8.2 Dynamic characteristics Ë 265Fig. 8.4:Typical vertical dynamic response of the HTS Maglev vehicle model at the B point after the
impulse force acting on the B point (FCH: 50 mm): (a) time and (b) frequency domains.
based on this two-dimensional dynamic model. Figure 8.4a and b shows the typical
dynamic response in the time domain and frequency domain analyzed by the free-
vibration experiments after a single impulse force excitation. The sampling time was
set to 1 s and the sampling frequency was up to 800 Hz. The FCH of the HTS Maglev
vehicle model was set as 60, 50, 45, 40, 35, 30, 25, 20, 15, and 10 mm, respectively. Each
field cooling (FC) duration time was 30 minutes.
The free vibration curve in Fig. 8.4a belongs to the typical damped free vibration
curve which decreases exponentially. The amplitude of the vibration curve decreases
quickly to zero after only 0.4 s. Figure 8.4b further verifies the distinct low-frequency
resonance characteristics of this HTS Maglev vehicle system since the resonant fre-
quency was 6 Hz and the amplitude of the vibration was very small with the maximum
of 16.2휇m. In fact, all the resonant frequencies were low: 6, 6, 7, 8, 7, 8, 9, 10, 11, and the
highest 13 Hz, respectively, for every FCH from the highest 60 mm to the lowest 10 mm.
Moreover, similar to the conclusion of some reports on HTS bearings, etc., the dynamic
characteristics of the HTS Maglev vehicle exhibited vibration isolation at a wide
high frequency range because of the strong flux-pinning nature [19, 20]. More time-
domain vibration experiments with the HTS Maglev system have comprehensively
validated the inherent dynamic characteristics of the low-frequency resonance and
high-frequency isolation from the viewpoint of both vertical levitation and horizontal
guidance [21, 22].
The experimental data were used with Eqs. (8.1) and (8.2) to determine the
dynamic stiffness and damping coefficient of the HTS Maglev vehicle. The relation-
ships with FCH are plotted in Figs. 8.5 and 8.6. The dynamic stiffness tends to decrease
with the increasing FCH. This can be explained by the flux-pinning forces between the
on-board HTSC and the PMG which increases with decreasing FCH. The lower the FCH
is, the more stable the vehicle system is. The maximum dynamic stiffness, 5408 N/m,
occurs at the lowest, 10 mm, FCH.