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Research Papers

Dynamic Modeling and Experimental Testing of a Piano Action Mechanism With a Flexible Hammer Shank

[+] Author and Article Information
Adel Izadbakhsh

Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L3G1, Canadaizadbakhsh@alumni.uwaterloo.ca

John McPhee1

Systems Design Engineering, University of Waterloo, Waterloo, ON, N2L3G1, Canadamcphee@real.uwaterloo.ca

Stephen Birkett

Systems Design Engineering, University of Waterloo, Waterloo, ON, N2L3G1, Canadasbirkett@real.uwaterloo.ca

Details are available in Ref. 16.

Maximum tip deflection during impact is about 1.5%.

For impact of a hammer on a flexible string, contact times of 23ms are more typical (12).

Details are available in Ref. 16.

1

Corresponding author.

J. Comput. Nonlinear Dynam 3(3), 031004 (Apr 30, 2008) (10 pages) doi:10.1115/1.2908180 History: Received March 25, 2007; Revised September 03, 2007; Published April 30, 2008

The piano action is the mechanism that transforms the finger force applied to a key into a motion of a hammer that strikes a piano string. This paper presents a state-of-the-art model of a grand piano action, which is based on the five main components of the action mechanism (key, whippen, jack, repetition lever, and hammer). Even though some piano action researchers (e.g., Askenfelt and Jansson) detected some flexibility for the hammer shank in their experiments, all previous piano models have assumed the hammers to be rigid bodies. In this paper, we have accounted for the hammer shank flexibility using a Rayleigh beam model. It turns out that the flexibility of the hammer shank does not significantly affect the rotation of the other parts of the piano mechanism and the impact velocity of the hammer head, compared to the case that the hammer shank has been modeled as a rigid part. However, the flexibility of the hammer shank causes a greater scuffing motion for the hammer head during the contact with the string. To validate the theoretical results, experimental measurements were taken by two strain gauges mounted on the hammer shank, and by optical encoders at three of the joints.

Copyright © 2008 by American Society of Mechanical Engineers
Topics: Hammers , Mechanisms
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References

Figures

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Figure 16

Two strain gauges mounted on the hammer shank

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Figure 17

Experimental versus theoretical strain measurement

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Figure 1

Action mechanism of the Boston GP-178 grand piano

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Figure 2

Components of a piano action mechanism and their rotation sequences

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Figure 3

Different parts of the piano action model

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Figure 4

Contact locations in the piano action mechanism

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Figure 5

Contact force during loading and unloading

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Figure 6

Motor force and corresponding key rotation

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Figure 7

Hammer and its flexible shank

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Figure 8

Predicted bending shape of the hammer shank

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Figure 15

Rotations of the hammer, key, and whippen

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Figure 9

Relative deflection of the tip of the hammer shank

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Figure 10

Rotation of the main parts of the piano action

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Figure 11

Difference between the rotation of the piano components for the rigid and flexible hammer shank cases

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Figure 12

Impact velocity and the rotation of the hammer for rigid and flexible shank. Instants A and B indicate the start and the end of contact.

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Figure 13

Scuffing motion of the hammer head

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Figure 14

Displacement of the hammer head tip during string contact

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