Experimental Validation of a Mechanistic Multibody Model of a Vertical Piano Action

Abstract

The validity and accuracy of a high-fidelity mechanistic multibody model of a vertical piano action mechanism is examined experimentally and through simulation. An overview of the theoretical and computational framework of this previously presented model is given first. A dynamically realistic benchtop prototype mechanism was constructed and driven by a mechanical actuator pressing the key. For simulations, a parameterization based on geometric and dynamic component properties and configuration is used; initial conditions are established by a virtual regulation that mimics a piano technician's procedure. The motion of each component is obtained experimentally by high-speed imaging and automated tracking. Simulated response is shown to accurately represent that of the real action for two different (pressed) key inputs using a single fixed parameterization. Various specialized model features are separately evaluated. Proper simulated dynamic behavior supports the accuracy of the friction representation; this is especially so for softer key inputs which demand a more actively controlled playing technique. The accuracy of the contact model is confirmed by the proper timing and function of the mechanism, as the relationship between components is strongly dependent on the state of compression of the interface between them. The value of including three flexible components is weighed against their significant computational cost. Compared to a rigid fixed ground point target, hammer impact on a compliant string reduces impact force, contact duration, and postimpact hammer velocity to improve accuracy. Flexibility of the backcheck wire and hammer shank also strongly affects postimpact behavior of the mechanism. The sophisticated balance pivot model is seen to be valuable in creating a realistic key response, with compression of felt balance punching and lift-off of the key, very important for achieving the proper key–hammer relationship. Finally, two components unique to the vertical mechanism—the bridle strap and butt spring—are shown to be essential in controlling the hammer for detached key inputs, where the key is released before it has reached the front punching. Accurate postimpact response is important for proper simulation of repeated notes, as well as the “feel” of the action. In general, the results reported can be considered as a validation of the method for constructing and parameterizing a dynamically accurate multibody model of a specific prototype mechanism or system including compliant contacts and flexibility of some components, as well as ad hoc components to cover unusual dynamic behavior.

A novel micromechanical model of nonlinear compression hysteresis in compliant interfaces of multibody systems

“…Since the micromechanical contact model represents the real hysteresis curves corresponding to hammer-string contact point, the results are very similar to the ones presented in Ref. [20] which is based on a math-based contact model, i.e. curve-fitting to the experimental felt compression data.…”

“…the math-based model presented in Ref. [20] and the physics-based model proposed in this work, are shown in Figs. 13 and 14 for piano and forte inputs, respectively.…”

“…The obtained overall contact pressure/force between the bodies (calculated by adding the hysteresis part to the elastic part), along with the generalized coordinates and speeds is fed-back to the input for the next step of simulation. Two different inputs introduced by Masoudi et al [3,20] are utilized to simulate the vertical action, incorporating the micromechanical contact dynamic model developed in previous sections for the hammer-string interaction. The input profiles have been derived from force sensor data attached to the key front, which imitate the pianist finger force when playing a note with different intensities, i.e.…”

“…A precise description of the experimental procedure has been presented in another work by the authors [20]. Displacements of different bodies were measured by tracking marking points (shown in Fig.…”

“…The obtained force sensor data and position data from different cameras were synchronized. All the parameters for the components, including mass and geometrical properties, flexible components and string parameters, and contact points parameters were measured experimentally [20].…”