Page 141 - Steam Turbines Design, Applications, and Rerating

122 Chapter Six

is equal to the natural frequency and when the accompanying excita-
tion forces at the circumference are simultaneously equal to the charac-
teristic mode.
Alternating bending stresses occurring in laced blades are lower
than stresses experienced in freestanding blades under resonant speed
conditions. This is due to the higher resonance frequencies and out-of-
phase vibration of laced blading.
If large vibration amplitudes occur, friction between the lacing bar
and the inside of the bore further dampens vibration amplitudes.
Since the lacing bars are well supported at both ends, coupling is
independent of typical fabrication tolerances of the bore; coupling of all
blades is thus ensured even at low speeds.
Damping coefficients and the influence of lacing bars on the natural
frequency of a row of blading are difficult to calculate. They are, there-
fore, generally determined by measurements (Figs. 6.14 and 6.15). This
is why strain gauge measurements of alternating bending stresses are
more typically made in actual blades under operating conditions. Fig-
ure 6.16 shows one set of results: no excessively high values over the
entire mass flow and speed range.
Slender case-stage blades are used in steam turbines ranging in speed
from 15,000 r/min to 3000 r/min. The blades are generally made as a
series of geometrically similar blades. If the same peripheral speed is

Figure 6.14 Campbell diagram of a freestanding blade. The
points of resonance were measured during turbine operation.
(Siemens Power Corporation, Milwaukee, Wis. and Erlangen,
Germany)