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

Analysis of critical shaft speed
With the use of turbines of rapidly revolving shafts a
phenomenonf called "critical rpm" was detected.
It was noticed that during the slow rotation of a rotor no
noticeable vibrations are observed. The rotor rotates smoothly.
With the achievement of a certain number of revolutions the rotor
begins, without visible cause, to vibrate sharply, which can lead
to the breakdown of a clearly strong shaft.
in revolutions the rotor again begins to rotate quietly.
With a further increase
The rpm at whic" a shaft loses stability and begins to vibrate
is called critical.
Stress analysis of shafts is studied in courses on the strength
of materials and machine parts. Therefore, in this section we shall
examine only the questions of transient stability of shafts.
Let us consider a shaft arranged vertically (for the elimination
of the effect of its weight) in the middle cross section of which
is attached a disk with mass m.
Let us assume that the mass of the
shaft is low as compared with the mass of the disk; however, the
shaft possesses elastic properties. Let us also assume that the
center of gravity of the disk c is displaced relative to the
geometric center 01 by quantity e (Fig. 3.62). We further assume that
supports allowing the shaft to rotate freely are absolutely rigid.
When the rotor only begins to rotate and the elastic axis of
the shaft is still a straight line (Fig. 3.62a), then, as a result
of the displacement of the disk's c¢nter of gravity with respect
to the axis of rotation, there appears centrifugal force mew 2 .
Under the effect of this force the shaft begins to be deflected,
which, in turn, leads to an increase in the centrifugal force
2
(Fig. 3.62b): PC m(y + eOw
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