Stiffness testing

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Ed Minch
Posts: 34
Joined: Sun Dec 24, 2017 1:59 pm

Stiffness testing

Post by Ed Minch »

Would this be useful in guitar building

https://www.msstate.edu/newsroom/articl ... st-lumber/

Ed
Alan Carruth
Posts: 1265
Joined: Sun Jan 15, 2012 1:11 pm

Re: Stiffness testing

Post by Alan Carruth »

It should be. It's basically doing the same thing as a Lucci Meter; measuring the speed of sound in the piece. Violin bow makers have been using those for years. If you know the density you can calculate the Young's modulus pretty easily. With dimensional lumber you'd have to have way to find the weight, and enter the dimensions. It's bound to be cheaper than a Lucci, at any rate. It would be interesting to try it on some guitar wood that had already been measured some other way, to see how reliable it might be on smaller stock.
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Beate Ritzert
Posts: 599
Joined: Thu Aug 02, 2012 8:20 am
Location: Germany

Re: Stiffness testing

Post by Beate Ritzert »

Btw, what about measuring Young's modulus directly, e.g. by deforming it under a controlled load (weight)?
Alan Carruth
Posts: 1265
Joined: Sun Jan 15, 2012 1:11 pm

Re: Stiffness testing

Post by Alan Carruth »

There are a number of methods of testing wood, and they all have drawbacks (wouldn't you know).

Probably the simplest in terms of setup is deflection testing with weights. A lot of makers do this. You support the piece to be tested, such as a half a guitar top, on something like pieces of pipe or round stock at a convenient distance apart, and load it with a weight in the center. The deflection is read off with a dial gauge or micrometer. With many makers this is pretty ad hoc: they will use the same setup every time, but nothing is calibrated. A top might be taken to some thickness based on 'feel' or the consensus of your favorite guitar group on line, and the deflection measured. If the instrument turns out well, then it's assumed that the stiffness was 'correct', and other tops can be thicknessed to get that same deflection with some assurance. No attempt is made to find the Young's modulus (E): there is no plan to share data with other makers. Both Gore and Hurd give formulas that allow for the derivation of E values if the thickness and width of the piece are known, along with the support spacing, weight used, and the deflection. This enables makers to pool data and possibly advance more quickly.

The biggest problem with any such test is 'stress relaxation' AKA 'cold creep'. Wood under bending loads will continue to deflect more as long as the load is maintained, eventually taking a 'set' in the deflected shape. This is, so far as I can tell, due to plastic deformation in shear of the lignin 'glue' that holds everything together; the property that allows to to bend sides. With deflection tests you're in a bind: you need a large enough load to produce a significant displacement, but that will often cause noticeable creep over fairly short time periods. To get an accurate reading you need to be quick. Often what people will do is to load the piece, zero a dial gauge, and then remove the weight, noting the reading immediately. There are a couple of other issues.

One is that you want to insure that the bending is uniform across the piece. Something as wide as a guitar top half could bend significantly across the grain if it was loaded at a single point in the center; you'd be getting more deflection at the load point than anywhere else. The same goes for the supports, of course. Usually parallel pieces of pipe are used for the supports, and a heavy pipe that spans the width, or something like a cast iron sash weight, is used as the load. Another issue is that wood with curvature in the grain or run out can give different deflection readings depending on which side is up. It's usually safest to measure a sample both ways and take the average. This is, of course, also a good way to find out if there are such 'flaws' in the wood; you might want to reject any tops that give readings that are too different.

Most deflection testing is done using that sort of 'freely supported' method. Recently on researcher has advocated using a cantilever for this. The sample is clamped at one end, and the weight is hung from the free end. I've never done it that way myself. In discussions of test methods years ago the objection that method was that in may not be as reproducible. There are two related issues. One is that the exact length of the beam is a major variable. You have to clamp it tightly enough so that you're sure the bending starts at the clamp, and not somewhere behind the edge. The problem there is that the difference between 'tight enough' to ensure that, and 'too tight', such that you start to crush the wood, may be hard to judge. Also, at least in my opinion, there is no gain in simplicity or accuracy with the cantilever, so it's hard to see the point.

I use a variation of the vibration method that Haines settled on when he did his tests. Again, there are several ways to do this. The simplest is to support the top half (say) at the node points for the fundamental bending mode. about 21% of the way in from either end, and tap it in the center. You record the pitch of the mode, and solve for E using standard equations (again, both Gore and Hurd give this, as well as Haines). You need to know the dimensions of the piece, and it's mass. There is no problem with crushing or deformation, or 'cold creep' either. It also has the advantage of allowing you to find a 'damping factor'; the loss rate within the sample. This ought to be useful information; just how useful is open to debate.

No measurement is going to be any more accurate than the least accurate input. With guitar top halves that's usually either the density or the thickness, which are related, of course. Thicker pieces allow for more significant digits, but we often don't have them. Also, this is limited to pieces that are pretty close to rectangular, and uniform in thickness. You can't get an E value from a top that's trimmed to shape, or (easily) from a wedge half of an archtop plate. The violin makers often test off cut strips, which bring up a whole set of issues of it's own. The big one there is that you can't always be sure that the strip you're testing is representative of the whole top.

A deeper problem is that, if you want to find the Young's modulus you need to be certain that you're looking at simple bending: only along or across the grain. If the piece is bending some in both directions you're seeing a mix of lengthwise and crosswise properties, and there's no simple way to sort them out. Testing narrow strips minimizes that issue, but then you're worried about how representative that strip is, and so on. If you just hold the piece at one point and tap on it, you have no way of knowing whether you're looking at a mix or not. Using a signal generator to drive the piece, and looking at the resulting Chladni patterns, gives you that information, but takes more time tan holding and tapping.

The really deep problem, which is probably common to all testing methods, has to do with the fact that bending doesn't just involve stretching and compression of the surfaces, so Young's modulus doesn't fully specify it. With wood,in theory, you'd need three Young's moduli (logitudinal, radial, and tangential), six shear moduli, and six Poisson ratios, with all the associated damping factors, to really capture it. And that assumes that each one is uniform throughout the piece. Right. As it is, the equations we solve to get these numbers from simple tests of single modes are simplifications that only get us to within, perhaps, 10% of the 'real' values. If you're using this to calculate the 'correct' thickness for a top, a 10% tolerance implies a change in thickness or brace height of 3% or so. Ask yourself if you really hold that sort of tolerance, either in getting the data to plug into the equations, or in final sanding.
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