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

The selection of any form of approximating dependence depends
on what kind of problem is being solved. For example, in solving
the problem of small vibrations in
an unloaded rotor we can limit
ourselves to a linear dependence if the form ( 3 .1 5 4). If, however,
we are examining the effect of forced vibrations on modes of autovibration
of currents or we are examining vibrations whose amplitudes
are commensurate with the value of the radial gap in the bearings,
we must take into account the nonlinearity of the characteristics
FrO ()
Dependences F to and Fc can be approximated by the linear
relationships:
PtAO=aU 2 eVo; FcaWVo. (3.155)
A transition from dimensionless quantities F, c, V0 and v0
to dimensioned quanti'ies F, r, w, 6 is effected with the aid of
the following relationships:
F.=F.pDL,; r=E. 0 to); w= D Q~;=~V
By themselves the dimensioned forces can be written in linear
form: F 1 = kIr; F 2 = k 2 wr; F3 = k 3 v, where subscripts 1, 2, 3
correspond to the former subscripts r, t, c, respectively.
Coefficients kl, k 2 , k 3 are connected with coefficients a,, c 2 ,
ca 3 by relationships:
) L L r 1)L
L o A ,;2=C2 2; 3==3
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