Page 258 - Tribology in Machine Design

Friction, lubrication and wear in higher kinematic pairs 243

3tp
on the piezo-viscous relation /i = /i 0e and reflects the change of viscosity
with pressure

fj. G is the lubricant viscosity at inlet surface temperature, V it V 2 are the
surface velocities relative to contact region

where the plus sign assumes external contact (both surfaces convex) and the
minus sign denotes internal contact (the surface with the larger radius of
curvature is concave), w is the total load on the contact and L is the length of
the contact.
The viscosity of the lubricant at the temperature of the surface of the solid
in the contact inlet region is the effective viscosity for determining the film
thickness. This temperature may be considerably higher than the lubricant
supply temperature and therefore the inlet viscosity may be substantially
lower than anticipated, when based on the supply temperature. Usually the
inlet surface temperature is an unknown quantity in design analyses. The
solution to this problem is to use the lubricant system outlet temperature or
an average of the inlet and the outlet temperatures to obtain an estimate of
the film thickness. It should be pointed out that the predicted film thickness
may be too large when the system supply temperature is used and the flow
of lubricant is not sufficient to keep the parts close to the lubricant inlet
temperature. Input data characterizing the lubricant, that is its viscosity,
pressure-viscosity coefficient and temperature-viscosity coefficient are
usually available from catalogues of lubricant manufacturers.
The best way to illustrate the practical application of eqn (6.27) is to solve
a numerical problem. Two steel rollers of equal radius R l = R 2 = 100mm
and length L = 100 mm form an external contact. Using the following input
data estimate the thickness of the lubricating film

Equivalent radius of the contact