3D Array of Spheres

[Anonymous]

I am trying to create a 3D cube of spheres, much like the picture attached. Best I could do was find: https://forums.autodesk.com/t5/inventor-customization/add-in-to-generate-a-3d-array-of-spheres/m-p/5... with no answer.

I have made a single array of 20 spheres, but would like this to form a 20x20x40 array of spheres. Is there an easy way to do this?

 

kelly.young has embedded your images for clarity.

[johnsonshiue · Accepted solution]

Hi! I thought you could do it with pattern of pattern. The trick is to pattern the sphere as a body but join occurrences together. Make sure Compute method is set to Optimized (click the double arrow to expand the dialog). Then repeat it in Z direction.

Many thanks!

[hncarle]

You could do this with a formula.  Set "count" for depth to the number of spheres per side of the cube.  Then make a pattern making it "count" number of occurrences.  Then make another pattern horizontal "count" wide and vertical "count" high. 

Shaazaaam you can have infinite variety of sizes of cubes. 

P.S.

or make a different count(vert), count(horizontal), count(depth) and make it any rectangular size.

[hosford]

If this is a sphere packaging problem, then the second layer should have 1 less ball per row and 1 less rows, its z position would be .707 R +R from first layer resting plane.

Check out this link

http://mathworld.wolfram.com/SpherePacking.html

[Anonymous]

Perfect, this is exactly what I was looking for. Thank you so much!

[Anonymous]

Since that solution worked for a rectangular array, how should one make a cylindrical 3D array? I tried the circular pattern, but it makes a hollow cylinder. Can you suggest a simple way to "fill" the hollow to look something like the attached? The picture has a random distribution of diameters, but I would be more interested in a uniform distribution.

[I_Forge_KC]

What is your end-goal?

The reason I ask is that if you're looking for visualization or 3D printable designs (i.e. meshes), then a tool like Meshmixer may be preferred because of its patterning tools (both stochastic and uniform).

[Anonymous]

We use Particle Flow Code (PFC Itasca) to generate a cell of spheres - the cylindrical cell above is one representation. These models are used for flow studies where the spheres represent grains of sand, rock etc. We would like to 3D print them for validation studies.

Most flow modelling programs have the ability to export the 3D representations into .STL format, but the file sizes can be well over several gigabytes, causing slicing programs to crash before being sent to the printer. The original question was to model a simple design (rectangular array) and then export to .STL. The PFC export was 12GB while the Inventor file was 60MB and printed just fine (Thanks @johnsonshiue). Based on how simple it was to make a rectangular array, I was wondering if there was an intuitive method to produce a 3D cylindrical array.

[I_Forge_KC · Accepted solution]

I had a feeling.

Here is an alternative workflow/tool for you to consider. It is designed for mesh modeling, so some of these kinds of operations are "lighter" and therefore faster to work with. It also includes a stochastic placement which may be of some use to you.

[Anonymous]

Absolutely brilliant @I_Forge_KC, you've saved me a lot of time and also opened up more questions! 

The second half of your video showing the random generation is intriguing in the sense that we are getting a more "natural" generation of particles. Is there a way to collapse the spaces between the spheres, but keep them from merging? Think of pouring marbles in a cup or, in my case, grains of sand in a cup. I realize we are moving more from mesh generation into porous media modelling, but I'm curious on the limitations of Meshmixer... 

Great video by the way, I'm old school and it was nice to see an example on my screen.

[I_Forge_KC]

As far as I'm aware there isn't much in the way of control with regards to the randomizer tool. While it certainly helps you out from a realism perspective to do stochastic, I think the hexagonal layout of normally tiled spheres is the best option to nest them super tight (but not touching). You can adjust the sliders in the random tool and it will vary the placement of the spheres, but you can't really control their 3D spacing very well.

One other feature of the tool that I did not highlight was the gradient feature. Basically, you can specify a range of sizes for the spheres based on a linear distribution or a spherical one. This may help to build additional realism by varying the size slightly (but not tons like your random example posted above).

I think for a truly randomized packing you will need some specialty tools (there is some free Matlab and Python code out there if you really want to get your hands dirty).

[WHolzwarth]

I did a quick search for this task using 3ds Max. In the tutorial equal sized marbles were used, but it seems to be possible with random sizes, too.

[WHolzwarth]

I've been playing around. See attachment ..

[Anonymous]

Great work @WHolzwarth - this helps even more!

[ahmedniri92]

Is there a solution to this in Fusion 360. I've been trying to get the same thing but was not able to do so in Fusion. Please help.

Thanks,

Ahmed