Page 214 - Steam Turbines Design, Applications, and Rerating

Campbell, Goodman, and SAFE Diagrams for Steam Turbine Blades 193

Figure 11.4 Vibration modes of a shrouded blade group. (Dresser-
Rand Company, Wellsville, N.Y.)

blade frequencies are found. The blade properties are not being approx-
imated as in an analytical determination. The disadvantages of testing
are that it is time-consuming and tedious, and the tests are done on a
stationary rotor, which does not include centrifugal stiffening and a
possible change in boundary conditions in the root.
Turbine manufacturers use a number of different finite-element
analysis computer programs to calculate blade natural frequencies.
The blading is generally modeled by a series of beam elements to sim-
ulate the actual configuration. By supplying properties such as areas
and moments of inertia to the beam elements, the natural frequency of
the model can be calculated. Along with the natural frequencies, the
displacements, forces, and moments within the model are given to help