ROLL CAGE: FINITE ELEMENT ANALYSIS
overview
Final Design FEA
Design 2-2 FEA
Design 1
Final Design FEA
Through 3 different design iterations, a finite element analysis (FEA) was conducted to ensure safety requirements are fulfilled. Analyzing how top, side, and backwards impacts effects the roll cage helped create future iterations of the design. Most elements that experienced the highest amount of force are the edges/points, which was indicated by red. The Upper bound axial and bending side help ensure that the design is staying within the ultimate yield strength where we want to be below the yield strength to ensure there is not permanently/plastic deformation during an impact. Overall, based on the results of the FEA, certain sections of the roll cage was changed to compensate for the high impact result at a specific section, leading to a final design.
Specifications:
Mass of Solar Car = 250 kg
Gravity = 9.81 m/s^2
5g of Force Applied = 12262.5 N
Ultimate Yield Strength = 4.60x10^8 N/m^2
Design Iteration #1:
Technical Skills Developed: Finite Element Analysis
The simulation must fulfill 5g of force in every direction to ensure the roll cage is safe. The stress of each of the simulation must not go beyond the indicated yield strength. The yield strength indicates the point where it changes from an elastic to a plastic deformation. A large yield strength indicates the model can withstand a high amount of stress without any permanent deformation. The scale on the results indicate the range of stress the model experiences. If an arrow is shown on the scale, the model will go through plastic deformation, as the stress experienced is above the ultimate yield strength. Additionally, how the model deforms will be taken into consideration to ensure the deformation post a roll over will not affect the driver in a harmful way.
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Top Impact:
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Large deformity which can negatively affect driver
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Driver Seat only slightly placed inside of roll cage
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Top impact results in downwards deformation
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Coincide with driver’s helmet = not safe
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Max. Stress: 3.222x108 N/m2
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Max. Stress < Ultimate Yield Strength
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Test Success
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Improvement: Although the FEA test was successful in terms of yield strength; the deformation is not ideal therefore; this model can not be considered safe
Side Impact:
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Large concentrated stress located at joint between the arch and vertical beam
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Max. Stress: 4.945x108 N/m2
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Max. Stress > Ultimate Yield Strength
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Joints experience plastic deformation
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Test Failed
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Improvement: The maximum yield strength is only slightly above the ultimate; adding additional supports to help disperse force may help reduce the yield strength it experiences
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Front Impact:
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Slight deformation towards the back
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Large stress concentration at the top two points on the arch of roll bar
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Max. Stress = 6.928x108 N/m2
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Max. Stress > Ultimate Yield Strength
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Test Failed
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Improvements: Adding supports disperse the force at the top and allowing the force to be diverted to different directions
Summary of Design Iteration #1:
From the last design a few points to reconsider:
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There is a large concentrated stress at the corner of the roll bar. Adding other supports connecting to the cage may reduce the force to be concentrated at that point
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There’s not much room for safety of passenger. Especially for the deformation of a top impact. This will create a large danger to the driver’s head as since the seat won’t fit into the roll cage itself which hinders the use of a roll cage.
In summary, some points to consider is adding an upwards lift at the back-supporting bars. This will allow the driver’s seat to be moved into the roll cage which will therefore allow the driver to be fully enclosed around the roll cage. As well as adding additional supports to disperse any concentrated force at a joint.
Design Iteration #2:
Added Component:
An upwards lift in the back-support bars were added. This lift consists of a rectangle-like shape for a direct 90 degrees vertical lift. This allows the roll cage to include more space internally allowing the seat to be immersed more into the cage.
Summary of Design Iteration #2:
The table above compares the maximum yield strength of the first design alternative to the second. The second design improved the results for the top and front impact. The deformity in each simulation was less intense than the first one; however, the side impact resulted in a greater maximum yield strength than the first design. Overall, of all the impact tests went beyond the ultimate yield strength except for the top impact.
The high concentrated force in each simulation showed similar results from the first design showing that additional supporting beams may be needed or a more drastic change in the design must be prompted.
Final Design:
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Summary of Final Design:
From the results, the maximum yield strength achieved for the top, side, front and back impacts, are all less than the ultimate yield strength of 4.6x108 N/m2. This fulfills the requirements for the roll cage as the minimum 5g of force (12262.5N) can be applied without causing permanent deformation. Permanent deformation is not the ideal situation for drivers, as in an event of a roll over, the roll cage must be able to withstand any impact force and protect the driver in all directions.
The results are realistic because comparing the results of the final design and the first two iteration designs; the force is more equally distributed as there are more supporting roll bars to help disperse any concentrated force. More supporting beams allows the maximum yield strength to decrease as less elastic deformation is experienced. At areas experiencing the highest amount of stress (indicated in red), the force can diverge out to the different beams. In an event of a roll-over, the impact force would not be directed right at the joint; an impact would involve the area the joint covers which would be expecting stresses less than what is shown on the FEA because the impact force is applied in a larger area.