## Saturday, 12 December 2020

### Sinkholes

Continuing my series of adventures in 3D printing holes the correct size, I turned my attention to countersink holes.

I don't normally use countersunk screws in 3D printed parts because they create lateral stress, whereas other forms of screw exert a purely compressive force, which can be spread by a washer. However, I am currently designing a part that needs flush screws in its base that is only 4mm thick, so there is no room for a counter-bore to bury a flat head.

First I had to improve my countersunk screw model because I previously just used a 45° cone with a sharp edge. In practice the edge has a nominal thickness of 1/10th of the screw diameter. That means if you countersink the hole with a normal conical countersink drill bit it has to be oversized to sink the head flush, and then leaves a gap around the circumference.

So the ideal shape for a 3D printed hole is an improvement because it can have a straight section at the top.

The complications are that, like horizontal holes, we have to take into account the rounded staircase produced by the filament layers and also, like vertical holes, we need to use polyholes to get the correct diameter when printed.

The cone makes contact with the rounded filament edge above, rather than the centre of the extrusion, where the slicer samples the model, as shown below:

In order for the extrusion to not overlap the cone it has to be offset outwards by a distance $x$, which is simply $(\sqrt2-1) r$ where $r$ is half the layer height. Applying that to the line equation of the cone and limiting the result to be in the range between the screw clearance radius and the screw head radius gives the correct placement for the rings of filament that just touch the cone without overlapping.

To make each of the rings print the correct size I make a stack of polyholes to subtract from the model.

These are double sided so they can be subtracted from the either the top or the bottom of a hole. As the slope is 45° they should be printable either way up.

This is what it looks like subtracted from a part:

I have added an OpenSCAD module called screw_polysink() to NopSCADlib to make printed countersinks. I haven't tried printing it yet but it should certainly work on a top surface. It might get a bit scrappy printed as an overhang without support.