The theoretical framework for constructing a fully mechanistic multibody dynamic model of a vertical piano action is described, and its general validity is established. Equations of motion are derived symbolically using a graph-theoretic formulation. Model fidelity is increased by introducing several novel features: (i) a new contact model for representing the compression of the felt-lined interfaces between interacting parts, capable of capturing the intermittent loading and unloading of these contacts occurring through the key stroke, as well as providing smooth transitions between these states; (ii) models for two important components that are unique to the vertical action, the bridle strap and the butt spring; (iii) a sophisticated key pivot model that captures both the rotational motion and the vertical translation of the key as it can lift off the balance rail under some conditions; (iv) flexible beam models for backcheck wire and hammer shank so as to predict observed vibrations in the response accurately; and (v) coupling of the mechanism model to a flexible stiff string model for realistic hammer impact. For simulation, parameters were obtained by experimental testing and measurement of a physical prototype vertical action. Techniques are described for the virtual regulation of the model to ensure that initial conditions and pseudostatic response accurately represent the precise configuration and desired relationships between the parts during the key stroke. Two input force profiles were used for simulations, a forte pressed (hard) and piano pressed touch (soft), typical of those measured at the key surface when activated by a pianist. Simulated response to these quite different inputs is described, and compared to experimental observations obtained from a physical prototype.
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July 2014
Research-Article
A Mechanistic Multibody Model for Simulating the Dynamics of a Vertical Piano Action
Ramin Masoudi,
Ramin Masoudi
Research Fellow
Department of Systems Design Engineering,
e-mail: rmasoudi@uwaterloo.ca
Department of Systems Design Engineering,
University of Waterloo
,Waterloo, Ontario N2L 3G1
, Canada
e-mail: rmasoudi@uwaterloo.ca
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Stephen Birkett,
Stephen Birkett
Associate Professor
Department of Systems Design Engineering,
e-mail: sbirkett@uwaterloo.ca
Department of Systems Design Engineering,
University of Waterloo
,Waterloo, Ontario N2L 3G1
, Canada
e-mail: sbirkett@uwaterloo.ca
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John McPhee
John McPhee
Professor
Department of Systems Design Engineering,
e-mail: mcphee@real.uwaterloo.ca
Department of Systems Design Engineering,
University of Waterloo
,Waterloo, Ontario N2L 3G1
, Canada
e-mail: mcphee@real.uwaterloo.ca
Search for other works by this author on:
Ramin Masoudi
Research Fellow
Department of Systems Design Engineering,
e-mail: rmasoudi@uwaterloo.ca
Department of Systems Design Engineering,
University of Waterloo
,Waterloo, Ontario N2L 3G1
, Canada
e-mail: rmasoudi@uwaterloo.ca
Stephen Birkett
Associate Professor
Department of Systems Design Engineering,
e-mail: sbirkett@uwaterloo.ca
Department of Systems Design Engineering,
University of Waterloo
,Waterloo, Ontario N2L 3G1
, Canada
e-mail: sbirkett@uwaterloo.ca
John McPhee
Professor
Department of Systems Design Engineering,
e-mail: mcphee@real.uwaterloo.ca
Department of Systems Design Engineering,
University of Waterloo
,Waterloo, Ontario N2L 3G1
, Canada
e-mail: mcphee@real.uwaterloo.ca
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 19, 2013; final manuscript received November 29, 2013; published online February 13, 2014. Assoc. Editor: Parviz Nikravesh.
J. Comput. Nonlinear Dynam. Jul 2014, 9(3): 031014 (10 pages)
Published Online: February 13, 2014
Article history
Received:
August 19, 2013
Revision Received:
November 29, 2013
Citation
Masoudi, R., Birkett, S., and McPhee, J. (February 13, 2014). "A Mechanistic Multibody Model for Simulating the Dynamics of a Vertical Piano Action." ASME. J. Comput. Nonlinear Dynam. July 2014; 9(3): 031014. https://doi.org/10.1115/1.4026157
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