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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.

In this paper, the finite strain plastic deformation of AM30 magnesium alloy has been simulated using the crystal plasticity finite element method. The simulations have been carried out using a rate-dependent elastic–viscoplastic crystal plasticity constitutive model implemented in a user defined material subroutine (UMAT) in the commercial software LS-DYNA. The plastic deformation mechanisms accounted for in the model are the slip systems in the matrix (parent grain), extension twinning systems and the slip systems inside the extension twinned regions. The parameters of the constitutive model have been calibrated using the experimental data. The calibrated model has then been used to predict the deformation of AM30 magnesium alloy in bending and simple shear. For the bending strain path, the effects of texture on the strain accommodated by the deformation mechanisms and bending moment have been investigated. For simple shear, the effects of texture on the relative activity of deformation mechanisms, shear stress and texture evolution have been investigated. Also, the effect of twinning on shear stress and texture evolution has been studied. The numerical analyses predicted a more uniform strain distribution during bending and simple shear for rolled texture compared with extruded texture.

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 Askenfelt and Jansson [1] 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, compared with the case that the hammer shank has been modeled as a rigid part. However, the flexibility of the hammer shank changes the impact velocity of the hammer head, and also 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.