Method of designing annular plate with even distribution of holes.
Method of designing annular plate with even distribution of holes.
(OP)
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
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





RE: Method of designing annular plate with even distribution of holes.
what's the objective? maximise hole area ??
another day in paradise, or is paradise one day closer ?
RE: Method of designing annular plate with even distribution of holes.
thanks
RE: Method of designing annular plate with even distribution of holes.
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 ?
RE: Method of designing annular plate with even distribution of holes.
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.
RE: Method of designing annular plate with even distribution of holes.
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
RE: Method of designing annular plate with even distribution of 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.
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RE: Method of designing annular plate with even distribution of holes.
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.
RE: Method of designing annular plate with even distribution of holes.
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.
RE: Method of designing annular plate with even distribution of holes.
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
RE: Method of designing annular plate with even distribution of holes.
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
RE: Method of designing annular plate with even distribution of holes.
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
RE: Method of designing annular plate with even distribution of holes.
RE: Method of designing annular plate with even distribution of holes.
RE: Method of designing annular plate with even distribution of holes.
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.