# Topology and Response Surface Optimization of a Bicycle Crank Arm with Multiple Load Cases
## 3 Results and Discussion
### Experimental Validation
Figure 21 shows the experimental procedure of the dynamic experiment. The bicycle is installed on a bicycle treadmill stand and a cyclist rides the bicycle as usual. The cycling load is obtained from the cyclist's foot during cycling in a low gear position. The average cycling speed is set to be 1 cycle/s or 60 rotations/min. Two types of cycling loads are applied. First, the load is applied only to the optimized crank arm which is placed on the left side of the crank as seen in the figure. The right-hand side crank arm is left to be rotated by itself without any load applied. The result of this experiment is shown in Figure 22 below. It is clearly seen that the stress value oscillates along the cycling period which indicates the maximum and the minimum stress value. Three maximum (peak) stresses indicated in the figure show the value of 2.31, 2.36, and 2.46 MPa, respectively. This also indicates that the multiple loads used in the simulation considerably match with practical situations and are possibly used for future dynamic investigation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**ANSYS Simulation (MPa)** & **Static Load Experiment (MPa)** & **\% Error** \\ \hline
1.078 & 0.98 & 8.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Static stress validation measurement. Figure 20: Static test result. The second type is the application of cycling load on both the left side (optimized) and right-hand crank arm. Now, the stress results considerably change in order to be multiplied since the crank arm suffers the cycling force from both pedals (see Figure 23). However, this inertial negative value from the other pedaling force is neglected here and our focus is merely on the pure positive pedaling force on the optimized crank arm. Even so, the maximum stress value indicated by the three-peak points in the figure shows a multiplying higher value. The maximum stress is 12.89, 12.91, and 13.46 MPa, respectively. It clearly indicates that the pedaling force gives a significant effect on the bike crank arm and plays a major role in cycling dynamics. For comparison, the experimental result of one arm operation from [PERSON] et al. [32] is plotted together with the author's present result in Figure 24. The maximum stress peak of the author obtained in Figure 22 at around 7 sec is replotted again in the form of a crank angle position by dividing one cycle experimental data into 0-180\({}^{\circ}\) angle evenly. Here, a normalized Von Mises stress is used in order to make an _apple-to-apple_ comparison between the two experiments since the experimental environment is not identical between each other. However, the comparison still can be made based on the normalized value to provide some useful insight. From [PERSON] results, the maximum cycling force occurs at around 60 to 120\({}^{\circ}\) crank angles shown by the stress peak at a 90\({}^{\circ}\) angle. While the author's result peak is obtained at the 120\({}^{\circ}\) angle. Even though the maximum stress from the author  
Figure 21: Dynamic load experiment. Figure 22: Dynamic test result (single crank arm operation). has a different position compared to [PERSON] et al. 's result, it can be seen that the overall Von Mises stress distribution has a similar pattern. This similarity does not only indicate that the present measurement procedure is considered acceptable, but also indicates the benefit of the optimized crank arm geometry. With considerably lesser mass and lighter material, it can provide similar performance with the conventional crank arm design. It can even be improved by choosing other materials with higher mechanical properties.