Hydrocarbon Processing - June 2021 - GP-24

TURBOMACHINERY
machines supported in oil bearings, which
is the focus of this article. Note: Axial motion
in the Z direction is not neglected for
active magnetic bearing control systems,
where they can play a significant role.
Every turboexpander vibrates at some
minimum level at least once per revolution
because no rotor can be perfectly
balanced. The OEM must, at a minimum,
ensure that the design can tolerate the
motions imposed by the residual imbalance
in the rotor. Therefore, the primary
objective of performing rotor dynamics
analysis is to predict the motion of the rotor
and ensure that the vibration levels are
contained within acceptable limits.
Vibration limits may be set by available
clearances between rotating and stationary
components (e.g., bearings and seals), or
by limitations on bearing load capacity. It is
important to avoid operating near a critical
speed, or natural frequency, to avoid very
high amplitude vibrations and stresses.
Vibration limits can also be set by experience
and empirical data. API-617,
for instance, limits overall vibration to
the lesser of 1 mil or √12,000/Nmc
, where
Nmc is the maximum continuous running
speed of the machine. However, the OEM
may find higher levels of vibration acceptable,
depending on the type of bearing
used, its clearances, and its stiffness and
damping properties.
The term " critical speed " is worthy
of comment. The definition of the term
itself is not uniform across the industry.
Therefore, it is important that the OEM
and end user have a common understanding.
For instance, API has slightly different
definitions across different standards
(e.g., API 616, API 617, etc.)
For the purpose of this article, the following
definition is adopted: A critical
speed is a shaft rotational speed at which
the rotor bearing support system is in a
state of resonance. This does not mean
that a critical speed is necessarily an unstable
operating point. A rotor running at a
critical speed will normally run at elevated
vibration levels. The level of vibration is
inversely related to the amount of damping
in the system. The level of magnification
is known as the amplification factor.
Rotor systems with sufficiently high
Ua
w4
w4
= 8
W4
N
w3
damping, and therefore low amplification
factor at around the critical speed, do not
require any separation margin, or avoidance
speeds, and therefore are typically ignored.
As such, these sufficiently damped
resonant frequencies are often not treated
as critical speeds. Another reason for not
considering sufficiently damped resonant
frequencies is that they sometimes cannot
be reproduced on the test stand.
Associated with critical speeds are
their vibration modes, which are the
shapes the shaft will take while running
at a critical speed (FIG. 3). These mode
shapes are commonly referred to as the
first rigid (translatory or bouncing)
mode, the second rigid (conical or rocking)
mode, and the nth (first, second,
third, etc.) bending mode.
It is not uncommon for engineering,
procurement and construction companies
(EPCs) or end users to request a rotor dynamics
analysis report from the OEM for
review during the design stage. The following
section provides an overview of the
components of such a report. For illustration
purposes, results from an actual case
study are included under each heading.
Case study machine. The machine in
question is a 5,395-hp turboexpander
processing approximately 170 MMsft3
d
Ua
1st
= 8
W3
N
Mode (W3 > W4)
Ua3
= 8
W4
N
w4
3rd
Mode
Bearing location and reaction
Unbalance placement
Overhung components (couplings, impellers, etc.)
FIG. 3. Rotor mode shapes (from API 617).2
24 MAY/JUNE 2021 | GasProcessingNews.com
Note: Rigid (solid) and flexible (dashed)
shaft modes shown
w3
2nd
Mode (W3 > W4)
Ua2
w3
= 8
W3
N
of natural gas feed (85.7% methane, 9.3%
ethane, 2.5% propane, etc.) at a supply
pressure and temperature of 865 psia and
-27°F. The expander is loaded by a centrifugal
compressor stage handling a flow
of mostly methane (97.9%) at a flow rate
of 285.61 MMft3
d and compressing at a
pressure ratio of approximately 1.21. The
rotor speed is 17,500 rpm at the design
point, but it can fluctuate between +2.74%
and -1.89% of that value, depending on
the off-design operating conditions.
Rotor model. This machine was required
to feature oil bearings. A rotor
dynamic analysis (RDA) based on the
finite-element technique was performed,
using a commercial software to determine,
among other issues, which design of
radial oil bearings was most appropriate.
The geometric model of the turboexpander
rotor-bearing system is shown in FIG. 4.
The rotor consists of a solid shaft with
one overhung wheel on each end. The
wheels are computer numerical control
(CNC) machined from forged aluminum
alloy and attached to the shaft via a tight,
slip-fit, polygon fit (which provides high
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Hydrocarbon Processing - June 2021

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