Page 208 - Steam Turbines Design, Applications, and Rerating

Rotor Dynamics Technology 187

10.16 Rotor Stability Criteria
After the dynamic characteristics of each component have been calcu-
lated, the components are combined into a comprehensive model where
either response to mass imbalance or rotor stability can be calculated.
When rotor stability is of concern, the logarithmic decrements of the
critical speeds (damped natural frequencies) are calculated. Generally,
the approach taken is to perform a sensitivity study of log decrement
for different levels of destabilizing force. Log decrements for the first
critical are calculated at different multiples of aerodynamic destabiliz-
ing force to provide a curve as shown in Fig. 10.14.
The curve represents a stable design where the log decrement is pos-
itive at the expected level of destabilizing force. In Fig. 10.14, at
approximately twice the level of destabilizing force gradient, the rotor
is on the verge of instability. When each of the dynamic characteristics
of components in the system are accurately known, the actual level of
rotor stability can be precisely predicted. To account for changes over
time in turbine operation, seal and bearing wear, and other important
parameters, turbines are designed to withstand at least twice the
expected level of destabilizing force before the calculated log decre-
ment goes negative. With this margin of safety, turbines will operate
free from rotor instability.

10.17 Experimental Verification
Any mathematical analysis is only as good as the results it produces.
The validity of the calculations must be verified by controlled tests.
The bearing oil film analysis is a key item in the overall rotor
dynamics analysis. State-of-the-art manufacturers use special labora-

Figure 10.14 Destabilizing force vs. logarithmic decrement. (Gen-
eral Electric Company, Fitchburg, Mass.)