Page 252 - Compression Machinery for Oil and Gas

238 SECTION II Types of Equipment

Mean stress factor, F mean , accounts for the observation that the endurance
stress decreases as mean stress increases. The modified Goodman formulation,
summarized above, provides a working method to account for mean stress. The
mean shear stress factor was calculated for each element from the mean torque
and the stress diameter. Note that the endurance limit calculations for the forced
response analysis include F mean , since the analysis produces purely alternating
stresses. For a transient analysis, F mean ,is not included for the endurance limit
calculation because the stress predictions account for both mean and alternating
stresses.
To account for stress raisers in the shafting, SCFs are applied to each ele-
ment. For example, SCF values for motor cores, keyways, and reciprocating
machinery shaft webs are typically assumed to be in the range of 2.0–3.0. These
values are considered reasonably conservative, based on experience with sim-
ilar machines, and “Peterson’s Stress Concentration Factors” [9].
Note that the shear endurance limits for the forced response and transient ana-
lyses are different, due to the mean shear stress factor, F mean , as discussed above.

Torsional Damping
The damping applied during the torsional analysis can have a significant effect
on the calculated forced response stress results, or cumulative fatigue predic-
tions for the transient events. The intent of this section is to give some brief
practical guidance for typical industrial systems, based upon the common
experience.
When typical disc pack or metallic flexible element couplings is utilized,
trains involving gearboxes, centrifugal compressors, and/or turbines are typi-
cally modeled with model amplification factors (Q values) in the range of
30–35. Trains with engine-driven reciprocating compressors normally involve
a Q value in the range of 35–50. For electric motor-driven reciprocating com-
pressors, Q values in the range of 50–70 are normally assumed.
It is very important to note that the Q values quoted above assume typical
disc pack or metallic flexible element couplings. If elastomeric couplings are
utilized, the resulting Q values will be much lower, and highly dependent on
the type of elastomers involved. Reciprocating engines also represent a special
case in that they may include viscous dampers, which are usually represented as
discrete damping components. Most torsional dampers in use on reciprocating
machines contain a highly viscous silicone fluid, which tends to solidify when
overheated, and must be maintained and/or replaced on a regular basis to ensure
that adequate damping is available to limit stress levels when operating on a
torsional critical speed. Similarly, many modern high power engines use
dampers with tuned steel springs that incorporate forced oil, supplied by the
crankshaft, as the damping fluid. These devices produce high damping levels
and allow high heat capacity, but planned maintenance intervals must also
be followed to ensure proper operation.