I bought an air belt grinder a while back which proved a little too air hungry for my compressor, so, rather than buy a bigger compressor I converted it to run off 12 volts.
The motor came from ebay as a 12 volt cordless drill spinning at 5000 rpm. I removed the air motor and as luck had it the 12 volt motor fitted perfectly in the grinder housing. I also turned up a 12 mm bush with a 3mm hole to fit over the motor's shaft and shrunk fit that into the belt drum, constructed a handle from 22 mm tube and inserted a switch in it. To protect the motor I turned down a PVC pip fitting and heat shrunk it over the motor leaving an air gap to coincide with the motors vents, Sikaflexed an end cap in place and cut some grooves under the cover to aid cooling.
The grinder works great and is certainly better than forking out $300 for a Makita belt grinder. some pics and a video: