## Bd2

Thus, if the cross-coupled coefficients are known, it is possible to determine the critical mass and the orbital frequency. If the mass acting on the bearing exceeds or equals the critical value, then an instability will occur.

Dynamic Stability of Various Bearing Types Several parameters can be used to establish the stability characteristics of a particular type of bearing. The most significant is the critical mass, derived above. It is also possible to get some feel for stability from purely steady-state performances by examining the bearing attitude angle. The larger the attitude angle, the greater the cross-coupling influence and the worse the stability characteristics. Interpreting attitude angles, however, can prove misleading.

Figure 22 shows plots of the attitude angle g versus the load parameter Wfor some of the different types of bearings previously described. The contradiction in these results is that the symmetric three-lobe bearing has higher attitude angles than the two-groove cylindrical bearing even though, as will be subsequently demonstrated, it has superior stability characteristics. The reason for the higher attitude angle is that the bearing is cavi-tating in the diverging region of the loaded pad, which results in a large shift in the journal. Whirl motion, however, is prevented by the accompanying lobes.

A more direct and accurate approach to establishing bearing stability is to determine the critical mass acting on the bearing. Figure 23 shows the results obtained for the fixed

FIGURE 22 Attitude angle versus load parameter for various bearing types.
FIGURE 23 Critical mass versus load parameter for various bearing types.

bearing geometries previously discussed. For any particular bearing geometry, if the critical mass attributable to the bearing exceeds that of the data plotted, the bearing will be unstable. Thus, if the plotted point falls to the right of the bearing line, the bearing is stable; if it falls to the left, the bearing is unstable.

The critical mass is defined as follows:

where M = nondimensional critical mass m = dimensional critical mass, lb • s2/in (kg • s2/mm) o) = shaft speed, rad/s R = shaft radius, in (mm)

c = bearing machined radial clearance, in (mm) m = lubricant viscosity, lb sec/in2 (Pa • s) L = bearing length, in (mm)

An examination of the curves in Figure 23 clearly indicates the superiority of the canted three-lobe bearing and the inferiority of the cylindrical configuration.

example Consider a high-speed bearing for which

The value of M is obtained from Figure 22 and indicated in Table 4 for the various bearing types considered. Dimensional units are also given. Table 4 clearly indicates that the lobe bearings can permit significantly more attributable mass than the cylindrical bearing can. If a symmetric rotor is being supported by two bearings, the cylindrical bearings would be unstable if half the weight of the rotor exceeded 14.7 lb (6.67 kg). The half weights go to 258 lb (117 kg) and 501 lb (227.2 kg) for the symmetric three-lobe and canted three-lobe bearings, respectively. No mention has been made of the tilting-pad bearing because, for all practical purposes, these bearings are always stable.

## Survival Treasure

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