Dynamic modeling of a flexible hub-beam system with an eccentric tip mass including nonlinear hysteretic contact is studied in this paper. In reality, the model is intended to represent the mechanical finger of an actuator for a piano key. Developing a device to achieve a desired finger-key contact force profile that realistically replicates that of a real pianist’s finger is the main objective of this research. The proposed actuation system consists of a flexible arm which is attached to a DC brushless rotary motor thorough a hub. The compliant arm behaves as a cantilever beam to which an eccentric tip mass has been attached at its free end. During the piano key stroke, the contact force input from the tip causes the key to rotate and impact the ground through an interface lined with stiff felt to suppress vibrations and noise. Euler-Bernoulli beam theory in conjunction with Lagrange’s method is utilized to obtain the governing equations of motion for the system. The finite element method is used as the discretization procedure for the flexible cantilever beam, which can be considered a distributed parameter system. To include contact dynamics at the stop, the nonlinear hysteretic behavior of felt under compression is modeled in such a way that smooth transitions between loading and unloading stages are produced, thus ensuring accurate response under dynamic conditions, and particularly with partial loading and unloading states that occur during the contact period. Simulation results show excessive vibration is produced due to the arm flexibility and also the rigid-body oscillations of the arm, especially during the period of key-felt contact. To eliminate these vibrations, the system was supplemented with various dashpot models, including a simple grounded rotational dashpot, and a grounded rotational dashpot with a one-sided relation. The results of simulations are presented showing the effect on vibration behavior attributed to these additional components.
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ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 28–31, 2011
Washington, DC, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
978-0-7918-5481-5
PROCEEDINGS PAPER
Dynamic Simulation and Vibration Analysis of a Mechanical Piano Key Actuator
Ramin Masoudi,
Ramin Masoudi
University of Waterloo, Waterloo, ON, Canada
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Stephen Birkett,
Stephen Birkett
University of Waterloo, Waterloo, ON, Canada
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Armaghan Salehian
Armaghan Salehian
University of Waterloo, Waterloo, ON, Canada
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Ramin Masoudi
University of Waterloo, Waterloo, ON, Canada
Stephen Birkett
University of Waterloo, Waterloo, ON, Canada
Armaghan Salehian
University of Waterloo, Waterloo, ON, Canada
Paper No:
DETC2011-48709, pp. 981-990; 10 pages
Published Online:
June 12, 2012
Citation
Masoudi, R, Birkett, S, & Salehian, A. "Dynamic Simulation and Vibration Analysis of a Mechanical Piano Key Actuator." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B. Washington, DC, USA. August 28–31, 2011. pp. 981-990. ASME. https://doi.org/10.1115/DETC2011-48709
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