4' x 4' x 8" Router Build

[routercnc]

I've found the 50 N force in X and Y directions to be a good guide but it is only the start. If under this simple load condition if you are <0.05 mm then I would call that a fair start point, and you would expect a fair amount of accuracy on the finished dimension.

But wait, this 50 N is a simple static force, and does not account for the repeated impacts of the cutting action in the material which will cause a ripple on top of this average force, say from 45 N to 65 N (making the numbers up to show the point) with every rotation. As the cutter rotates very fast this will cause vibrations in the machine, not only at the main impact frequency but across a wide frequency range with amplifications where the machine frame resonances are and this may show up in the finished part.

This is where the wall thickness will help you as Jazz is advising, and this is money well spent. It adds significant stiffness (more than might be suggested is required by the simple static load analysis), which will lower the vibration levels as higher frequencies decay quicker and as they are stiffer they also deflect less initially with each impact. It also adds mass which will also lower the vibration (acceleration) levels as shown by re-arrangement of the famous F=ma equation ; a = F/m). So it is a win-win up to the limit of what your steppers can accelerate around.
Technically you would not have added much damping (energy absorption through friction, e.g. damping pads or sand) but you will still have reduced the vibration amplitude through the mass and stiffness which is all that matters.

If it helps I went through the same thought process on my mk4 machine for the upper box section members on the bed. I went with 5 mm wall in the end, as every mm costs £, but I know it makes a difference.