Bowed string simulation using a thermal friction model

Abstract

In the past, theoretical modelling of the motion of a bowed string has assumed that the frictional force due to the rosin on the bow was determined by the sliding speed only. Recently, it has been proposed that a better constitutive law would be to assume that the friction force is a function of the contact temperature. The predictions of these two models are compared, using the best available calibration data for the properties of the rosin and the instrument string. The main conclusion is that the thermal friction model predicts bowing behaviour which is more "benign", in that the desired Helmholtz motion of the bowed string is established more reliably and more quickly than with the old friction model. The two models also predict different detailed behaviour of the frequency of the string oscillation as a function of normal force, the "flattening effect". These predictions are amenable to direct experimental check, and it is hoped that measurements will soon provide evidence to test the predictions, discriminate between the models, and fine-tune the more successful model.