In an air tool, compressed air enters the inlet port which is plumbed to the smallest compartment of the vane-housing inside. The compressed air should be at least at the minimum operating pressure for that air tool to work properly.
The compressed air is moving from an area of high pressure as it enters the air tool, to an area of relative low pressure, that being back to atmospheric pressure outside the air tool. As the air moves inside the tool, it too moves the vanes.
As the shaft in the vane-housing rotates due to the air movement, the vanes inserted into that housing slide in or out, depending on where they are in the cycle.
Centrifugal force ensures that the vanes are always keeping contact with the inside of the outer cylinder, creating a seal. This forms air-tight compartments within the vane housing.
As mentioned, compressed air always flows from an area of high pressure to an area of low pressure, so the high pressure air in the small vane-compartment wants to get to the larger area vane, and ultimately, out of the tool back to a stable, lower, pressure.
The shaft inside of the vane-housing extends through air-tight seals up into the air tool, and is attached to tooling on the end or to gearing of some sort. The result is rotary motion of that tooling.
The power that drives the air tool is compressed air.
Not to generate rotary motion of a shaft to drive an air tool, but use the rotary motion of the vanes to draw in free air, and compress it so that you then can use compressed air power to run a huge variety of compressed air-driven equipment.
Road repair / builders and building construction crews can use rotary vane compressors too. These are typically powered by a gasoline, diesel or sometimes even a propane motor.
The vanes, installed in the eccentrically located centre housing, are able to slide in and out. The vanes length depends on where it is in relation to the outer barrel. Centrifugal force presses the vanes against the inner-wall of the outer barrel. This seals each vane against the outer surface, creating relatively air tight compartments within.
Where the volume between the vanes is largest, free air is drawn into the compressor vane-housing through an inlet valve.
As the center shaft continues to rotate, and since it is off-center to the cylinder, the succeeding compartments are smaller and smaller as the vanes cannot extend as far, being closer to the outer wall. The result, higher volume of air is compressed into a smaller volume.
When the vane-housing volume is the smallest, the air is as compressed as it can be in the cycle, and it is released through another valve into a compressor tank / receiver or into the shop air mains.
Vane Compressors can come equipped with an external enclosure, so the compressor looks like a large metal crate. Aside from the cosmetic value, the housing usually provides sound attenuation. It is usually needed.
Rotary vane manufacturers suggest their units are more compact than other types of compressors, yet can provide more compressed air output than similarly sized reciprocating units.
Rotary vane compressors claim a longer life expectancy in continuous duty applications. Mind you, the same claim is made by some manufacturers of rotary screw air compressors too.
Manufacturers claim that Rotary Vane units are easier to service than other types of compressors, and that they are ideally suited for moderate-pressure applications.
It is my impression that rotary vane compressors are not the typical first choice for industrial compressed air applications.
The rotary vane compressor users seem to lean towards specialty gas requirements, hobby trade, pumping, vacuum generation, and other areas outside of industrial compressed air supply. This is my impression, at least.
Regardless, there is every reason to think that you will find a Rotary Vane type compressor for your application, should you determine that this compressor technology is your choice.