Handbook of Turbomachinery Second Edition Revised - Ventech!

Centrifugal Bending Stresses
This stress component arises when the cross-section centroids at different
blade heights do not fall on the same radial line. Especially in long blades,
designers typically use this effect to help offset the steam-bending stresses, as
illustrated in Fig. 39.
Steam-Bending Loads
Both steady-state and dynamic bending loads are induced on the blade as a
result of the flow of steam within the blade path. Steady steam-bending
loads are discussed here, the effect of nonuniform flows in the next section.
Steam-bending loads are important in both HP/IP and LP blade design.
Steady steam-bending stresses in the blade airfoil are typically low, less
than 10% of the centrifugal stresses in rotating blades. In the lashing wires,
steady steam stresses may be several times higher than in the airfoil because
of stress concentration effects, but the centrifugal stresses are lower.
A method for calculating steady steam-bending forces in rotating
blades has been reported by Hong et al. [60, 62, 63] based on a streamline
curvature method. Values of the thermodynamic and aerodynamic
properties of the steam as it moves through a stage are calculated and
then used to evaluate static pressure and velocity distributions, which are in
turn used to determine the steam-bending forces in both axial and
tangential directions.
Steady steam-bending stresses can significantly affect stationary blades
or diaphragms as the differential pressure across the section tends to try to
bend them in the axial direction; this effect is greatest in the HP turbine,
where interstage pressure differentials are the highest, particularly in
impulse designs. However, because the blades are shorter, the maximum
stresses may not occur in stages with the highest pressure differentials.
Synchronous Resonance of a Blade with a Harmonic of the
Unit Running Speed
A primary goal of blade design is to tune the longer turbine blades away
from multiples of unit running speed (harmonics). Blades typically have a
sharp frequency response, typically the bandwidth being on the order of + a
few Hz, and thus virtually no vibrational amplitude unless the exciting force
is relatively close to, or at, a resonance frequency. Thus, even a nominal
degree of tuning off resonance by 3 to 5 Hz for lower modes (less than
300 Hz) can dramatically reduce the dynamic stresses that develop. If such
tuning is not performed, high cycle fatigue failures caused by resonance can
occur within a relatively short period (several weeks to less than a year). A
Copyright © 2003 Marcel Dekker, Inc.