Modeling of a piano hammer
Hideo Suzuki · The Journal of the Acoustical Society of America · 1985
From the measurement of the force-time pattern and the acceleration-time pattern, a simple model that describes the action of the hammer, when it hits an ideally rigid string, was established. It was found that the relation between the force (f) and the deformation (x) is approximated by the form f = kX4 for the specific hammer used for the measurement, where k is a constant. This shows that the hammer stiffness S(x) has a nonlinearity of the third order. Then, the effective mass Mh was calculated using a single mass-spring model. It is fairly constant during the time when the hammer is moving toward the string. The force-time patterns of this model were calculated using S(x) and Mh for different hammer velocities. The agreement between the measured and calculated force-time patterns is good (within 15% near their peaks). As a second model, a double mass-spring system was considered. The force-time patterns calculated from this model are in better agreement with the measured curves.