Mode 1/0

[WebPilot]

A 15 node, 8 quad FE model is beginning to converge to the Barton solution.

[WebPilot]

With a 28 node, 18 quadrilateral FE model, we are almost within 5-6% of Barton's analytical solutions. This is considered 'adequate' in engineering circles but I shall do one more refined mesh model for demonstration purposes.

[WebPilot]

With a 45 node, 32 Quad FE model,

1. the % error in Mode 1 did increase a little bit, but those for Modes 2 and 3 dropped.
2. all % errors are now within the requisite 5.0-6.0 range.
3. I am going to stop here.

[WebPilot]

We were fortunate in the previous case to have a 'target number' to shoot for, but this is unusual. How do we know when 'enough is enough' mesh refinement?

Let's forget we have Barton's formulae, and look at the modal frequency predictions for each of the FE models I developed.



Click here to see image in its entirety.

[WebPilot]

[WebPilot]

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.

[WebPilot]

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.

[Mike Everman]

Beautiful, man. That's a keeper, thanks.

[WebPilot]

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.

[WebPilot]

Click here to see entire image.

[larry cottrill]

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

[WebPilot]

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

[WebPilot]

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.

[Mike Everman]

That is cool. Nice mesh.

[WebPilot]

Thanks Mike E.

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


view entire image