# Topology and Response Surface Optimization of a Bicycle Crank Arm with Multiple Load Cases
## 3 Results and Discussion
### Experimental Validation  
Figure 18a below shows the three-dimensional model result from 3D printing. The model is taken from the optimization result (Figure 12a, coarse model, compliance minimization by 50% mass constraint). This model has a similar performance to the fine mesh model in terms of the value of compliance and also offers the simplest fabrication to avoid geometry limitation in the 3D printing process. The geometrical result from the 3D printing is quite precise and acceptable, yet, the surface roughness might have a little difference with the CAD model due to the PLA fiber fabrication process. The effect of the surface roughness is, therefore, excluded from the discussion. However, during strain gauge placement, the surface has been smoothened by using sandpapers to avoid noise and measurement bias due to roughness issue. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Topology**} & \multicolumn{2}{c}{**Response Surface**} & \multirow{2}{*}{**Reduction (\%)**} \\  & & **Optimization (MPa)** & & **Method (MPa)** \\ \hline \multirow{4}{*}{Compliance Minimization} & 30\% Mass constraint & 127.5 & 126.4 & 0.80 \\ \cline{2-5}  & 40\% Mass constraint & 105.8 & 105.7 & 0.10 \\ \cline{2-5}  & 50\% Mass constraint & 91.09 & 71.2 & 21.8 \\ \cline{2-5}  & 60\% Mass constraint & 85.01 & 71.4 & 16.0 \\ \hline \multirow{2}{*}{Mass Minimization} & 80\% Stress Constraint & 92.0 & 87.2 & 5.21 \\ \cline{2-5}  & 90\% Stress Constraint & 133.6 & 133.3 & 0.22 \\ \hline \multirow{4}{*}{Compliance Minimization} & Uphill Angle Case 1 & 101.3 & 99.9 & 1.38 \\ \cline{2-5}  & Uphill Angle Case 2 & 115.9 & 113.9 & 1.72 \\ \cline{2-5}  & Uphill Angle Case 3 & 124.3 & 120.3 & 3.21 \\ \cline{2-5}  & Carbon Fiber & 187.8 & 186.2 & 0.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Maximum equation Von Mises stress comparison. Figure 18b shows the strain gauge installment on the crank arm, as well as the Arduino Nano package. The placement of the strain gauge follows the maximum stress resulting from the simulation result, as discussed in the previous subsection. It has been known that it is located at the bottom of the narrow section of the topological hole near the crankshaft hole. In order to be able to read the stress data more accurately, the strain gauges are placed using the Rosette arrangement, as seen in Figure 19.  
From the figure, it is seen that this arrangement provides a simpler and tidier measurement compared to the previous work [24] since only less electric cables are involved. Moreover, the wireless connection provides a more effective and convenient procedure for both static and dynamic measurements. The validation process is conducted using 1 kg weight as a static load given to the crank arm in the horizontal (0\({}^{\circ}\)) position. The crankshaft is set to be fixed at this position so that  
Figure 19: The Rossette strain gauge. Figure 18: (**a**) Three-dimensional (3D) printing result, (**b**) strain gauge, and Arduino installation. the stress data from the strain gauge can be processed by the Arduino Nano. This measured data is then compared with the result from ANSYS simulation using the same static load of 1 kg weight. The strain gauge measurement has been calibrated before the experiment that the static test is conducted to ensure the experimental process. The measurement time is conducted for about 1 min to get a steady-state reading from the strain gauge. The obtained stress range is between 0.983 to 0.989 MPa. For clearer observation, Figure 20 shows the overall result of the static test result from 0 to 70 s. If we take an average of this stress as 0.98 MPa, the percentage error between simulation and experimental result is only around 8% as provided in Table 6. Therefore, it can be said that both simulation and static validation experiment shows considerable agreement and can be validly used for further investigation. In order to enhance the discussion, the dynamic test result has also been obtained.