Introduction: Fused Pyramid
The Cheops pyramid in Egypt is a stack of 201 layers of stones. What could be more natural than to use Fused Filament Fabrication, since the inherent drawback of visible layers, in this case becomes an asset, as this makes the print more realistic. My work consists of studying how to set the slicing parameter (layer thickness, scale), taking into account the printer constraints, (bed size) in order to print the pyramid in a way that corresponds with the actual thickness of the layers of the real Cheops pyramid.
Step 1: Model Construction
In order to modelize the thickness of the stone layers, I used the study from the French archeologist Georges Goyon entitled "Les rangs d'assises de la Grande Pyramide" BIFAO 78 (1978), p. 405-413.
There are 201 physical layers ranging between 49.5cm for the thinnest layer no. 173 to 150cm to the thicker layer no.1. I therefore introduced 201 boxes into Blender, each of them having the measure given by the report at a scale of 1/10000. Then I stacked the boxes along the z-axis. The X-Y dimensions of each box were set such to follow the slope of the apothem. (14/11/) and the first box (base of the pyramid) measures 230.35m. Thus, at the end, I obtained a model which has the same number of boxes as the physical layers of the pyramid. To finalize the model I merged all the boxes (modifier "union" in Blender) together to obtain a single watertight shell that passed the 3D toolbox of Blender.
Step 2: Slicing the Model
Here comes the main target of this work which attempts to reproduce the layers of the pyramid using the printed layer height set into the slicer.
Let's find now the scale and the printing layer thickness that make a print which has the same number (n) of layers as the pyramid (201) and that fits inside the printing bed. The printer I use is a PrusaI3 with a heated bed which has a print area of 18cm by 18cm.
First of all I took the average stone thickness (l) of 69cm given by the study of G.Goyon and made it correspond with the printing layer height (l'). The printed layer height l' and the total print height z' of the pyramid are linked by the relationship z'=n x l' . For instance with a layer height of 300u, we will get a print which is 201x0.3mm= 60.3mm which is a good dimension to print.
Then, since 0.3mm (300u) corresponds with 690mm (69cm), the scale is 0.3/690=4.35/10000. Therefore we can calculate the printed base lenght as the real length 230.35m multiplied by the scale 230.35 x 4.35/10000=0.1102m or 10.02cm. Again a good dimension for most FFF printers.
Finally I used Cura to slice the model, with walls of 1.2mm (3x noozle size of 0.4mm)) and an infill of 10%. I added a brim of 30 loops around in order to prevent warping and obtain a nice flat base. One can see on the screenshots of Cura that the scale of 4.35 and a layer height of 300u ends up with exactly 201 printed layers with the dimensions calculated above.
Step 3: Printing the Model
As already mentionned , I have used a PrusaI3 for that print. This open source printer is quite accurate and thanks to the heating bed allows a good adhesion of the print. I took a PLA filament from ColorFabb which was the nearest color to the pyramid that I found on my shelf and set the printing temperature to 220°C for the filament and 60°C for the bed. The print time is 3hours15 and the print weight is 60grams.
Step 4: Print Results
Here we are.
The overall impression of the pyramid geometry is well reproduced by the print. The print layer number being the same as the real stone layer number brings an additional touch of reality, which in my opinion is more authentic than a pyramid made of flat surfaces. Thanks to this feature, the print can be used as a teaching support to illustrate how the external shell of the pyramid was made.
On the print quality side, one can see that the pyramid has a little warp on one corner, because the printed lines of the brim were not touching closely to each other. As a consequence, the print started to lift up because the brim was not sticking well enough. A bed levelling to bring the nozzle closer to the bed allowed to me to resolve this issue, and there was no more warping.
Step 5: Conclusion
This work is an attempt to reproduce the pyramid construction using the inherent drawback of the FFF technology where the printed layer thickness is in relationship with the average thickness of the real stone layer of the pyramid. A further study would be to exactly emulate each of the stone layers by a dedicated printed layer height. This may be possible by editing the GCODE such that the layer thickness changes during the print. I feel that the project succeeded in using the FFF drawbacks to give an authentic and textured surface that corresponds with the actual appearance of the Pyramid of Cheops.
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