[CAUT] low friction bearings

[Stephen Birkett]

David:
>St three days without posting, I know this thread seems to have 
>gracefully gone it's way, but I'll try, nevertheless, to cobble 
>together the various thoughts I had had.

8 days now and counting. I think it's dead. Let's try moving it to to 
pianotech and see what comes out of the woodwork. I love hypothetical 
pianos.

Lots of questions....Some speculative answers, and a comment on some 
experiments with low friction bearings.

>Your hypothetical piano questions address tunability, tuning 
>stability, and the effect of bearing point friction upon the wave 
>form and wave duration. What is it you are trying to accomplish? 
>The Boston model that inspired this thread would seem to have some 
>significant design issues in this area, but is the implication that 
>the basic concept (pin block, tuning pin, etc.) is inadequate?

The specifics of the Boston problem (obviously important to the 
original question) aren't relevant to my hypothetical piano. I'd say 
this addresses the first two questions directly, and the last point 
indirectly (and unpredictably). It also allows you to use a long 
backlength without the concern it will unduly affect stability.

>Tunability would depend upon the level of refinement of the 
>mechanical system that would control the tension.  I don't have the 
>information readily available that correlates tension with 
>frequency, but such a system would have to be able to acheive, in a 
>linear fashion, what we do with the combination of turning the pin, 
>flexing the pin, test blows, etc.

Not necessarily. A regular tuning system, as long as it was 
reasonably secure, would work just as well as for a regular 
configuration. As for test blows, you wouldn't need any, because 
tension would instantly equalize in the various string sections as 
soon as it is changed.

>Tuning Stability - I don't remember if a recent (?) past thread ever 
>determined exactly why strings go out of tune.  Is the assumption 
>that, by reducing friction at bearing points, the tension of the 
>various lengths will be more equalized than what we generally 
>achieve, and thus, less prone to change?

Longest strings (overall wires) minimizes the effects of any 
instability on pitch.

>What tension values (or range of values) would you insert into a 
>formula that described the tension relationships between the various 
>sections in a stably tuned string?  How much variation in tension 
>would be viable between the front section and vibrating section; 
>between the latter and the back length?  How do you measure that 
>tension?

First two points would depend on whether friciton at the bearing is 
actual zero, or just minimal. Tension is easy to measure in 
experiments, simply by monitoring pitch. I've done experiments with 
minimized friction bearings. You set up two equal string segments and 
equal pitches, then crank the tension up and down. The extent to 
which the pitch in the segments varies is a proxy for the tension 
variation and that is a measure of how low the friction is in the 
bearings. Several cycles up and down will give a hysteresis loop, 
unless the bearing friction is zero.

If this topic is interesting I would consider writing up the results 
for the journal.

>Does the friction at the agraffe and bridge pin have any role in the 
>definition and containment of vibrational energy or is that solely a 
>function of deflection?

I suspect not, since the string is stiff, and the motion is primarily 
in the directions perpendicular to the string. Longitudinal 
virbrations will pass through bridge pins anyway, friction of not.

>Why do you say that the longer the non-speaking length, the better?

Because, with say zero friction bearings, any change in string 
tension from sideways excursion (e.g. when struck), will be 
(temporarily) distributed over the entire wire, not just the speaking 
length. So the the proportional change in length (strain) is less, 
and so is the change in stress, and so is change in pitch.

>Why, from what's been discussed, do you find "same total string 
>lengths within trichord" to be advantageous?

Because any instability in the length will transfer to a strain 
change. If the instability is about the same for each string in the 
trichord, the strain change in each will be similar, and so will the 
pitch change. The trichord would stay locked, even it it goes out of 
tune a bit.

Stephen
-- 
Dr Stephen Birkett
Piano Design Lab
Department of Systems Design Engineering
University of Waterloo, Waterloo ON Canada N2L 3G1
tel: 519-888-4567 Ext. 3792
Lab room E3-3160 Ext. 7115
mailto: sbirkett[at]real.uwaterloo.ca
http://real.uwaterloo.ca/~sbirkett