Tension Resonator

[Robin Hufford]

Phil
     Thanks for the link, which I will go to this weekend,  and an interesting analysis.  I am reading my own Machinery's Handbook, 25th ed, in particular, the section entitled "Torque
and Tension in Fasteners" in anticipation of composing a reasoned answer when I have time this weekend.  Offhand, I am still unconvinced that the plate does not impart substantial
strength to the inner rim as I have said earlier but in arguing this I  am not contending that metal braces could not be used efficiently with the effect, as you say, unless I
misunderstand you, of reducing the bracing.
       I have often wondered if there was, indeed, any reason for calling the "centripetal tension resonator" beyond that served for sales purposes.  This, particularly,  when its
purpose, according to the literature of M&H that I have seen years ago,  was to prevent spreading of the rim and subsequent loss of crown.  The details of the patent you have posted
here make the name understandable, although, and I have not yet had time to go to the link you sent and read the patent entirely, it seems its use in M&H is considerably different than
that which the patent depicts.   More on this later.
Regards, Robin Hufford

> Robin,
> On thinking about this post afterwords I realized that I had made an error in my calculations.  My conclusion is still the same, but the numbers are a bit different.  Details below.
>
> > >I don't think the holes are that loose fitting, nor in a high quality
> > >piano the
> > >bolts  flimsy and, particularly, in comparison to the normal loads placed
> > >upon the
> > >rim.
>
> >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.
>
> Here's the error.  That should be 7 - 8 thousandths, not 78 thousandths.  That makes more sense.
>
> >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).
>
> That would make this 3900 lb of load on the rim to close the gap, not 39,000.
>
> >So, all things
> >considered, I still stand by my contention that the plate is not doing much
> >to keep the rim from deflecting.
>
> My conclusion is still the same, but the numbers supporting that are now down closer to earth, rather than in the stratosphere.
>
> Phil F