Page 237 - Compression Machinery for Oil and Gas

226 SECTION II Types of Equipment

viscous damper conditions for engines (if applicable). The resultant compressor
or engine cylinder excitation is applied to the train during the forced response
stress analysis. With trains involving motors, slip and/or VFD frequencies are
normally evaluated in addition to mechanical orders of running speed.
During the forced response calculations, stress concentration factors (SCFs)
are developed to account for keyways, major diameter changes, fillet radii, etc.
based on shaft geometry provided by the equipment manufacturers and/or expe-
rience with similar machines. The resultant intensified stress and/or dynamic
torques developed at each station in the model are then compared against allow-
able values (provided by the OEM or independently developed) to determine
acceptability.
A torsional analyst will typically evaluate the provided train configuration
and make recommendations for modifications, if necessary, to shift the calcu-
lated torsional critical speeds or otherwise improve the damage tolerance of the
shafting.

Torsional Mass Elastic Models
Torsional models are normally prepared by lumping major system masses (e.g.,
motor cores, piston/rod inertias, flywheels, etc.) and connecting these with tor-
sional stiffness values to represent the shafting and couplings. It is important to
maintain sufficient fidelity in the model to accurately reflect the dynamically
important modes. It is also prudent to lump the model in such a way as to main-
tain constant diameters within each interconnecting stiffness value when prac-
tical, thereby limiting the effects of stress concentration to the parts of the
shafting that will experience it. This latter practice avoids overly conservative
forced response stress and cumulative fatigue results.
For typical solid shafting, the stiffness of the shaft may be estimated by
using the following formula:
∗ ∗ 4 ∗
K ¼ JG=L ¼ π G D = 32 Lð Þ
Likewise, the following formula may be used to estimate the polar mass
moment of inertia for solid cylinders or discs:
∗ ∗ ∗
Ip ¼ π=32 ρ L D 4
In many cases, torsional stiffness and inertia information is available from
the OEM involved (EG: coupling stiffness, hub inertias, motor core inertia,
reciprocating throw inertias, etc.). In most cases, these values are not considered
controversial. Although calculating torsional stiffness values for the webs of
reciprocating machines can be challenging for some geometries, several
resources exist to provide guidance in mass elastic model generation, including
the book by W. Ker Wilson entitled “Practical Solution of Torsional Vibration
Problems” [8]. If necessary, solid models and/or FEA calculations may be uti-
lized to confirm or estimate these values.