Page 138 - Tribology in Machine Design

124 Tribology in machine design

The object is to ensure that the thrust block and the collar or rotating
pivot maintain an unchanged form after wear. At any radius, r, where the
intensity of pressure per unit area of bearing surface is p, work expended in
friction is proportional tofp V, volume per unit area worn away by a vertical
displacement, 6 = d sin a, so that/p V is proportional to 6 sin a. Since/and 6
are constant, we have

Figure 4.28
where V = rco is the circumferential velocity of the pivot surface at radius r,
and co is the angular velocity of the pivot in radians per second. If it is
desired that the pressure intensity p should be constant, then, writing
K = rco, eqn (4.66) becomes

Referring to Fig. 4.28, CD is a half-section through the axis of the bearing
surface and AB is the tangent to the profile at radius r, where AB = r/sin<x..
Hence for uniform pressure and uniform wear the profile must be such that
the length AB of the tangent is the same for all values of r. If the bearing is of
any other shape it will tend to approach this condition after a lapse of time.
Equation (4.66) may be applied to any profile. Thus if a is constant and
equal to 90°, then for uniform wear:

pF = prco=const,
so that the pressure intensity p is proportional to 1/r and becomes infinite at
the centre where r=0.

4.9.2. Pivot and collar bearings

Two alternative methods of calculation are given below, based on the
following assumptions:
(i) for a new well-fitted bearing the distribution of pressure is uniform;
(ii) for a well-worn bearing under conditions of uniform wear

or since V = rco, and a is constant for the bearing surfaces,

(A). Flat pivot or collar - uniform pressure
Figure 4.29, cases (b) and (c), represent a flat collar and pivot in which the
external and internal radii of the bearing surfaces are r t and r 2 respectively.
Under an axial load Q the bearing pressure is assumed uniform and of