Handbook of Turbomachinery Second Edition Revised - Ventech!

Figure 34 Rotor-bearing-support structure model.
cp, respectively. This simple modeling scheme (i.e., lumped mass pedestals) is
often used by designers/analysts to obtain a ‘‘rough sense’’ of the influence
of the support structure frequency response on the rotordynamic
performance of the system.
The critical speed map for this system without inclusion of the pedestal
mass and stiffness is presented in Fig. 28. For example, with abearing
stiffness of 10 MN/m (5.71 10 4 lbf/in.), the first three forward critical speeds,
as shown on the critical speed map, are 10,358, 17,369, and 65,924 rpm. If
the pedestal mass and stiffness are included for each bearing support as
illustrated in Fig. 35, these critical speeds may change considerably
depending on the natural frequency of the support structure.
For instance, if mp is chosen as 91.75 kg (202.3 lbm) and kp as 367 MN/
m (2.10 ? 10 6 lbf/in.) the natural frequency of each pedestal, as a stand-alone
structure, is approximately 19,098 rpm. This natural frequency is roughly
10% higher than the second forward critical speed of the system with rigid
supports. A whirl speed map for this system is shown in Fig. 35. Whenever it
is observed that a natural frequency of a rotor-bearing-casing system does
not change significantly with rotor spin-speed, it is highly probable that the
associated mode is associated with the nonrotating portion of the system.
The inclusion of additional flexibility to the system, by adding the
pedestal masses, changes the forward critical speeds of the system to 10,184,
16,515, 19,424, 20,086, and 65,930 rpm. The first two forward critical speeds
are lowered in comparison with those associated with a rigid support, and
two additional critical speeds enter the operating range of the system. These
two new modes are essentially foundation modes with relatively large
Copyright © 2003 Marcel Dekker, Inc.