Non-smooth dynamics for an efficient simulation of the grand piano action
Dynamique non-régulière pour une simulation efficace de la touche de piano à queue
Résumé
The main function of a grand piano action is to throw the hammer up to the strings by pushing down the key. In the line of previous studies, a model based on rigid body approximations and nonlinear junctions is proposed. The rigid body approximation is discussed in some details. The major challenges addressed here pertain to the simulation of the model: (i) predicting the force exerted by the key on the finger in reaction to a given displacement at the end of the key, (ii) efficiently and accurately capturing the non-smooth character of the motion due to contact and dry friction, which are known to be crucial for the touch of the pianist. The presented predictions of the key force (in other words, the haptic characterization of the piano action) are successful. Combined with a high sensitivity to the complexity of the model, this comparison between measured and simulated forces to a given motion constitutes an excellent validation of the model, as opposed to the usual comparisons between motions in response to prescribed forces. Regarding (ii), non-smooth numerical methods have been used instead of regularization. This allows for the time step being chosen according to physics only and avoids the reduction needed for numerical reasons, resulting in computations about a few hundred times faster than those reported in recent literature. The use of non-smooth dynamics hence opens doors to industrial and haptic applications.
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