Plate and Rim (was Re: Tension Resonator)

[Delwin D Fandrich]

Phil,

If I'm understanding you correctly, you're assuming that there is some
substantial amount of load being transferred from the string plane through
the plate to the rim. I've not found this to be the case. String tension is
nearly all supported and contained within the plate--trace the lines of
force. Even with the Steinway design with its plate horn and wedge there is
not all that much string load transferred to the rim--especially when the
wedge left out or lost.

I once joked that if all we had to worry about was the string load a few #10
wood screws would be sufficient to hold the plate in the rim. Of course
there's a bit more to it than that. The greatest strain is placed on the rim
bolts/screws during moving or shipping. Even a lightly built plate is rather
heavy and dumping a wheel in that first pothole would probably rip those #10
wood screws right out of that Select Hardwood rim and the whole thing would
end up on the floor. While it is a formidable task holding a 200 to 500
pound (90 to 230 kgf) iron casting in place and it would seem that a good
friction fit between the plate and the rim would be essential, even the
Baldwin system seems to do an adequate job.

Among the primary functions of the plate are (first) to support string
tension and (second) to establish and maintain a desired relationship
between the string plane and the soundboard/bridge assembly. If nothing was
changing or shifting my #10 wood screws might well be adequate. But even the
most well-designed rim assembly is going to shift and twist with changes in
relative humidity--at least they will as long as they are made of wood. If
the rim is able to do this independently of the plate there will be changes
in the string plane to bridge/soundboard relationship that will result in
tuning instability. If the plate is fastened to the rim such that the two
essentially form an integral whole these changes in relationship will be
minimized and tuning stability will be improved.

Taken from this perspective there are any number of fastening systems that
are adequate to the task.

Regards,

Del


----- Original Message -----
From: "Phillip Ford" <fordpiano@earthlink.net>
To: <pianotech@ptg.org>
Sent: May 07, 2002 10:43 AM
Subject: Plate and Rim (was Re: Tension Resonator)


> >Date: Mon, 06 May 2002 14:51:43 -0700
> >From: Robin Hufford <hufford1@airmail.net>
> >
> >Phillip Ford wrote:
> >
> > > 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,
>
>
> Yes, correctly speaking, a screw.
>
>
> >  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.
>
>
> I was ignoring friction.  If there were no friction then the only load
path
> is a physical contact between the plate and the screw.  In order for this
> to happen the plate would have to deflect enough for the edge of the plate
> hole to come into physical contact with the screw.  As you say, if the
> screws have sufficient preload, then the load can transfer to the screws
or
> the dowels by friction.
>
> >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.
>
>
> The plate has to load the screws (and/or the dowels) in shear to transfer
> load to the rim, since the screws and dowels are the only physical
> connection between the plate and the rim.  The load I'm talking about here
> is the load in the plane of the plate (more or less parallel to the string
> plane) - the string load, not the axial load on the screws that would
> result from the plate trying to bow up due to string load.  If the rim is
> going to assist in resisting this load, which it must if the rim and plate
> are supporting each other as you say, then the path from the plate to the
> rim is through the screws and dowels in shear.  Regardless of whether the
> load transfers to the screw by physical contact between the plate hole and
> the screw or by friction between the screw head and the top surface of the
> plate the load on the screw is a shear load.  This shear acting over the
> distance between plate and rim will result in a bending moment on the
> screws and dowels at the rim (another way to put this would be to say that
> the screws and dowels are acting as cantilevers off the rim).  I don't
> understand what you mean by the screw rotating and transferring a
> substantial part of the load.
>
>
> >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.
>
>
> Yes, there can be a preload.  I wouldn't agree that the preload is
> resisting the joint loading.  The screw is doing that.  If the screw was
> snugged down so there was no clearance between the screw head and the
> plate, but there was no preload, the screw would still be able to resist
> this axial load.  If the preload is high enough, then the screw can resist
> this axial load without relaxing the preload.
>
> >    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.
>
>
> Agreed.
>
> >      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.
>
>
> The lug nuts are tapered to form a close fit between the nut and the wheel
> rim so that there is a direct shear transfer from the wheel rim to the lug
> bolt.  The auto manufacturers also seem to feel that this close fit is
> necessary for transferring shear.
>
> >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.
>
>
> I'm not sure what you're saying here.  If a designer gave consideration to
> the plate and rim sharing the load or needing to share load, then
designing
> a full perimeter plate and leaving off the rim braces would seem to
> indicate to me that the designer didn't feel that the frame support was
> necessary and that the entire load was going to be taken by the plate
(this
> is assuming that he felt that the rim braces weren't necessary to stiffen
> the rim for acoustical reasons - that they are merely structural
> elements).  Even assuming the load transfer mechanism you've described
> above I wouldn't think that the rim in this case was giving much support
as
> it would be fairly flexible without the rim braces.  In spite of that, you
> say that the piano was exceedingly stable.
>
>
> >    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.  .
>
> I concede.  IF there is adequate preload on the screws then this joint
> provides a structural connection between the plate and the rim.  How much
> load would be shared would depend on the stiffness of this joint and the
> relative stiffnesses of the plate and rim.  I can't say whether that would
> be a lot or a little.  I'm presuming a little but I might be wrong.  If I
> were a designer and was depending on the connection between plate and rim
> to be structurally effective I wouldn't use the standard design.  For
> reasons discussed above this design is only effective if the preload is
> maintained.  Since the wood of the rim and the wood of the dowels on which
> the plate is set will creep under load and move with changes in humidity
it
> is inevitable that the preload will be lost and then the connection that
> you describe will be lost.  Then you're in the position of depending on a
> technician to tighten plate screws at regular intervals.  You also would
be
> accepting a gradual sinking of the plate as you slowly compress the dowels
> over time.
> I would either design the plate so that it is heavy enough to handle
string
> loads by itself, or use a different kind of connection between plate and
> rim.  The Baldwin system seems good to me.  It provides a direct
connection
> between plate and bolt (no gap between plate hole and screw), it doesn't
> depend on preload to transfer load, and the position of the plate (and
thus
> bearing) doesn't change with time.  However, if I wanted to depend on this
> system to transfer string load between plate and frame I would make the
> bolts bigger and also arrange things so that the plate ended up being
> suspended a short distance above the rim.
>
>
> 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.
>
> What do you mean by 'stability accumulates over time'?  I have trouble
> seeing how load sharing between the plate and the rim would make the piano
> more stable.  If substantial load sharing occurs between the plate and the
> rim if the bolts are tight, then if the bolts become loose and lose their
> preload this load sharing would fail to occur.  This would seem to me to
> make the plate less stiff than the plate and rim assembly.  So it might
> take longer to get the piano to stabilize, since the plate would be moving
> more due to string load.  But once it was stabilized, I can't see that it
> would make any difference to long term stability whether the plate was
> sharing load with the rim or not.
>
> 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 alwaysbe 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 stress
>
> Yet another reason to add to the ones I gave above not to use this design
> if you're depending on load sharing between plate and rim.
>
> Phil F
>
>
>
> Phillip Ford
> Piano Service & Restoration
> 1777 Yosemite Ave - 215
> San Francisco, CA  94124