Phil,
Phillip Ford wrote:
That CFT Steinway thought that soundboard compression was 'humbug' is interesting to me as I have great admiration for his work. However, reading the Gertz patent makes it
seem to me that they, at least, believed that soundboard compression was necessary and this device was going to help them achieve and maintain it.
>
To be accurate, the quote was, I think, in the context of an ongoing discussion as to whether Steinway & Sons should produce a cheaper piano, or persist in the high
quality, "artistic" designs they were using. As I have not seen the actual letter I don't know the extent, really, of his views on this, only the fact of the quote
attributable to him. I mentioned it only to indicate that there were creditable figures that had opinions that were contrary to what is usually thought of as unanimity on
this subject. Another, perhaps equally creditable figure in this context is Mathuschek. It may have been that Steinway thought soundboard compression superfluous only
in the context of building a cheaper piano. I agree that Gertz believed that it was either necessary or an improvement and hence the utility of the device. However, I am
still not able to see how M&H have actually used it to induce or maintain crown.
> Relatively speaking. You have several holes in a cast iron plate spread
> out over a distance of 3 or 4 feet with corresponding holes drilled in a
> piece of wood and with bolts that have to drop a vertical distance of 1/2
> in to 1 in or so from the plate to the rim. Most likely those holes are
> drilled by hand or with a fairly imprecise machine. By definition (or at
> least by my definition) these have to be loose fitting holes or you'd never
> be able to install the bolts.
As the fit, in fact, in what is in reality a screw even though we use the conventional term bolt, is an interference fit where the threads are self forming through elastic
compression of the material of the rim I don't think this argument holds up. Once the plate bolt(screw) is tightened the grip of the screw threads is on the formed threads
in the material of the rim and vice versa; there is no lateral play needing closing as you suggest. If there is the joint is not correctly closed. However, were there,
and should the plate be loading the bolt in shear then, in fact, the bolt would merely rotate in the hole, close the gap, and thereby transfer a substantial part of the
load.
In a structural application where you expect
> fasteners to carry shear the clearance between fastener and hole would be
> something like .001 or .002 in clearance to a few thousandths
> interference. The only way to hold those sorts of tolerances on a dozen
> holes spread out over several feet would be with a very precise machine
> tool drilling both parts (the plate and the rim) with the two parts
> precisely indexed to each other and with fasteners that are manufactured to
> precision tolerances (plus or minus a thousandth, let's say). Also, for a
> shear application you would not have a separation between the load
> application point and the load reaction point (in other words the plate
> would sit directly on the rim - not on dowels elevating it above the
> soundboard).
The screw threads grip, and are gripped, as indicated above, through elastic compression of the material of both media. Torquing the head of the screw causes compression of
the media of the threads and an increasing axial stress, or preload, develops in the screw, along with torsion which is partially released when wrenching ceases. The
preload is the balance between the axial stress in the body of the screw and the compression of the threads and external material resisting this stress. It is this that
creates the clamping pressure that closes the joint and prepares it to take the joint load that may be axial, shear or a combination of these. The preload, through the
strenth of the screw itself and the material of the rim can resist joint loading that is axial to the screw. It can also transfer shear. In so doing it does not require
the clearances between the hole in the plate and the stem of the screw to be such that these are in contact, or nearly so, with one another, as you seem to suggest. The
bulk of shear is transmitted by friction developed on the mated bearing surfaces of the head of the lag screw and the plate created by the preload in the screw. Such
friction is a function of the preload.
For example, the bolts holding the rim to the hub of the wheel on a car develop a similar axial preload which in turn creates friction between the bearing surfaces in
turn, which then is efficient at resisting the nearly pure shear loads placed upon them by the car; they are not closely fitted, particularly in machine terms, again, as
you seem to say is necessary for resisting shear.
To use a familiar example, the top of a leg on a grand piano should be well fitted to the underside of the piano. The leg plates are not designed to take the shear
load themselves; their function is to hold the two well fitted surfaces together and allow friction between the two surfaces to resist shear.
How much shear, or axial loading or the degree of combination of the two, which exists in a plate attached at the rim, I don't have much sense of, although, I believe,
the plate is more than adequately coupled to the rim in such a manner that it is able to effectively strengthen it and so doing creates, as I have said before, a structural
unit of substantial strength. The effect of the flange cast in most plates near and following the rim must, I think, tend to transmit whatever portion of the string load
that is in fact transmitted as mostly shear or mostly axial loading of the joint, and, perhaps, favor one over the other although I am not sure which. Apparently, this
view, rightly or wrongly, has been shared by others some of whom have designed pianos using a full perimeter plate which is used in lieu of rim bracing under the
soundboard most or all of which is essentially left off. I had a piano, a Wurlitzer, if memory serves me, grand in the shop ten or twelve years ago with just such an
arrangement. It was, upon completion, an exceedingly stable piano.
With all due respect to you, I think the predicate of your argument, that is, that the rim must close a gap due to an allowance in the fit of the screw joint for the
plate to effectively transmit loads to the rim, and that it could not do so were such a gap extant, is not borne out for the reasons I have given above, and perhaps
others. Additionally, upon reflection, the fasteners used in most high-quality pianos are 4 to 6 inches long, or, occasionally longer and deeply embedded into the rim.
Some, for example, older Mason & Hamlins have large countersinks where the large screw head fits into the plate, something, that may be overkill but probably answers some
of your objections which the conventional bolt head upon a boss might not, although I think both are sufficiently effective. Yamaha, and Young Chang, are the only Asian
manufacturers at this moment to use the larger size fasteners, that I am aware of, there may be others, as this is,. of course, subject to change.
Even though the plate may sit off the rim with the bosses on dowels, or platforms of some kind, the effectiveness of the bolts, operating even as cantilevers, is
adequate and particularly so in the larger fasteners used upon most high-quality pianos. .
.
To my knowledge no piano is built like that. Say the bolts
> are 1/2 inch. My Machinery's Handbook lists a Close Fit hole for this size
> fastener as .5156 inch. A Free Fit is given as .5312 inch. So, there's 78
> thousandths of clearance between the bolt and the hole for even a close fit
> hole.
> Let's say that you assume the plate and rim are immobile at the point where
> the plate lug meets the rim brace collector. Apply a load on the rim at
> one of the rim braces. Assume only the rim brace is resisting the load (in
> other words ignore the bending stiffness of the rim itself which is
> significant). The compression of the rim brace, which is also the
> deflection of the rim at this point, is Pl/AE. Assume a 1000 lb load. A
> is 18 square inch given above,
> E = 1,500,000 psi given above, and assume a length of 4 ft (48
> inch). Deflection is
> .002 inch. So, to deflect the rim enough to close the clearance between
> bolt and plate hole would take 39,000 lb of load on the rim at that point
> (assuming that the fastener is centered in the hole).
> Also, let's look at the bolts themselves. Let's assume 1/2 in. diameter
> bolts (not flimsy, as you say). Most plates are fitted so that they float
> above the rim. For the load to transfer from the plate the bolt would have
> to bend from the load application point (the center of the plate) to the
> load reaction point (let's say the top of the rim - the soundboard material
> is so soft it can't really take this bolt load). This could amount to an
> inch of length (for the Baldwin style of plate suspension I think it could
> even be more). So each bolt is acting like an inch long .5 inch diameter
> steel cantilever (assuming that the rim is perfectly rigid so that the bolt
> can't rotate at all - not a very accurate assumption, but I'll use
> it). Deflection of a cantilever is Pl^3/3EI. Assume
> E = 30,000,000 psi. Once again assume load is 1000 lb. Deflection is .004
> inch. Not as much as I expected but still twice as much as the rim
> deflection for the same applied load (or in other words twice as flexible as the rim at the same point for the same applied load). This, of course, is assuming that the
> bolt is in a zero clearance hole, so that it starts picking up load
> immediately. Also, many pianos have bolts smaller than 1/2 inch diameter
> which will be considerably more flexible, as the bending stiffness is
> proportional to the fourth power of the diameter. So, all things
> considered, I still stand by my contention that the plate is not doing much
> to keep the rim from deflecting.
>
Judging from previous posting on this subject this will be heavily contended, but my experience has been that pianos with loose plate bolts are unable to develop adequate
stability, suggesting that part of the string load in stable pianos is in fact transmitted into the rim. A substantial, marked improvement in stability accumulates over
time after the bolts have been properly tightened. Tightened bolts can be deceiving, for example, I have had the experience, mostly on Asian pianos, of tightening bolts
then letting the tension down only to find the bolts I thought were tight were now loose. This suggests to me the 10 mm or small plate bolt used on most Asian pianos is in
fact inadequate and cannot pull the plate down against the load without approaching to close to stripping or fracturing, both of which I have experienced. I would always
be cautious in assuming that the preload in tightening a plate bolt has, in fact, created sufficient clamping force to close the joint when the joint load itself, that is
axial or shearing stresses from the strings, is operating on the joint at the time of tightening. What one thinks is closed may or may not be once the joint load is
removed.
Regards, Robin Hufford
>
> Phil F
This PTG archive page provided courtesy of Moy Piano Service, LLC