Page 66 - Tribology in Machine Design

Basic principles of tribology 53

2.13.6. High-speed unloaded journal
Here it can be assumed that eccentricity is zero, i.e. the journal is placed
centrally when rotating, and the fluid film is in a state of simple shear. The
load P, the tangential resisting force, F and the frictional moment, M are
measured per unit length of the bearing.
Referring to Fig. 2.21, co is the angular velocity of the journal, so that
V= cor

Figure 2.21

This result may be obtained directly from the Petroff eqn (2.128).
Theoretically, the intensity of normal pressure on the journal is uniform, so
that the load carried must be zero. It should be noted that the shaded area in
Fig. 2.21 represents the volume of lubricant passing the section X-X in time
6t, where a = Vdt, so that

The effect of the load is to produce an eccentricity of the journal in the
bearing and a pressure gradient in the film. The amount of eccentricity is
determined by the condition, that the resultant of the fluid action on the
surface of the journal, must be equal and opposite to the load carried.

2.13.7. Equilibrium conditions in a loaded bearing
Figure 2.22 shows a journal carrying a load P per unit length of the bearing
acting vertically downwards through the centre 0. If 0' is the centre of the
bearing then it follows from the conditions of equilibrium that the
eccentricity OO' is always perpendicular to the line of action of P. The
journal is in equilibrium under the load P, acting through 0, the normal
pressure intensity, p, the friction force, q, per unit area and an externally
applied couple, M', per unit length equal and opposite to the frictional