Finite Element Analysis

Of a Skateboard Truck

2

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.

3

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

4

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 Repair’ function in ABAQUS.

Calculations

Assumptions:

• Maximum rider weight 250 lbs

• Elastic Deflection upon landing .1 in

• Relevant conical contact 1/3 area of inner cone

• Mass of Skateboard neglected

Circular Area

( )( ) 222

22

6597.2.5. in

Arr actCircleContholesolid

=−

=−

π

π

Conical Area

7

2291.415.3

104.23

104.2335.22

inininAhCininrC

tConeContac =⋅==⋅

=⋅== ππ

Normal Riding

psiin

lbsA

FP

psiinlbs

AF

P

lbsFlbslbsFF

lbsFinFlbsinM

lbsFF

lbsF

tConeContac

actCircleCont

Y

truckN

N

25.387291.

69.112

56.566597.

31.3769.112

031.3712531.37

0675.11255.

1252

250

21

1

23

3

1

1

3

31

===

===

=

=+−=

=

=⋅+−⋅=

==

=

∑

∑

8

One set of Wheels

All pressure on circular area

psiPin

lbsA

F

actCircleCont

N 96.3786597.250

32 ===

Impact Loading

psiinlbs

AFP

psiinlbs

AF

P

lbsFlbslbsFF

lbsFFlbsinM

lbsF

F

lbsin

inlbsd

mahF

xxavv

mvdF

tConeContac

actCircleCont

Y

impactpactTruck

impact

impact

180797291.

26306

64.339366597.

2238894.52611

0223887500022388

0675.1750005.

750002

1500001.

60250)(2

21

21

1

23

3

1

1

3

31

Im

02

02

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.

psiPpsiP

28.67837361594

3

1

==

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

0.0685

0.069

0.0695

0.07

0.0705

0.071

0.0715

0.072

1000

0

1600

0

2200

0

2800

0

3400

0

4000

0

4600

0

5200

0

5800

0

6400

0

7000

0

7600

0

8200

0

8800

0

9400

0

1000

0

1060

0

1120

0

1180

0

Number of Elements

Stra

in E

nerg

y

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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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