Finite Element Analysis
Of a
Skateboard Truck
Executive Summary:
Engineering is and always has been an integral part of the sporting scene. This
can be seen in nearly all sports since their conception. Downhill skis have gotten
faster, Lacrosse sticks have gotten lighter, Adidas even has a pair of shoes that
adjusts the cushioning according to a small microchip. There is no limit to what
can be improved upon. This report strives to analyze the forces present on the
baseplate of a skateboard, which is an element of the ‘truck,’ which holds the
wheels. Finite Element analysis will be conducted on this piece using a number
of calculated forces and contact pressures representative of a skateboard being
ridden normally, on one set of wheels, as well as an impact from 5 ft in the air.
After viewing the results of the analysis, an impact from 10 ft in the air was also
calculated.
The analysis for this piece was done using a combination of SolidWorks (for
modeling) and ABAQUS (for finite element analysis). It is evident from the
results that stress concentrations do not get very intense in this structure, which
leads to the conclusion that a strategic re-design of this baseplate could save on
material as well as expense. This strength could also potentially be sacrificed for
weight, which could lead to easier manipulation of the board while in use.
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Table of Contents
Cover Page……………………………………………………………………...…………1
Executive Summary………………………………………………………….…..………..2
Table of Contents………………………………………………………………...………..3
Introduction………………………………………………………………………………4
SolidWorks Modeling……………………………………………………………………5
Finite Element Model……………………………………………………………………6
Model Importation to ABAQUS…………………………………………………...6
Calculations……………………………………………………………………….6
Loading……………………………………………………………...…………….8
Constraints………………………………………………………………………...9
Finite Element Analysis and Results……………………………………………………9
Conclusions…………………………………………………………………………...…11
Appendix A……………………………………………………………………………...13
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Introduction:
This project strives to understand the stress present in the baseplate of a
skateboard through computer aided finite element analysis. The baseplate is
constructed of aluminum with a Young’s Modulus of 1E7 (in lbs)/in 2 and a
Poissons ratio of .3. First, it is relevant to understand exactly where this
component fits in to the assembly of a skateboard and the types of forces that the
piece withstands during regular use.
Figure 1 – Assembled Truck
Figure 2 –Separate Baseplate
The baseplate withstands forces from the ‘hanger,’ or the axle piece. These forces
are transferred through two small pieces of rubber, which allows for slight
flexibility in the hanger and the ability to steer a skateboard. This results in two
pressures being applied to the baseplate in different magnitudes.
There are a number of variables that should be brought to light considering the
analysis of this piece. It should be noted that this analysis was not done for all the
potential forces that could be incurred by this piece due to the sheer volume of
skateboarding tricks that exist. In addition to this, the baseplate of the trucks
modeling in this analysis are bottom of the line components. The major
difference in trucks seems to be the weight, material (some materials are better for
grinding tricks because they slide better), and center of gravity (which makes the
board easier to flip in the air). The only of these issues relevant to this analysis is
the material due to Young’s Modulus and Poissons’ Ratio. Lastly, the forces and
pressures present on the baseplate are hardly static. The analysis done here was
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done for the most extreme of the considered conditions (assuming the rider of the
skateboard was 250 lbs, heavy for the typical skateboarder) in attempt to get the
most accurate results without the use of dynamic loading.
SolidWorks Modeling:
SolidWorks 2005 was used in the modeling of the baseplate due to the ease of use
and the ability to import .igs files into ABAQUS. While this later proved to offer
some difficulties, such problems will later be discussed with other conclusions.
The modeling of this piece turned out taking significantly longer than originally
thought. The piece was measured in English units using a set of digital calipers,
accurate to .001”. Modeling of the baseplate began with the thin metal extrusion,
followed by two separate lofts to create the basic profile for the plate. Additional
loft-cuts, extruded cuts, fillets, as well as some other minor details were added to
produce the final product seen here.
Figure 3 – CAD Model of Baseplate
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Finite Element Model:
The construction of the finite element model consists of a number of steps. First,
the model must be inserted into ABAQUS in order to create a mesh and perform
the analysis. Calculations must be performed in order to determine the forces
applied during analysis. All calculations were done in English units, simply
because the part was originally modeled in English units. Forces and applicable
pressures for 3 situations have been calculated and modeled including data
analysis with an increasing number of elements in the mesh to display
convergence. The issues of loading and constraints will also be discussed.
Model Importation to ABAQUS
In order to properly import the model from SolidWorks to ABAQUS, the file
must be saved in SolidWorks as a ‘.igs’ file. Problems were experiencad duing
the importation due to the part being ‘invalid.’ This means that some of the edges
and intersections were not modeled friendly to the mesh algorithm that ABAQUS
uses to analyze the system. With some help from the TA, this problem was
eventually overcome using the ‘Tools Æ Repair’ function in ABAQUS.
Calculations
Assumptions:
•
Maximum rider weightÆ
250 lbs
•
Elastic Deflection upon landing Æ
.1 in
•
Relevant conical contact Æ
1/3 area of inner cone
•
Mass of Skateboard neglected
Circular Area
π (r 2 solid − r 2 hole ) = ACircleContact
π (.5 2 − .2 2 ) = .6597in 2
Conical Area
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C = 2πr = 2π ⋅ .335in = 2.104in
C
2.104in
⋅ h = AConeContact =
⋅ .415in = .291in 2
3
3
Normal Riding
FN = 250lbs
FN
= Ftruck = 125lbs
2
∑ M 1 = .5in ⋅ −125lbs + F3 ⋅1.675in = 0
F3 = 37.31lbs
∑F
Y
= F1 − 125lbs + 37.31lbs = 0
F1 = 112.69lbs
P3 =
P1 =
F3
ACircleContact
F1
AConeContact
=
=
37.31lbs
= 56.56 psi
.6597in 2
112.69lbs
= 387.25 psi
.291in 2
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One set of Wheels
All pressure on circular area
FN
ACircleContact
=
250lbs
= P3 = 378.96 psi
.6597in 2
Impact Loading
1 2
mv
2
+ 2a ( x − x 0 )
Fimpact d =
v 2 = v0
2
mah 250lbs ⋅ 60in
=
= 150000lbs
d
.1in
Fimpact
FTruck Im pact =
= 75000lbs
2
∑ M 1 = .5in ⋅ −75000lbs + F3 ⋅ 1.675 = 0
Fimpact =
F3 = 22388lbs
∑F
Y
= F1 + 75000lbs − 22388lbs = 0
F1 = 52611.94lbs
P3 =
P1 =
F3
ACircleContact
F1
AConeContact
=
22388lbs
= 33936.64 psi
.6597in 2
=
26306lbs
= 180797 psi
.291in 2
Extreme Impact Loading (10 feet)
P1 and P3 from the other impact loading is simply doubled for the
difference in a 5 to 10 foot drop.
P1 = 361594 psi
P3 = 67837.28 psi
Loading
The loading in this element was reasonably straightforward, with the only major
assumption being that pressure in the conical area of the baseplate loading took
place on the bottom third of the circumference of the surface. The only other
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loading area for the element was the circular area (with a hole) at which loading
was assumed to be distributed evenly. Again, while the loading of this element in
reality is far from a static loading, the potential dynamic loading for this element
will not be discussed in this project paper.
Constraints
The constraint that was applied for this element was simply the bottom face of the
baseplate in all directions. In reality, the element is screwed in to the board;
however, the horizontal forces present in this piece are negligible to its overall
function.
Finite Element Analysis and Results:
After the finite element analysis was completed in ABAQUS, it became clear that
the only scenario that had any noticeable affect on the baseplate (on the finite
element level) was the impact loading. This, however, still did not have as large
as an affect as was anticipated. Therefore, the height from which the impact
initiated was doubled in order to see a larger loading. In order to not be repetitive
in information, the only analysis that will be covered in depth is the impact
loading from 10 feet with a rider of 250 lbs. Pictures for the other analysis steps
can be seen in Appendix A (low element number of ≈ 20000 elements).
Stress distribution (as seen in Figure 6 and 7) was reasonably smooth as the piece
has few right angles (or close to 90o) and a reasonable amount of fillets. Stress
was highest in the element towards the bottom of the conical region, which was
taking a large majority of the force exerted on the piece over a smaller area.
However, this is not of concern due to the location of the stress, which is only
separated from the constrained region by a thin section of aluminum. It should
also be noted that these stress concentrations do not come close to a dangerous
level of stress for aluminum. While the conical region of the piece has the highest
stress concentration, the area of more interest is the base of the circular loft near
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the rib. Even with the rib there, there is a noticeable concentration of stress in this
region. This makes sense physically due to the slight angle of the lofted surface
itself and the normal forces creating pressures on that surface. In other words, it
seems as if this rib is more crucial to the design than the average person could
know. Here are two figures representative of the Von Mises stresses occurring
due to the impact loading of a 250 lb rider from 10 feet in the air.
Figure 6 – 250 lb Rider, 10 foot impact loading, Isometric View
Figure 7 – 250 lb Rider, 10 foot impact loading, Top View
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Analysis was also performed to show that convergence occurred. This helps to
show that the finite element analysis is truly a accurate model of elemental
stresses. Six mesh sizes, ranging from 10000 elements to 120000 elements were
graphed with their total strain energies below. As one can see, the graph
approaches a finite solution logarithmically with an increasing number of
elements.
Strain Energy Convergence
0.072
0.0715
Strain Energy
0.071
0.0705
0.07
0.0695
0.069
Number of Elements
Figure 7 – Strain Energy Convergence
Conclusions:
While it is evident that this analysis does not show every possibility for stress
concentrations in this element, I do believe that it is safe to say that this piece is
over-designed. Perhaps innovations in material choices or even more optimal
designs could be done (and have been, compared to this cheap set of trucks) to
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11800
11200
10600
10000
94000
88000
82000
76000
70000
64000
58000
52000
46000
40000
34000
28000
22000
16000
10000
0.0685
increase the performance, as well as the weight of these trucks. If I were to do
this analysis over again, I would most likely choose not to import from
SolidWorks to ABAQUS, as it caused difficulty in the ‘validity’ of the baseplate.
In the future, I would prefer to use one program for the entirety of the modeling
and analysis. In closing, I’d like to admit that this project was originally intended
as an assembly, considering the entire truck as opposed to just the baseplate.
Unfortunately, a day and a halfs’ worth of work was squandered in attempt to
make model the hanger. In one last valiant attempt to hope that efforts were not
completely wasted, I have included a picture of the model with the loft that did
not want to execute. It makes me shed a tear.
Figure 8 – The hanger that wasn’t meant to be
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Appendix A:
Figure A.1 – 250 lbs Rider, Normal Riding, Isometric View
Figure A.2 – 250 lbs Rider, Normal Riding, Top View
Figure A.3 – 250 lbs Rider, Riding on one Set of Wheels, Isometric View
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Figure A.4 – 250 lbs Rider, Riding on one Set of Wheels, Top View
Figure A.5 – 250 lbs Rider, Impact from 5ft, Isometric View
Figure A.6 – 250 lbs Rider, Impact from 5ft, Top View
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