Page 61 - Tribology in Machine Design

48 Tribology in machine design

where o r is the applied stress at x = a and <T O is the applied stress at the crack
point. For four intervals

If the effective stress on the crack calculated in this way is denoted by a xy

where S is the non-dimensional form of a xy. Values of S were calculated for
two different friction coefficients, tan /?, of the opposing faces of the crack.
The case of no friction on the wear surface was used since S is relatively
insensitive to tana.

2.13. Film lubrication 2.13.1. Coefficient of viscosity
Relative sliding with film lubrication is accompanied by friction resulting
from the shearing of viscous fluid. The coefficient of viscosity of a fluid is
defined as the tangential force per unit area, when the change of velocity per
unit distance at right angles to the velocity is unity.
Referring to Fig. 2.18, suppose AB is a stationary plane boundary and
CD a parallel boundary moving with linear velocity, V. AB and CD are
separated by a continuous oil film of uniform thickness, h. The boundaries
are assumed to be of infinite extent so that edge effects are neglected. The
fluid velocity at a boundary is that of the adherent film so that velocity at
AB is zero and at CD is V.
Let us denote by v velocity of fluid in the plane EF at a perpendicular
distance y from AB and by v + dv the velocity in the plane GH at a distance
y + dy from AB. Then, if the tangential force per unit area at position y is
denoted by q

and in the limit

Figure 2.18