## 4 Electromagnetic Analysis of the Proposed Damper
### Analysis Results
Figure 14 shows the induced current, induced voltage, and power of the circuit connected to the  
Figure 12: Field results: (**a**) mesh configuration; (**b**) magnetic flux density; (**c**) magnetic flux lines; (**d**) current density. Figure 13: Changes in the driving force of the damper model over time. damper with respect to time. The induced voltages of the windings were generated by an alternating electromotive force, and the maximum voltage was 16.42 V. The maximum current flowing through the circuit was 2.53 A, and the voltage and current waveforms applied to the respective coils (resistance nodes #224 and #183) exhibited almost identical changes. The maximum power of the winding was calculated to be 41.51 W.  
In the current measurement test for the coil-type electromagnetic damper, the maximum current and power were 1.31 A and 23.32 W, respectively. The maximum current and power of the proposed damper were 93% and 78% higher, respectively, than those of the coil-type electromagnetic damper. The feasibility of energy harvesting based on the wind-speed data measured on a cable of a real bridge was evaluated using the coil-type electromagnetic damper prototype employed in this study [36]. According to a previous study, the generated power of the proposed damper model satisfies the power required for vibration monitoring of the cable. However, because the amount of power of the proposed damper model is an analytically derived value, it is necessary to examine the loss and efficiency when implementing an energy-harvesting circuit including a storage battery. Changes in the flux linkage of the windings affect the driving force, inductance, and induced electromotive force of the damper [37]. The function of the winding in the proposed damper was to ensure controllability, but when the energy-harvesting performance was first considered, it was necessary to determine the number of turns of the coil according to the voltage to be induced and the amount of power required. Figure 15 shows the changes in flux linkage and inductance of the two windings over time. The maximum flux linkages of the windings were 0.59 Wb and 0.39 Wb. The flux linkages changed with the same period as the excitation, while maintaining a constant difference of 0.2 Wb. Figure 14: Changes in the electrical properties of the damper over time. Figure 15: Changes in the magnetic flux linkage and inductance of each winding: (**a**) flux linkage; (**b**) winding inductance. The average self-inductance of the windings calculated according to the flux linkage was 29.96 mH, and the mutual inductance was 6.67 mH. Changes of \(\leq\)0.37 and \(\leq\)0.05 mH, respectively, were observed; thus, the values remained almost constant over time. The amount of magnetic flux per unit current varies according to the inductance and affects the damping force of the damper. Additionally, the damping coefficient of the electromagnetic damper is affected by not only the inductance of the winding but also the damper's device constant, circuit resistance, and excitation frequency. Hysteresis curves indicating the damping force according to the displacement and speed of the proposed damper are presented in Figure 16.  
The hysteresis loop of the proposed damper model was similar to that of a viscous fluid damper. Compared with the previously discussed electromagnetic dampers, the amount of dissipated energy was relatively large, and the damping coefficient remained almost constant. The estimated damping coefficient was 2687.60 N-s/m, representing an improvement of approximately 80% compared with the damping coefficient (1491.55 N-s/m) estimated according to the major-axis slope of the composite-type electromagnetic damper under the same excitation conditions. In general, as the coil inductance decreased, the ellipse reflecting the velocity-force relationship became thinner (while maintaining a constant slope) and eventually approximated a straight line [38]. Therefore, the damping coefficient did not change, but the maximum damping force increased slightly.