Page 75 - Compression Machinery for Oil and Gas

66 SECTION II Types of Equipment

amplification factors (AFs). According to the API 617 [8], if the foundation
flexibility is less than 3.5 times the bearing stiffness, then a foundation model
should be included.
An unbalance response analysis is used to determine the rotor vibration
amplitude from start-up through the maximum continuous speed and all the
way up to 150% of the maximum continuous speed. The magnitude and place-
ment (location) of the unbalance will affect the rotor response. For centrifugal
compressors, the common unbalance amount is typically the amount described
by API, 4*W/N oz-in, where W is the rotor weight in pounds and N is the rota-
tional speed in rpm. In general, the unbalance placement is oriented with respect
to the points of maximum amplitude for the subject mode shape. API 617 and
684 offer recommendations for unbalance configurations for various example
mode shapes.
The unbalance response calculation produces amplitude and phase-response
plots. Critical speeds are identified where the system’s sensitivity to unbalance
excitation is maximized. Fig. 3.33 shows an example unbalance amplitude
response plots for the first and second critical speeds for the subject example
rotor. The first critical speed is well excited by mid-span unbalance, meeting
API separation margin (SM) requirements. The second critical speed for this
example is excited by quarter-span unbalance, with the unbalance amounts
placed 180 degrees out-of-phase. Damping notably increases the second critical
speed as compared to an undamped analysis. In addition, no SM is required for
the second critical speed since the AF is below 2.5.
Fig. 3.34 describes the API SMs and AF calculations for rotor unbalance
response. It is noted that SM requirements defined by API are a function of
AF, and are provided in equation form in 617 and 684 [7]. For a lightly damped
response, the AF will be higher and require a larger SM. When damping
increases, the AF is lowered and the SM requirement decreases. API considers
any AF below 2.5 to be well damped and does not require a SM.
As part of the unbalance response calculation, the response amplitude at the
seals (in addition to the bearings) should be considered. As per API 617 [8], the
major axis of the rotor response orbit cannot exceed 75% of the design seal
clearances. In order to verify that a rotor design meets these requirements,
the rotor orbit should be calculated at the annular seal locations, at the speed
of maximum displacement (i.e., the first critical speed). Bearing eccentricity
should be included for this seal clearance check. In addition, rotor sag should
be considered, especially for larger compressors, such as those in liquefied nat-
ural gas (LNG) applications, where the rotor static deflections due to gravity can
become notable.
Rotordynamic stability is assessed through the calculation of damped eigen-
values (or damped natural frequencies) and associated log dec values. For cen-
trifugal compressors, it is necessary to include potential destabilizing forces
from all close-clearance components, including journal bearings, annular seals
(including labyrinth and damper seals), and impellers.