I was thinking about doing this to my compressor, but came to the conclusion that there is just too much heat involved. I normally wear earplugs while using any power tool, so the compressor doesn't really bother me.
When I was thinking about doing this, I thought that an old 'office cubicle' would be ideal as a sound dampening material. They are readily available on CL, they are built to reduce noise in a busy office and can be pretty inexpensive on the used market. You don't care what they look like, since you are likely putting sheet metal or plywood or pegboard on the outside.
The key here, I believe, is to get the air to change direction THROUGH sound insulating material (gives you potential for enough air flow and makes the most of your enclosure's ability to reduce sound.) The problem with that is you need to increase the size of your air path quite a bit for every bend you make to trap noise.
I think it would be best for one vent to be low and one vent near the top.
Of course, I've scrapped my idea for an enclosure, because I think the heat is an obstacle which would just take too much time, money and space to overcome effectively. Instead, I plan to redesign the cheap plastic cover for the top of the machine, using better sound deadening materials and designs.
Here are a couple of pics of me measuring the sound levels on my machine, as a baseline, before any changes are made. This project has hit the back burner big time, since earplugs are cheap and I pretty much have them in any time I am working in the studio...
My measuring rig...
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The intake on this compressor (the source of the majority of the noise), without the cheap, black-plastic cover...
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With the cover on, just for reference...
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The components which make up the 'noise reducer...' the cheap, plastic cover with a molded-in, sound-redirecting channel, the piece of foam which fits in that channel, and the cover...
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A couple of different pics without the cover on...
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Just over 104 dB with the factory cover ON ('C' weighting, slow response)...
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Right at 110 dB with the factory cover OFF (C-weighting, slow response)...
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So, the factory design is somewhat effective (if I remember my theory, every 3 decibels reduces the impression of loudness by half), but nowhere near the 87 dB we need for longer exposure to this sound pressure level (It is recommended that you not be exposed to the sound level for more than 4 hours at a time. The recommended exposure time cuts down drastically for every few dB you go up after that.
Anyway, my though is that a better 'bolt on' head design would control sound better than a cabinet and get rid of the heat problems you have, when you enclose the compressor.
My other recommendation would be to just build a 'sleeve' of sound reduction material around JUST the head of the machine (think a box, about 2 feet tall, without a top or bottom, supported so it is at the level of the air intake). That would allow significant air flow, but also cut out a lot of sound.
I haven't tried any of this yet...just my musings on what I plan to do to reduce noise in my studio.
Kev