domain experiences no displacement in either x- or
y-direction. This is boundary condition is essential to solving the solid mechanics
problem as if the road domain was allowed to displace in the y-direction, the model
could not be solved (domain would continue to be pushed further and further down with
nothing preventing its motion). The next boundary condition set was that the top surface
(1)
of the tire domain has a set displacement of 0.001 m in the negative y-direction. This
displacement causes the stresses in the model by pushing the tire and therefore the stud
into the road. Since there was an initial offset of 0.0005 m between the stud and the
road, the net realized displacement is 0.0005 m. Initially this was the only boundary
condition applied to the tire and stud assembly, however this resulted in an undesired
deflection in the tire surface in contact with the stud (see Appendix A for the comparison
between initial and final model results).
To remedy this, an additional boundary
condition was applied to the bottom edge of the tire. This condition was a boundary
load, in the form of pressure, of 40 psi. This boundary load was set to simulate the
internal tire pressure which serves to maintain the tire rigid (in addition to the tire
properties). The last boundary condition that had to be set was establishing the contact
pair between stud and road.
3.2 Meshing
Before solving the COMSOL model, the finite element mesh had to be defined. Due to
the relatively simplicity of this model, the general physics meshing tool was used using
the “Finer” mesh option. This resulted in a maximum element size of 0.0012 m, a
minimum element size of 4.05e-6 m, a maximum element growth rate of 1.25 and a total
number of elements of 1,295. Figure 5 shows the meshing pattern for the model.
Figure 5: Tire, Stud, and Road Model Meshing
4. Results and Discussion
Approach angles were varied from -10° to 10°. The results from the runs associated with the
varied approach angle were compiled into Table 4 and Figure 6 to better show trends and
general system behavior as a result of each variation. Appendix B contains the 2D plots
created by COMSOL Multiphysics for the each approach angle case shown in Table 4.
These plots are intended to be visual aids to the data included and discussed herein.
Table 4: Tabulated Resulting Stress Based on Approach Angle
Von Mises Stress (N/m^2)
Approach Angle
(degrees)
-10
-8
-6
0
6
8
10
Max Stress Y
(N/m^2)
7.70E+06
7.40E+06
1.39E+06
-7.56E+05
5.40E+05
5.65E+05
1.01E+06
Max Stress X
(N/m^2)
8.36E+06
1.20E+07
1.59E+06
1.83E+05
1.85E+05
1.45E+06
3.38E+06
Max Stress Von
Mises (N/m^2)
5.49E+07
8.06E+07
9.53E+06
9.38E+05
1.04E+06
2.34E+06
4.03E+06
8.50E+07
8.25E+07
8.00E+07
7.75E+07
7.50E+07
7.25E+07
7.00E+07
6.75E+07
6.50E+07
6.25E+07
6.00E+07
5.75E+07
5.50E+07
5.25E+07
5.00E+07
4.75E+07
4.50E+07
4.25E+07
4.00E+07
3.75E+07
3.50E+07
3.25E+07
3.00E+07
2.75E+07
2.50E+07
2.25E+07
2.00E+07
1.75E+07
1.50E+07
1.25E+07
1.00E+07
7.50E+06
5.00E+06
2.50E+06
0.00E+00
-10
-5
0
Approach Angle (Degrees)
5
Figure 6: Von Mises Stress Based on Approach Angle
10
As is evident by comparing the data in Table 4 and the Figure 6 plot, varying the approach
angle of the metal stud has a significant effect on the maximum stress applied to the surface
of the stud. This data from these seven cases can be interpreted as a depiction of the
stress behavior as the wheel rotates and each stud starts and stops coming in contact with
the road. This assumes that the tire is rotating in the counter-clockwise direction (i.e. the
car would be moving forward). The -10 degree position, shown in Figure 7, is when the
stud is just starting to come in contact with the road. As such the stress is initially
concentrated near the leading edge (i.e. the bottom right corner of the stud).
Figure 7: -10 Degree Stress Case
As the tire continues to rotate counter-clockwise, the approach angle goes to zero. As
this happens, the stress becomes more evenly distributed in the stud. This is evident
successively comparing Figure 7 through Figure 9.
Figure 8: -6 Degree Stress Case
Figure 9: -2 Degree Stress Case
When the approach angle is equal to zero, shown in Figure 10, the stress in the stud is
shown to be very close to equally distributed about the vertical center axis of the stud.
Figure 10: 0 Degree Stress Case
Once the tire rotates past the zero degree approach angle and starts to increase, the stress
concentrations now start to approach the bottom left edge of the stud. When the stud
being evaluated is about to rotate out of contact (as exemplified in the 10 degree case),
the maximum stress concentration is now clearly in the bottom left corner which now
must bear most of the load. Figure 11 and Figure 12 depict the transfer of stress
concentration from being equally distributed about the center axis to being heavily
concentrated towards the bottom left edge of the stud.
Figure 11: -6 Degree Stress Case
Figure 12: -10 Degree Stress Case
5. Conclusion
The results of this project show two very important phenomena with regards to the
stressing and wear of metal studs used in winter tires. The first phenomenon is that
depending on the approach angle, i.e. the angle of the bottom stud surface compared to
the road, the stresses can vary significantly. This is an important to consider because if
the stud continually comes in contact with the road primarily at an angle and increase in
localized stress and therefore wear can be experienced. This is especially important to
consider during stud installation. If the stud is not properly set into the tire, there is a
potential that for a greater than zero approach angle or for the stud to become dislodged
from its desired perpendicular position therefore forming an approach angle. The second
phenomenon is that even with proper installation and ensuring the stud surface can be
perfectly parallel with the road, the stud can still experience the varying stresses
associated with approach angles as the tire rotates and the stud comes into and out of
contact with the ground. This means that during the design and analysis of stud wear,
the designer must make sure to consider all of the possible approach angles when
evaluating stress and wear. Even though the stress pattern when the stud is parallel to
the ground is evenly distributed across the bottom edge and may not cause significant
wear, a potential could exist that the outer edges of the stud will wear faster due to the
increased stress concentration resulting from the approach angles as the tire rotates.
Although the results of this project shed light of two important aspects of tire wear, this
project does not fully evaluate this subject. The potential exists to expound and improve
upon the results presented herein. One way which these results could be expounded
upon would be to consider the cases where the road has asperities in it. This project
modeled the ideal case where the road was assumed to be perfectly flat. Although
possible and a valid case to evaluate, it is more likely that there will be debris on the
road or divots/indentations which would skew the analysis. This foreign material or
divots/indentations in the road, i.e. asperities, would affect the angle with which the stud
comes into contact with the road. By doing so, the stress concentrations would change
along with the wear patterns.
Another possibility to expound upon the evaluation
presented herein would be to consider both the friction as the tire and therefore the stud
rotates in and out of contact with the road and the adhesion between the road and stud.
Both of these additional forces could increase the wear rate of the stud and decrease the
performance capabilities of the stud.
6. References
[1]
Peal Race Tyres, "Kumho Tyres Motorsports; S700 Slick," 2011. [Online]. Available:
http://peakracetyres.com.au/products/s700-slick-2/. [Accessed 09 May 2015].
[2]
MW Motor Werke, "Winter Tires VS All-Season Tires," 2012. [Online]. Available:
http://www.motorwerke.ca/blog/winter-tires-vs-all-season-tires. [Accessed 09 May
2015].
[3]
eArio,
"Winter
Snow
Tires,"
[Online].
Available:
http://www.eario.com/winter_snow_tires.html. [Accessed 09 May 2015].
[4]
Tire
Rack,
"Winter/Snow
Tire
Tech,"
2015.
http://www.tirerack.com/winter/tech/techpage.jsp?techid=151.
[Online].
Available:
[Accessed
10
[Online].
Available:
May
2015].
[5]
Grip
Studs,
"Grip
Studs
Technical
Info,"
2012.
http://www.gripstuds.com/Info.php. [Accessed 12 May 2015].
[6]
General Carbide, "Introduction to the Designer's Guide to Tungsten Carbide," General
Carbide, Greensburg, 2008.
[7]
CoorsTek, "Durable Tungsten Carbide for Extreme Service Applications," CoorsTek,
Inc., Golden, 2014.
[8]
TireRack,
2015.
[Online].
Available:
http://www.tirerack.com/tires/TireSearchResults.jsp?tireIndex=0&autoMake=Kia&auto
Year=2012&autoModel=Forte+Koup&autoModClar=2.4L+SX&width=215%2F&ratio
=45&diameter=17&sortCode=49500&skipOver=true&minSpeedRating=S&minLoadR
ating=S. [Accessed 13 May 2015].
[9]
TireRack, "Tire Specs Explained: Tread Depth," 2015. [Online]. Available:
http://www.tirerack.com/tires/tiretech/techpage.jsp?techid=197. [Accessed 13 May
2015].
[10] L. A. Wood, N. Bekkedahl and F. L. Roth, "Measurements of Densities of Synthetic
Rubber," Journal of Research of the National Bureau of Standards, vol. 29, pp. 391396, 1942.
[11] Geosyntec, "Guidance Manual for Engineering Uses of Scrap Tires," Maryland
Department of the Enviroment, Baltimore, 2008.
[12] Roger Johnson Consulting Limited, "Construction Tables and Calculators (metric)," 19
April 2000. [Online]. Available: http://www.rjcsolutions.com/calculators/grav-den.htm.
[Accessed 13 May 2015].
[13] "Chapter
7;
Asphalt
Pavements,"
[Online].
Available:
http://www.citg.tudelft.nl/fileadmin/Faculteit/CiTG/Over_de_faculteit/Afdelingen/Afde
ling_Bouw/-_Secties/Sectie_Weg_en_Railbouwkunde/_Leerstoelen/Leerstoel_Wegbouwkunde/-_Onderwijs/_College_Dictaten/doc/CT3041_UK_Hoofdstuk_7.pdf. [Accessed 13 May 2015].
[14] E. R. Brown, P. S. Kandhal and J. Zhang, "Performance Testing for Hot Mix Asphalt,"
National Center for Asphalt Technology, Auburn, 2001.
[15] The Science Tool Box, "Mohs' Hardness Scale," Arden Services, 2004. [Online].
Available:
http://www.sciencetoolbox.com/articles/Mohs-Hardness-Scale.html.
[Accessed 14 May 2015].
APPENDIX A: Comparison of 0 Degree Model with and Without Tire
Pressure Boundary Condition
Case without accounting for tire pressure on lower tire boundary:
Case with tire pressure on lower tire boundary:
APPENDIX B: COMSOL Model Output Figures
-10 degrees:
- 8 degrees:
-6 degrees:
-2 degrees:
0 degrees:
2 degrees:
6 degrees:
8 degrees:
10 degrees: