Handbook of Turbomachinery Second Edition Revised - Ventech!

Figure 4 Forward (a) and backward, (b) whirl circular orbits.
Backward Circular Whirl. This special whirl condition exists when us ¼ vc
and vs ¼ uc. Again, for illustration purposes, let uc ¼ f and vc ¼ g. The
orbit Eq. (2) then simplifies to
uðtÞ ¼f cos ot þ g sin ot
vðtÞ ¼ g cos ot f sin ot
and describes a backward-whirl circular orbit as illustrated in Fig. 4(b). For
this case, the precessional rate of the radius vector op is also constant over
the orbit and is equal to negative the whirl frequency o of the orbit.
Superposition of Elliptic Vibrations
The steady-state motion of a rotor system frequently involves the superposition
of several frequency components, e.g., natural frequencies of whirl,
rotor spin-speeds, and external excitation sources. This situation can often
be represented at a typical structural point as the superposition of several
elliptic vibration components of the motion.
If all the frequencies are commensurate (i.e., the ratios of all possible
frequencies are rational numbers), then the resulting superposed motion is
periodic. If any one ratio is not commensurate, the resulting motion still
possesses a discrete frequency content; however, the motion is not periodic.
Several special cases exist in the superposition of elliptic vibrations
that are often of interest to rotordynamists.
1. Identical frequency superposition. If all the frequencies in a
superposition of elliptic vibrations are identical with whirl frequency o, then
the resulting motion is also an elliptic vibration with the same whirl
frequency.
2. Subharmonic superposition. This situation occurs when an elliptic
vibration with whirl frequency o is superposed with a second elliptic
Copyright © 2003 Marcel Dekker, Inc.
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