## 5 Conclusions  
Through a magnetic-circuit analysis of an electromagnetic-damper model, major equations related to the dynamic behavior and performance of the damper were derived, including equations for the magnetic flux of the damper, the electromotive force induced in the active coil, and the total damping force of the damper. Additionally, characteristic tests were conducted on prototypes of electromagnetic dampers with different stator structures, including coil-type electromagnetic dampers, to which the optimal values for the main parameters were applied, to examine the hysteretic dynamics according to the excitation conditions and structure types. For all the dampers, as the excitation frequency increased, the amount of dissipated energy and the damping force increased non-linearly, but the damping coefficient decreased slightly. As the excitation amplitude increased, the amount of dissipated energy increased significantly, and the damping force increased linearly, but the damping coefficient remained almost constant. Figure 16: Hysteresis loops of the proposed damper: (**a**) position–force curve; (**b**) speed–force curve. The eddy current-type electromagnetic damper exhibited the best damping performance among the dampers under the same excitation conditions, but as the excitation conditions were strengthened, the damping force and damping coefficient approached the maximum values and tended to converge. The damping force began to decrease after the frequency reached a certain value, and strong convergence was confirmed. The maximum damping forces for the coil-type and composite-type electromagnetic dampers were 60% and 80%, respectively, of those for the eddy current-type electromagnetic damper. According to the considerations of the electromagnetic-damper model and the characteristics test results, an RHED was proposed that can apply various control methods, allow energy harvesting through self-generation, and exhibit improved damping performance compared to typical electromagnetic dampers. The physical and electromagnetic behaviors and characteristics of the proposed damper model were examined through electromagnetic finite element analysis. The results confirmed that the enhancements in the damping and energy-harvesting performance were due to pole shoes considering magnetic saturation, the tubular oxygen-free copper inside the stator, and the magnetic paths utilizing the teeth structure. The maximum damping force of the proposed RHED model was 1.01 kN, and the estimated damping coefficient was 2687.60 N-s/m, which was improved by \(\geq\)80% compared with a controllable coil or composite-type electromagnetic damper. The maximum induction voltage and production power of the RHED model were 16.43 V and 41.51 W, respectively. This production power is sufficient to build a vibration monitoring system for cables according to a previous study on the feasibility of energy harvesting using the same coil-type electromagnetic damper, wind vibration data for the cable of an actual bridge, and wireless sensors. However, it is necessary to consider that the actual wind environment is not the condition of having a constant wave excitation, such as in experiments or simulations. When implementing an actual energy-harvesting circuit including a storage battery, it is necessary to examine the loss and efficiency. Additionally, because the hysteresis-loop analysis results indicate that the resistance value for inductance is relatively large, it is expected that the attenuation performance can be improved by optimizing the winding design according to the required voltage and power. Through this study, we proposed an electromagnetic damper, a key element in realizing an autonomous damping and vibration monitoring system, and analyzed the feasibility of an improved damper model. It is necessary to verify the performance experimentally in the future by connecting the energy-harvesting circuit, including the control circuit, and analyzing the prototype applied to the cable.