Hammer Shank Research Articles

Linearly implicit time integration scheme of Lagrangian systems via quadratization of a nonlinear kinetic energy. Application to a rotating flexible piano hammer shank.

This paper presents a general and practical approach for nonlinear energy quadratization based on the Euler-Lagrange formulation of the physical equations. A Scalar Auxiliary Variable -like method based on a phase formulation of the equations is applied. The proposed scheme is linearly implicit, reproduces a discrete equivalent of the power balance. It is applied to a rotating and flexible piano hammer shank. An efficient solving strategy leads to a quasi explicit algorithm which shows quadratic space/time convergence.

„denn er arbeitet nur zum nutzen der Musique, und nicht seines nutzens wegen allein, sonst würde er gleich fertig sein“ – Die Analyse von handwerklichem Aufwand beim Bau von frühen Hammerflügeln

The collection of musical instruments at the Technisches Museum Wien (TMW) contains a fortepiano dated c. 1782. A number of details point to the builder having been Anton Walter. That said, the action is unique among Walter’s early pianos and its specific characteristics suggest that it is his oldest surviving type of action. Two other early fortepianos – one of them in the possession of W. A. Mozart – were later modified but show signs of having originally had similar actions. The discourse concerning Mozart’s fortepiano in the 1990s assumed that the TMW-fortepiano’s action was the low-grade work of an early 19th-century piano builder. Reconstructing the steps of the building process can help us to classify the details of historical instruments in a new way. In fact, the interaction between capsule and hammer shank in TMW-fortepiano is an excellent technical solution to a musical demand, and the capsule’s handcrafted production is much more complex than it might initially seem. Thus, analysis and reconstruction by hand can give us deep insight into the technical mastery and the inventive spirit of historical piano builders.

Experimental Validation of a Mechanistic Multibody Model of a Vertical Piano Action

The validity and accuracy of a high-fidelity mechanistic multibody model of a vertical piano action mechanism is examined experimentally and through simulation. An overview of the theoretical and computational framework of this previously presented model is given first. A dynamically realistic benchtop prototype mechanism was constructed and driven by a mechanical actuator pressing the key. For simulations, a parameterization based on geometric and dynamic component properties and configuration is used; initial conditions are established by a virtual regulation that mimics a piano technician's procedure. The motion of each component is obtained experimentally by high-speed imaging and automated tracking. Simulated response is shown to accurately represent that of the real action for two different (pressed) key inputs using a single fixed parameterization. Various specialized model features are separately evaluated. Proper simulated dynamic behavior supports the accuracy of the friction representation; this is especially so for softer key inputs which demand a more actively controlled playing technique. The accuracy of the contact model is confirmed by the proper timing and function of the mechanism, as the relationship between components is strongly dependent on the state of compression of the interface between them. The value of including three flexible components is weighed against their significant computational cost. Compared to a rigid fixed ground point target, hammer impact on a compliant string reduces impact force, contact duration, and postimpact hammer velocity to improve accuracy. Flexibility of the backcheck wire and hammer shank also strongly affects postimpact behavior of the mechanism. The sophisticated balance pivot model is seen to be valuable in creating a realistic key response, with compression of felt balance punching and lift-off of the key, very important for achieving the proper key–hammer relationship. Finally, two components unique to the vertical mechanism—the bridle strap and butt spring—are shown to be essential in controlling the hammer for detached key inputs, where the key is released before it has reached the front punching. Accurate postimpact response is important for proper simulation of repeated notes, as well as the “feel” of the action. In general, the results reported can be considered as a validation of the method for constructing and parameterizing a dynamically accurate multibody model of a specific prototype mechanism or system including compliant contacts and flexibility of some components, as well as ad hoc components to cover unusual dynamic behavior.

Modeling the influence of the piano hammer shank flexibility on the sound

A nonlinear model for a vibrating Timoshenko beam in non-forced unknown rotation is derived from the virtual work principle applied to a system of beam with mass at the end. The system represents a flexible piano hammer shank coupled to a hammer head. A novel energy-based numerical scheme is then provided and coupled to a global energy-preserving numerical solution for the whole piano (strings, soundboard, and sound propagation in the air). The obtained numerical simulations show that the pianistic touch clearly influences the spectrum of the piano sound of equally loud isolated notes. These differences do not come from a possible shock excitation on the structure, nor from a changing impact point, nor a “longitudinal rubbing motion” on the string, since neither of these features are modeled in our study.

Energy based simulation of a Timoshenko beam in non-forced rotation. Influence of the piano hammer shank flexibility on the sound

A nonlinear model for a vibrating Timoshenko beam in non-forced unknown rotation is derived from the virtual work principle applied to a system of beam with mass at the end. The system represents a piano hammer shank coupled to a hammer head. An energy-based numerical scheme is then provided, obtained by non-classical approaches. A major difficulty for time discretization comes from the nonlinear behavior of the kinetic energy of the system. This new numerical scheme is then coupled to a global energy-preserving numerical solution for the whole piano. The obtained numerical simulations show that the pianistic touch clearly influences the spectrum of the piano sound of equally loud isolated notes. These differences do not come from a possible shock excitation on the structure, or from a changing impact point, or a “longitudinal rubbing motion” on the string, since neither of these features is modeled in our study.

Experimental investigation of the piano hammer-string interaction

Experimental techniques for investigating the piano hammer-string interaction are described. It is argued that the accuracy, consistency, and scope of conclusions of previous studies can be compromised by limitations of the conventional methods relating to key inputs; physical distortion; numerical distortion, particularly when differentiation or integration of measured signals is used to derive primary response variables; contact identification; and synchronization issues. These problems are discussed, and experimental methods that have been devised to avoid them are described and illustrated by detailed results from a study of the hammer-string interaction in a vertical piano. High resolution displacements are obtained directly by non-contact high-speed imaging and quantitative motion tracking. The attention focused on achieving very accurate and consistent temporal and spatial alignment, including the objective procedure used for contact identification, allows meaningful comparisons of responses from separate tests. String motion at the strike point and on each side of it, as well as hammer motion, is obtained for eight dynamic levels from 1.06 to 2.98 m/s impact velocity. Detailed observations of the force-compression behavior of the hammer interacting with real strings are presented. The direct effects of hammer shank deflection and agraffe string pulses on the interaction are also highlighted.

Modeling the dynamics of a compliant piano action mechanism impacting an elastic stiff string

A realistic model of the piano hammer-string interaction must treat the action mechanism and string as a single system. In this paper an elastic stiff string model is integrated with a dynamic model of a compliant action mechanism with flexible hammer shank. Action components represented as rotating bodies interact through felt-lined interfaces for which a specialized contact model with hysteretic damping and tangential friction was developed. The motion of the hammer during string contact is governed by the dynamics of the action mechanism, thereby providing a more sophisticated hammer-string interaction than a simple transverse impact hammer model with fixed contact location. Simulations have been used to compare mechanism response for impact on the elastic string as compared to a rigid stop. Hammer head scuffing along the string and time in contact were predicted to increase, while hammer shank vibration amplitude and peak contact force were decreased. Introducing hammer-string friction decreases the duration of contact and reduces the extent of scuffing. Finally, significant differences in hammer and string motion were predicted for a highly flexible hammer shank. Initial contact time and location, length of contact period and peak force, hammer vibration amplitude, scuffing extent, and string spectral content were all influenced.

Considering the effect of hammer shank flexibility using a multibody dynamic simulation model of a piano action mechanism with string contact

A piano action mechanism converts a pianist's mechanical input into acceleration of the piano hammer, which impacts the string for tone generation. We present a multibody dynamic model of the mechanism, considering the differences when hammer shank flexibility is included as compared to a rigid shank. The model is developed using the graph theoretic approach and includes the hammer‐string interaction. A Rayleigh beam model including complete second order deformation field is used for simulating hammer shank flexibility. The governing partial differential equation is discretized using Ritz approach considering Taylor monomials as assumed modes. A convergence study confirms that two bending modes and one axial mode are sufficient to represent the hammer shank deformation. The vibrating string is modeled using a standard modal analysis procedure. The many contacts between components of the mechanism include significant sliding during contact; for these contacts a modified Hunt‐Crossley law is used to represent the normal force, and interface friction is handled using a Cull and Tucker friction model. The results of parametric studies show the effect of hammer head friction on the dynamics of the mechanism during string impact, as well as the influence of hammer shank flexibility on the frequency response of the string.

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

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.

Piano hammers and their force compression characteristics: does a power law make sense?

We have studied the force characteristics of a collection of piano hammers, through studies of the acceleration of the hammer head, the force due to the compression of the hammer felt, Fh, and the associated bending of the hammer shank which occurs when a hammer strikes a rigid object. By integration of the acceleration one can estimate the compression of the felt, and thus obtain a force-compression Fh(z) relationship; our results for this function are compared with previous experiments and theoretical models. Close examination of our findings suggests that bending of the hammer shank, and also the time required for the force to be transmitted from the outer edge of the hammer to its core, play significant roles in the hammer dynamics. The data are used to estimate the quantitative impact of these effects on the derived Fh(z) relation. The implications for physical modeling of a piano tone are briefly discussed.

On the acoustics and psychology of piano touch and tone

By way of ‘‘the touch,’’ a pianist is able to achieve two degrees of freedom in the control of the key motion. Besides the final hammer velocity, the pianist can control, to some extent independently, the force history between the key and finger. By controlling the acceleration history of the key, while keeping the final hammer velocity constant, the pianist can vary the duration of the key and hammer motion and the forces between the interacting parts of the action. This will influence the intensity of vibrations in the hammer shank and of a noise precursor in the radiated sound. This report addresses the pianist’s ability to change the touch parameters and to control them (at will) for musical purposes. The traditional controversy between physicists and some pianists raises a psychological question: ‘‘Why do some pianists think they are able to control a timbre of the individual tone by touch?’’ One hypothesis is that variations in touch change the perception of a tone for the pianist, but not for a listener, because for the pianist the tone perceived starts at finger–key contact, while for a listener it starts when the hammer hits the string.

Combined acoustic and electronic piano in which the acoustic action is disabled when played in the electronic mode

An improved combination acoustic-mode and electronic-mode piano is provided which includes a hammer shank stop rail that intercepts the hammer shank, when in the electronic mode, so that the hammer cannot complete its normal travel and cannot strike its corresponding string(s) when its piano key is actuated. The hammer shank stop rail is actuated by an intermediate crank that, in turn, is actuated by a pedal dowel attached to one of the pedals of the piano. When operated in the acoustic mode, the stop rail occupies a position that will not interfere with the hammer shank's movements, and when in the electronic mode, the stop rail intercepts the hammer shank so that its associated hammer will not be able to travel all the way into contact with their associated string. A second embodiment operates the stop rail by use of a cable and cam mechanism. A third embodiment uses a hand-actuator to operate the stop rail via a dowel and intermediate crank. In a fourth embodiment, a fluid-actuated hammer shank stop rail is located in a position similar to the mechanical hammer shank stop rail described hereinabove. The fluid-actuated hammer shank stop rail includes a rigid portion that provides support across the width of the piano and an expandable portion that is resilient and can be enlarged by the use of an internal fluid pressure, which intercepts the hammer shank before the associated hammer can strike their associated string. A fifth embodiment of a combination dual-mode piano is provided that utilizes a spring-loaded wippen-disabler to prevent the wippen from being actuated by the key tail when the associated key is struck. When placed into the electronic mode, the wippen-disabler is rotated into a position in which one of its extended members is forced against the bottom portion of the wippen and raises the wippen high enough into a position so that the capstan screw of the key tail cannot come into contact with the bottom surface of the wippen. In addition, a different portion of the wippen-disabler is rotated so that its associated spring comes into contact with the top of the key tail, thereby providing the person playing the piano with some mechanical feedback that will approximate the feel of a standard key action.

Keyboard musical instrument hammer movement detection apparatus

First Page

Action for upright piano

An action for an upright piano which emulates or simulates the action of a grand piano is provided. In the action, a back check lever is positioned above the back of the key, and a grand piano whippen is positioned above the back check lever. The grand whippen acts on a knuckle provided on a catcher arm integrally connected with the hammer shank at a substantial angle. Depression of the key produces upward movement of the back of the key, the back check lever, and the grand whippen, in turn producing rotation of the catcher arm which drives the hammer towards the string. The catcher arm has a catcher at its forward end and the back check lever has a back check for catching the catcher after the hammer has rebounded from the string. A vertically-acting gravity-activated damping action is provided. The hammer action is mounted independently from the damping action, and a shifting lever connected to a foot pedal permits lateral shifting of the hammer action with respect to the strings. A hammer return spring is positioned between a hammer spring rail and the hammer shank to bias the hammer away from the string.

計装化シャルピー衝撃試験における計測上の問題点

Some difficulties inherent in the measurements by an instrumented Charpy impact testing apparatus have been studied by using aluminum alloy and mild carbon steel specimens in order to solve the disorderly oscillation of load and displacement observed during the measurement.The measurements by the instrumented apparatus showed a remarkable oscillation of the measured load in the Charpy impact test under the condition of the standard initial tapping velocity. The load oscillation was effectively mitigated and a successful smoothing of the load-time records was obtained when the initial tapping velocity was lowered to about 75% of the standard value.The load oscillation behavior was also effectively avoided by attaching a buffer material, such as a fat clay sheet, to the specimen tapping portion, and an effective smoothing of the load-time records was achieved simultaneously. The sensing error of the absorbed energy due to the attachment of the fat clay sheet was negligibly small.It was confirmed that the cause of the displacement oscillation observed during the course of the impact test was the vibration of hammer shank of the testing apparatus due to the elastic deformation generated by tapping the specimen. It was also proposed that the increase in rigidity of the hammer shank is an effective procedure to reduce the displacement oscillation.

Key touch adjuster for a keyboard musical instrument

First Page

Method and apparatus for measuring the dynamics of a piano performance

The dynamics of a piano performance are measured by measuring the dynamics of each individual note played. This measurement is accomplished by measuring the "near terminal velocity" of the hammer shank associated with each note, the velocity determining the "loudness" of the note. In order to make this velocity measurement without affecting appreciably the "feel" of the piano, a notched shutter is secured to the hammer shank for the particular hammer associated with each note for cooperation with an optical switch (light source and photo cell). When any one note is played, the corresponding hammer shank will move upwardly to cause the hammer to strike the appropriate piano string and in the upward movement, the top of the shutter will intercept the optical switch to generate an initiating signal. This initiating signal starts a count in an electronic counter. As the shank continues to move upwardly, the bottom edge of the notch will generate an end-of-count signal which will terminate the count in the electronic counter. The time increment defined by the count is inversely proportional to the "near terminal velocity" of the hammer.

A Precision Study of Piano Touch and Tone

The loudness and tone quality of a piano note are determined by the motion of the hammer at the time of its impact with the string—theoretically, by its velocity, acceleration and higher time derivatives. Practically, due to the great rigidity of the hammer shank, the influence of the acceleration and higher derivatives is negligible. This study presents exact quantitative confirmation of the findings of other investigators that the loudness and tone of a piano note are uniquely determined by the velocity of the hammer at the time of impact with the string.