Modeling the dynamics of a compliant piano action mechanism impacting an elastic stiff string

Abstract

A realistic model of the piano hammer-string interaction must treat the action mechanism and string as a single system. In this paper an elastic stiff string model is integrated with a dynamic model of a compliant action mechanism with flexible hammer shank. Action components represented as rotating bodies interact through felt-lined interfaces for which a specialized contact model with hysteretic damping and tangential friction was developed. The motion of the hammer during string contact is governed by the dynamics of the action mechanism, thereby providing a more sophisticated hammer-string interaction than a simple transverse impact hammer model with fixed contact location. Simulations have been used to compare mechanism response for impact on the elastic string as compared to a rigid stop. Hammer head scuffing along the string and time in contact were predicted to increase, while hammer shank vibration amplitude and peak contact force were decreased. Introducing hammer-string friction decreases the duration of contact and reduces the extent of scuffing. Finally, significant differences in hammer and string motion were predicted for a highly flexible hammer shank. Initial contact time and location, length of contact period and peak force, hammer vibration amplitude, scuffing extent, and string spectral content were all influenced.