Page 72 - Tribology in Machine Design

Basic principles of tribology 59

2.13.10. Reaction torque acting on the bearing
The journal and the bearing as a whole are in equilibrium under the action
of a downward force P at the centre of the journal, an upward reaction P
through the centre of the bearing, the externally applied couple M' and a
reaction torque on the bearing, M r acting in opposite sense to M' as shown
in Fig. 2.23. For equilibrium, it follows that

Figure 2.23

Substituting for M' and P from eqns (2.146) and (2.148), the reaction torque
(on the bearing) is given by

The variation of the load P together with the applied and reaction torques,
for varying values of e = e/c is shown in Fig. 2.24. It should be noted that the
friction torque on the journal is equal and opposite to M'. Similarly, the
friction torque on the bearing is equal and opposite to M r. Theoretically,
when e/c — Q, P is zero and M' = M r. Alternatively, when e/c approaches
unity, M' and P approach infinity and M r tends to zero, since the flow of the
lubricant is prevented by direct contact of the bearing surfaces. It will be
remembered, however, that this condition is one of boundary lubrication
Figure 2.24 and the foregoing theory no longer applies.

2.13.11. The virtual coefficient of friction
If/is the virtual coefficient of friction for the journal under a load, P per unit
length, the frictional moment, M per unit length is given by eqn (2.127),

The magnitudes of M and P are also given by eqns (2.146) and (2.148), so
that

Differentiating with respect to e and equating to zero, the minimum value of