## 4 Design Optimization
### Results of Optimal Design and Verification  
For efficient design, the design of experiments (DOE) was used. A meta-model was created first to explore the design area, which requires a large number of analyses, and to proceed with an optimal design. In order to create a meta-model with PIAnO, which is integrated optimal design software, an orthogonal array enables efficient design and analysis with only a small number of experiments among various experimental design methods. As shown in Table 5, the design variables were defined as three factors related to the holes in the rotor and one ventilation blade that helps improve the internal heat dissipation performance (shape of holes, number of holes, diameter of holes, and diameter of ventilation blades), and each design variable was defined to have three levels. \[\text{min}\bigg{[}\frac{(ndv+1)(ndv+2)}{2},\ 100 ndv\bigg{]}+[5 ndv]<number\ of\ data \tag{8}\]  
\(ndv\) is the number of design factors. \[\text{min}[total\ of\ data\cdot 10\%,\ 10 ndv] \tag{9}\]  
The test points to be used in the meta-model were derived through the standards provided in PIAnO [21]. The standard for use of the test points is shown in Equation (8), and the selection of the number of test points is shown in Equation (9). The number of data (81) and the number of design variables (4) were substituted into Equation (8) to calculate the number of design factors, and the smallest value was selected among the resulting  
values. As the selected value was identified to be smaller than the number of data, the test points can be used. Thus, eight test points were created. The initial finite element model was modified to fit the design variables, and structural and thermal analyses were carried out in ANSYS. It was also repeated to derive the stress and temperature. For orthogonal arrangement, a minimal experiment was conducted for design efficiency. As shown in Figures 9 and 10, the effects of the design variables were identified on the sensitivity plot through the analysis of the sensitivity of major design variables that affect the objective functions in optimization. The factor which has the largest effect on the stress obtained through structural analysis is the diameter of the ventilation blades. Other factors have little effect. The factor that has the largest effect on the temperature obtained through thermal analysis is the hole type, followed by the hole size and ventilation blade. The design variables and objective functions were defined to minimize stress and temperature through the Hybrid Metaheuristic Algorithm (HMA) to formulate the optimal design problem and derive the results. It was identified that the stress decreased by 18.19 MPa, from the initial value of 64.04 MPa to 45.85 MPa, and the temperature decreased by 6.57 \({}^{\circ}\)C, from 45.90 \({}^{\circ}\)C to 39.33 \({}^{\circ}\)C, compared to the plain solid disc. In addition, it was identified that the optimal values of the design variables were 30 holes, a diameter of holes of 4 mm, slit-shaped holes, and a diameter of the ventilation blades of 8 mm. The optimal values of the design variables are shown in Table 6.  
In the design of orthogonal arrangement, there is a high possibility that there may be design points that can be further improved in the design area, because only the minimum experiment was conducted with only three levels in the design area for design efficiency. Therefore, additional optimizations were performed to consider only the ventilation blade, which is the variable that has the largest effect on stress. The ranges of design variables in the additional optimizations were set as shown in Equation (10). The shape of the blade is shown in Table 7. The values of three variables other than the blades were defined in the \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Design Variables**} & \multicolumn{1}{c}{**Optimal**} \\ \hline  & Shape & Slits \\ Hole & Number & 30 \\  & Diameter & 4 mm \\ Ventilation Blade & Diameter & 8 mm \\ \hline \hline \end{tabular}
\end{table}