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Stiffness and Graduation of Plates

 
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Dave Chandler
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PostPosted: Sat May 22, 2010 7:32 pm    Post subject: Stiffness and Graduation of Plates Reply with quote

I've been reading that stiffer wood can be guaduated a bit thinner. Without a bunch of samples to compare is there some formula to determine how stiff a piece is? I'm a weak old man, I can't bend anything till I've already got it pretty well graduated. Seems I read somewhere its a ratio of tap tone and weight of the plate, but I can't seem to find anything definitive.

If, lets say you have a piece of extremely curly hard maple, how much would you allow, perhaps instead of 2.7mm thick average (I'm just grabbing a number out of the air), you'd go to 2.5mm? Is there any rule of thumb?

Does tap tone take into account stiffness?
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rs
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PostPosted: Sat May 22, 2010 11:47 pm    Post subject: Reply with quote

Hi Dave,

I'll share what I do. I cut a small sample from the piece I will make for the back and thin it to 1mm. I then free hand bend it and simply compare it to what I have bent before. There could be a formula derived, but I like this approach of just subjective comparison. If it tends to be more flexible, this shows the sample to be less "stiff", hence of a lower "spring constant" composition. I then approach cutting the back with two options in front of me. I can either thin the back a little more than I would if it was "stiffer", or I can increase the arch about 1 to 2 mm more to superimpose a higher "spring constant". I have found that either works, but the route I prefer is to arch it a little more as I like the look of a slightly more aggressive arch than not.

If the wood is stiffer, I simply reverse the above; heavier grad and slightly less arch.

For what it is worth, I have found that the curlier the maple, the less the "spring constant" tends to be. I like this curlier wood not only for appearance, but it allows for a little more arching and a little thinner back, which tends to be prettier with a slightly advanced arch, I think, and the thinner back tends to be lighter. A fine instrument that is also light to the hands is not only a more responsive instrument, I believe, but also does not wear out the player.

After I string it up, I trim out the back to complement the top. This last step, I have found, greatly improves the instrument in every detail.

As for the tap tone and stiffness, the stiffness greatly changes the tap tone. If a back is cut in every detail the same as a predecessor, but has a higher stiffness, or spring constant, while maintaing the same mass as its forerunner, the tone will be higher when tapped. This is simply because no two pieces of wood are the same in every detail. Pitch has long been defined by the effect of force to mass that is constrained by spring constant. Hence, changing the spring constant requires changing the mass, or vice versa.

But this is just my approach. Others approach violins differently with good results, also. This is why I love the instrument!

Best wishes
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Dave Chandler
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PostPosted: Sun May 23, 2010 8:20 am    Post subject: Stiffness and Graduation of Plates Reply with quote

RS:

Very much appreciated, had not thought of approaching it from the arching standpoint, but that sounds like a good option.
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violinarius
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PostPosted: Tue May 25, 2010 4:25 pm    Post subject: Re: Stiffness and Graduation of Plates Reply with quote

Dave Chandler wrote:
I've been reading that stiffer wood can be guaduated a bit thinner.
Seems I read somewhere its a ratio of tap tone and weight of the plate, but I can't seem to find anything definitive.



Is this what you are looking for?

http://www.platetuning.org/
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L P Reedy
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PostPosted: Wed May 26, 2010 6:27 pm    Post subject: Reply with quote

Dave,

John Masters multiplies (mass of the plate in grams) by (mode 5 frequency squared). I believe the frequency is Khz and the numbers he looks for are about 0.8 for the top and 1.2 to 1.4 for the back.

I tried it once and it probably works, but my plates are not trimmed to size until after they are glued to the ribs so the weights are high. I just flex the plates and guess at it.

Lyle
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Dave Chandler
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PostPosted: Fri May 28, 2010 1:27 pm    Post subject: Plate tuning and stiffness Reply with quote

These are both worth exploring. The Plate Tuning site is going to keep me busy for a while.

So here's a new but related question. I'm currently working on a one-piece spruce top. Needless to say one side of the plate has annual rings that are so close together I can barely see seperation between them, while the other side gets pretty wide. Is the stiffness related to the growth rings, or are they irrelevant?
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rs
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PostPosted: Mon May 31, 2010 4:08 pm    Post subject: Reply with quote

There is a general correlation.

Generally, if pressure is applied to spruce samples equally cut and hanging over a table edge, it will be found that the wider the grain, the more force that is needed to deflect the piece. This demonstrates that generally, the wider the grain, the greater the spring constant or stiffness.

If the piece was absolutely uniform in its grain, a maker could compensate for the overall anomoly of each top he made with general thickness adjustment. The reality is, that spruce tends to vary on every sample cut in that very few samples are absolutely uniform. Typically on two-piece tops, the inner part is thinner grain, the outer bout areas broader. On one-piece tops, the variance is exaggerated further still.

This was a red herring for me for a while. I was on the right track, I came to find, that adjusting the top in areas of grain variance produced very good results. But the reason I found, was not because of the stiffness variance, but rather, the variance in mass.

If there is one thing I will pass on about tops it is this. The best tops are uniform, not necessarily in thickness, but more correctly in mass. I found that the narrower grain tends towards more density and therefore mass. If a maker knowing this, simply removes a little more wood where he finds narrower grain, his tone will tend towards uniformity. The quality is then adjusted by the cut of the back and finally the adjustment of the back to the already existing top.

I compare it this way. A gut string has little use when it has nodules or knots or irregularity as all of the notes will not be uniform. The nodule itself, by its own inertia, or unwillingness to move, will cause certain notes to drop out as the string is fingered at different stops, depending on where the nodule is. A perfectly drawn string, on the other hand, does not possess this aberration. If a top has abnormal MASS distributions, the results tend to be the same as the bad string, that is, the violin has some good notes, some mediocre, some bad. If this problem is addressed, and the top is cut uniformally, not as to thickness, but as to mass, the maker will find that the instrument is uniform in tone, for good, mediocre or bad, but still, that ALL the notes will be of the same calibre, as a rule. This, I found, was the most important aspect of correctly cutting a good top.

As your question is directly related to tops, and to variance of grain width on tops, I will pass on how I would treat the top you described. My experience without seeing your top tells me that I should expect the narrower grain to be denser than the broader grain. I therefore would be prepared to remove slightly more wood in the areas of narrower grain. I have found that if I use a little cross-cut motion on the scraper in these areas, more of the wood is raised and removed between the harder part of the grain.

For what it is worth, I give my highest attention to the above when I cut a top, that is, I spend the most time on top making simply refining the uniformity across the top. Sometimes the graduation shows the opposite, and will vary somewhat, but the reality is, it is MASS uniformity I am after, not necessarily graduated uniformity.
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Janito
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PostPosted: Mon May 31, 2010 9:51 pm    Post subject: Reply with quote

rs wrote:
Generally, if pressure is applied to spruce samples equally cut and hanging over a table edge, it will be found that the wider the grain, the more force that is needed to deflect the piece. This demonstrates that generally, the wider the grain, the greater the spring constant or stiffness.


Some would say the opposite.
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Michael Darnton
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PostPosted: Tue Jun 01, 2010 7:59 am    Post subject: Reply with quote

There's also a published study showing no difference at all. Brain work (without wood) indicates that the greater the proportion of hard stuff (dark grains) the stiffer the wood should be, but apparently it turns out that stiffness doesn't hinge on grainlines at all, but rather on something else, so depending on the specific pieces of wood you try the "over the edge of the table" thing with, you could get different results. That's what the research said, anyway.
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mikemolnar
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PostPosted: Fri Jul 16, 2010 8:55 pm    Post subject: Reply with quote

Michael, I am told that the optimum grain count per inch is 15.

Does that seem right?
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Michael Darnton
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PostPosted: Fri Jul 16, 2010 11:30 pm    Post subject: Reply with quote

I'm not sure there is any kind of real optimum, but that certainly is a size that looks nice and varnishes up well.
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jethro
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PostPosted: Sun Jul 18, 2010 2:15 am    Post subject: wood stiffness tester Reply with quote

Dave :
I happen to have an article here by Mr. Charles Woods called
"wood testing"
Found at " http:www.scavm.com/Woods.htm
It describes making a device to test a small beam of wood sawed off you
plate before you cut it into a top/bottom. I have not built/ tried it.
Perhaps someone else may have !
Tim
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