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Rotor Dynamics Technology 183

areas or until some other nonlinear restraint changes the system and
prevents further amplitude increases. In a stable system, the exciting
force does not increase with increasing amplitude. Therefore, the
amplitude is limited to a low level by the restoring damping force.
Again, the presence of limited amplitude, subsynchronous vibration
in operating turbines has probably always existed but has not been
documented by frequency spectrum analyses.

10.14 Service Examples
The amount of spectrum data available for turbines in service is lim-
ited to relatively few installations. This is particularly true for the
older turbines. However, some examples of subsynchronous vibration
in turbines having long service times are shown in Figs. 10.10 through
10.12. This type of vibration has existed for many years, and no prob-
lems because of it have been reported to date.
The first example (Fig. 10.10) is a six-stage extraction turbine rated
14,000 hp at 12,915 r/min. The unit went into service in 1967. In 1981,
a frequency spectrum analysis was made while the turbine was oper-
ating at 98 percent of rated output at 12,225 r/min. The synchronous
shaft vibration amplitude is labelled 1X. The subsynchronous vibration
is at slightly less than 0.25X running speed. The first critical speed had
previously been observed at 80 r/s, but no indication of this appears in
the spectrum plots. The high-pressure and low-pressure shaft ends
show 1X amplitudes that are much different relative to one another,
but the other vibration components are about the same. This turbine
has tilting-pad journal bearings.

Figure 10.10 Frequency spectra for large steam turbine show relative
amplitudes of vibration at 23 percent of running frequency. (General Electric
Company, Fitchburg, Mass.)