Page 85 - Compression Machinery for Oil and Gas

Centrifugal Compressors Chapter 3 75

Blade and Disk Vibrations
While impellers are primarily selected based on their aerodynamic perfor-
mance, they also have mechanical limitations that must be considered in their
selection. An impeller will experience centrifugal stress and deflection due to
rotation. An impeller will also experience thrust force due to differential pres-
sure, and vibratory force due to disturbances in the flow field. Stresses and
deflections must be managed to remain within allowable values, which are
determined by the design, material, and the method of manufacture.
A review of traditional methods of impeller mechanical design have been
presented by numerous authors including Kushner et al. [13, 14] and Singh
et al. [15]. The following are typically examined:

l mean stress,
l disk critical speeds,
l leading edge impeller blade resonance, and
l disk interaction resonance
Impeller mechanical design typically begins with an evaluation of the mean
stress and bore growth. The maximum mean stress must remain within safe
limits during an API 617 impeller overspeed test [8]. In addition, the impeller
to shaft junction must safely transmit the required horsepower either through a
key, hirth, curvic, or bore-to-shaft frictional contact. Once manufactured, the
impeller is overspeed tested at 115% of the maximum continuous speed. After
testing, critical dimensions such as the bore, eye seal, and outside diameter are
reviewed for deviations that would take the part out of tolerance.
Manufacturers have typically avoided disk critical speeds. The term disk
critical speed was defined by Wilfred Campbell [16]. Disks vibrate in a pattern
defined by nodal lines. The resonant operating speed is equal to the natural fre-
quency divided by the number of diametrical nodal lines. When operating at a
disk critical speed, the relative amplitude of the disk around the circumference
in stationary coordinates would form a standing wave in stationary space thus
being easily excited by pressure variations around the impeller. The modes of
concern are from two (2) up to the number of rotating impeller blades divided by
two (B/2). Fig. 3.40 provides a specific example of a predicted and tested three-
nodal diameter for an impeller. In this case, the natural frequency was 774Hz by
prediction and 796Hz by test. Dividing these frequencies by the number of
nodal lines yield the disk critical speeds. In this case, operation near 15,487–
15,920rpm could be disastrous. Overall, there have not been many disk critical
speed problems in the past 50years because all manufacturers try to avoid them.
Blade resonance for the impeller blade’s leading edge can be a concern.
Fig. 3.41 illustrates this concern where the inlet guide vane and blade leading
edge are close to one another. Fig. 3.42 shows an example of Campbell diagram
for a first leading edge blade mode. For this specific impeller, large SM was
present from the 16 upstream return channel vanes as well as the 14 sideload
guide vanes.