DESIGN AND ANALYSIS OF THE STEM TUBE OF THE BIKE (Part 2)
5. Meshing
As the model are not so wide or complex, therefore, we have the luxury to use fine meshing so we will get more accurate results, and the calculations will not take much time. See figure 4.
Table 2 shows the mesh parameters for the used mesh for the initial solution.
Mesh type
|
Solid Mesh
|
Mesher Used
|
Standard mesh
|
Automatic Transition
|
Off
|
Include Mesh Auto Loops
|
Off
|
Jacobian points
|
4 points
|
Element size
|
5 mm
|
Tolerance
|
0.25 mm
|
Mesh quality
|
High
|
Total nodes
|
26158
|
Total elements
|
15715
|
Maximum Aspect Ratio
|
16.117
|
with Aspect Ratio < 3
|
97.5
|
with Aspect Ratio > 10
|
0.121
|
(Jacobian)
|
0
|
Remesh failed parts with incompatible mesh
|
Off
|
Time to complete mesh(hh:mm:ss)
|
0:00:03
|
Table 2
6. Initial Solution
Now, the model is prepared for solution. In the initial solution, the thickness of the main body tube is used as 8mm as initial thickness. Then, the model will be solved to check if it satisfy the requirements or it needs some adjustments. The analysis will be made for Von-Mises stresses, displacement of the deformation and for the factor of safety that should not be below 2.5. As this solver is approximate solver and the model not very big, therefore the meshing not big, the time for the analysis was very fast. It takes approximately 7 seconds. The following is the results for the initial solution.
6.1 Von-Mises Stress Result
Figure 5 shows the initial Von-Mises stress result. The figure is viewed with a deformed shape with a scale of around 20 time comparing to the actual deformation. The results show maximum stress at the root of the main body tube with a value of 111 MPa, this value is far lower than the yield stress, therefore, the body will deform in the elastic region of the elasticity curve so there will not be a failure in the body at this point of tube thickness regarding to this analysis. In addition, the results show minimum stress at the flat plat which is the tip of the body. Therefore, the results show reasonable values.
If the results are checked transversally (figure 6), they will show max. stress above and lower a neutral region. The should be a neutral line passing through the center of area point where the stresses will equal zero and the above stress is tensile and the lower is compressive, therefore, the result is consistent with bending stress force, and the stem can be dealt as a cantilever beam.
6.2 Displacement results
Figure 7 is viewing the displacement result with the same deformation scale of 20. The result shows displacement of zero value at the root of the main body which is a fixed area. In addition, the result show a maximum value of around 1.24 mm at the tip of the part where the flat plate exists, the result shows a good value as the lower displacement will make the rider does not feel it so it will not affect the bike function. This result also supports the idea of cantilever similarities and application of bending force. There result also shows that the flat plat does not leave or move respect to the main body, therefore, the chosen type of bolts are doing it function very well.
6.3 Factor of Safety Result
The factor of safety is shown in figure 8. The results shows that the root of main body where the fixation and the tip have bulk of materials as the factor of safety exceeds 15. The minimum factor of safety is at the root of the tube where the value of maximum stress exists, the value of it is around 2.4 which is lower that the required factor of safety of 3.7. Therefore, the initial value for tube thickness (3 mm) will be rejected and optimization method of trials and errors will be done till reaching the requirements.
7. Optimization
A trials and errors technique will be done till reaching the optimum tube thickness. The initial thickness of 8 mm gives higher result of factor of safety than the required, therefore, the thickness will be decreased with a step value of 0.5 mm till reaching. While each trail, the mesh will be recreated and the results will need to be resolved. A tangency relation between the hole in the plate and the hole of the tube are added so its diameter will be updated automatically (figure 9).
The next table shows the results of the optimization process till reaching the final results.
trial
|
thickness (mm)
|
total nodes
|
total elements
|
max. stress (Mpa)
|
factor of safety
|
1
|
8
|
26158
|
15715
|
111
|
3.7
|
2
|
7.5
|
25923
|
15533
|
113
|
3.67
|
3
|
7
|
25328
|
15090
|
116.8
|
3.556
|
4
|
6.5
|
26238
|
15638
|
115.6
|
3.59
|
5
|
6
|
25851
|
15363
|
120.3
|
3.45
|
6
|
5.5
|
24335
|
14208
|
125.9
|
3.297
|
7
|
5
|
23402
|
13507
|
132.5
|
3.13
|
8
|
4.5
|
22737
|
13020
|
140.1
|
2.96
|
9
|
4
|
23856
|
13699
|
146.7
|
2.83
|
10
|
3.5
|
23525
|
13433
|
158.2
|
2.62
|
11
|
3
|
23454
|
13379
|
173.9
|
2.38
|
Table 3
The Previous table shows that the best result is between 3.5 and 3. We will try other optimization trails by changing the material of the stem (table 4)
thickness
|
material
|
Yield stress (Mpa)
|
FOS
|
4
|
2014-T6
|
415
|
2.8
|
4
|
2024-T3
|
345
|
2.3
|
4
|
2024-T361
|
395
|
2.6
|
3.8
|
2024-T362
|
395
|
2.561
|
3.6
|
2024-T363
|
395
|
2.446
|
3.7
|
2024-T364
|
396
|
2.51
|
Table 4
The table shows the best result at thickness of 3.7 mm using 2024-T364 as a material for the steam.
8. Final solution
In this section the final result of the optimized design with tube thickness of 3.7 mm is shown.
8.1 Final Von-Mises stress results
With a deformation scale of 20, figure 10 shows the Von-Mises result for the optimized design. As expected, due to the thickness decrease in main body tube, the stress maximum value is slightly increased to reach a value of around 157 MPa. However, the position of it is still in the same place at the root of the tube. In addition, the minimum stress is still at the tip of the stem where the flat plate exists. Transversely, the position of neutral region does not changed as the distribution of mass is not changed transversely.
8.2 Final Displacement Results
The maximum displacement is still at the tip which is the free end. Its value is decreased very slightly to 1.74 mm. This value is still low so it will not affect the bike functions. Figure 11 shows this discussed result with a deflection scale of 20 as usual.
8.3 Final Factor of Safety results
After the trials and errors process the factor of safety of 2.5 is reached as shown in figure 12. The minimum value is still at the tube root where the maximum stress exists. The value is linearly increasing till reaching large value (exceed 15) at the end of the tube. Transversely, the result at the neutral region exceeds 15 as the stresses at this region is very low almost zero. The results at the ends of the stem are very high (more than 15), therefore, this parts is very stiff with material and its shape can be optimized.
9. Verification
The hand calculations will be done at the end of the tube where the maximum stress exists. Then, this value will be compared with output results from the simulation so we can verify the correction of the results.
The moment of area and maximum height will be calculated using section properties tool in the Solidworks.
The error percent seems to be big, however, the hand calculations have many assumptions as it considers it is pure bending and ignore the other torsional effects. So, the result is acceptable.
10. References
SOLIDWORKS Simulation. (n.d.). (SOLIDWORKS ) Retrieved from https://www.solidworks.com/product/solidworks-simulation
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