Hydrocarbon Processing - June 2021 - GP-27

TURBOMACHINERY
bearings, the bearing pedestals and the
skid (i.e., the machine support structure)
can handle the loads imposed on them.
Unbalance response plots. Until this
point in the analysis, the designer has not
accounted for excitation forces, such as
unbalance. The unbalance in the rotor
will generate a dynamic load at the same
frequency as the rotation of the rotor (one
excitation per revolution). The shape of
the unbalance force will be related to the
amount and distribution of unbalance (in
terms of weight). Three unbalance weight
configurations are typically considered in
an analysis for any turbomachine, and they
must follow API guidelines. The amount
of balance is determined by the balancing
tolerance applicable for each machine,
and the unbalance weights are arranged
spatially in such a way as to excite the predominant
modes. A single weight in the
middle of the rotor (which may be called
a purely static unbalance) would tend to
excite the cylindrical or bounding mode.
A " couple " unbalance (i.e., one in which
the weights are separated axially but opposite
exactly 180°) will excite the conical
or " hinging " mode.
The simulation in FIG. 9 shows the
speed at which the vibration will peak as
the rotor goes up in speed. This is the critical
speed, and it is an important parameter
to predict and monitor during field startup.
The shape of the curve itself is important
because it indicates the rate at which
the vibration will increase as the machine
ramps up. Well-damped, smoothly increasing
curves with a wide base and a " dull "
peak like the one pictured in FIG. 9 are
preferable over one with a sharp and narrow
peak. In the latter, which is a result of
poor damping, the vibrations will quickly
jump for a small increase of rotor speed,
rendering the process of ramping up to
speed somewhat unreliable and unpredictable.
The shape of the curve is quantified
by a parameter called " amplification factor. "
From an API 617 perspective, those
speeds with amplification factors greater
than 2.5 are considered critical speeds.
Another issue to consider is that the
rotor must not run too close to the critical
speed. The parameter to watch is the
separation margin, which is the amount
of separation between the critical speed
(Nc) and the rated speed.
The data generated by the response
analysis (i.e., vibration response magnitude
and phase angle) can be validated
with field measurements as long as the machine
is equipped with proper instrumentation
and data acquisition equipment,
either in the field or in a factory test stand.
Clearance checks. The analysis must
show that available clearances between rotating
and stationary components are not
exceeded, with considerations for margin.
For instance, API 617 requires that shaft
vibrations must not exceed more than 75%
of minimum design diametral clearances.
In summary, a successful rotor dynamics
analysis should ensure that the overall
2.5
1.5
2
1
0.5
-0.5
-1
KXY
, lb/in.
FIG. 8. Influence of cross-coupling stiffness in log dec. KXX
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
5,000
stiffness in the horizontal and the vertical direction, respectively. In this case study, KXX
and KYY refer to the direct bearing
= KYY
.
10,000
20,000
30,000
40,000
50,000
60,000
70,000
vibration levels will not exceed clearance
or load limits, and that the overall rotor
bearing system is stable throughout the
operating speed range.
Conclusion. Rotor dynamics analysis is a
key part of turbomachinery design. Ensuring
that a rotor is stable and will operate
within acceptable levels of vibration is necessary
for long-term, reliable operation.
API 6172
such an analysis to make sure that all parties
agree to what defines a suitable design.
Log dec vs. KXY
can be referenced for reviewing
Nc = 8,000
AFy = 0.89
SMa = 0%
SMr = 0%
10,000
FIG. 9. Rotor dynamic response plot.
Gas Processing & LNG | MAY/JUNE 2021 27
15,000
Rotor speed, rpm
20,000
25,000
30,000
Response (at expander-side pickup), mils p-p
Log dec
RatedCOS
MaxCOS

Hydrocarbon Processing - June 2021

Table of Contents for the Digital Edition of Hydrocarbon Processing - June 2021