Plate Bushings - was Re: Bushing vs. bigger pin?

Ron Nossaman RNossaman@KSCABLE.com
Wed, 31 May 2000 13:23:40 -0500


>So... you are gonna make me take a stance eh ??? I gotta bad feeling about
>this...grin.. but here goes..
--------------------------------------------
>Grin... so there you have it.. my humble musings on the matter for what
>they are worth. Now go ahead... :) tear me apart.. hehe..


I don't think you did badly at all. I agree that it's unlikely that poor
flange fit is all that likely a cause of long term tuning instability. I
can envision a block fit so badly to a flange that all those tons of string
tension will pull it, or sections of it, forward until it either
accumulates enough flange contact, or tuning pin to plate contact, or
bushings compacting enough to provide enough cumulative resistance, to stop
further movement. This should happen during approximately the same time
period when all the other new piano new piano tuning stability problems are
settling down, and may even be part of what we're seeing during that
process.   

The biggest conceptual problem I see in all this is the notion that string
tension, with the tuning pins being levers, and the plate bushings being
fulcrums, will force a previously fitted pinblock away from the plate
flange. I don't believe it. 

The easiest place to start would probably be with a plate without bushings.
Say you have a 2 1/2" (63.5mm) tuning pin in an 1 1/2" (38.1mm) pinblock.
Assume a plate webbing thickness of 10mm. Assume also that the centerline
of the string coming off the bottom of the coil, going to the
counterbearing bar, is 3mm above the plate surface and under 180 pounds of
tension. That leaves 25mm of tuning pin in the pinblock. If the pins aren't
contacting the plate, the string tension is pulling the block to the plate
flange. It's also applying a much lower rotational force that the plate
screws are easily able to contain, so we shouldn't have to worry about that
much from here on. Let's look at what sort of forces the hole in the block
is being subjected to, and where.

For now, let's assume the pin isn't contacting the plate. All the string
tension is pulling the block toward the flange. Plain old leverage (moments
of force) will tell us something about the distribution of forces in the
block. At the top of the block, we have 180*38/25= 273.7# (lbs), where 180
is string tension, 38 is total lever length from the bottom of the tuning
pin thread to the centerline of the string, and 25 is the distance from the
top of the block to the bottom of the pin threads. At the bottom, we have
13/25*180 = 93.6#, where 13 is the distance from string centerline to
pinblock top. It doesn't work exactly this way, since the pin isn't a free
lever, and is supported throughout the length that's in the block, but the
compressive force of the pin at the block surface will still be
considerably higher than at the bottom of the pin threads, which will be
180° from the direction of string pressure. The center of pitch rotation
will be somewhere toward the bottom of the pin. This means that the slow
compression creep of the wood in the pinblock will eventually let the pin
lean forward. So what happens when the pins lean forward enough to contact
the plate?

If the pin was a free lever, fulcrum at the bottom, we'd have 180*38/35 =
195.43# at the top edge of the plate, and 3/35*180 = 15.43# at the bottom,
trying to push the block away from the flange. The pin, however, has it's
bottom 25mm imbedded in the block. The center of pitch rotation moved from
near the bottom of the pin, to 3mm below the string plane, at the point
where the pin contacted the plate. While there is negative 15.43# at the
bottom of the pin, trying to force the block away from the flange, there is
( assuming a free lever ), of 25/10*15.43 = 38.58#. This would be the
leverage equivalent of  23.11# of resistance at the pin/plate contact
point, in the direction of the plate flange. That's in addition to the
resistance already present in the compressed wood of the pin block just
before the pin contacted the plate. All this is working to hold the plate
to the flange in spite of the negative leverage resulting in the pin
contacting the plate. Even with a bushing around the pin, the situation
would be similar.

My conclusion from all this is that I don't see how tuning pins, with or
without bushings, can possibly lever a pinblock away from a plate flange. I
also don't see how, given a reasonable number of screws holding block to
plate webbing, a pinblock to plate flange fit can have a noticeable long
term negative effect on tuning stability. This leads me back to my original
opinion that plate bushings improve the feel of tuning by lessening
flagpoling, and keeping the pin away from the plate. They won't make up for
sloppy plate fit, nor will they allow the pins to lever the block away from
the plate flange. I also don't see the rocking of the pinblock resulting
from the above center string tension load being a factor in anything at all
unless there aren't any screws holding the block up to the plate webbing.
If that were the case, I would be worrying about more than tuning stability.

I hope some of this makes sense to anyone hard headed enough to have
dragged themselves through it and tried to make the concepts fit the
reality. It's hard for me to try to describe without being able to sketch
and point during the process. If I could just project the little video I
can picture in my alleged mind, it would be so much easier. Maybe with the
next generation of Linux...


Ron N


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