Design and Stress Analysis of Extraterrestrial ... - The Black Vault

! t
I
The frequency characteristic is
symmetric relative to the
origin of coordinates.
This means that the curvesicoincide exactly'
in the ! and III and in the II and IV quadrants. Therefore, they
are bounded by its representation only in the two neighboring
quadrants: in I and II (Fig. 3.73a') or in I and IV (Fig. 3.73b).
The latter representation more accurately eýresses the physical
essence: for a given direction of shaft rotation'(we assume it is
positive) both forward (positive values of X),
(negative values of X) occur.
anrd reversp precession
However, from the mathematical point
of view, it is more convenient to deal with continuous curves, i.e.,
with the representation of characteristics as shown in
Fig. 3.73a.
Analysis of the frequency characteristic shows that in the
examined single-disk system each value of angular velocity
corresponds to two natural angular frequencies (velocities') in the!
region of forward precession and two in the region ofreverse
precession. For the entir, set of angular shaft velocities-there -
is an infinite number of natural angular frequencies.
Fig. 3.74. Shapes of the elastic
line during the vibration of a
rotating shaft with one disk.
a~ .(a) 6)(b) '
When w = 0 there are two frequeucies of bending vibrations for
forward and two for reverse precession.. Since the shaft is
turning there is no gyroscopic moment and the frequencies in the
regions of forward and reverse precession, by pairs, are equal
(in
absolute value).
not
When w > 0 in the region of forward precess'ion, the ntimerical
values of X are greater than when w = 0, an in the region of reverse,
precession are less. This is explained by the effect of:the gyroscopic
moment which, during forward precession, increases shaft rigidilty
and during reverse decreases it.
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