Page 258 - Compression Machinery for Oil and Gas

Reciprocating Compressors Chapter 5 243

Torsional Vibration Analysis
Demonstration Case - Synchronous Motor 2 Phase Short
Shaft section 8
Amplification factor = 30
Maximum shear stress
Effectiv radius = 7.35 in
Low cycle failure stress
Inner radius = 0.00
shear endurance limit
Length = 80.00 in
Sped ratio = 1.0
Shear modulus = 1.18 e+7 Psi
16,000
12,000
Predicted number of tolerable events: 491
Stress (psi) 4000 0
8000
–4000
–8000
–12,000
–16,000
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
FIG. 5.54 Representative transient torsional results—two-phase short circuit. (From SwRI results
with University of Virginia ROMAC code TORTRAN.)

6
3
and sloping linearly on a log-log plot between the 1 10 and 1 10 cycle
points. While stress limits are used to evaluate the shafting elements, the pre-
dicted torque levels are typically used to evaluate the couplings.
Typical output from this type of analysis includes calculated dynamic torque
and stress plots for key portions of the trains, a summary of shaft stress results
for the transient analysis, and an evaluation of dynamic torque developed at the
couplings during the transients. Fig. 5.54 provides a representative dynamic
stress history for a synchronous motor two-phase short circuit event, along with
the associated cumulative fatigue results.

Resolution of Typical Torsional Problems

Many torsional issues can be resolved through the practice of frequency avoid-
ance, which generally involves tuning the predicted critical speeds such that an
adequate separation margin is maintained from excitation energy present in a
system. This approach is most useful for fixed-speed applications, but may
not be fully effective for some machines operating over a wide speed range.
In existing reciprocating systems, the frequency shifts are most often accom-
plished by modifying system inertias or interconnecting stiffnesses. Examples
of inertia values that can be most readily adjusted in a reciprocating system
would include external flywheel inertia, or internal flywheels placed between
compressor throws. A common torsional stiffness change would involve a