Page 199 - Tribology in Machine Design

184 Tribology in machine design

the usual practice to assume no side leakage, i.e. a bearing of infinite
dimension / such that velocity w and dp/dz are zero. Equation (5.23) is then
simplified to

Integrating once

For the bearing of Fig. 5.10 with a film thickness at the entrance of h { and at
the exit of h 2 (shown greatly exaggerated), let the inclination be
a = (/ij — h 2)/b. Then h = h 1— = h 2 + <x(b — x) and dh/dx= — a. Hence

The boundary conditions p=0 at x=0 and x=b are utilized to obtain

where the latter is in terms of the minimum film thickness h 2. The total load
P is found by integration over the surface.
Machining or mounting the pads within the tolerances required for the
very small angle a is difficult to attain and thus the pads are usually pivoted.
The relationship between pivot distance, x p, and the other variables may be
found by taking moments about one edge of the pad. Since side leakage
does occur, correction factors for the derived quantities have been
determined experimentally and are available, for instance, in ESDU-82029.
The theory for flat pads indicates that the maximum load capacity is
attained by locating the pivot at x p =0.5786, but there is no capacity if the
motion is reversed. For bearings with reversals, a natural location is the
central one, x p = Q.5b, but the flat pad theory indicates zero capacity for this
location. However, bearings with central pivots and supposedly flat
surfaces have been operating successfully for years.

5.4.1. Flat pivot
The simplest form of thrust bearing is the flat pivot or collar. In such cases
the separating film of lubricant is of uniform thickness everywhere and the
pressure at any given radius is constant, i.e. the pressure gradient is only
possible in a radial direction. If the oil is introduced at the inner edges of the
bearing surfaces it will flow in a spiral path towards the outer circumference
as the shaft rotates. It is clear, however, that maintenance of the film will