Page 89 - Compression Machinery for Oil and Gas

78 SECTION II Types of Equipment

In addition to disk critical speeds, significant minor resonances can also be
excited due to the interaction of stationary vanes and rotating blades. Parametric
equations have been developed for evaluating these interaction resonances. For
certain combinations of the two numbers, the coupled blade/disk modes with
diametric nodal lines are either phase canceled or excitable when an excitation
source coincides with a resonant mode. These equations are represented as fol-
lows [13]:
When not at a disk critical speed,

|y S| |z B| ¼ n
y S ¼ h (3.1)
f n ¼ y S ω
Whereas when at a disk critical speed,
For B >1
h ¼ n (3.2)
f n ¼ n ω

such that B is the number of rotating blades, S is the number of stationary ele-
ments, f n is the natural frequency (Hz), h is the harmonic of speed, n is the num-
ber of diameter nodal lines, y and z are the integers >0, and ω is the rotating
speed (Hz).
An interference diagram as applied to impellers is essentially a graphical
representation of these equations. This type of interference diagram is also
called a “SAFE diagram” [15]. Such methods are used to determine whether
a certain number of stator vanes could excite the impeller to resonant vibrations.
As an example, Fig. 3.43 shows a Campbell diagram of an example impeller
showing all possible modes of vibration. The Campbell diagram indicates that it
is essentially impossible to avoid every mode in this case. However, the equa-
tions of Kushner [13] would indicate that only certain modes are of concern as
the rest would experience phase cancelation. Fig. 3.44 shows test results con-
firming phase cancelation [17]. Phase cancelation was noted to reduce the
response to excitation by as much as having good SM.
On rare occasions, impellers that meet all design criteria may still fail. Konig
et al. [18] and Petry et al. [18a] discuss the potential for Tyler/Sofrin modes
coinciding with an acoustic eigen-frequency coinciding with an impeller mode
shape. These situations are sometimes referred to as “triple coincidence.”

Deflection
Temperatures and pressures can change considerably through compressor start-
up and operation. Thermal deflection of the piping, the casing, and the support
must be managed to keep forces within allowable limits hence preserving equip-
ment alignment.