Method of designing annular plate with even distribution of holes.

[asimpson]

I am looking for a method of designing an annular plate with equal diameter holes that are evenly spaced.

See attached image as rough attempt using circular pattern of holes. Spacing between holes varies considerably.

I think there is a geometric process called circle packing which may achieve this .

https://www.google.ie/search?q=circle+packing+in+a...

Many thanks

 

[rb1957]

arranging the holes is one thing, spacing is another (how much load?)

what's the objective? maximise hole area ??

another day in paradise, or is paradise one day closer ?

 

[asimpson]

The application is heat recovery. Heat is transferred from mass by fluid flowing through holes I wish to maximise the ammount of material around each hole and avoid un-even that transfer.

thanks

 

[rb1957]

these plates would work like radiator fins ?

you want to minimumise the steady state temp of the fluid ? how about fins on the pipes ?

each hole is effectively a heat source for the plate, with heat being radiated by the plate material around the hole.

more holes mean more heat removed from the fliud, holes closer together mean a higher steady state temp.

another day in paradise, or is paradise one day closer ?

 

[asimpson]

Thanks rb1957

No the plates are not fins.

I am just interested in a drafting method of evenly disributing holes so that I can play around with size and number. I can't go into further details of application.

 

[drawoh]

asimpson,

This sounds like a question for the forum for your CAD software. In SolidWorks, for each row, I would place the first hole on the pitch circle with an angle offset. I would apply circular arrays. The offsets and arrays can be controlled from a design table or the equation editor.

If your CAD package cannot do this somehow, get another CAD package.

--
JHG

 

[IRstuff]

Is there a fixed ratio in size between the annulus and the holes? Is there a constraint on the total area of the holes? Is there a constraint on the minimum area left on the annulus? Where does the heat go in the annulus, i.e., the ID or the OD or both? Why doesn't the fluid contact the flat sides of the annulus? Is it going through tubes that go through the holes?

Seems to me that the desire should be to have the smallest holes possible, since the critical issue is the area of the hole relative to its perimeter that's exchanging heat. Given that the ratio of perimeter to area is 2/r, the ratio maximizes as r goes to zero. So, it would seem to me that the answer requires holes so small that their exact distribution is not particularly important. I would think some sort of oriface plate equation would need to be worked.

TTFN
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[tbuelna]

asimpson-

With a good parametric CAD system you can probably get a satisfactory result with a bit of trial and error using parameters, relations, formulas and constraints. A good place to start would be to determine the optimum hole size and edge distance between holes based on things like plate thickness, plate material, fluid properties and flow conditions. Once you determine an optimum hole size for your conditions, you can layout a pattern of these holes/spacing in CAD starting at either the inner or outer edge of the flange.

While figuring out a geometric array of the max number of holes for a given annular area is not too difficult once you have determined the hole size and spacing, once you add the requirement of maintaining a uniform temperature throughout the plate the problem becomes much more difficult. For this case, the size and spacing of the holes will not likely be uniform throughout the array.

 

[JStephen]

Depends on what you need to accomplish, exactly.
I'm not aware of a general solution for circle-packing problems. But seems you could take your hole size, offset it by half the desired wall thickness between holes, and start packing those circles in there as tight as they go. If you want a symmetric pattern, try filling a quadrant and mirroring it. If you get a quadrant filled, it may be possible to then expand all the circles slightly to minimize wasted space and get more uniformity.

 

[zdas04]

Asking this question in a Mech Eng forum gets you Mech Eng answers. As several people above have commented, if all you want is the CAD tip to place the holes evenly, then you should be asking in a CAD forum--many of the same people will be in both places, but we all wear many hats. I opened AutoCAD and had an drawing of evenly spaced array of holes in a plate within 3 minutes (with a 0.39 β-ratio, which is probably approaching a strength limit) without doing anything really fancy. Another 5 minutes dimesioning it and I could give it to a machinist.

If you want to share some of your constraints here, a number of the participants could give you good advice on sizing, spacing, and limitations. If you can't share those details, then you really should move this discussion to a CAD forum.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. —Galileo Galilei, Italian Physicist

 

[asimpson]

I have had no luck in forum of my own cad system (SolidEdge). Others may fare better.

It is really ageometery problem so maybe a mathematics forum would be the way to go.

The constraints are fixed annular shape. Fixed number of holes. Maximise spacing between holes

 

[drawoh]

asimpson,

So this is a math problem.

In your model, could you separate your holes using sketch segments of equal length? Or approximately equal length?

--
JHG

 

[btrueblood]

Do you need to simultaneously maximize spacing to the edges? If not, is there a minimum edge distance to maintain?

 

[btrueblood]

And another question - do the hole patterns need to be symmetric (i.e. can there be jumps/breaks in the pattern).

 

[3DDave]

You are looking at an optimization for hole spacing - the problem statement is more like:

For N holes of diameter D in an annulus between R1 and R2 how can holes be placed such that there is a maximum distance between hole centers (should be the same concept as between hole edges + D)

Is there a second condition - such that the distance between hole edges and from hole edges to R1 and R2 is maximized? Or, third, can the holes be tangent to R1 and R2?

If it's always the edge distance, between holes and R1 and R2, then you can look at packing solutions for N, D+d, R1, and R2 where 'd' is a factor that would cause the circles to be tangent to each other and to R1 and R2.

If the number of holes isn't great (<100), this could be done with a spreadsheet, starting with all the holes at a random delta R, delta theta, and then looking to increase the distance from the nearest neighbor until all the distances were the same. The increment is along a vector between mutual centers that tends to increase the distance, perhaps by including an amount to approach the next nearest neighbor at the same time.