Handbook of Turbomachinery Second Edition Revised - Ventech!

Figure 21 Generalized Laval–Jeffcott rotor.
This system is a 4-degree-of-freedom model with two translations ðu, vÞ and
two rotations ðb, gÞ at the disk center. The translations at both boundary
points are constrained to zero. The excitation force for this model includes
both rotating unbalance and rotating disk-skew terms.
The four precessional modes are circular with two of the natural
modes whirling in the same direction as the rotor spin (forward modes) and
two whirling in the opposite direction (backward modes). Typical first
forward and second forward mode shapes are illustrated in Fig. 22 for a
rotational speed of 3,000 rpm. The backward modes are similar in shape to
the forward modes.
The natural frequencies of whirl, and associated modes are a function of
the rotor spin-speed, and the system parameters. A typical whirl speed map
for this system is illustrated in Fig. 23 for the following selection of
parameters: m ¼ 10 lbm (4.5359 kg), Id ¼ 90 lbm-in. 2 (0.0263 kg-m 2 ), Ip ¼ 0.5 Id,
E ¼ 30 ? 10 6 lbf/in. 2
(206.84 GPa), r ¼ 0.5 in. (1.27 cm), and L ¼ 12 in.
(30.48 cm). The shaft mass is neglected in this example system. The
translational and rotational coordinates are statically coupled for this system.
As a result, all natural modes of motion are affected by the gyroscopic
moments associated with the spinning of the disk.
Copyright © 2003 Marcel Dekker, Inc.