Page 261 - Tribology in Machine Design

246 Tribology in machine design

(i) the applied load MK producing a circular contact of radius a:

where p max is the peak pressure at the centre;
(ii) the contact radius a is found from the relationship

where R is the equivalent radius defined by l/R = l/R^ + l/R 2 and £is
the equivalent materials modulus

where v denotes the Poisson ratio and the subscripts 1 and 2 refer to the
two materials in contact;
(iii) the gap outside the main contact region at any radial distance r is (see
Fig. 6.6)

The expression in square brackets can be approximated over the region
a^r^2a by

By denoting that e = (11.43 W)/4aE/i 0, eqn (6.32) becomes

By writing a non-dimensional version of the Reynolds equation in polar
coordinates, and considering the quadrant of the annulus ADCBA, only the
final differential equation can be derived. Obviously, the equation does not
have an exact analytical solution and it is usually solved numerically. This
has been done by many workers and the solution in a simplified form is as
follows

where /i 0 is the oil viscosity at atmospheric pressure, a is the pressure-
viscosity coefficient and V is the surface velocity. Equation (6.34) has been
verified experimentally and it is now clear that despite an unfavourable
geometric configuration, an elastohydrodynamic lubrication film exists at
the nominal point contacts over a very wide range of conditions.

6.10. Cam-follower The schematic geometry of a cam-flat-follower nose is shown in Fig. 6.7.
system The film parameter X for a cam-follower system can be calculated by the