FREE REED PHYSICS - 2

[ttonon]

Greetings again to free reed enthusiasts.  In this post, I’d like to show results comparing steel to carbon fiber.  In thinking about this issue yesterday, I did a web search and found that people are now selling carbon fiber material in thin sheets – for very reasonable prices.  This opens the possibility of experimenting with this material as tongue material.  Though, I'm sure some makers already know this.

 

I say this because of the very interesting results from the free reed physics model I’m working on.  I put up another .docx file showing the difference between steel and carbon fiber vibration spectrum in the same way I showed for steel and brass, and the link is below.  The results indicate that the primary material property that affects tongue vibration is the ratio of Young’s modulus to density. 

 

In 2012, I posted a survey of materials that one might consider making tongues from, based on the hypothesis that E/rho is the only material property you need to know as a measure of what the musical tone would be.  The link is:

 

https://www.concertina.net/forums/index.php?/topic/14568-reed-tongue-materials-a-survey/&tab=comments#comment-138942

 

and the original table is still available.  That hypothesis is valid rigorously only for the free vibration of the tongue, which occurs after the transients have died out when you start vibration by plucking.  I didn’t know what effect it would have in forced vibration; i.e., excitation by a bellows pressure.  The physical model I now developed shows that there’s an influence by both E and rho separately, apart from their appearance in the ratio. 

 

But now with this complete theory we can calculate the effects of E and rho, along with all the other important parameters, and these calculations give support for the simple idea that the ratio is the primary influence. 

 

If we normalize the ratio E/rho for different materials using that for steel (divide all ratios by that for steel), we get 1 for steel, 0.497 for brass, and 6.8 for carbon fiber.  There’s considerable variation for carbon, but I think this is a representative value. 

 

I’m assuming here that steel sounds brighter than brass, as reported.  I assume further that the reason is because steel has about twice the ratio E/rho that brass has.  This is true IF the character of these harmonics in tongue motion carry through to the musical tone, and the difference in harmonic amplitude is now firmly established.  From the plots, we see that carbon, with an E/rho ratio over six times that of steel, produces higher harmonics that greatly dominate those for steel, even at relatively low bellows pressure.  In FREE REED PHYSICS – 1, plots show that higher harmonics for steel dominate those for brass at higher bellows pressure.  But with carbon vs steel, the dominance is much more, with carbon favored.  As the reasoning goes, we thus expect that carbon would sound much brighter than steel, even much brighter than steel sounds in relation to brass. 

 

Of course, I could be wrong, and these tongue vibration harmonics don’t translate to musical tone.  I’d be surprised because I don’t see any other way that tongue material could affect musical tone.  The fact that players report clear differences in the sound of brass vs that of steel strongly indicates to me that plots such as these can lead to an educated guess on what different tongue materials sound like, just from knowing these two key properties.    

 

I did simple calculations on the tongue geometry required for a carbon tongue material.  Using available thicknesses (0.5 mm and 1 mm), the lowest concertina pitches would require lengths around 4 inches at 0.5 mm thickness for 100 Hz.  These lengths are probably too large, and thinner sheets would be required for shorter lengths.  Perhaps the 0.5 mm size could be sanded down.  Carbon is a material very easy to work with.  The high end is more accommodating, requiring lengths around 5/8 inch at 1 mm thickness for 8700 Hz.  A 1 mm thickness is also much thicker than existing steel construction, and that might introduce interesting issues with such short lengths, perhaps in connection with the plate thickness.  We can of course now use the model for calculations involving different plate thickness.  Another alternative is to make tongues at the extreme pitch ends out of steel. 

 

Of course, we can wonder just how bright a carbon fiber tongue could sound, and I encourage makers to give it a try, if they haven’t already.

 

The docx file for Carbon and Steel is at:

https://app.box.com/s/zchj1y5d4l65fttok3n4sofupzx2gsio

 

 

Best regards,

Tom

 

 

 

 

 

[maccannic]

I'm no scientist, but I find myself wondering about the longevity of a carbon fibre reed.  I'm remembering the problems Rolls Royce had with carbon fibre aero engine blades, which basically vibrated themselves to bits.

[ttonon]

2 hours ago, maccannic said:

I'm no scientist, but I find myself wondering about the longevity of a carbon fibre reed. 

Maccannic, that's a reasonable concern, and the question is, how long would carbon fiber last as a free reed tongue?

 

The short answer is, very long (comma is important here).

 

The long answer is that we need to first understand a little about Fatigue Limit and Fatigue Strength.  Titanium and Ferrous (Iron) alloys usually have a Fatigue Limit, which is a stress level below which cyclic motion is unmeasurably large.  Above that limit, cycling will cause breakage after a number of cycles, typically in numbers above one or ten million.  For steel, that limit is roughly 40% of the materials tensile strength.  In an analysis I did, it's not too likely that steel tongues will be stressed above that limit, and thus, steel reeds can last seemingly forever. 

 

Nonferrous alloys such as brass and aluminum do not have a Fatigue limit, and Fatigue Strength is used to characterize their performance, often with a Stress-Number (S_N) diagram, which predicts the number of cycles to failure for a given stress level.  But still, these numbers can be quite large in many applications.  Thus, aluminum is a useful material in aircraft construction.  

 

Carbon and other composites are a different story.  They don't possess a Fatigue Limit, but that doesn't mean their Fatigue Strength isn't high.  Carbon fiber composites are usually in the highest performance level here.  There are charts that show fatigue cycles going into 10^8 cycles.  That would mean a tongue playing continuously at 1000 Hz would last a month, 24-7.  In addition, we'd have to calculate just what the stresses are, and if they are not too much compared to the materials tensile strength, the tongue would probably last indefinitely.  

 

Another issue is that the performance of composites depend greatly on the direction of the fibers in comparison to the direction of stress, being much weaker in directions across the grain.  Thus, I wouldn't make a tongue with fibers running perpendicular to the long axis.  For fibers in the long direction, maximum fatigue life can be expected.

 

The story about Rolls Royce and other anecdotes that involve widely different applications aren't show stoppers.  The specific application is key and proof is in the pudding.  It's true that in general, composites often fail catastrophically, but that's not really a concern here.  

 

There may be a concern on how long the tongue could hold tuning.  I've read that, near fatigue failure, Young's Modulus could lessen. 

 

Here's a quote I got from Quora, by Thomas Moura, M.S. Mechanical Engineering & Aerospace and Aeronautical Engineering, University of CampinasGraduated 2015:

 

"CFRP has a benign behavior in fatigue when compared with metals with fatigue strength around 80–90% of the static strength in tension, compared to below 50% of steel. As noted by other answers CFRP [Carbon Fiber Reinforced Plastic] doesn't has a fatigue limit, however its fatigue strength for a given number of cycles and loading is a lot better than any metal more so if you normalize by the materials density.  For instance, helicopter blades made from aluminum have a finite life of 6000 hours for example, where when those were replaced by CFRP ones, they considered to have infinite life, or at least greater life than the airframe itself."

 

For those interested, in 2012 I posted on the reasons why brass tongues break: 

 

 https://www.concertina.net/forums/index.php?/topic/14533-why-do-brass-tongues-break/&tab=comments#comment-138648

 

Unfortunately, the attachment for the figures is no longer available.  If one is interested, I may be able to find them.

 

Best regards,

Tom

 

Edited June 14, 2019 by ttonon
Separate paragraphs.