Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

116 Fluid Mechanics, Thermodynamics of Turbomachinery
design in which none of its natural frequencies coincides with any excitation frequency.
The subject is complex, interesting but outside of the scope of the present text.
Centrifugal stresses
Consider a blade rotating about an axis O as shown in Figure 4.15. For an element
of the blade of length dr at radius r, at a rotational speed W the elementary centrifugal
load dFc is given by
where dm = rmA dr and the negative sign accounts for the direction of the stress gradient
(i.e. zero stress at the blade tip to a maximum at the blade root),
F c+dF c
FIG. 4.15. Centrifugal forces acting on rotor blade element.
F c
o
dr
r
W