A refined bow-string interaction model considering hysteresis

In order to accurately model the bow-string interaction, a friction model is necessary that will correctly predict the friction force during stick-slip phases.This force has been estimated from experimental measurements.It appears to be at its highest at the start of slipping, and it decreases as the slipping speed increases.On the way back towards the sticking phase, the force is lower than on the way towards the slipping phase.It has been hypothesized that the temperature fluctuations of rosin are responsible for this hysteretic behaviour [Smith, J. and Woodhouse, J., The tribology of rosin.J. Mech.Phys.Solids, 48(8), 2000].In this work, a model is proposed that directly incorporates the temperature changes of rosin during bowing.It is shown that the friction force resembles the one estimated from the measurements.