# Multi-Step Design Optimization for the Improvement of an Outer-Rotor Brushless Direct Current Motor
## 2 Configuration of Reference Model's Design and Materials  
The design calculation of the outer-rotor BLDC motor can be used in the following equation. This motor can be calculated using the torque development equation; Tmax is the torque development of the motor in Nm, P is the number of poles, Bg is the air gap flux density in the electrical degree of 120 in Wb/m2, Ic is the current through a conductor in amperes, ns is the number of stator slots, L is the conductor length in mm, and Rinner is the inner radius of the stator in mm [14]:  
\[\text{T}_{\text{max}}=2\text{ P Bg Ic ns L Rinner} \tag{1}\]  
\[\text{B}_{\text{g}}=\mathcal{O}_{\text{magnet}}\text{ A}_{\text{g}} \tag{2}\]  
\[\mathcal{O}_{\text{magnet}}=\frac{\mathcal{O}_{r}}{1+k\frac{R_{z}}{R_{m}}} \tag{3}\]  
The magnetic flux density is shown in Equation (3). The magnetic flux density is the relation between the resistance of the air gap and the magnet. The coefficient of reactance \(\mathbf{k}\) is a constant value of the magnetic material [15]. A higher efficiency percentage means that the motor is more efficient, with less power lost to inefficiencies, while a lower percentage indicates higher losses and less efficient energy conversion. The efficiency of a motor is expressed in percentages. Pout is the output power of the motor and the mechanical power generated by the motor in Watts (W), typically measured at the shaft. Ploss is the total power lost within the motor due to various inefficiencies like the electrical resistance in W, friction, windage, iron losses, and other factors contributing to energy loss. The Pin is the total electrical power consumed by the motor from its power source in W [14; 15]. We can calculate the efficiency as follows:  
\[\eta=\frac{P_{out}-P_{loss}}{P_{in}} \tag{4}\]  
Equations (5) and (6) show the relative permittivity of the material in terms of the electric displacement vector {D} in (C/m2); [e] is the Piezoelectric stress constant matrix (C/m2), [eS] is the permittivity matrix (F/m), [S] is the Strain vector, and {E} is the vector for the electric field intensity (N/C) [16]. \[\{\text{D}\}=[\textbf{e}][\text{S}]-[\textbf{e}^{\text{S}}]\{\text{E}\} \tag{5}\]  
\[\left[e^{S}\right]= \begin{bmatrix}E_{11}&E_{12}&E_{13}\\ E_{21}&E_{22}&E_{23}\\ E_{31}&E_{32}&E_{33}\end{bmatrix}  \tag{6}\]  
Figure 2: Result of our market survey on using energy-saving electric fan. The material of China steel 50 CS1300 [17; 18] can be used in the reference motor model of the stator and rotor parts. According to the information provided by the JMAG, the specifications for the configuration of the China steel material are shown in Figure 3. This material has a magnetic flux range of 1.5 T to 1.8 T. In the reference motor, the magnetic flux does not exceed the 1.8 T value. In this study, we used this material in the proposed motor design. The magnet is magnetized to the saturation point in a closed circuit, and the B-H curve characteristics of the Ferrite magnet and the NMF-6C magnet are used in the rotor part in the reference motor design. Figure 4 provides a hysteresis loop of the relationship between the magnetic induction (B) and the magnetizing force (H). This curve describes the magnetic field strength of the negative coercivity value of \(-\)270 kA/m, which is an approach to the zero value of the magnetic flux density based on the information provided by JMAG. In this case, the coercivity of the magnetic field strength reduces the magnetization to zero after the magnet has been saturated [17; 18]. The parameter of this reference motor was measured, and the measured parameter results are shown in Tables 1 and 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Outer diameter & 55 & mm \\ Inner diameter & 45 & mm \\ Stator bore diameter & 20 & mm \\ Gap length & 0.3 & mm \\ Number of slots & 12 & \\ Number of poles & 10 & \\ Rated voltage & 24 & V \\ Rated current & 3 & A \\ Speed & 5500 & rpm \\ Connection type & Y & \\ \hline \hline \end{tabular}
\end{table}