Page 207 - Tribology in Machine Design

192 Tribology in machine desigr

Substitution into eqn (5.47) gives

This equation indicates that pressures will be distributed radially and
axially somewhat as shown in Fig. 5.14; the axial distribution being
parabolic. The peak pressure occurs in the central plane z=0 at an angle

and the value of p max may be found by substituting @ m into eqn (5.48).

5.5.2. Mechanism of load transmission
Figure 5.14 shows the forces resulting from the hydrodynamic pressures
developed within a bearing and acting on the oil film treated as a free body.
These pressures are normal to the film surface along the bearing, and the
elemental forces dF=pr d0 dz can all be translated to the bearing centre O b
and combined into a resultant force. Retranslated, the resultant P shown
acting on the film must be a radial force passing through O b. Similarly, the
resultant force of the pressures exerted by the journal upon the film must
pass through the journal centre Oj. These two forces must be equal, and
they must be in the opposite directions and parallel. In the diverging half of
the film, beginning at the & = n position, a negative (below atmospheric)
pressure tends to develop, adding to the supporting force. This can never be
very much, and it is usually neglected. The journal exerts a shearing torque
Tj upon the entire film in the direction of journal rotation, and a stationary
bearing resists with an opposite torque T b. However, they are not equal. A
summation of moments on the film, say about 0 }, gives Tj = T b + Pesin 4>
where 0, the attitude angle, is the smaller of the two angles between the line
of force and the line of centres. If the bearing instead of the journal rotates,
and the bearing rotates counterclockwise, the direction of T b and Tj
reverses, and T b = Tj + Pe sin </>.
Hence, the relationship between torques may be stated more generally as

where T r is the torque from the rotating member and T s is the torque from
the stationary member.
Load P and angle <£ may be expressed in terms of the eccentricity ratio e
by taking summations along and normal to the line O bOj, substituting for p
from eqn (5.48) and integrating with respect to 0 and z. Thus