Page 253 - Compression Machinery for Oil and Gas

Reciprocating Compressors Chapter 5 239

Forced Response Analysis
Torsional forced response analyses are used to document the stress and/or tor-
que levels generated in the interconnecting stiffness elements in the model, as
the unit runs at various operating conditions. For reciprocating engines or com-
pressors, the torque generated in the swept volume of the cylinders must be
determined and applied to the model as a forcing function. The resultant stress
is evaluated on a station-by-station basis to determine acceptability using
methods such as those outlined in the Allowable Stress Methodology section.
Fig. 5.51 provides representative cylinder torque effort and frequency con-
tent information. The individual cylinder torque effort histories are utilized to
generate the total applied torque plot, and determine the magnitude of the var-
ious orders involved based upon the phasing of the throws. In this particular
case, significant 1 and 3 are generated.
Fig. 5.52 presents the resultant dynamic torque and stress distribution within
the train. The dynamic torque levels are typically compared to the OEM pro-
vided coupling and/or shaft torque ratings. The dynamic stress levels for the
shafting are typically plotted against the allowable stress limits described in
the Allowable Stress Methodology section for design factors corresponding
to 1.5 and 2.0. For the methodology presented here, design factors equal to
2.0 or above are considered to correspond to infinite life. Changes to operating
conditions, speeds, or mass elastic characteristics (to shift critical speeds) are
generally recommended in cases where a design factor below 1.5 has been cal-
culated, in order to improve long-term reliability.
For reciprocating machines, it is frequently useful to conduct the stress cal-
culations over a range of speeds in order to document the effects of operating on
the flank of a critical speed. Fig. 5.53 provides a typical graphic for displaying
this type of information in a waterfall format.

Transient Torsional Analysis
Transient torsional analyses are usually conducted for trains involving electric
motors. The transient events most often studied include start-up, two-phase
short circuit, and three-phase short circuit. It should also be noted that genera-
tor/motor synchronization events may also be studied, along with the varying
effects of soft start strategies (as opposed to across-the-line or line-to-line start-
ing events). A significant difference exists between synchronous and induction
motors during the start-up event. Generally speaking, a synchronous motor pro-
duces more significant dynamic torque during start-up, and involves a forcing
function which varies with respect to speed (generally twice the line frequency
at zero speed, dropping to 0Hz at synchronization speed). However, in most
cases the resultant shaft stress levels are tolerable if the total driven inertia
(compressor, flywheel, coupling hubs, etc.) is less than the motor inertia (see
Ref. [5], section 3.4.2.1). Induction motors tend to generate forcing torques
at various frequencies and relatively lower amplitudes during the start-up event.