The exposure time for one cycle (tc) can be expressed as a track length (L) divided
by the sliding speed (V), tc = L/V, and the number of cycles can be expressed as the
product of the sliding speed (V) and the cumulative run time (T) divided by the track
length (L), n=VT/L. The fractional coverage of the surface entering the contact as a
function of run time, track length and velocity (parameters normally measured during
tribological experiments) is given by eqn 2.9.
SVT( VTvPL)
. = [0 [e JJ + -e 1LA eqn 2.9
1 e 1-A e )
The relationship between the entering fractional coverage (0,,) and the average fractional
coverage (0) under the pin can be derived from the fractional removal equations
developed by Blanchet and Sawyer [18], as shown in eqn 2.10.
0= (-A, ) eqn 2.10
-ln(A)
The average fractional coverage under the pin contact at any cumulative run time is found
by substituting eqn 2.9 into eqn 2.10, which is done in eqn 2.11.
(-A) Lr LVA( (e/ 1VT ( vPL
1-A e-L v}\
1- oA ( )t( e VT vPL PL
0= () +V V e(VL ) eqn 2.11
Two nondimensional groups can be defined: normalized time T* = VT / L, and
normalized deposition D* = vPL / V. Substituting these two nondimensional groups into