Page 238 - Compression Machinery for Oil and Gas

Reciprocating Compressors Chapter 5 227

It should be noted that the torsional stiffness and damping properties of elas-
tomeric couplings are nonlinear, and require special consideration since they
typically become the controlling stiffness for (at least) the first mode when
installed in a train.
For systems with gearboxes, the effects of the speed ratio(s) must be taken
into account in order to accurately calculate the critical speeds. In practice, one
end of the model becomes a reference speed, and the inertia and stiffness values
of the remaining portions of the model are referenced with respect to (gear ratio)
[8]. Input torques and interpretation of calculated torque/stress must also take
speed ratio into account. Another issue that arises with gearboxes is how to rep-
resent the gear mesh stiffness. For most industrial gearboxes, with a fixed ratio
defined by a mechanical connection between pinon and bull gears, the gear
mesh stiffness is sufficiently high that the first several modes are not usually
affected by this parameter. Although the gear mesh stiffness can be estimated,
the controlling springs in typical systems are usually located in the couplings
and driver/driven shaft ends. For variable speed devices (e.g., torque converters,
planetary gear arrangements, etc.) a more in depth analysis is needed to accu-
rately determine the torsional effects on the attached system.
The following Fig. 5.41 provides a table and representative graphics
describing a typical torsional mass elastic model.
A common issue that arises when preparing torsional models for systems with
interference fit couplings is how to appropriately represent the torsional stiffness
contribution of the hub to shaft interference. The most common industry recog-
nized approach to dealing with this issue is referred to as the “one-third shaft pen-
etration rule.” Fig. 5.42 provides an illustration of how this approach is applied.
Each interference fit length is divided into a section 1/3 of the total length, and
another 2/3 of the total length. For the section 1/3 of the overall length, the shaft is
assumed to be free to twist (unattached to the hub). In the remaining section (2/3
of the overall length), the shafting is assumed to be fully bonded to the shaft.
In some cases, preparing an FEA of a torsional model may be advantageous.
One example of this would be when significant localized stress concentrations
exist, such as those located within a reciprocating compressor shaft with unusual
web construction. Fig. 5.43 provides a comparison between FEA and lumped
parameter frequency prediction results for a typical reciprocating compressor
shaft. In this instance, reasonable calculated frequency agreement was found
(within about 4%) for the subject mode. For most typical configurations, a
lumped parameter model is more cost effective and sufficiently accurate.
Peterson’s Stress Concentration Factors [9] provides an excellent resource
for estimating the SCF for common shafting geometries. Fig. 5.44 illustrates
methods for estimating the stress concentration effects for shafts with shoulder
fillets at diameter changes, and for shafts containing keyways. The charts indi-
cate that shoulder fillets can roughly double the dynamic stress developed in
shafting for some geometries, and that keyways have the potential to intensify
stress by a factor of 4. These findings demonstrate the importance, from