I use a 4 axis CNC foam cutter for cutting wings that I made from scratch.
If using white foam, such as you find for insulation, you should get the ones that some brands designate "300". They are higher density and usually cannot be made with regrind. They are usually certified to Type 3 or Type 4. The higher compressive strength is mainly used under concrete floors.
Type 3 Expanded Poly Styrene or EPS has higher compressive strength and greater moisture resistance.
A site with a lot of resource information for building and cutting, including firmware, is rckeith.co.uk
When I took some of my wing cores to a local foam manufacturer, I showed the production manager a sample. He took one look at it. Without hesitation his first words were "too slow, too cold". The appearance was enough to tell him what was wrong. He has a lot of experience manufacturing foam products. I was using their Type 3 foam.
He then took me to a small foam cutting machine in their production facility. He threw a large block of white EPS foam on it. The machine had multiple wires tensioned by large springs. When it heated up he turned on the motion. It sliced the foam and it had a much smoother finish then my example. It was hot enough that the foam seemed to be sealed a bit.
I achieved a similar appearance when I made a quick and dirty 8 foot bow to cut up 3 inch thick sheets. The bow was connected to an ordinary light dimmer and 120v AC. When the wire gets to the correct temperature it stretches a surprising amount. About 2 inches over an 8 foot length.
Using a 12 or 24 volt power supply, sometimes just doesn't get the wire hot enough. I use Rene wire as does the foam plant. I use a 24 volt transformer with a bridge rectifier and a large capacitor. That results in about 34 volts ouput. I am still struggling to get the wire hot enough. The thinner and hotter the wire, the better your cut results will be.
Most wires between 10 and 20 thou should work fine. Cutting takes place with radiant heat, NOT contact with the wires. The wire should never touch the foam. If it touches the foam, the speed is too fast or the wire is not hot enough. Excess stringing can mean the wire should be hotter.
My existing 4 axis foam cutter is a modified version of this one on Thingiverse.
https://www.thingiverse.com/thing:1672015
I modified it several ways. It is essential to NOT use the bearings in the stepper motors if using a lead screw design. You must use thrust bearings. The stepper motor shaft is held in position internally by magnetism. The bearings are only for side load on the shaft, not end load.
This is important if you are using using a gantry on parallel tracks or rods. It is essential that the length of the guides or carriage running on the tracks or rods be 1.5x to 2x as long as the distance between the tracks or rods. If the carriage is shorter than it is long, it can jam more easily. On mine the distance between the rods was 70mm but the length of the carraiges was only 50mm. They would rack slightly and jam. When I lengthened the carriages to 105mm, it ran smoothly without jamming. With a short carriage, it jams. When it jams, it then jumps when the threaded rods push hard enough to overcome the jam. The result is lines on the finished cut.
Here is an example of such a modification.
https://www.thingiverse.com/thing:4604186
Here is a link to a gallery of foam cutters.
https://rckeith.co.uk/builders-gallery/
Mine is labelled
Jim’s Foam Cutter using 3d Printed parts.
It has pictures of the thrust bearing I used on the horizontal axis.
For an aircraft foam that is virtually indestructible, there is HYBRID EXPANDED POLYPROPYLENE (HEPP). A local vendor of flying wings uses this type material from
www.polyform.com in Quebec.
You cannot believe how tough this stuff is.
Just my experience cutting foam. YMMV.
Jim Haliburton