Handbook of Turbomachinery Second Edition Revised - Ventech!

Disk-Skew Excitation
As was established earlier, a rotating unbalance force provides a spin-speed
squared translational force at the connection of the disk to the shaft. A similar
excitation exists if the disk happens to be assembled on the shaft such that the
disk is skewed, at an angle e, relative to the shaft as illustrated in Fig. 19.
The ‘‘disk-skew’’ moment vector, associated with the ðx, yÞ rotatory
displacement coordinates ðb, gÞ, for this imperfect configuration is given by
O 2 ðId IpÞ sin e cos e
0
cos Ot þ
0
ðId IpÞ sin e cos e
sin Ot ð22Þ
Thus, the disk-skew excitation forces are similar to unbalance forces
associated with a mass center that does not coincide with the spin axis. The
difference is that a disk-skew produces a moment of force at the connection
of the disk to the shaft while a mass eccentricity produces a translational
force. The steady disk-skew amplitude response, normalized with respect to
the skew-angle e, is shown in Fig. 20 for aLaval–Jeffcott rotor with a
positive disk-skew angle. A resonance condition is pencountered
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi when the
pspin-speed
ffiffiffiffiffiffiffiffiffiffiffi equals the first critical speed, Of ¼ or= 1 Ip=Id , where or ¼
kr=Id represents the disk rotatory natural frequency for a nonspinning
shaft. As the spin-speed increases to very high speeds, the gyroscopic
stiffening effect of the disk dominates, and the amplitude of the disk angular
rotation approaches the disk-skew angle. In effect, the disk spins, without
nutating, about its axial principle axis that becomes co-aligned with the
bearing centerline.
Figure 19 Typical disk-skew configuration.
Copyright © 2003 Marcel Dekker, Inc.