What you’re doing there is very similar to what people try to do with home music studios. Basically there’s two aspects to dealing with sound,
- Managing reflection and reverberation to manage the sound within a space
- Absorbing or isolating the sound energy to reduce the leakage out of the space.
I can’t recommend this guy enough as a starting point to understand how this stuff works, he’s a real pro and talks sense not expensive products.
I’m a bit of an audio nerd so I’ve already got some strategically placed audio panels and bass traps to clean up the sound in my room. I’ve also done the measurement and fighting in a friends studio to try to position the monitor speakers properly to avoid the worst 1/4 and 1/2 wave resonances and level out the sound as much as possible before electronic EQ. If you put the noise making device in any of the ‘wrong’ places in a room it will just resonate and nothing you do will usefully damp that noise inside or outside the room compared to just altering the resonance modes.
As for construction materials… Wow, that a rabbit hole, if you go look at forums like gearslutz you’ll find an easy years worth of reading and argument on that topic.
In summary…
Mass is what stops sound, then isolation, but it really needs to work, sound leaks through tiny gaps. Rockwool is really not that effective because it doesn’t have enough mass to do much absorbtion in realistic thicknesses, stud walls are mostly transparent to sound because they transmit the sound through their rigid frames. floating floors and stud walls with separate frames for each side of the wall start to isolate the sound.
For a sound absorbing material, foams and egg-crates are just useless, regular rockwool isn’t much better. There are much heavier grades of rockwool which are used to make sound deadening panels, GIK acoustics sell both the panels and the materials. The panels I have are GIK. You can locate the heavy duty rockwool but not at your local building supplier.
There’s also a whole plethora of domestic sound absorbtion products which you might want to look at. These typicall work on a mixed heavy layer and spongy layer sandwich approach. This is what you could put under a ‘floating’ bench top for your machine.
I made a box to keep my shop vac in, but it has an outlet which let me put a 4" hose on the exhaust to go out a window, I also put a cyclone settler on the input to keep the worst of the dust out of the vac. It makes quite a lot of difference.
If you want to keep the noise inside the room I’d suggest using something heavy as the supports for the Shapeoko, even concrete paving slabs would be worth considering along with one of those floor isolating products and then use proper industrial grade vibration isolating mounts to isolate that frame from the floor. A few people here have used vibration absorber / isolator mounts between their machine and the table too, that’s a good double strategy if there is enough mass in the table.
HTH