Handbook of Turbomachinery Second Edition Revised - Ventech!

Furthermore, in practice each manufactured and assembled blade has
a slightly different natural frequency, which complicates the analysis for a
row of blades but does reduce the aerodynamic coupling between blades and
therefore makes the row less unstable than if all blades were perfectly
matched. In fact, it is possible to stabilize an aerodynamically unstable row
by deliberate mistuning if the average self-damping of a single fixed blade is
positive, but not if it is negative. The variation in individual blade natural
frequencies also explains why, in a potentially unstable row, some blades fail
while others do not: adjacent blades that are not aerodynamically coupled
will vibrate independently of one another.
The implication to blade design is that blade rows should be
aerodynamically stable with the use of deliberate mistuning (or mixing) of
actual blade natural frequencies to achieve stability if necessary. Mechanical
damping, primarily a result of mechanical friction, decreases with increasing
amplitude and should not be relied upon unless specifically confirmed in
rotating tests under worst-case operating conditions. Monitoring of all
blades in a suspect row is necessary, and tests should be run under worstcase
flow conditions. In situ blade vibration can also be measured by
noncontacting methods using strain gage, telemetry, electromagnetic, eddy
current, or optical devices. Use of such methods are the preferred means of
measurement of nonsynchronous vibration.
Vibratory stresses can also arise from variation in the geometry of the
steam inlet passages in the stationary blades. There is no practical way to
tune the blade against these high-frequency per-rev harmonics. The
deflections and stresses that result are fortunately generally low; however,
poor environmental conditions can lower the life of the blade under such
loadings.
Asymmetric variations in the flow path that are both temporally and
spatially periodic result in flow-induced vibrations in the blade by buffeting
from random fluctuations in the flow, by aerodynamic instability (which can
lead to blade flutter), or by a combination of the two. Such excitations are
the result of random fluctuations in the flow and, as a result, the frequency
spectrum is continuous or broad band and the Campbell-type plot and
methods cannot be used to guard against failure.
The Campbell diagram can, however, be used to predict the
frequencies of individual blades, or some groups of blades. Where the
blade groups are attached to rigid drum-type rotors, finite-element models
and a plot of the Campbell diagram are sufficient to detect potential
conditions of resonance. However, in turbines with more flexible disks, there
may be structural interaction between the blades and the disks that is not
easily detected using only the Campbell diagram. The dominant shapes of
the deformation of the disk tend to be sinusoidal waves around the
Copyright © 2003 Marcel Dekker, Inc.