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Enthalpy

Percussion Instruments

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Hello dear music lovers!

Church bells are still made today like in the Middle Age: Cu80Sn20Pb0 bronze cast in a one-way clay mould. One batch of varied middle-sized bells takes six weeks of hard work to ten persons. I propose instead to electroform them.

A well-developed technology, electroforming can deposit varied metals and alloys, from ultra-thin to thick, on diversely shaped mandrels, bulk conductive or not, and separate the created item from the mandrel. Here bronze and the bell shape are easy.

ElectroformChurchBell.png.7ae29663cd4a888576a18b40e457ef25.png

Maybe the mandrel can be of wax on wood, or talcum-loaded paraffin... In one interesting option, the mandrel itself would be obtained by electroforming on the inner face of a good existing bell. For the parting film, ask a specialist.

The current density varies with the rest, let's take 500A/m2 as an example. This grows 11mm/week copper and slightly more bronze, faster than traditional mould making. The current in copper and tin electrodes, and initially the electrolyte composition, control the alloy composition; I ignore if the electrodes can be bronze.

A D=0.8m bell has around 1.2m2 surface, needing 600A (or less since some parts are thinner) and roughly 3V and 1.8kW only. The anodes are closer to the created item than depicted, their shape and number is not representative. Maximum 30mm thickness take 3 weeks, mean 25mm just 700kWh costing 150€. Upsizing is easy.

Schottky diodes could provide the DC current, but I prefer MOS to reduce the losses and regulate the current, for instance by pulse swallowing. Electronics can produce a square single phase around 24V (safer than 500V) distributed to local transformers, at 400Hz for laminated iron cores or higher for iron powder or ferrite. Some processor can distribute the swallowed pulses smartly. The currents must be monitored automatically, the thickness could be measured manually from time to time but is better monitored automatically too. The bath needs limited cooling.

Rotating the electrodes (or the bell) during the growth may achieve a rounder shape. Then, the transformers better rotate with the electrodes, so fewer contacts pass less current.

I've no opinion about the internal stress of electrodeposited bell bronze nor its acoustic qualities. It can be heat-treated afterwards. Titanium parts are isostatically hot-pressed (in silicone) after casting, this may apply here too.

Impurities from the mandrel or parting agent must be removed from the bell.

Marc Schaefer, aka Enthalpy

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Electroplating alloys isn't trivial.
One traditional method for providing the low voltage high current for electroplating was a homopolar generator run from an AC motor.

I think the biggest challenge you will face is that the churches are richer than they usually admit, and more interested in tradition.
Just because your method is better doesn't mean they will use it.

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Considerations about the 3V*600A DC supply. Beyond, church bells, most apply to any electrochemical apparatus, and can be scaled up or down.

The intermediate square wave at 24V*75A can travel cheaply over 5m or 10m while 600A conductors are uneasy to move. The conversion from three-phase mains is in a separated room, clean and dry, prefiribly a floor higher than the bath (as opposed to the nuclear power plant in Fessenheim). A 24V shock has the (legal) reputation to be survivable even in a wet environment, more so at 400Hz. The waveform should be smoothened.

400Hz makes a reasonable transformer to 3.2V: with 50µm Fe-Si tape, the core can have the double AMCC-500 size and weigh 6kg, while each 3.2V winding has two turns of 3mm thick Cu foil and the primary thinner foil. Losses are around 45W.

A nanocrystalline core of AMCC-250 size and single-turn secondaries would reduce the losses to 20W, which electricity saved over few hundred bells may pay. Iron powder or ferrite cores would reduce the transformer with frequencies over 20kHz but are fragile, and switching components would waste more power.

Multiple 3.2V transformers would save cable volume if the 3.2V current returns over a shorter path. For a church bell, it means contacts inside the mandrel near the rim, and transformers nearby. This might get interesting at bigger bells. Contacts distributed on the fresh deposited surface are more difficult: they should move regularly for even deposition, and make sense with immersed transformers.

ElectroformCircuit.png.29ba68de89f9a900c9178f0e4cbe0e2a.png

MOS rectifiers waste far less voltage than diodes, they can swallow pulses to tune the deposition rate locally, and also reverse the DC voltage, all by individual gate control. Possible upgrade for apparatus still using diodes. Unless some manufacturer avoids it, the parasitic diode demands MOS pairs. The dual secondary transformer saves MOS and losses. For 3.2V output, the gate control can be referenced to the mandrel potential.

Some deposition processes apply periodically a short and strong reverse current to even and smoothen the deposited layer. The sketched circuit achieves that; I'd limit the intermediate voltage to 24V even during the reversed current, hence use a smaller voltage for the normal polarisation, and increase the frequency during the increased voltage periods.

Marc Schaefer, aka Enthalpy

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Power Mosfet were introduced historically (when I was young) with a channel length defined by a double diffusion instead of lithography which was too coarse at that time. They also offer a higher drain-source voltage.

But low-voltage synchronous rectifiers don't need the huge Vds capability, and meanwhile lithography is much finer than necessary for transistors operating at 5V or 20V. So maybe a manufacturer could make power Mosfet with channel length defined by lithography, just like low-power Mosfets are made, but with a wider channel, low contact resistances and low thermal resistance? The symmetric transistors with an independent bulk connection would be nice in the above diagram, where one transistor would replace two of Rdson twice as low. Since pairs of Mosfet connected as above due to the parasitic diode appear from time to time at other circuits, maybe there is a market. For low power, the transistors exist already, but for a few amps, my quick search didn't find any.

Marc Schaefer, aka Enthalpy

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On 8/12/2018 at 8:03 PM, John Cuthber said:

Electroplating alloys isn't trivial.
One traditional method for providing the low voltage high current for electroplating was a homopolar generator run from an AC motor.

I think the biggest challenge you will face is that the churches are richer than they usually admit, and more interested in tradition.
Just because your method is better doesn't mean they will use it.

Hi JC, thanks for your interest!

Electroplating alloys isn't trivial, I believe so! I've cautiously avoided to suggest anything about how to do that. I've only read that Cu-Ni is regularly done, Sn has a redox potential farther away from Cu than Ni has, but bronze can be electroplated too. Well, that's a job for specialized people and companies, like making seal rings or gears.

I just love homopolar generators. Pity they are less fashionable presently, but maybe they'll come back. While low-voltage power electronics is tricky, every computer motherboard contains some, so designers must be less difficult to find than for a homopolar machine.

Sure, inventions need luck to be adopted, improving over existing methods doesn't suffice. To my understanding, "church bell" designates a design of bells even if used by seculars, but about all big items must be in churches, and small ones have some efficient casting method. On boats maybe?

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I know who would buy church bells: symphonic orchestras, simply.

Presently they use tubular bells. All composers and conductors complain that their sound is weak, meager and sinister. Wagner for instance specified true bells but is often played on tubular bells, sometimes helped by a piano. Other orchestras try to develop plates and other shapes, which are less bad than the tubes but don't equal church bells.

True bells, affordable and sounding good, would seduce the orchestras.

Marc Schaefer, aka Enthalpy

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4 hours ago, Enthalpy said:

True bells, affordable and sounding good, would seduce the orchestras.

Right up until they tried to move them.

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I haven't checked what notes composers specified. Could be a challenge, sure. Worse than a grand piano.

Taking a symphonic orchestra on tour is already a headache. Not just the visas for 150 people. Most airlines ignore if one can take a violin in the cabin, but musicians don't want their instrument in the cold nor at low pressure, even less lost.

And what about the materials? Violins use Pernambouc wood (Pau Brasil) and blackwood, both being prohibited to export or import in many countries. Woodwind use grenadilla and rosewood, same story. Then you have flutes of silver and gold not pure enough for France, whose law doesn't consider musical uses.

Other funny laws may impose to fumigate all wood that enters a country as a protection against insects. Pssch pssch on the cello.

Then you have the scores. Intellectual property differs among the countries, and a score acquired lawfully in Europe can bring you trouble in the US.

I say: headache.

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22 hours ago, Enthalpy said:

Intellectual property differs among the countries, and a score acquired lawfully in Europe can bring you trouble in the US.

Not much. They are both signatories of the Berne Convention (as are most countries).

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Bartók died over 70 years ago so all his compositions are in the public domain in Europe. This differs in the US, where property can last 100 years under some conditions.

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On 9/2/2018 at 11:03 PM, John Cuthber said:

Right up until they tried to move them.

Church bells at the height written for Parsifal are too big. Wagner wants E G A C where C is the height of the 20t bell on Vienna's Stephansdom, so the E would weigh 80t. Bells of that size were made, but not moved on a stage.

Wagner later let build a "Glockenklavier" for that, a kind of grand piano with four notes of many strings each, hit by wider hammers moved by the fists on big keys (I've found no equivalent sites in English)
Glockenklavier at de.Wiki
hear the instrument
qUfo1szjPIc at Youtube
br-klassik.de
but orchestras aren't pleased with the power nor the sound, so they still experiment
wiener-staatsoper.at
this isn't solved yet.

==========

For notes less low, orchestras investigate alternatives to church bells with a decent sound
FaxGwZRKpao at Youtube, sounds at 0:54, 2:16, 3:10, 3:27, 3:47, 4:06, 4:50
or they buy authentic church bells from traditional founders, possibly over a store
2MaoAOhxbdQ at Youtube, sounds at 0:09, 1:52
schlagzu.com
so if electroforming is cheaper, a market exists.

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Can the Glockenklavier improve? It will never sound like a church bell, but it's half manageable and affordable, and Wagner wanted it for Parsifal
de.wikipedia - wiener-staatsoper.at - br-klassik.de
Steingraber made the 1882 instrument with bits of his grand pianos, and the loudness and sound resemble more a piano than a bell, so here a a few proposals.

  • Felted wood hammers can't imitate an iron clapper against a bronze bell. Better bare plastic, beechwood or bronze.
  • 8 piano strings per note make the sustain fainter and even longer, wrong choice for low notes. 1 string per note.
  • The 1914 instrument had no keyboard but hand hammers, enough to play single notes in Parsifal.
  • The 8 strings still needed hand hammers of ridiculous piano style. Have good heavy rods instead.
  • Or move the hard and heavy hammers with foot pedals, sturdy as for a bass drum. Hydraulic transmission is an option.
  • Strings make a brighter sound if they propagate the wave faster than air does. At D=5mm, Röslau delivers 1720MPa steel. 18-12-5 maraging steel gives 2400MPa at any diameter. No copper overspinning. I don't care about harmonicity.
  • At 380m/s, strings are 4.5m long for E=42Hz but cold-drawn steel has only 1.5* strength margin. Maraging achieves 420m/s for 5m strings with 1.7* margin. 6m bars are standard and the instrument fits in a lorry.
  • The soundboard can be vertical. If the sound is more brilliant sideway, consider reflectors. The strings should face the public. The musician can have a mirror.
  • End fasteners can be welded on maraging strings. Friction can hold cold-drawn carbon steel, but with self-blocking shapes like pairs of cones, as the string thins under tension.
  • At the two bridges, maybe slit or split cylinders can be screwed tight on the already stretched strings.

A single instrument can have its frame similar to a grand piano but of welded steel tube.

The soundboard is wider than the 5m string speaking length and tall. I'd have a closed soundbox to radiate the 42Hz. It could consist of spruce planks and ribs like at a piano, or maybe of aluminium as we want a metallic sound anyway. For flexural propagation speed similar to spruce, aluminium sheets must be milled thin with tall integral ribs, and can be welded butt.

Can instead a thin soundboard get its sound speed from tension? The strings move more easily a very light soundboard, and propagation faster than in air radiates all frequencies well. Cold-rolled steel achieves is easily (>920MPa tension), composites even more (>200MPa for 1700kg/m3), aluminium with little margin (>330MPa), some plastic films (>150MPa for 1300kg/m3) and even luthier-quality Picea abies (>42MPa for 360kg/m3). I suppose the board must be thin enough so radiation dampens the resonances, and its resonances tuned outside the spectrum of the four notes. Side reflectors seem necessary. The bridge and frame may have to slow down the energy transfer from the strings to the soundboard.

Tensile soundboards exist already at banjos, qanuns and many more, but with a slow propagation. Fast tensile soundboards would apply to more instruments if they sound well.

As a hypothetic killer option, extra items could be made to knock at the note's frequency against the strings or other vibrating parts. At the snare drum, the banjo, the tromba marina and others, it takes power from the fundamental to replenish the high harmonics that make the sound much more powerful and brilliant. The knocker needs an extremely accurate adjusted position (the tromba marina lifts one foot of its bridge), or it may have a spring and rely on its inertia, or few knockers among many can have by chance the proper position.

Would the usually strident effect fit a Glockenklavier? Less hard materials nearer to vibration nodes have a less extreme effect.

The development of this instrument requires luthier skills only if the soundboard is of wood. It's more acoustics and mechanical engineering, not very costly. Delicately megalomaniac thesis topic for instance.

Marc Schaefer, aka Enthalpy

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10 hours ago, Enthalpy said:

Can the Glockenklavier improve?

Isn't the Vibraphone an evolution/improvement on the same family of instruments?

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Hi DrP and all,

While the Glockenklavier was designed (and failed) to replace church bells, it is a string instrument adapted from a grand piano, and it does sound like a grand piano. Here it there:
3mNMUNJIS3Q at 0:30 with keyboard
pcpkp13juVA at 0:36 with hand hammers

The vibraphone has metal resonating bars, much like the glockenspiel, but it's lower and it adds tubes to amplify the sound. You can view it as a marimba or xylophone where metal replaces the wooden bars.

And because Sapiens sapiens have imagination, here's an attempt to replace low bells with metal plaques and a vibraphone on steroids:
5SvuGtaU3Co at 0:42, 0:55 and 1:09
the sound is less clean than from a bell, but it definitely resembles, far more than the Glockenklavier does. Passing over a symphonic orchestra's fortissimo is quite doubtful, what the Glockenklavier can't neither.

Edited by Enthalpy

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Here are attempted flexural soundboards for the Glockenklavier evolution.

To radiate low frequencies well, a soundboard must spread the vibration wave over much area, and if several locations have opposite phase, they should be far apart with different areas or amplitudes. This favours a big flexural propagation speed. At high frequencies, the many locations with opposite phase can still reinforce an other in directions where their path difference is a half-wave, which needs a flexural propagation faster than the sound in air. This justifies Picea abies (spuce) among usual materials and shapes, with ribs and domes.

The E=41.4Hz Glockenspiel, with a 5m string, woud have a soundboard about as long.

GlockenklSoundbFlex.png.762c4cee9990371f6f9a0c73b550957f.png

========== Wood

Picea abies could have transverse fibres in a 10mm plate and tall lengthwise ribs. The bridge shall spread the vibrations sidewise, big assumption. With rho=360kg/m3 and E=11GPa, I find flexural 342m/s in the plate at 1.2kHz and lambda/2=0.14m, and take ribs spaced by 0.12m. Ribs 20mm wide and 63mm tall give EI=3.8*104 and µ=8kg/m2 for the complete soundboard, so EI/µ=4.8*103 m4s-2.

At 52.1Hz, the mean of E=41.4Hz to C=65.7Hz, lambda/2=1.4m, wasting a longer soundboard, and the cutoff frequency is 269Hz, not exceeded until the 7th harmonic of 41.4Hz. This reveals an inefficient soundboard, and it's heavy too.

Even grand pianos have a stiffening bulge in the soundboard despite the many strings in a plane, so the above attempt isn't optimum. Strong camber gives its plate much stiffness, so the koto instead should inspire the Glockenklavier
wikipedia
make the hull a good portion of a cylinder but flexible at the sides, put transverse ribs from place to place, tall at the middle, and fasten a tall keel under the top's centre. The keel must reach the hull, it can have apertures and be thicker at the bottom. Roughly, if this design puts wood 4* farther apart and better spread, it's 100* stiffer, so waves are 3* longer. Hugely better, but I won't detail it.

I suppose a wooden soundboard wastes in internal losses >90% of the input vibration and radiates the tiny rest, worse at low frequencies even with a better design. Neither do I want the piano's wooden sound for the Glockenklavier.

========== Milled aluminium

I limited to 40mm the dimensions of 1mm milled walls, and then aluminium brings only EI/µ=2.7*103 m4s-2, worse than Picea abies. Though, a refined design with a few taller parts would improve, and AA5083 or AA6082 are easily welded. At least, aluminium loses less power than wood and should sound metallic. Irregular cell size shall limit the resonances.

========== Graphite fibres sandwich

Flexural waves run slower in graphite composite (CFRP) alone than in wood, so here's a sandwich with 60mm balsa core of 100kg/m3 and 2*1.5kg/m2 skins of 1550kg/m3 and isotropic E=90GPa for total µ=9kg/m2. I doubt balsa transmits shear stiffly enough, especially for shorter waves, so it's probably interrupted by tilted fibres resembling corrugated cardboard.

EI/µ=18*103 m4s-2 improves over wood. At mean 52.1Hz, lambda/2=2.0m, nothing magic, and heavy too.

At violins, cellos and pianos, present CFRP soundboards sound horribly because they resonate too low, which the core improves. Balsa should also limit the wild resonances. Or it's wishful thinking.

========== Graphite fibres with ribs

Between lengthwise ribs, transverse fibres and 20mm balsa shall transmit the vibrations over 2*0.1m. 80mm*20mm balsa ribs spaced 0.2m hold lengthwise (190GPa) 0.2kg/m CFRP at the outmost faces, and thin isotropic CFRP covers everything, for total µ=6.6kg/m2 and EI/µ=300*103 m4s-2. At mean 52.1Hz, lambda/2=4m gets usable, and the soundboard is lighter. The cutoff frequency is below 41.4Hz, perfect.

40kg are still a bit much for 1kg contrabass strings. PU foam is lighter than balsa, but is it stiff enough? This plate too can adopt the koto shape with ribs and keel. Or a bridge, for instance cable-stayed, can inspire its shape.
wikipedia

Marc Schaefer, aka Enthalpy

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For the evolved Glockenklavier, tensile soundboards promise efficiency: they store hence dissipate little vibration energy, and their minimal mass couples well with the strings and the air.

========== Materials

Somehow I don't trust wood under permanent extreme tension. It's also too fragile and, under achievable thinness, too stiff to my taste: any residual bending at a bridge would break it under tension. Maybe I'm unfair.

Plain polymer films aren't strong enough. PEN (polyethylene naphthalate) outperforms now PETP
de.wiki - en.wiki
1360kg/m3 and 380m/s sound speed would need 196MPa tension, but PEN films break at 200MPa and creep well before. The films still elongate by 60% at break, and I suspect much stronger deformation at production would make them stronger.

Graphite or polymer fibers are by far strong enough. Unidirectional graphite composite weighing 1550kg/m3 needs only 273MPa for 420m/s and guarantees often >1200MPa. At least in ropes, some polymer fibres offer similar strength-to-mass with better flexibility and good (sufficient?) creep resistance. Rather than using some epoxy matrix, one could ask a sails maker to embed the fibres between two polymer films: the usual thickness fits the soundboard better, and sail makers design with stress in mind.

My clear choice is cold-laminated stainless steel. 7900kg/m3 and 380m/s need only 1141MPa while austenitic steel band can guarantee >2000MPa and more, with negligible creep. Carbon steel showed a frightening notch sensitivity in my trials, but AISI301 was very tolerant even at >2000MPa strength, and gained further resilience and strength after a short 180°C bake. I stressed such bands at 1000MPa for months and they performed perfectly.

Such a band resists corrosion, is easy to process at 50µm and 100µm thickness and is available from industry suppliers. Other alloys, like duplex stainless steel, PH 15-7 Mo, Maraging or CoCr20Ni16Mo7 can be strong enough but I discern no advantage to them.

========== Sound radiation

Individual mills limit the width of ultra-strong bands; I take a soundboard 1m high, to be checked. Width is for instance 5m and the deformation taken as a sine.

At the E=41.4Hz fundamental, the soundboard is not so big, so I take 5.6mohm*F2=10ohm radiation resistance. 1m/srms at the centre moves 3.2m3/srms air, so with a closed soundbox, the radiated power is 100Wrms.

100µm steel is sturdy and easy to process. The 1m*5m soundboard weighs then 4kg, so the same vibration stores 2J. A free vibration decays in 20ms or one cycle of E=41.4Hz. Higher frequencies radiate even better as they propagate faster in the band than in air, and will decay in fewer cycles, that is, before reaching the end of the band. The slow membrane of a banjo radiates slowly and its densely packed resonances create a completely different sound.

Since usual metals Q-factors are in the thousands, if the rest is properly built, this soundboard is nearly 100% efficient, while flexural wood achieves 10% or less. Loud instrument.

This soundboard is essentially aperiodic. I expect it to add no colour to the sound of a bare steel string heard by skull contact. Nice sound, resembling more a bell than a piano does.

========== String coupling

Usual soundboards of flexural wood are heavy and stiff, so a very light bridge transfers little string power to them. Here the soundboard is but heavier than one string and radiates immediately any received energy, so something like the bridge must limit the power transfer for good power and duration.

A stiff bridge looks better than a heavy one for that, as it transfers better the higher frequencies, so the high partials will be stronger at the beginning of a sound and vanish more quickly, as from a bell and most instruments. The bridge's resonances should be damped. The non-speaking string length contributes stiffness too.

Such a soundboard seems useful to more instruments.

Marc Schaefer, aka Enthalpy

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On 3/3/2019 at 6:50 PM, Enthalpy said:

The E=41.4Hz Glockenspiel, with a 5m string, would have a soundboard about as long.

Glockenklavier.

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Here are acoustics elements and a possible aspect of the evolved Glockenklavier.

GlockenklLook.png.9f788eeeda68a6a4da8131a8642e8e9c.png

The lower strings are about as high as the musician's head for good mallet length. With excellent ear protection and a mirror, the musician faces the strings that face the public and conductor.

Maraging 18Ni-12Co-5Mo-1Ti seems the best string alloy: yield=2344MPa in good diameter, weldable and solderable at full strength. 1293MPa tension achieve 400m/s with 1.8* margin. Over 4.83m for E=41.4Hz, the strain is 32mm. A D=10mm string, stretched with 102kN, stores 1.6kJ: some resilient net must catch the debris at the ends if a string or the soundboard breaks.

The musician can inject 150J in a string for fortissimo: as much as a 1kg stick thrown 30m far. 1.6kJ stretch energy shall let the string resonate decently. If the fundamental's displacement decays as exp(-t/1.5s), the mostly radiated power is 100W, or more since the harmonics decay faster: the percussive sound passes well above a symphonic orchestra, and 40dB decay take 7s, good for one note per second and 4s repetition period.

If the deformation were a symmetric triangle, 150J would displace by 60mm the middle of the E string. For 300MPa added stress, the D=10mm string takes 81mm length to turn by these 60mm/2.4m, but the string tension alone would achieve a sharper turn. The mallets must be wide with a domed contact, but the bridge and saddles thin enough to let the strings yaw freely, and they shouldn't bend the strings.

Stainless steel 17Cr-7Ni can make the tensile soundboard. Cold rolling provides yield>2000MPa with good resilience. 1141MPa tension achieve 380m/s with 1.7* margin. Alternately, Maraging may be available as wider sheet and is easier to weld or braze. 100µm*1m need 114kN stretch.

To radiate 100W, the soundboard moves at 1m/srms by 5.4mmpk at 41.4Hz sine, distributed as a constant over 0.8m width and a sine over 6m. The half-string shakes 4kNpk for 60mmpk displacement, so the stiffness goal is 781kN/m. As the strings and soundboard extend 1m beyond the bridge, their tension contribute 522kN/m, leaving 259kN/m to the bridge. Simple shapes suspending the bridge at the frame achieve the stiffness and deformation.

Neither the strings nor the soundboard deviate at the bridge, so to transmit traction, the strings are clamped, a pre-stressed beam runs between the frame sides to press the soundboard right under the bridge, and the bridge's suspension can have the opposite pre-stress. These forces must be eased or released before tuning, sorry.

To resonate at 35Hz a 100µm*6m2 soundboard without tension, the soundbox should contain 22m3, or 6m*2m*1.8m, bigger than drawn. This stiffness combines with the soundboard's tension, so even more capacity would be needed. Though, efficient radiation limits Q to ~4 only, and the bridge controls the transmitted power, so the box can probably be smaller. 5% conduction losses would need only 1m3. The long box has some resonances.

Because the soundboard moves much, sufficient clearance to the frame would leak too much, so the soundboard's sides hold to the frame. The bridge moves most width uniformly, and the sidemost 0.1m taper the amplitude to zero, advantageously under the bridge's suspension. The lengthwise tension is to propagate this shape far from the bridge, or transverse stiffeners may help, like small metal sheet omegas soldered on the soundboard, or glued light wood bars. No transverse tension up to now, but how does that sound? Limited tension is possible, if a transverse half-wave resonates much lower than 41Hz.

Resisting the 0.5MN tension, more than a grand piano, is difficult and may bring adjustments to the sketch above.

Marc Schaefer, aka Enthalpy

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The Glockenklavier's soundboard radiates the harmonics over one wavelength or less, so it's very little directional. The strings propagate the sound at 400m/s, emitting the highest components mainly at 31° from them.

Reflectors would then extend a lot from the instrument. Orienting the instrumen's plane around 30° from the public seems better than a reflector. Experiment shall tell, as a concert hall brings many reflections anyway.

Being about lambda/2 long, the soundbox combined with the soundboard could radiate the fundamental as a dipole, but this needs more thoughts. As a monopole, it's very little directional. Both cases are compatible with the sideways plane.

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To add at most 300MPa bend stress to the Glockenklavier's 10mm thick strings, the mallets need 3.3m curvature at their head, hence be broad, for instance 200mm for 60mm deflection at the middle of a 4.83m string. This width weakens the harmonics above 1kHz roughly.

A short impact on a 102kN 0.635kg/m string can be modelled (...at least prior to experiments) as a 254ohm resistor that brakes a 0.2kg mallet head in 0.8ms exponential decay, whose harmonics weaken roughly in the same range. A 0.6m shaft should then achieve a good velocity. The mass and length, together with the head hardness and the impact position on the string, influence the sound and must be experimented.

The sketch shows on the left a wooden mallet meant to survive the playing style. Thin fibre composite could reinforce the impact face. Polymer could look similar, while aluminium would be milled thinner and with more ribs and make lighter mallets.

An elastic stick would give a lighter head more speed, provided it's accurate enoug for music. Additional weight at midheight acelerates further, as in a spear-thrower
wikipedia
Playing with the feet would give guided hammers even more energy. For instance, four hand valves can direct to hammers the accumulated hydraulic energy produced by both feet.

GlockenklMalletPluck.png.05becfc7d4bd04bb514959925e9fd95b.png

Plucking gives a warmer, purer, more direct sound. Leverage shall adapt human force to 5kN for 60mm at the string's centre. Two lever stages may overcome some limits and achieve a non-linearity that reduces the effort at maximum deviation. On the right, the sketch proposes principle ideas for one plucker per string, with no significant thicknesses.

The jaws too must be rounded with 3.3m radius. If the lever comes back in 3s, the string's amplitude has decayed from 60mm to 8mm, which some material at the jaws must damp down silently: silicone, polyurethane, cork... The jaws can have interleaved teeth. The shown nonlinear grasping action is quick at big openings and strong to close the jaws. Something not displayed must define the jaws' inclination, for instance a rod at the axle tagged "Grip", whose other end's position would adjust the height of the jaws during their movement.

The musician can stand in front of the instrument or sit below. A bicycle brake action could control the jaws. Playing in a seat with the feet would give more power, with a different jaw control.

Can a percussionist play the plucked version, or does |: Ding-Dang-Deng-Dong :| demand a guitarist then? And is the tubist available at that time?

Marc Schaefer, aka Enthalpy

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Elements of Glockenklavier mechanical design.

The sounding part of the strings is better as drawn, for ease and for uniform thickness. The strings need thicker fastenings at the ends which could be forged or are welded. D=14mm tailor-made Maraging screws can stretch D=10mm strings. A usual thread achieves the 40mm strain of a 6m string over 23 turns, so a turnbuckle would help. Tuning to 0.1% needs 16° accuracy or 0.3m at a 1m wrench. Something must prevent the rotation of the string ends. At µ=0.14 friction, 102kN would need some uncomfortable 220N*m; I got µ~0.03 with a coating and MoS2 grease, it's corrosive but graphite grease is good too.

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The tensile soundbooard needs end parts too. A contractor electrodeposited locally Ni then Sn on my cold-rolled X12-Cr17Ni7: the layers adhered even when curving the sheet, and SnPb soldered them easily. Sadly, I know no shear strength for the Ni layer nor SnAgCu solder, but at 10MPa, 2*10mm solder joint suffice. Inspect the solder joints by ultrasound. Maraging needs no Ni layer but I feel 100µm too sensitive to corrosion.

GlockenklSheetEnd.png.defdfd4dce05fe0f6f5832b59ca3d8c8.png

Cu-Ni18Zn27 matches the expansion coefficient of X12-Cr17Ni7, while alpha steel would match a Maraging sheet. Available side milling cutter are too thick, so block(s) fill the groove and reduce the solder's creep. The assembly procedure would be:

  1. Block the groove's ends. Protect the threaded holes. Protect optionally the metal around the groove.
  2. Coat the end part, blocks and sheet end with flux.
  3. Heat the end part and blocks, for instance in an oven.
  4. Lay the hot end part with its groove on top.
  5. Melt solder in the groove. Coat optionally the block(s) with solder.
  6. Introduce the block(s) in the groove.
  7. Introduce the sheet in the groove.
  8. Cool.
  9. Clean.
  10. Ultrasound testing wouldn't hurt.

Six M8 threaded rods suffice, for instance of 600MPa stainless steel stopped with glue. The nuts or turnbuckles can be of Cu-Ni18Zn27 too, as a music instrument is built for a century and more.

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The 6m long frame must resist 0.5MN compression, half a railway engine weight. It shall have 3* margin so the strings or soundboard break first. A truss would be lighter, but two independent wide tubes, unsupported over 6m, would suffice in a first approach. With D=240mm e=10mm, they make bad use of AA6060 and weigh 240kg together.

Marc Schaefer, aka Enthalpy

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