Page 56 - Tribology in Machine Design

Basic principles of tribology 43
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Because Q = T /16K and therefore T= (16QR)\ Substituting the expression
for T into eqn (2.100) and rearranging gives

and finally,

and C 2 is a constant of integration. Equation (2.102) gives the dependence
of Q on L. The dependence of Q on the other parameters of the system is
contained in the quantities C t and C 2 of eqn (2.102).
Equation (2.102) implicitly defines the allowed ranges of certain
parameters. In using this equation these parameters cannot be allowed to
assume values for which the assumptions made in obtaining eqn (2.102) are
invalid.
One way of determining C l and C 2 in eqn (2.102), is to perform a series of
controlled experiments, in which Q is determined for two different numbers
of operations for various values and combinations of the parameters of
interest. These values of Q for different values of L enable Ci and C 2 to be
determined. In certain cases, however, C t and C 2 can be determined on an
analytical basis. One analytical approach is for the case in which there is a
period of at least 2000 passes of what may be called zero wear before the
wear has progressed to beyond the surface finish. This is done by taking C 2
to be zero and determining C t from the model for zero wear. C t is
determined by first finding the maximum number L l of operations for
which there will be zero wear for the load, geometry etc. of interest. L t is
then given by:

where t max is the maximum shear stress computed using the unworn
geometry, t y is the yield point in shear of the weaker material and y R is a
quantity characteristic of the mode of lubrication. The geometry of the wear
scar produced during the number L 1 of passes, is taken to be a scar of the
profile assumed in deriving eqn (2.102) and of a depth equal to one-half of
the peak-to-peak surface roughness of the material of the pin. In the
particular case under consideration it is assumed that

7^=0.20 (fatigue mode of wear),
f—Q.26 (coefficient of friction).