## 4 Electromagnetic Analysis of the Proposed Damper
### Design Orientation and Model Configuration  
Coil-type electromagnetic dampers can be controlled actively, passively, or semi-actively, but need reinforcement in terms of damping force. In contrast, the eddy current-type electromagnetic damper has a strong damping force, but has a limit that can only be controlled passively. An eclectic type of damper was proposed, where the damping level was increased while combining the functions and advantages of coil-type and eddy current-type electromagnetic dampers. The damping level depended on the maximum damping force and damping density [23]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **Amp.** & **Freq.** & **4 Hz** & **5 Hz** & **6 Hz** & **7 Hz** & **Remarks** \\ \hline \multirow{6}{*}{Eddy current} & 3 mm & 215.19 & 234.14 & 242.49 & 240.66 & - \\  & 6 mm & 421.47 & 458.95 & - & - & - \\  & 9 mm & 615.98 & 669.36 & - & - & - \\  & 12 mm & 798.31 & 826.67 & - & - & - \\  & 15 mm & 935.05 & - & - & - & 100\% \\ \hline \multirow{6}{*}{Coil} & 3 mm & 125.22 & 136.64 & 144.81 & 145.25 & - \\  & 6 mm & 238.09 & 264.73 & - & - & - \\  & 9 mm & 351.25 & 390.60 & - & - & - \\  & 12 mm & 452.56 & 496.52 & - & - & - \\  & 15 mm & 538.26 & - & - & - & 60\% \\ \hline \multirow{6}{*}{Composite} & 3 mm & 170.91 & 182.43 & - & - & - \\  & 6 mm & 335.91 & 367.56 & - & - & - \\ \cline{1-1}  & 9 mm & 506.64 & 550.21 & - & - & - \\ \cline{1-1}  & 12 mm & 670.79 & 729.11 & - & - & - \\ \cline{1-1}  & 15 mm & 842.62 & - & - & - & 88\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum damping forces (N) of the dampers according to the excitation conditions. The drive part of the proposed damper is constrained by steel rods, permanent magnets, and pole pieces that move linearly under external excitation. In the stator surrounding the driving part, a coil for the control function, an oxygen-free copper tube for generating eddy currents, and a stator tooth for reinforcing the damping force were arranged. The outermost side of the stator was surrounded by an iron shell and functioned as a stator yoke, forming a magnetic circuit. The shape and analysis model of the proposed damper are shown in Figure 9.  
The driving part comprised permanent magnets magnetized in the axial direction and pole shoes that induced a magnetic flux in the radial direction [24; 25]. Because the permanent magnets maintained a permanent magnetization state when magnetized, they could be maintained without losing magnetic force or receiving electrical energy from an external source. These features are advantageous for use in semi-permanent attenuator development and monitoring-system construction. Among the magnets currently used as permanent magnets, neodymium (NdFeB) magnets used have the strongest magnetic force [26]. A neodymium magnet has good processability and a relatively low price but rusts easily; thus, it is usually plated with nickel. However, there is a disadvantage: the magnetism is weakened by heat owing to the low temperature coefficient [27]. Therefore, the magnet grade should be determined according to the temperature of the environment in which the damper is to be installed. The width of the air gap is a critical variable influencing the absolute magnitude of the damping force [28; 29; 30]. The width of the air gap was set as 0.5 mm (the minimum length for ensuring permanent operation), as it is feasible to manufacture a prototype with a constant width in the axial direction. The stator located outside the air gap comprised two solenoid coils, an oxygen-free copper tube, and an outer shell [31]. The coils reduced the absolute damping force owing to series resistance and inductance, but were essential for circuit construction and control. Each coil was insulated and separated. In addition to the coils, the stator was provided with an oxygen-free copper tube and regularly spaced teeth to increase the damping force [32].