# Multi-Step Design Optimization for the Improvement of an Outer-Rotor Brushless Direct Current Motor
## 3 Taguchi Method and Response Surface Methodology (RSM)
### Taguchi Method  
The Taguchi method is a prominent experimental design technique that can enhance a product's quality by optimizing the design parameters [19]. Table 4 shows the variance in the control factors. The factors obtained for the Taguchi method to optimize the design parameters of the control factor are selected for the reference motor part of the dimension parameters. Each control factor has different levels, representing the different settings or values that it can take. The selection of the control factor of the Taguchi method is the first consideration in the process to improve the performance of the motor design. The Taguchi method uses these specially designed matrices to study a large number of variables with a minimal number of experiments. This approach significantly reduces the time and resources needed for experimentation. The main objective is to improve the performance of the product or process, like a BLDC motor, by optimizing the control factors. This involves finding the best combination of the control factors' levels, which produces the most robust and high-quality outcome. By focusing on the control factors and seeking a design that is less sensitive to noise factors, the Taguchi method helps us achieve an economically efficient design. It reduces the need for expensive alterations to handle noise factors, as the optimized design inherently copes better with these variations. In the Taguchi method, noise factors are variables that cannot be controlled or are too costly to maintain. These might include environmental conditions or usage variations in a BLDC motor. In contrast, control factors are those that can easily be adjusted. The goal is to minimize the impact of noise factors to optimize control factors [7; 8; 9; 10; 13; 19; 20]. In our experiment, the selected control factors for the proposed model's stack height, a value range of 3 mm to 4 mm, have been chosen. This range is determined by the motor's operating speed and its performance characteristics. At a stack height of 3 mm, the motor's speed reaches 8700 rpm. This range provides a suitable configuration for balancing the proposed model's characteristics, ensuring optimal motor performance. The control levels of the number of turns, width of slot opening, depth of stator slot, and angle of the stator tooth tang also correspond to the increased and decreased range of the torque, efficiency, and magnetic flux, which will happen within the range, as described in Table 4.  
Using the Taguchi method, Table 5 shows the FEM analysis of the simulation result. This result can be the rated speed in the range of 5400 rpm, and we cannot use the exceeded value within a range. The S/N ratios of the efficiency, torque, and output power are shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Constant**} & \multirow{2}{*}{**Control Factors**} & \multicolumn{4}{c}{**Orthogonal Array Levels**} \\  & & **1** & **2** & **3** \\ \hline A & Stack height & 3.5 mm & 4.5 mm & 5.5 mm \\ B & Width of stator tooth & 2.8 mm & 3.8 mm & 4.8 mm \\ C & Depth of stator slot & 8 mm & 10 mm & 12 mm \\ D & Width of stator slot opening & 1.5 mm & 2.25 mm & 3 mm \\ E & Angle of stator tooth tang & 17 deg & 27 deg & 37 deg \\ F & Number of turns & 72 & 82 & 92 \\ G & Magnet thickness & 3.5 mm & 4.5 mm & 5.5 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Design variance of the control factors. The outer-rotor BLDC motor involves various control factors: magnet thickness, stator tooth tang angle, stator slot depth, stator slot opening width, stack height, and number  
Figure 7: S/N ratios of mean to control factor for proposed model design: (**a**) S/N ratios for maximum efficiency; (**b**) S/N ratios for maximum output power; and (**c**) S/N ratios for maximum torque. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**A** & **B** & **C** & **D** & **E** & **F** & **G** & **n (\%)** & **P\({}_{\text{out}}\) (W)** & \(\tau_{\text{max}}\) (Nm)** \\ \hline  
\hline \hline \end{tabular}
\end{table}