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

through the critical mode during acceleration and stopping of such
a rotor, special devices which limit the deflections of the shaft
are used.
A shift of the critical modes to lower rpms ca*x be accomplished
by introducing into the design of the supports special devices which
restrict the rigidity of the support while preserving slifficient
rigidity and strength of the shaft itself,
Usually, "elastic" supports are not purely elastic since they
are also the location of vibration dampers. In order to show the
effect of an elastic support, let us examine the diagram in Fig. 3.80.
Critical velocity of a rotor with an elastic support can be
determined from the equality (without allowing for gyroscopic moment)
Cp
I/(3.142)
where cnp is the cited coefficient of rotor rigidity at the point of
disk attachment (with allowance for the pliability of the support).
The coefficient of rigidity
C. = -- ,.
"C yp
(3.-143)
where y = y 6 + Ynn is the displacement of the shaft at the
point of disk attachment under the effect of the force P;
YB and y on.np are the displacement of this point because of the
deflection of the shaft and the deformation of the elastic support,
respectively.
We shall express displacement yon.np in terms of the deformation
of the support itself (Fig. 3.80a): yon(11/1). On the other hand,
Yon Pon /c on, where Pon = P(Il/1) is the reaction of the elastic
support.
Consequently,
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