# A New Multi-Axial Flux Pm Motor-Generator System for Flywheel Energy Storage
## 2 Materials and Methods  
In this study, a new FESS design for CML is suggested. One of the two AFPM machines in the design operates in the low-speed stage (12 poles) and the other in the high-speed stage (2 poles). Moreover, the prominent feature is the separate generator winding in the 12-pole AFPM machine structure to obtain high energy in a short time and that there is a separate smaller powered 2-pole AFPM motor design to keep the flywheel at reference speed. With the use of windings in FESS's conventional motor-generator set, high energy cannot be obtained in under two seconds. Thus, a separate generator winding is placed in the 12-pole AFPM machine structure. Also, at lower speeds, the multi-pole machine structure is ideal. At a high-speed stage, a few poles and a small-power AFPM motor structure could keep the flywheel at the reference speed. FESS stores energy kinetically in a rotating flywheel. Since there is no chemical reaction, there is no change in the material due to charging and discharge. Thus, the cycle life of the material becomes longer. Therefore, FESS is useful in short-term high life cycle areas. FESS has traditionally been used for short-term energy fluctuations in power transmission lines, energy fluctuations in renewable energy production systems, and energy recovery in electric vehicles. In this study, the FESS design for CML was carried out with a compact AFPM machine that provides high torque and power density instead of a radial flux machine. To avoid friction losses, FESS is operated in a vacuum environment. FESS, with a radial flux motor-generator set placed on the same shaft, is given in Figure 1. In Figure 1, the motor winding in FESS is also the generator winding. The discharge current is similar to the charging current since single winding is used. The existing motor must operate at a lower load to keep FESS in standby mode. Hence, the motor operates at a lower efficiency point. FESS has over 20 years of lifetime [24]. Since the centrifugal forces are large in high-speed FESS, materials with high degree of hardness should be used [24]. Maximum energy amounts per unit volume and weight in FESS are given in Equations (1) and (2) [24]. \[\mathrm{e_{v}}=\mathrm{K}\sigma_{\mathrm{\theta,u}} \tag{1}\]  
\[\mathrm{e_{m}}=\mathrm{K}\frac{\sigma_{\mathrm{\theta,u}}}{\rho} \tag{2}\]  
In Equations (1) and (2); \(\sigma\), \(\rho\), and K, are the tensile strength, specific weight, and shape factor, respectively. The shape factor represents the maximum energy that can be stored depending on the shape of the flywheel. Shape factor is equal for the thick ring, thin ring, solid disc, and laval disc of 0.305, 0.5, 0.606, and 1, respectively [24]. In this study, the material used for energy storage is in the form of a solid disc (K = 0.606). Table 1 provides the unit weight for various materials, along with their respective constant and energy amounts per unit volume. \begin{table}
\begin{tabular}{l c c c c} \hline
**Material** & \(\mathrm{e_{v}}\) [MJ/m\({}^{3}\)] & \(\mathrm{e_{m}}\) [kJ/kg] & \(\mathrm{\rho}\) [kg/m\({}^{3}\)] & \(\mathrm{\sigma_{\mathrm{\theta,u}}\) [MPa] \\ \hline Aluminum & 251 & 93 & 2700 & 500 \\ Steel & 399 & 51 & 7800 & 800 \\ Glass Fiber/Epoxy & 500 & 250 & 2000 & 1000 \\ Grafit HM/Epoxy & 374 & 237 & 1580 & 750 \\ Grafit HS/Epoxy & 752 & 470 & 1600 & 1500 \\ \hline \end{tabular}
\end{table} 
Table 1: Values for different materials [24]. Figure 1: The general structure of FESS [23]. When Table 1 is examined, it is seen that the energy stored per kg and volume is proportional to the tensile strength, and the steel, which is the heaviest material, stores the lowest energy per kg. Since this study aims not to store material-related energy per unit volume or unit weight, aluminum material is preferred for ease of production. FESS is an important component, especially in space applications. The comparison in terms of discharge depth, energy density, and life cycle in NASA's study on FESS and NiH2 batteries are given in Table 2[25].