expressions in a form similar to the position-dependent steady-state equations for
reciprocating motion published in [23], where tc = tf + t,.
, =[1-(1-[A)e -vP]e-'" 1 eqn 2.20
( 2)ePAe-, vp'] [ e-vp( 2 e-vp, )] 2 -vP (-'
A) = 1-(1- -P ] e- L -- i_] eqn 2.21
11 2 e-vPtI
The first check for the validity of eqns 2.20 and 2.21, which are spatially dependent
(through tf and tr values) and time dependent (through the cycle number, n), was to
evaluate the limit of these functions as n -+ oo and compare this with the previously
developed steady-state expressions, which were created by balancing the deposition and
removal rates at steady state. As expected, eqns 2.20 and 2.21 are identical to the steady-
state equations published earlier [23]. The second check was that this model matched the
time-dependent model in eqn 2.8 developed in the pin-on-disk/reciprocation midpoint
section at the midpoint of the track (when t, = t,). The final verification step was to take
the limit of the model as n -> oo when tf = t, and compare this to the steady-state
coverage expression in eqn 2.4, derived using the pin-on-disk model. In all of these
cases, the model was able to be expressed in an equivalent form to the previously
developed models. To predict friction coefficients at specific pin locations, the average
fractional coverage within the contact, 0, is calculated according eqn 2.10