Are there any users who have tried using expanding foam in extrusions to deaden noise?
An interesting notion… my first question is how much noise is being generated by the extrusions? If they are vibrating at the resonant frequencies generated by your milling motor, there could be some point to this approach. I suspect changing the resonant frequency at which you mill materials, would be a whole lot easier and much more effective. If the extrusions are producing a lot of sound by way of resonance, this could potentially be deadened by using sound deadening materials that are used inside the cargo bodies of trucks, to reduce the amount of movement the body panels can make.
I don’t have a LongMill machine so I cannot say much about the extrusion pattern. I would hazard a guess and say that the noise you are hearing is far more likely to be generated by your vacuum system first and your milling motor secondly. Call these your primary noise sources for want of better words. Secondary noises are generated by blunt milling cutters, inaccurate toolpathing, material selection and feeds and speeds. Given these findings, I would think that extrusions contribute very little additional noise to resonant frequencies generated by a working machine. Additionally solid structures such as walls may reflect any sounds that are generated.
Noise may be generated by loud machinery (typically) a Makita trim router generates about 85dBA when running at maximum speed. This drops to around 75 dBA when run at its slowest speed. Vacuum systems that I have used tend to hover around 87dBA when being used. The cutter should not generate loud noises and if it is doing so, then it is blunt or the wrong cutter for the material being machined or the feeds and speeds are too high. If you want to deaden noise and you have sufficient space to work and can plumb in the vacuum system, you could make an anechoic chamber to cover your machine. It may need illumination and inspection windows but it is a possibility. I suspect that solid extrusions (dead to sounds reverberating within the body of the extrusion) would not really make much of a reduction in the noises you are hearing.
Possibly a sound engineer will happen along and tell you that I am completely wrong on all counts and then you will get better advice.