Hello! This is the huge sounproof box with the inside faces covered by rockwool.
How are you planning to observe your cnc in action?
I’ll made two small “windows” (one per door). Those windows will be made by 2 pieces of transparent polymer, one inside and one outside of at least 5mm of thickness. All the control electronics will be put outside the box.
Remember that you’re not just going to need to see it, but get at it as well. I’ve got mine on wheels just so I can get to all sides of it. If I were to add an enclosure, it’d have to be something that lowered from the top, or was big enough for the CNC to rotate on a turn table as needed.
You may want to maybe put your CNC on drawer slides or something there, so you can get at it…
Yes, I already though about slides, but I’ll implement them in a second time. About the accessibilty all around : IMHO in order to make a very effective soundproofing (moreover in a cheaper way), fullfill the box of doors is not advisable 
Uh and the box is very huge. The inner space height is bout twice the height of the CNC itself (80cm). There is the space for 2 people inside 
@Gabriele_Rossetti Remember that sound is vibrations. The most effective sound barrier I’ve ever made was a cheap carpet sandwiched between the wall studs and regular drywall (plasterboard, wallboard, gypsum board). But just plane carpet would work infinitely better…
But I’m just saying, you’re going to need to get at it a lot. And you already have the doors, so sliders would be a good addition. Plus they would isolate the CNC’s vibrations from the box, somewhat…
The sounds are high frequency, so most any barrier will make a huge difference…
@Mat_Helm Thank you for all your advices, I’ll take in account each suggestions … at the moment I’ll finish the project as is because a finished project is better than a number of unfinished ones! By the way… the idea to use the doors to support the sliders may be very interesting!
this is interesting idea. I have used some soundproofing foam for audio studio was thinking about trying that, I am curious what result you will achieve.
@Darko_Bulatovic Foam would be best sound wise, not so sure about clean up wise though…
Right, but shape is important as well.
For audio recording studios they use foam triangularly shaped to break and absorb sound waves and prevent reflections of the sound. As many annoying sounds are actually reflections combined with original vibrations and amplify them self’s (like echo)
@Darko_Bulatovic Yes, but it only matters from inside the box with a sound studio. In this case you’re just trying to keep the sound in the box. And only high frequency sound, for the most part, with a CNC…
Nice box. I would plan for dust collection also as it makes everything better.