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Comprehensive SolidWorks Simulation Analyses for CAE Study of Consumer Skateboard

Team Huge Deflections Mohsin Farooqui 13043825 Saffi Khan 43363922 Maaz Syed 75287222

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Contents

Cover ................................................................................................................................................1

Contents ...........................................................................................................................................2

Purpose .............................................................................................................................................3

Closed Form Solution ......................................................................................................................5

Boundary Conditions for Analyses .................................................................................................6

Skateboard Deck Static Analysis .....................................................................................................7

Truck Static Analysis .......................................................................................................................9

Modal Analysis ............................................................................................................................. 11

Buckling Analysis ......................................................................................................................... 12

Nonlinear Analysis ....................................................................................................................... 13

Modes of Failure ........................................................................................................................... 14

Failure: Excessive Frontal Impact Load ....................................................................................14

Failure: Excessive Loading ........................................................................................................15

Fatigue S-N Curve ........................................................................................................................ 16

Defining Orthotropic Material ...................................................................................................... 17

Design Iteration ............................................................................................................................ 17

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Purpose The intent of this project is to simulate and understand the common operating conditions of a skateboard using SolidWorks Simulation software. Skateboards are commonly used for transportation, mainly by teenagers and young adults. They are ridden on both street pavement as well as on sidewalks and in skate parks. The design the team will be analyzing was developed by a member of GrabCAD, an online community distributing CAD models for similar use purposes. The assembly allows the team to analyze separate parts and analyze components individually.

The above drawings represent the model the team found online. Generally, competitors will employ similar materials and design schemes, as seen below.

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Figure 5: Pictures of Skateboards

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Closed Form Solution For a closed form solution we assume a cantilever beam which is simply supported. The length of the beam will be flat part of the board and we not consider end lips, which comes out to be 0.52 m. The force applied will be the weight of the rider, which the team will consider to be in the normal range of 100lbs to 200lbs with the extreme case of 300 lbs.

Figure 6: FBD of Simply Supported Skateboard

Table 1: Closed Form Solution Displacement

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Boundary Conditions for Analyses The team will incorporate various loading conditions for static analysis. These are shown below in the following free-body-diagrams. Figure 7 shows a free-body-diagram in which the boundary condition is simply supported on the truck bolts, and a total load of P is applied. The team will compare the result to that of Figure 9. The load is chosen as 180lbs because it is in the range of the 100lbs-200lbs that the skateboard experiences in normal condition, and one of the team member wanted to see how his weight impacts the skateboard.

Figure 7: Free-Body-Diagram 1 Simply Supported Fixture with 2-Point Loading

Figure 8: Free-Body-Diagram 2 Fixed Restraints with Distributed Loading

Figure 9: Free-Body-Diagram 3 Fixed Restraints with 2-Point Loading

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Skateboard Deck Static Analysis Static analyses were conducted with different materials: suggestions) and red maple wood (isotropic). The reason for using alloy steel as a comparison material was to show the better light-weight performance of the red maple relative to the alloy steel.

Figure 10: Stress Plot with Red Maple Material

FBD Diagram with Material of Red Maple (Isotropic)

Boundary Condition

Max Displacement [mm] from

FEA

Max von

Mises Stress [MPa]

Max Displacement [mm] from Closed Form

Solution

% Error

Simply Supported 0.886 47.6 0.865 1.73

Fixed 0.820 41.7 0.8 2.5

Fixed 0.523 38.3 0.51 2.5

Table 2: Data Results from Static Analysis for Red Maple Skateboard

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The factor of safety (FOS), which highlights the design safety of a model, can be calculated from the results of Table 2 for red maple wood.

The FOS range of 1.11-1.38 definitely shows the safety of the design of the skateboard in terms of yielding to large loads.

FBD Diagram with Material of Alloy Steel

Boundary Condition

Max Displacement

[mm]

Max von Mises Stress

[MPa]

Simply Supported 0.0515 52.76

Fixed 0.0463 45.44

Fixed 0.0302 41.31

Table 3: Data Results from Static Analysis for Alloy Steel Skateboard

Based on Figure 10 and Tables 2-3, the stress and displacement results are valid, because the expected deformation of a skateboard under a normal scenario will be minutely small. If a result where the displacement was 50mm (roughly 2 inches) was reached, then there would have been a problem in either the fixture or load definition, which would require a nonlinear analysis because of large deformation. The stress results also make sense because it is expected that the maximum stress produced be lower than the yield strength. Little deformation and stress accumulation were expected when applying a total load of 800 N.

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Truck Static Analysis Static analysis was applied on the truck, because it is an integral part of the skateboard: it holds the skateboard deck to the wheels. Moreover, the analysis was simulating dropping the truck from different heights to illustrate how the stress is distributed on the structure when it hits the ground and the ground transfers a force equal but opposite to the truck. Height of 1ft, 5ft, and 20ft were applied in which the forces were calculated as seen below. The heights of 5ft and 20ft are considered extreme cases. Assumptions

o mTRUCK = 0.05521 kg o Mass of other skateboard components is negligible o Truck is released from height, H, with zero initial velocity ( vO = 0 m/s )

Use Conservation of Energy to find impact velocity, vIMPACT.

Use Impulse to find force, FIMPACT.

Figure 11: FBD of Truck in Drop Test

Conservation of Energy (H = 1 ft.)

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Impulse Over 0.1 s Time From vIMPACT

Values of FIMPACT for H = 5, 20 ft. can also be calculated using this same procedure.

Figure 12: Truck Static Analysis from H = 20 ft.

Scenario Load [N] Max

Displacement [mm]

Max von Mises Stress

[MPa] H = 1 ft. FImpact = 1.42 1.016*10-5 0.2 H = 5 ft. FImpact = 7.1 5.078*10-5 1.1 H = 20 ft. FImpact = 28.4 2.031*10-4 4.5

Table 4: Drop Test Result for Truck Static Analysis Using Alloy Steel (Yield = 620.4MPa) as the material composing the truck, the analysis are valid and something the team expects. The reason for this is because even though the truck is being released from H=1ft, 5ft, and 20ft, the team expect the smallest deformation and von Mises stress to be the 1ft drop test, and for the other cases, be a factor of multiple from the 1ft drop test. Low deformation and below yielding confirms the linearity of the problem which is further enhanced by the results.

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Modal Analysis In order to ensure that the rider is safe from severe vibration during operation, we performed a modal analysis on the skateboard deck to determine resonant frequencies.

Figure 13: Mode of Vibration 1 of Skateboard Deck (Red Maple)

Figure 14: List of Resonant Frequencies The resonant frequencies are very high and that is something that the team expected because under the normal riding conditions, the board will never resonant.

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Buckling Analysis Buckling analysis calculates the critical failure loads of slender structures under compression. In the simulation, the long, thin direction of the skateboard is applied with a frontal impact load.

Figure 15: Buckling Analysis for Red Maple Material with 3rd Mode Number

The buckling plot for the 3rd mode number when a frontal load of 45N is applied. This force is calculated using the impulse formula F = m*delta(v)/delta(t) in which the mass of the skateboard is 0.837kg, the normal speed of a skateboard is 15mph, and the impact time is 0.1s.

Table 5: BLF for Skateboard Deck with Red Maple Material

Table 5 shows the BLF (buckle factor safety) and it suggests that the skateboard will not buckle since BLF for mode 3-6 are greater than 1. Modes 1 and 2 are negative suggesting that the load must be applied in the opposite direction, and therefore, have no significance. Based on fundamental mechanics of materials, wood is a brittle material that hardly under goes any plastic deformation which means that no buckling will happen as is proven with the BLF table.

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Nonlinear Analysis

Simulation. The intent of this analysis is to understand how the board deforms through large displacements by analyzing the stresses and the deformation structure. Mesh quality of 5mm element sizes was used in this analysis.

FBD Max Displacement [mm] Max von Mises Stress [MPa]

Yield Strength [MPa]

Applied Load

0.7687 62.19 53 300lbs (1334N)

Table 6: Nonlinear Static Analysis Results

Figure 16: Nonlinear Static Analysis Stress Plot

As expected, the maximum von Mises stress passes the yield strength. However, it is important to note that the material defined is isotropic in nature. Also notice the maximum displacement seen in Table 6 is the highest among the static skateboard deck analysis at 0.7687mm due to the

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Modes of Failure The team expects that the skateboard may show crack if a high enough force is applied, however, issues such as reactive environment or temperature will not produce any failure because the board is highly unlikely to experience these factors. Also, even though skateboards are expected to last for a long time, with wear and tear from excessive years may cause fracture. Failure: Excessive Frontal Impact Load For example, the frontal impact scenario is important to consider because often times a skateboard hits a wall and understanding how the stress distributes can help the team design a better version of the skateboard. The calculation of determining the force exerted by the wall onto the skateboard is as followed:

A 45N was applied to the frontal part of the skateboard. Normal riding conditions favors a speed of 12 mph (5.37 m/s). Based on research, the normal speed range is between 5mph-15mph, therefore, the team decided to use scenarios of 22 mph and 40 mph to simulate the how the skateboard will deform and the stresses associated with it. Table 7 summarizes the results and Figure 17 shows the stress plot of the skateboard under the 45N loading. Please note that for a speed of 40mph, the impact time was halved to obtain a high load.

Figure 17: Stress Plot of Frontal Loading 45N

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Speed [mph] Time of Impact [sec] Force of Impact

[N]

Max Displacement

[mm]

Max von Mises Stress [MPa]

12 0.1 45 0.08496 2.3 22 0.1 187 0.3531 9.6 40 0.05 300 0.5664 15.4

Table 7: Results of Frontal Impact Loading with Worst Case Scenarios The results are valid because when a rider slams their skateboard into the wall, there is little deformation occurring which is seen in the table, and the maximum stress must be lower than the yield strength because the skateboard should not snap if a rider is going downhill and reaches speed of 40mph. Failure: Excessive Loading Another mode of failure presented is the excessive load placed on the deck of the skateboard. Currently, many of the static analysis were carried out with a load of 180lbs to simulate a

However, the team decided to go past the normal riding range of 100-200lbs weight, in order to assess if the skateboard deck breaks and understand if the deck can support such weights. The weights chosen were 300lbs and 400lbs, and below is a figure of the result for the 300lbs scenario and a table that summarizes the results.

Figure 18

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Weight [lbs.] Max Displacement [mm] Max von Mises Stress [MPa] 180 0.2317 22.72 300 0.3882 40.86 400 0.5041 53.01

Table 8: Results for Over Loading Skateboard Deck From the above plots, the team views that a 400 pound user cannot be accommodated by the skateboard without failure. However, it is important to note that in actuality, the board will be able to accommodate such a result because the skateboard is made of epoxy resonant that is layered thereby increasing the strength of the deck. Furthermore, the analysis was conducted with red maple wood assuming that it was isotropic material. Fatigue S-N Curve For comparison purposes, S-N curve of Alloy Steel is used. The max stress from the simulation is 24.15MPa (Table 3), and the team expects a total number of cycle (N) of 36,500 (with an assumption of 20 cycles/day for a max usage of 5 years).

Figure 19: SN Curve

Based on Figure 19, the skateboard will not experience crack with the number of cycles and max stress specified as it is far below the SN curve for steel.

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Defining Orthotropic Material The team was unable to simulate a static study where orthotropic material was defined because of the unavailable resources on the topic either online or meetings with the professor. However, the team expects a great reduction of stress once orthotropic material is defined. Design Iteration The team noticed high stress buildup near the bolt area, and to combat this, the team decided to increase the radius of fillet on the boundary of the bolt hole as seen in the following figure.

Figure 20: Before and After with Fillet