Page 185 - Compression Machinery for Oil and Gas

174 SECTION II Types of Equipment

in cycles/min, n the synchronous speed in rpm, P r the synchronizing torque
coefficient, this is the stiffness of the electrical field applying torque to the rotor to
restore it to the neutral position in units of kW/rad, and f the electrical line frequency
2
2
in Hz, WK in units lbs-ft (see [2a]).
The electrical natural frequency obviously must be separate from the
running speed in order for the current pulsation to be below 66%. Usually it is
between 0.5 and 0.75 running speed. Also referring to NEMA MG1 21.38
2
4
8
there is a term called the compressor factor C where C ¼0.746 WK n /(P r f 10 )
so the term compressor factor gives a dimensionless measure of the inertia in the
motor and driven system. At C ¼9.24 the system is in electrical resonance and the
1/2
natural frequency is proportional to 1/C . Generally for the multiple throw
machine such as a six throw, satisfactory current pulsation will be achieved at
C ¼20 (f n ¼0.68 running speed) and for a two throw at C ¼30 or greater
(f n ¼0.55 running speed). It is typically acceptable to have a motor with
minimum C ¼20 for a two throw and C ¼15 for four or more throws (consid-
ering the bare motor inertia only). Any additional inertia required will be in
the compressor or can be added to the compressor flywheel. The current pulsation
for both induction and synchronous motors should always be checked during the
engineering phase by the motor manufacturer using the full-load and part-load
crank effort and the driven inertia (supplied by the packager). Most motor
manufacturers will calculate the current pulsation for both induct and synchro-
nous motors using a simple single degree of freedom model, electrical
bus-magnetic field stiffness-inertia of motor and driven equipment lumped as
one mass. This is accurate for most systems where the torsional natural frequency
is above 4 running speed. However, for applications where the first torsional
natural frequency is below 4 then a more accurate result can be obtained using
a two degree of freedom model, electrical bus-magnetic field stiffness-motor
inertia-equivalent shaft stiffness-flywheel and compressor stiffness lumped as
one mass. Not all motor manufacturers can do this calculation, but it will show
more accurate and lower current pulsation for torsionally soft systems. The motor
manufacturer will determine the minimum amount of system inertia required to
achieve 66% for synchronous and 40% for induction motors. The required inertia
can be added using a compressor-mounted flywheel if the motor inertia is not
adequate. Note for a synchronous motor it is recommended that the driven inertia
always be less than the motor inertia. This is because of the strong (up to 40% of
nameplate torque) 2 slip frequency pulsating torque that is induced during
acceleration. During acceleration this 2 slip frequency torque will inevitably
coincide and excite torsional resonance at some brief point during start-up
assuming that torsional resonances occur between 0 and 120Hz (for a 60Hz
electrical frequency). Reciprocating compressor drives are torsionally robust
so if the driven inertia is less than the motor inertia then the resulting torsional
stresses are unlikely to exceed permissible limits. See this chapter for a further
discussion of torsional analysis.