Page 137 - Improving Machinery Reliability

Machinery Reliability Audits arid Reviews 109

EQUIVALENT SYSTEM WODE GRAPES
WODE XO. 1 31.80 HZ ieo7.e3 CPW
1

WODE XO. 2 114.49 HZ 6869.44 CPY

WODE XQ. 3 307.04 HZ 18476.23 CPW

WODZ WO. 4 382.29 HZ 2~37.17 CPW

Figure 3-23. Torsional natural frequencies and mode shapes.

An interference diagram for the turbine-driven compressor with a gear box is given
in Figure 3-24. The rated speeds are 5,670 rpm for the gas turbine and 10,762 rpm for
the compressolr. In this system, excitation at 1X and 2X the gas turbine and compres-
sor speeds are possible. The 1X excitation of gas turbine speed excites the first critical
speed at 1,907 rpm; however, it will not reach the second natural frequency at 6,869
rpm since maximum speed would be less than 6,000 rpm. The compressor speed (1X)
excitation would excite the first torsional natural frequency at 1,005 rpm and the sec-
ond natural frequency at 3,619 rpm on the gas turbine.
Once the system has been modeled and the natural frequencies have been deter-
mined, the forcing functions should be applied. The forcing functions represent
dynamic torques applied at locations in the system that are likely to generate torque
variations. Identification of all possible sources of vibration is an important step in
diagnosing an existing vibration problem or avoiding problems at the design stage.
The most likely sources of dynamic torques include reciprocating engines, gears,
fans, turbines, compressors, pumps, motors (synchronous and induction), couplings,
fluid interaction (pulsations), and load variations.