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

Fig. 3.64. Mutual arrangement
of the 0 axis of bearings, the
01 axis of the shaft at the disk
attachment point, and the center
of gravity of the disk at various
angular velocities: a .
w Kw ;b-P. 00 X
a) (a)5)b
Y
We
As experimental and theoretical studies have shown, at angular
velocities less than and greater than critical, the shaft is
dynamically stable. At critical angular velocity the shaft is
dynamically unstable.
It
is conditionally accepted to call shafts operating in the
subcritical region rigid and in the supercritical region flexible
(Fig. 3.65).
As seen from formula (3.103) and the graph in Fig. 3.63, when
W = W the shaft obtains an infinite deflection. Actually, at an
angular velocity near critical the shaft deflections increase but
remain finite (see Fig. 3.65). This is caused by the fact that with
great deflection the centrifugal force of the disk is balanced not
only by the transverse force of elasticity but also by the force
directed along the axis of the deflected shaft.
Turbine operation at rpm near critical is not permissible.
practice we assume that the opepiating angular velocity must be
w < 0"7wp or w > 1.3w p.
In
The effect of gyroscopic moment on critical
angular velocity. The concept of shaft
precession
35