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

When analyzing the natural frequency (or natural angular
velocities) of rotors with distributed mass, the mass of the sha"'-.
can be taken into account by reducing it to the mass of the disk.
A simple adding of the mass of the shaft to the mass of th,
disk is too rough an approach. 'The best approach is the method
.•
of reducing the mass of the shaft to the mass of the disk basc" 3n
the assumption that the kinetic energy of a rotating shaft is "qual
to the kinetic energy of a certain reduced mass concentrated r
the spot where the disk is attached to the shaft. With thic ,(
assume
that the elastic line of the vibrating shaft has the same
form as during static deflection under the effect of a unifo,,t'.y
distributed load. This method of presentation does not tak., into
account shaft rotation.
A stricter accounting for the mass of the shaft at certain
critical velocities, proposed in reference [20], requires a very
large amount of computation.
As studies have shown,
the critical velocity of a system without
taking the mass of the shaft into account will be higher than the
first
natural angular frequency of the system with mass taken into'
account.
Disregarding the mass of a shaft can lead to particularly
large errors (up to 50%) in systems with long shafts.
The mass of short rigid shafts with a low frequency of vibrations
can be disregarded and this, of course, appreciably simplifies the
problem of determining critical velocities.
Critical angular velocities of complex systems
The frequency equation (3.121) makes it
possible to calculate
critical angular velocities and vibration frequencies for a. shaft
of a single-disk system with allowance for gyroscopic-moment.
equation of the 4th power relative to A is
obtained.
An
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