## Mode 1/0

Moderator: Mike Everman

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### Re: Mode 1/0

In summary, I have done a finite element analysis of one example of a cantilevered thin plate and compared it to those frequencies predicted by the Barton formulation. I get 'good agreement' between the two.

There is no need to do a FE analysis of this type of valve, so before I go on, here is a present.

I developed an Excel spreadsheet to 'do the math' for the Barton formulation of cantilever, thin plates in vibration. It can be downloaded here, Barton-forum.zip.
1. it is good only for steel
2. there is sufficient accuracy for thin plates of a/b ratios, 0.5:1 through 5:1.
3. I used the English Engineering System for units. If you are using the MKS system, convert your dimensions to inches before entering them into the data sheet. [2.54 cm/inch]
4. simple directions are inside the sheet.
5. it passed one test, so I think it is correct.

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### Re: Mode 1/0

I have added a mm to in feature to my Barton spreadsheet, so you may want to download it again if you plan on working with metric sized thin plates.

To better grasp what I am writing here, the reader is encouraged to reread this part of my dynamic modeling of a strip valve thread.

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### Re: Mode 1/0

Beautiful, man. That's a keeper, thanks.
Mike
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### Re: Mode 1/0

Thanks ... gentlemen.

Now, let's turn our attention, finally, to the DynaJet petal valve.

Again
1. Mode 1 is the first flexural.
2. Mode 2 is the first torsional.
3. Mode 3 is the second flexural.
The reader should verify this for himself (or herself) by inspection of the eigenvectors as I showed you how to do, previously.

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### Re: Mode 1/0

larry cottrill
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### Re: Mode 1/0

Forrest -

Keep in mind when looking at the Dynajet valve that, when mounted in the engine, it does not flex around the 'root' of the petal (meaning, the section across the petal between the bottom of the two adjoining grooves). This is because the central flat zone of the retainer is slightly larger in diameter than the "diameter" formed by the bottoms of the ten interpetal grooves (and in fact, probably a larger diameter than the circle formed by the narrowest zone of the petals, though I have no way of measuring this accurately). Therefore, the base of the petal is captured farther out, and the frequency will be higher.

You may have already taken this into account, of course, so my apologies if I'm beating an old drum.

L Cottrill

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### Re: Mode 1/0

Thanks ... but I already took that into account.

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### Re: Mode 1/0

I had to give this some thought in order to come up with an irregular nodal layout for the quadrilaterals. Triangular meshes are easy.

To me, the mesh now resembles an insect wing.

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### Re: Mode 1/0

That is cool. Nice mesh.
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### Re: Mode 1/0

Thanks Mike E.

Mode 1/0 (f2) convergence is still pretty low (10.61%), so, another refined mesh is in order.

view entire image

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### Re: Mode 1/0

I am pretty busy right now, but am letting you know I haven't forgotten and am working on a refined mesh.

This mesh is looking like a Trilobite.

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### Re: Mode 1/0

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### Re: Mode 1/0

At the expense of a slight divergence in predictions for f1 and f3, the prediction of f2 is finally within my % error tolerance. IOW, we can stop refining the mesh, here.

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### Re: Mode 1/0

I am now ready to turn my attention to the Argus V-1 folded valve.

To my knowledge there is NO analytical solution for what I call a 'folded' valve. The finite element method is a natural candidate to use in estimating the V-1's valve frequencies. I have a hard time even predicting its fundamental frequency, let alone Mode 1/0's (if there is such a thing).

However, if I use the results of my thread, dynamic modeling of a strip valve, I can make an estimate for the fundamental frequency for the valve.

The driving frequency of a V-1 is 40 Hz. By using the maximum dfr that allows the valve to close before +tive pressure occurs in the combustion chamber, namely, 0.59, for driving frequency ratio, I estimate the fundamental natural frequency to be 67.8 Hz . Mind you this is an upper bound.

From a scant few, poor images of the original drawings, I was able to glean the following dimensions. The dimensions were unclear in various areas, so I had to guessimate at times. I think I'm close.

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### Re: Mode 1/0

I find this absolutely wonderful to be able to calculate this!
1. You might think I am saddened to calculate a fundamental of 115.6 Hz, but I am not. It makes good engineering sense.

I am off by a factor of 115.6/67.8 = 1.705. Why? Well, if you look back at my other thread, a dfr of 0.346 will work (the wigglies occurred at 0.3, remember?), but the amplitude of the valve is not as great. The important thing is that the endurance stresses in the valve will be LOWER! This results in a LONGER lifetime. The flow per valve is diminished, so what do you do? Add more valves!

Crafty Germans.
2. The fundamental mode shape is 2 dimensional!
I should know better than to get too excited, since I still have to run some convergence tests but ... I am! Things are making sense!

SFP!