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Non-smooth model of the grand piano action

Anders Thorin 1, 2 
2 LIS - Laboratoire Interfaces Sensorielles
DIASI - Département Intelligence Ambiante et Systèmes Interactifs : DRT/LIST/DIASI
Abstract : The grand piano action aims at propelling the hammer up to the strings. This mechanism provides the pianist with a high-controllability of the time of impact of the hammer with the strings and the hammer's velocity at the impact. This controllability is believed to be due to the dynamic behaviour of the piano action. The present thesis proposes a simulation method of a complete model of the mechanism, which opens doors to improvements of the haptic rendering of digital keyboards. The sound following the impact of the hammer on the strings is not analysed. In the last fifteen years, various models of the piano action including several degrees of freedom, friction and intermittent contacts, have been proposed. Our approach differs from existing work in that it is based on a new viewpoint for model validation and simulation. Indeed, using a in-depth study of a model with a single degree of freedom, it is shown that the simulation of a complete dynamic model must be driven with a displacement whilst, until now, only force driven simulations have been presented. Velocity discontinuities, occurring during the descent of the key, raise numerical issues which are analysed. They are overcome by non-smooth numerical methods that have been implemented in the computer program XDE. The results of the simulation are presented and compared to experimental measurements. For both piano and forte keystrokes, most of the irregularities in the measured force are reflected in the simulated force. The kinematics of the bodies is also correctly predicted. Eventually, a sensitivity analysis of the dynamic behaviour to the model's parameters is proposed.
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Submitted on : Thursday, January 30, 2014 - 7:31:05 PM
Last modification on : Thursday, February 17, 2022 - 10:08:03 AM
Long-term archiving on: : Thursday, May 1, 2014 - 9:35:12 AM


  • HAL Id : pastel-00939493, version 1


Anders Thorin. Non-smooth model of the grand piano action. Solid mechanics [physics.class-ph]. Ecole Polytechnique X, 2013. English. ⟨pastel-00939493⟩



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