Page 217 - Steam Turbines Design, Applications, and Rerating

196 Chapter Eleven

TABLE 11.1 Comparison between Vibration Testing and NASTRAN Analysis
of a Particular Design
NASTRAN
1st rotor 2nd rotor Maximum
test fn, test fn analysis estimated
Mode Hz Hz fn, Hz Error,* % error, %
1 1st TAN 835. 790. 799. 2 5
2 1st AXIAL 1420 1423. 1274 10 10
2 AXIAL ROCKING — 1675. 1447 14 15
4 TAN FIXED 3020 2860 2879 2 5
SUPPORTED
5 2931
6 3007
7 3047
8 3090 3153 3058 2 5
9 Axial “U” 3580 3546 3531 2 5
10 2nd TAN 4047 — —
11 AXIAL, FIXED — 3880. 4483 16 20
SUPPORTED —
12 4688
13 — 4125. 4765 16 20
* Error is that compared to be average test value.
SOURCE: Dresser-Rand Company, Wellsville, N.Y.

quency above the fourth harmonic of running speed excitation for vari-
able speed turbines. For constant speed turbines it is conceivable to
have a blade frequency that is less than four times the running speed,
but it will be tuned between exciting harmonics at the operating r/min.
Nozzle-passing frequency excitation is caused by the steam wakes at
the trailing edges of nozzle vanes as the blade passes from one nozzle
to the next. The first harmonic of nozzle-passing frequency is equal to
(r/min/60 × number of nozzles in 360°) in units of Hertz.
Partial admission excitation is similar to nozzle-passing frequency
excitation, except instead of each nozzle causing one pulse of excita-
tion, a group of active nozzles will be causing the exciting force. As a
blade passes from inactive nozzling to an active group of nozzles back
to inactive nozzling, it will receive one pulse of excitation. Partial
admission nozzling will provide a low harmonic of running speed exci-
tation that is dependent on the number and spacing of the nozzle
groups.
There are other exciting frequencies that occur in turbines besides
these three most common discussed earlier. Struts or support ribs in
casings can cause disturbances in the steam flow. Diaphragm manu-
facturing variations can cause both nozzle passing and low harmonics
of running speed excitations; sharp turns in the steam path can cause
random excitations.
The vibratory stress at a resonant condition depends on the
strength of the exciting force, the resonant mode shape of the blades,