## Introduction: Comparing 3d Printed Voronoi Structures With Shell Structures (TfCD)

Pictures of 3d printed shapes consisting of Voronoi-based structures are seen a lot on the web lately. In this instructable we want to show how to create and print these structures, and compare the printed results of two similar shapes to explore the possibilities of Voronoi-based shapes.

As basic test object we used a sphere with a diameter of 50mm, with two 8mm (diameter) cylinders added to both the top and the bottom of the sphere.

We tested two shapes: A solid shell with a thickness of 3mm, and a Voronoi pattern sphere with a tube thickness of 3mm.

The looks, strength and weight are compared.

## Step 1: Set Up the Model for the Shelled Print

The first step is to create the models. This can be done using any CAD program. The solid shell model can be loaded into to the printer software right after a .stl file is created. Above the exact sizes of the shelled sphere are given.

## Step 2: Set Up the Model for Voronoi Printing

The Voronoi shape requires some more attention.

First a shelled sphere is created. This sphere is then converted in Autodesk Meshmixer to a Voronoi-based shape, similar to the way presented in this instructable: https://www.instructables.com/id/Make-Voronoi-Patt...

An important thing to take into account when creating these Voronoi shapes is the outer-and inner dimensions change a little (the process did not match our expectation that the tubes would be created in the middle of the surface). In our case this resulted in a decrease of diameter of 2.3mm.

Combining Voronoi shapes with solid shapes proves to be a little tricky. In our case we imported the Voronoi model in Rhino, and manually added the two solid cylinders. Combining these shapes requires close attention, as the interferences between the shapes play a large role in the eventual strength of the object. It might be necessary to model some custom connecting surfaces.

Once the model is done, it can be exported as an .stl file and loaded into the printer software.

## Step 3: Printing

For the 3d printing, a Wanhao Duplicator 4x was used. Above the settings are shown. We did use the same settings for both structures. Because of some problems with configuration the printer was set to 50% speed. 3d printers are all different in configuration so just copying the settings will not always result in good quality prints. Some things to take into account for printing spheres (overhang) are:

- Print quite warm (depends of course on material) it will make a better connection between the layers. For the Voronoi structures it is also better because the nozzle will move from one 'leg' to another all the time
- Especially the first part of the sphere should printed slow (more time to cool so less warping)
- When available, use a fan for especially the first quarter (bottom) of the sphere. (because it prints overhang, the edges tend to warp. With cooling this should be less)

After some hours of printing, the spheres where ready to test and compare.

## Step 4: Analysing and Comparing the Shapes

For the analysis we wanted to check different things:

- SHAPE
- WEIGHT
- STRENGTH

SHAPE

As the Voronoi shape is build up of ‘tubes’, there is far less support for the structure during printing in comparison with the solid shell where the rings support both each other and themselves by shape. We therefore expected the Voronoi-shape to show some dimensional deviations.

Both the shell and the Voronoi shape showed some inconsistencies due the overhang at the bottom of the sphere. However, the basic outer dimensions of both objects proved to be very close to the original models, contrary to our hypothesis.

These are the dimensional results:

· Height shell model: 52mm

· Height shell measured: 51.8mm & 52mm

· Diameter shell model: 50mm

· Diameter shell measured: 50mm & 50mm

· Hight Voronoi model: 49mm

· Height Voronoi measured: 48.9 & 49mm

· Diameter Voronoi model: 48.7mm

· Diameter Voronoi measured: 48.5 & 48.3mm

Looking to the deviation of the size we conclude that de deviations are standard 3d printing variations, and the performance of the Voronoi shape was better than we expected, almost as good as a solid shell.

WEIGHT

The Voronoi structure weighed 10.14 grams, whereas the shelled structure weighed 15.31 grams.

So, the wheight of theVoronoi (influenced by the % of mesh reduction in Meshmaker) and based on a tube thickness of 3mm (similar to the thickness of the solid shell) was about 2/3rd of the shelled structure.

STRENGTH

To get an indication of the difference of strength between both printed models, we examined how much compression force the structures could resist. Both structures where submitted to a compression test, and the peak load was measured. A very basic test setup was used, consisting of a drill-stand like mechanism and a pressure sensor.In the first test, the printed layers were positioned horizontally, while applying force in a vertical direction. In this setup, the shell structure could resist 2200, while the Voronoi structure only could resist 860N. A remark that has to be made here is that we were unable to determine when exactly the first significant plastic deformation occurred when testing the solid shell. Large deformations appeared around 2200N. When we continued, the peak force increased to 2776N, which was the maximum we could apply.The Voronoi structure bursted at 860N.

As the orientation of the way in which the layers were stacked seemed to influence the admissible force, we conducted a second test with the printed layers parallel to the load direction. In this orientation, the shell structure started to show large deformations around 1790N while the Voronoi structure could resist 594N.

These results lead to the conclusion that the maximum load depends on the direction of admission. Based upon these tests, the strength of the solid shell appears to be 2,5 times larger than the Voronoi shape at a load perpendicular to the layers, and 3 times larger for parallel loads.

## Step 5: Conclusions

The dimensions of both shapes matched the 3D models quite well, so in this respect the Voronoi patterns proved to be a dignified alternative.The weight of the Voronoi structure, given the settings presented was 2/3rd of the weight of the solid shell. On the other hand, the strength was 2,5 – 3 times less. This leads to the overall conclusion that Voronoi-based shapes can be potent replacements for shell structures, in situations where strength is not the primary objective.