Why slicers get the dimensions wrong

People using Slic3r often complain that holes come out too small, see forums.reprap.org. This blog post is in reply to the question here.

The issue is not just with round holes (which shrink for reasons I described here) but rectangular or hexagonal holes as well. I got my rectilinear dimensions correct with Skeinforge nearly three years ago and blogged the maths here. I now design exclusively in OpenScad using polyholes to get cylindrical holes the correct size as well.

I have tried Slic3r, Cura and Kisslicer but none of them print the Mendel90 calibration part the right size, so I have stuck with Skeinforge. It is looking a bit old now as Enrique seemed to stop developing it around the time people started saying "Slic3r is nicer", but at least it is stable and has very few bugs.

Looking at the G code produced by Slic3r and Cura, they both assume the extruded outlines have a rectangular cross section. I.e. if I work out the volume of plastic extruded from the E number and feedstock diameter and divide it by the length of the line then I get an area. This is equal to the layer height times the intended filament width and the outline is offset by half the intended filament width. The problem is the filament does not form a rectangle if the edges are not constrained. It forms a rectangle with semi circular ends due to surface tension. The actual width of an outline of a given area is therefore slightly more than it would be if it was a rectangle.

The cross sectional area of a filament with height h and width W is that of a circle with diameter h plus a rectangle of width (W - h) and height h. A = πh²/4 + h(W - h).

Solving for W gives W = A / h + h(1 - π/4).

But slicers output enough filament to fill the rectangle, so A = intended w × h. Substituting that value for A we get W = w + h(1 - π/4). So we have an additional width that is just a fixed multiple of the layer height.

I print a lot of things with 0.4mm layers, so the error is very significant. To fix it in Skeinforge I set the outline flow rate to be enough to fill the rounded rectangle, rather than the full rectangle. I achieve this by setting the "Perimeter Flow Rate Multiplier (ratio)" on the Speed tab. A value equal to the "Perimeter Feed Rate Multipler (ratio)" gives an area equal to the full rectangle. To correct for the fact that it is actually a rounded rectangle one has to multiply the feed rate by the ratio of the areas, which is 1 + (π/4 -1) h / w, a value which only depends on the w / h ratio.

As you can see, when the w / h ratio is high the reduction in flow rate necessary is only about 4%. I assume the reason a lot of people don't notice this is that they use a high w / h ratio and then calibrate a thin wall box, so that the flow rate is low enough to compensate without making the infill too sparse. I generally print with lower values of w / h and prefer to just put in numbers, rather than measure thin wall thickness.

An alternative way to compensate would be to keep the flow rate the same but offset the outline by W/2 instead of w/2. I.e. by an additional h(1 - π/4)/2.

If objects are printed with multiple outlines then the error appears much worse if the inner outlines are printed first working outwards (or the opposite for holes). Looking at the area of plastic this is not obvious mathematically because an additional area of plastic equal to w × h will extend the width by w, preserving the original error but not adding to it.

However, if you consider the practicalities of the process it is obvious that you can't squeeze viscous plastic into the infinitely sharp point under the overhang of the previous outline, particularly when the opposite edge is completely unconstrained. In practice I think you get something like this: -

The plastic that fails to fill the overhang causes the opposite edge to bulge a bit further and this effect then gives the cumulative error that I experience. I don't think the correction factor is easily calculated because it depends on the viscosity of the plastic as well as layer height, etc.

So if you want accurate dimensions and multiple outlines then do the outer perimeter first. For better seam hiding on objects where the dimensions don't matter do the inner perimeters first. I tend to print most things with one outline as you effectively get an extra one free with Skeinforge because it joins the ends of the infill, see hydraraptor.blogspot.co.uk/2008/04/python-beans-make-object.