Page 66 - The Tribology Handbook

ROTOR CRITICAL SPEEDS

The speed of a rotor at which a resonant lateral vibration occurs corresponds to the natural resonant frequency in bending
of the rotor in its supports. This frequency corresponds closely to the ringing tone frequency which can be excited by hitting
the rotor radially with a hammer, while it is sitting in its bearing supports. If the supports have different flexibilities in, for
example, vertical and horizontal directions, such as may occur with floor mounted bearing pedestals, there will be two
criticai speeds.
The critical :speed of a rotor can be reduced substantially by adding overhung masses such as drive flanges or flexible
couplings at the ends of the rotor shaft. Figure 10.4 gives guidance on these effects.

U

Nco =: Critical speed
without m2 1 .o
Ncw = Critical speed
with mz added

o.6 0.5 0 u
0.7

0.05
0.25
0.15
0.20
0.10

To determine the effect of additional mass at the shaft end, calculate and h4
Li DSI4
for the rotor, and also the mass ratio -, and read off an approximate value for
ml
the critical speed reduction from the graph.

Fig. 10.4. The effect of an overhung mass such as a flexible coupling on fhe critical speed of a shaft

ROTORDYNAMIC EFFECTS

A full rotordynamic analysis of a machine tends to be complex largely because plain journal bearings give cross coupling
effects. That i?;, a force applied by the shaft to the oil film, produces motion not only in line with the force, but also at right
angles to it. This arises from the nature of the action of the hydrodynamic films in which the resultant pressure forces are not
in line with the eccentric position of the shaft, within the bearing clearance.
Basic points of guidance for design can, however, be stated:

1 The most important pedormance aspect is the rotor response, in terms of its vibration amplitude.
2 The response is very dependent on the design of the journal bearings and the amount of damping that they can provide.
Bearings with full oil films provide the most damping.
3 The likely mode shapes of the shaft need to be considered and the bearings should be positioned away from the expected
position of any nodes. This is because at these positions the shaft has negligible radial movement when vibrating and
bearings positioned at these nodes can therefore provide very little damping.

AI 0.5