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

y
ii
y0
\
1
0-1
H t ieemNw
idn 5ai7
(1)
o NW, (2) U)
'
Fidl'iul
Fig. 3.65. The concepts of Fig. 3.66. The precession
"rigid
of a
shaft" and "flexible shaft with a disk.
shaft".
KEY: (1) Rigid shaft, (2)
Flexible shaft.
Formula (3.104) for critical. angular velocity is valid only
for the case when a disk is located precisely in the middle between
supports and during rotation the shaft is displaced in a parallel
manner without rotation relative to the diameter.
In the overwhelming number of cases a disk is locate2 a!,ymmetri-.
cally on the shaft and, simultaneously with the revolution around
its own axis with angular velocity w, it rotates along with the
elastlc line relative to the axis of the bearings with angular
velocity X. This can be represented as the vibrations of a shaft
rotating along with the disk with angular velocity w relative to
axis 01 - 01 in a plane rotating with angular velocity X relative to
axis 0 - 0 (Fig. 3.66). The projection of the disk onto a thick
plane will complete the oscillating motions (to rotate around its
own diameter).
I
Such qomplex motion of bodies in mechanics is called precession
while angular velocity X of the elastic line with the disk is called 7
the angular velocity of precession or the angular frequency of
natural (free) vibrations of the rotating shaft.
precessive motion are:
Two cases of
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