Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)

462 Centrifugal Pumps: Design and Application
vibrations by absorbing some of the vibrational energy. A positive log
dec indicates that a rotor system can damp the vibrations and remain stable,
whereas a negative log dec indicates that the vibration may actually
increase and become unstable. Experience has shown that due to uncertainties
in the calculations, the calculated log dec should be greater than
+ 0.3 to ensure stability. The damped eigenvalue and log dec are sometimes
plotted in a synchronous stability map. The frequency of damped
eigenvalues is generally near the shaft critical speeds; however, in some
heavily damped rotors it can be significantly different from the unbalanced
response.
Rotor stability programs are available that can model the rotor stability
for most of the destabilizing mechanisms; however, some of the mechanisms
that influence it are not clearly understood. It has been well documented
that increased horsepower, speed, discharge pressure, and density
can cause a decrease in the rotor stability. Many rotors that are stable
at low speed and low pressure become unstable at higher values. To predict
the stability of a rotor at the design operating conditions, the rotor
system is modeled and the log dec is calculated as a function of aerodynamic
loading.
Torsional Critical Speed Analysis
All rotating shaft systems have torsional vibrations to some degree,
Operation on a torsional natural frequency can cause shaft failures without
noticeable noise or an obvious increase in the lateral vibrations. In
geared systems, however, gear noise may occur that can be a warning of
large torsional oscillations. Therefore, it is important to ensure that all
torsional natural frequencies are sufficiently removed from excitation
frequencies.
A torsional analysis should include the following:
* Calculation of the torsional natural frequencies and associated mode
shapes,
* Development of an interference diagram that shows the torsional natural
frequencies and the excitation components as a function of speed.
* Calculation of the coupling torques to ensure that the coupling can handle
the dynamic loads.
* Calculation of shaft stresses, even if allowable margins are satisfied.
* Calculation of transient torsional stresses [39] and allowable number of
starts for synchronous motor drives.
Torsional natural frequencies are a function of the torsional mass inertia
and the torsional stiffness between the masses. The natural frequen-