  The influence of out-of-plane oscillations on friction is a well-known
phenomenon that has been studied extensively with various experimental methods,
e.g. pin-on-disk tribometers. However, existing theoretical models have yet
achieved only qualitative correspondence with experiment. Here we argue that
this may be due to the system dynamics (mass and tangential stiffness) of the
pin or other system components being neglected. This paper builds on the
results of a previous study (Popov M. et al. Friction, 2016, submitted) by
taking the stiffness and resulting dynamics of the system into account. The
main governing parameters determining macroscopic friction, including a
dimensionless oscillation amplitude, a dimensionless sliding velocity and the
relation between three characteristic frequencies (that of externally excited
oscillation and two natural oscillation frequencies associated with the contact
stiffness and the system stiffness) are identified. In the limiting cases of a
very soft system and a very stiff system, our results reproduce the results of
previous studies. In between these two limiting cases there is also a resonant
case, which is studied here for the first time. The resonant case is notable in
that it lacks a critical sliding velocity, above which oscillations no longer
reduce friction. Results obtained for the resonant case are qualitatively
supported by experiments.
