Gantry design and FEA analysis

[routercnc]

Agree with Voicecoil.
Analysis 2 is closer to worst case as this puts a twisting moment on the gantry as the force is applied at some distance away from the structure and will usually cause the biggest deflection.

I wrote a spreadsheet a long time ago just to play with the numbers and I looked at 3 load conditions.
Vertical load at the centre of the gantry due to the mass of the Y and Z axis and estimate the sag.
Lateral load applied at the tool tip as this will want to turn the gantry into a parallelogram- one reason why raised bed sides is stiffer than tall gantries.
Foreaft load at the tool tip to twist the gantry. This usually causes the most deflection and you need to make the gantry have a shape with material around the outside not 2 isolated beams. So yes plate them together is an option.

I used 80N load for cutting aluminium.

Remember this is all to see relative performance and get a feel for what aspects are important as it will assume perfect joints and you would need to model the whole machine and the cutter to get close to the actual deflection and even this is the steady cutting force not the deflection caused by vibration which will add some more.

The stiffest gantries in terms of numbers are raised bed sides with a large box section as this gives good stiffness for all load cases. But practical considerations mean other options are good including the famous L shape gantry with 2 good sized rectangles joined in an L shape.
In the end you want a single shape with as much material as possible away from the central axis it is trying to twist or bend about (the neutral axis). Once you have the largest outline you then up the wall thickness for many reasons including getting the load into the section from discretely mounted components. Depending on the design the very large sections may need baffles or subdivisions.

It’s fun to look at the numbers and get a feel for it but also look at successful machines to see what has worked before and bare in mind the practicalities of building it and having adjustment capability.