When stick-slip oscillation is deliberately sought, in bowed violin strings
or in other systems, it is well known to help if the contacting surfaces
are given a thin coat of rosin, a resinous substance obtained from the sap
of coniferous trees by solvent extraction or distillation. Nearly all
theoretical modelling of stick-slip motion has used a constitutive model in
which the frictional force is assumed to be a nonlinear function of
instantaneous sliding speed. This model has had considerable success in
predicting at least the qualitative features of observed stick-slip motion,
and yet there is apparently no physical justification for its use.
This talk will describe efforts to find a physically-based constitutive
model for rosin friction. Experiments in which the friction force was
measured during stick-slip oscillation will be described, showing clearly
that the traditional model is not correct. It will be suggested that a
better model would use not sliding velocity but contact temperature as the
key state variable governing the friction force. Simple models constructed
on this basis will be described, and comparisons with the measurements used
to select the most plausible. Simulation studies using this "best" model
will then be described, both for a frictionally-excited harmonic oscillator
(as was used in the friction measurements) and for a bowed string. The
results so far are somewhat mixed - some observed features are captured
much better by the new model, but paradoxically one particular phenomenon
in the bowed string seems to fit the traditional model better than the new
one.
