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

The angular velocity w Aof natural vibrations,, with rotation
taken intc account, is
determi.ned from formula
A
w+Bw C
2 (3.48)
where w. is the angular velo,,viy of natural vibrations in a nonrotating
blade;
w is the angular velocity;
B is the coefficient allowing for the effect of centrifugal
forces on the natural frequency of a blade.
Coefficient B depends on the geometric dimensions of the blade
and can be determined from formula
F(ro+ z) dz
dz'•
(3.4 9)
where F is the current cross-sectional Area of the blade.
Figure 3.28 shows the character of variation in w as a function
of the angular velocIty of the rotor.
The effect of blade heating on the frequency
of its natural vibrations
During turbine operation from the moment of starting up to the
steady run the gas temperature and blade temperature vary.
Due to the increase in blade temperature with a change in w
the modulus of elasticity for the material is reduced, which leads
to a reduction in the frequency of natural vibration, as shown in
Fig. 3.28 (dashes).
If the blade temperature for each mode is known then we can
account for the effect of heating from formula
282