Page 70 - Tribology in Machine Design

Basic principles of tribology 57

In these equations p 0 is the arbitrary uniform pressure of simple shear. The
constant £ = e/c is called the attitude of the journal, so that

The variation of p around the circumference, for the value of e = e/c=0.2, is
very close to the sine curve. For small values of e/c we can write A = c and
cos0'= — (3/2)(e/c), so that k = 6(e/c)sin® and the pressure closely
follows the sine law

For the value of e/c = 0.7, maximum pressure occurs at the angle 0' = 147.2°
and /c max = 7.62. Also at an angle 0'=212.8°, the pressure is minimum and,
if po is small, the pressure in the upper half of the film may fall below the
atmospheric pressure. It is usual in practice to supply oil under slight
pressure at a point near the top of the journal, appropriate to the assumed
value of e/c. This ensures that p min shall have a small positive value and
prevents the possibility of air inclusion in the film and subsequent
cavitation.

2.13.9. Equilibrium equations for loaded high-speed journal
Referring now to the equilibrium equations discussed earlier, the uniform
pressure p 0 will have no effect upon the value of the load P and many be
neglected. In addition it can be shown that the effect of the tangential drag
or shear stress, q, upon the load is very small when compared with that of
the normal pressure intensity, p, and therefore may also be neglected. The
error involved is of the order c/r, i.e. less than 0.1 per cent. Hence

where

and

The integrals arising from prcos© and grsin© in eqn (2.132) will vanish
separately, proving P is the resultant load on the journal, and that the
eccentricity e is perpendicular to the line of action of P. The remaining