## 3 Characteristics Test of Electromagnetic Dampers
### Comparative Analysis of Test Results
Therefore, to determine the required damping coefficient, the amplitude of the cable in the real wind environment and the driving stroke length of the damper should be considered. However, because the stroke length of the damper affects the lengths of the permanent magnet, coil, and magnetic material, these factors must be considered together. The changes in the maximum damping force with respect to the excitation amplitude and excitation frequency of the electromagnetic dampers are shown in Figure 6 on the same \(y\)-axis scale. For all the electromagnetic dampers, the maximum damping force increased linearly as the excitation amplitude increased at a constant excitation frequency. However, at a constant excitation amplitude, the maximum damping force exhibited a non-linear increase with an increase in the excitation frequency. The convergence of the maximum damping force was most pronounced (and the damping force was strongest) for the eddy current-type electromagnetic damper. Figure 5: Hysteresis loops of electromagnetic dampers with an excitation frequency of 5 Hz: (**a**) displacement–force curve for the coil type; (**b**) displacement–force curve for the eddy-current type; (**c**) displacement–force curve for the composite type; (**d**) velocity–force curve for the coil type; (**e**) velocity–force curve for the eddy-current type; (**f**) velocity–force curve for the composite type. The maximum damping force when the eddy current-type electromagnetic damper was excited at an amplitude of 12 mm and a frequency of 5 Hz was increased by 28.36 N (4%) compared with that for the same amplitude and a frequency of 4 Hz. This was the smallest increase among the three dampers under the same excitation conditions. The eddy current-type electromagnetic damper had a stronger damping force than the other dampers under the same excitation conditions but approached the maximum damping force at a relatively low frequency. Therefore, it is necessary to design a damper with consideration of the corresponding frequency range. The results of comparing the velocity-force hysteresis loops under different excitation conditions are shown in Figure 7. When the excitation amplitude and frequency were small and low, respectively, the non-linearities and delays of loading and non-loading were significant. The effect of the error due to the friction of the drive shaft and the noise of the shaking table was observed. The history of motion was similar to that for the magnetorheological (MR) fluid damper, where shear and yield stresses act. As the excitation frequency and amplitude increased, the history became elliptical, similar to that for a viscoelastic damper. A comparison of Figure 7b,c confirmed that a larger excitation amplitude corresponded to greater similarity between the damping forces of the composite- and eddy current-type dampers. This is because the increase rates of the damping force for the eddy current- and coil-type dampers were relatively low, and that of the damping force for the composite-type damper was relatively high. Previously, it was confirmed that the increase rate decreases as the eddy current-type electromagnetic damper force approaches the maximum damping force when the excitation amplitude and frequency are increased. However, when the maximum damping force at an excitation frequency of 4 Hz and an excitation amplitude of 15 mm was compared with that at an amplitude of 3 mm, increments by factors of 4.3, 4.3, and 4.9 were observed for the eddy current-, coil-, and composite-type dampers, respectively. This implies that the excitation conditions cannot be presumed to be the cause for the convergence of the eddy-current type damping force and the maximum damping force.