Handbook of Turbomachinery Second Edition Revised - Ventech!

otating assembly for these modes, the external damping at the bearing
supports will be less effective and the response will be significantly larger
than at the rigid-body critical speeds. Mass eccentricity limits may need to
be reduced and rotor–structure clearances increased in order for a
supercritical rotor to be reliable.
Double Overhung Rotor: Disks Outside the Bearings
Next, consider the same rotor-bearing system except with the disks at the
ends of the rotor instead of between the bearings. The critical speed map of
Fig. 40(a) shows how the first four synchronous whirl speeds change with
bearing support stiffness, and the corresponding mode shapes are shown in
Fig. 40(b) for abearing support stiffness of 100,000lbf/in. (17.51 MN/m).
The critical speed associated with the ‘‘cylindrical’’ mode does not change
significantly, but the critical speed associated with the ‘‘conical’’ mode is
three times lower than in the ‘‘straddle-mounted’’ configuration. The
‘‘cylindrical’’ mode does not change because it is controlled by the weight of
the rotor and the bearing stiffness. The ‘‘conical’’ mode changed because it
is controlled by the diametral mass moment of inertia of the rotor assembly
(which increased significantly) and the coupled stiffness of the bearing
supports.
Note that the node points for the ‘‘bending modes’’ again coincide
with the disks and their relatively large inertias. Due to the change in its
mode shape, the first bending mode of this configuration is reduced about
67% from that of the ‘‘straddle-mounted’’ configuration. The nodes in the
first ‘‘bending mode’’ are located closer to the bearings, thus increasing the
percent strain energy in the rotating assembly. ‘‘Supercritical’’ operation
through this critical speed would result in increased response compared to
that of the original straddle-mounted configuration.
Single Overhung Rotor
Next consider a rotor configuration with both disks overhung at the aft end
of the rotor and the aft bearing moved forward 4.0 in. (10.16 cm). The critical
speed map of Fig. 41(a) shows how the first four synchronous whirl speeds
change with bearing support stiffness. The corresponding mode shapes are
shown in Fig. 41(b) for a bearing support stiffness of 100,000lbf/in.
(17.51 MN/m). The critical speed associated with the ‘‘cylindrical’’ mode is
significantly reduced since the aft bearing now effectively supports the inertia
of both disks. The critical speed associated with the ‘‘conical’’ mode is
roughly the same as in the straddle-mounted configuration because both the
diametral mass moment of inertia of the rotor and the coupled stiffness of the
Copyright © 2003 Marcel Dekker, Inc.