the hunt for an easier way …

[WebPilot]

Personally, I feel petal valves are inefficient.

I showed on my other threads how to determine the the first flexural and first torsional frequencies of a DynaJet petal valve using the finite element method. A year has passed and I realize that the FE method is a difficult one for the uninitiated.

So, I am going to post another way to estimate them.

[WebPilot]

I'm readying a post, so in the meantime I would suggest to the interested reader to:

1. draw the DynaJet petal valve in your favorite CAD program and
2. brush up on your knowledge of your spreadsheet of choice.

[WebPilot]

I found enough data on the CURTIS DYNAFOG® Ltd plan to draw the above. I can
now determine those pertinent locations I need by using the CAD program.

Figure 1. CAD drawing of DynaJet petal valve


NOTES:

• ø 0,562" is what I call the 'root dia' of the petal valve array.
• ø 0,625" is the dia of the retainer 'face'.

[PyroJoe]

Looking good.

[WebPilot]

⬎ Nice work, Joe. Thanks for checking my work.

Figure 2. Determination of Area and CM of a triangle


NOTE: One has to be able to calculate areas and centers of mass with some degree of accuracy for my proposed method to work. The above is a test case for the reader to perform with his/her favorite CAD program.

QCaD can determine the area of a polygon (or triangle) by selecting vertices. It can also ID co-ordinates of a point. If your CAD cannot determine areas, then it can be computed by using the formula:

Area of a ◺ ≡ base × altitude / 2

where the altitude is defined as the ⊥ (or perpendicular) distance from the vertex opposite the base, to the base.

You should be able to determine these lengths by selecting the segment and clicking, somewhere, entity properties.

Note:

• The CM of a ◺ is where the medians intersect and
• the CM of a ▯ is where the diagonals cross, ICYDK.

[WebPilot]

Version: 2.0.5.0 [Community Edition]

• it's free
• works natively in Linux; no need for wine or dosbox
• has all the tools to do what is needed for this problem;
  it computes areas, id's co-ordinates and computes
  distances from point to point.

[WebPilot]

Figure 3. ZOOM of previous CAD drawing


As you can see, I split the petal valve in half and subdivided the ½ area into 2 rectangles and 5 triangles.

NOTES:

• the centralized 'dot' in each area is the centroid of that particular ▯ or ◺.

[WebPilot]

Figure 4. Partial of the spreadsheet I used for computation

[WebPilot]

We are computing the center of mass of the total area, a2 ... a7, here. This is where a spreadsheet is superior to hand calculation. The above is a printout of my spreadsheet calculation.

Notes:

1. skip the 'a1' row for now.
2. the 2nd column are the areas. CAD program computed these.
3. 3rd and 4th columns are the centroids relative to the origin (in this case pt 0 or the center of the circles in Fig. 1). Again this was done by CAD program.
4. 5th column is the centroid 'x' distance times area. The sum is in the next to last line. Divide this by the total area and you will obtain xcm.
5. 6th column is the centroid 'y' distance times area. The sum is in the next to last line. Divide this by the total area and you will obtain ycm.

[WebPilot]

In the spreadsheet calculation, the co-ordinate pair, (xcm, ycm), was
computed relative to the origin, O.

Figure 5. Side wing center of mass location


I have taken those co-ordinates and drawn in the CM. Here the displace-
ments are relative to the center of the strip at the clamp. The relative origin
is the point, β.

[WebPilot]

Figure 6. Individual parts and their CM's


So, I've split the petal valve into 3 pieces; a central strip and two
"wings". I have determined the mass and center of mass for each
by computing areas.

Why all the trouble? What can we do with this?

[vturbine]

Great tutorial, WP.

You just made me open a box I haven't for a long time. All dusty. It's tempting to follow along with it. Just to do it one more time.

Eagerly awaiting your next step.

[WebPilot]

That's a nice planimeter you've got there. I don't remember ever using one, but I have an appreciation for analog devices. I own several slide rules and an abacus, or two.

⇨

I am still working on my next addition to this thread; I'm mucking about with the graphics.

[vturbine]

I bought it new 33 years ago. It was used with tables in determining areas of cross sections of boats to find displacement, centers of bouyancy, coefficients, moments, centroids, and stability calculations. Back when Simpson ruled, pre-Homer.

[WebPilot]