Effect of Forces on Gantry Cross-Sections?

[Jonathan]

For instance if Jonathan were to build a new machine and dosh wasn't a limitation, I wonder if he would still use box section, what size it would be, and why?

The simple answer is wait and see ;)

That is an extremely difficult question to answer since it depends primarily on the intended purpose and size of the machine. If the machine was required to do everything I could ever want, i.e. 5-axis able to cut most metals, then I would consider a steel and epoxy granite construction since it offers great versatility and strength in the design. Next step down perhaps would be a gantry made from aluminium plate. Neither of these would follow a style remotely similar to what has been posted. If the machine was only ever intended to cut woods and plastics with a short Z-axis then I would use multiple pieces of steel box section for the gantry, after appropriate FEA to ascertain and suppress potential resonance issues. None of this really helps you though since your budget is regrettably finite, so I'll leave it at that.

Jonathan's gantry uses 80x80 box section probably 3-4mm wall thickness. But as he says in other posts, the ball screw is not in an ideal location, the distance from the ball screw to the cutter is too far.

Mine is 80x80x3mm since that was cheap at the time. It is adequate since the SBR20 round rails introduce a far greater error than deflection of the box section. With profile rails then something stronger is warranted.

I would discount purple and blue due to the potential problems with accurately mounting the rails on material that may not be made to sufficient tolerances to maintain an accurate rail spacing. Additionally the ballscrew position is sub-optimal on these, since there is a horizontal distance between the ballscrew an the rails which allows the bearing blocks to move (slightly since they are mounted on something that is not perfectly stiff) without the ballnut moving. This is a significant limitation on my machine, made more significant by presently not having profile rails on the Y-axis.

It's harder to say between green and red, in my opinion they are both fit for purpose. I'll post more about them later.

Edit: In fact, if you send me or post the drawings (ideally just the cross section as a .dxf) I will run a FE stress analysis simulation since as irving has pointed out it would be good to get some idea of the torsional stiffness and calculate the second moment of area.