Equating the vertical applied force expressions in the forward (eqn 4.12) and reverse (eqn
4.14) directions results in a relation between the actual surface applied normal forces in
the forward and reverse directions.
(cos # cosf + p sinf) eqn 4.19
(cos # cos f p sin f)
Using expressions from eqns 4.11-4.14, the horizontal force read by the tribometer when
sliding in the forward and reverse directions (FHf, FHr) can be expressed in terms of the
vertical force applied by the tribometer (Fv) the coefficient of friction at the surface (g)
and the misalignment angles (3, 4).
(pcos -cossing)F --F (p/cos + cos#sin /)
(cos#cos + psin p) (cos cos psinlp)
eqns 4.20,4.21
Using relations in eqns 4.15-4.21 the tribometer read friction coefficients in the forward
(pf') and reverse (gr') directions can be expressed in terms of the actual coefficient of
friction (p) and the misalignment angles (3, ().
(p cosfl-cos#singf) (. cosfl+cos#sinf)
/ (cos # cos f +p sin f) = (p sin? coscos) eqns 4.22,4.23
From eqns 4.22 and 4.23 expressions for the actual coefficient of friction (p) in terms of
the tribometer read forward (pif') and reverse (pr') values and the misalignment angles (3,
() can be found.
(,1ucosfl+sinfl) (pr, cosfi+sinfl)
pu = cos# P,/. = -cos# o
(cosi pf sin f) (cos? -u, sinfi)
eqns 4.24,4.25