Rotary Vane Air Motor - Torque, Force, Power

Interesting paper, plus a lot of references at the end:

http://www.improve2011.it/Full_Paper/48.pdf

Torque will be generated not by the pressure impacting on the vane, but, rather, the difference in pressure between two faces of the vane. This pressure differential will vary significantly over the face of the vane (unless the vanes are very, very small). One needs to integrate over the surface fo the vane to determine how much of the energy in the air is actually converted to torque.

Air vane motors I am familiar with (sliding vane styles, eg Gast Manufacturing, up to 5 HP) are expansion motors. They are powered largely by input moment of the incoming air (which is due to pressure differential in the piping anyways) & the differential pressure between the chambers created by the vanes sealing against the cavity walls, seperating the intake & exhaust.

They typically are very compact, powerful, relatively quite, explosion proof & inefficient compared to an equivalent electric motor. You can try googling Gast to get data. If you are trying to derive this compared to an IC type engine, look at a Wankel.

A typical vane motor is pictured below. (This is from the Modec website.) You can see that space C1 in the left drawing is completely enclosed. As the rotor turns, this space will increase in volume, so the air must expand. Pressure will drop from (for example) 4 bar to 3 bar. In the right picture the rotor has advanced to the point at which one vane is just about to cross the edge of the exhaust port. As you can imagine, if the exhaust ports are small (as they are when just uncovered) the pressure will remain high for a while. A similar effect occurs at the intake side. The two effects combine to reduce the pressure differential at the vanes tending to turn the motor.

You can probably see that this motor would lock up if it were hydraulic. You can probably also see that there would be losses associated with getting air to move through the motor without restriction. So efficiency will vary with design details, and with the speed at which the motor is run.

For stall torque, you can imagine full pressure being applied to the exposed vane area at P1 in the left picture, and 3/4 of full pressure being applied to the (vane area at P1 minus the vane area at P1). But that number will be fairly close to full pressure at the vane are P1 alone times a fudge factor. (Given enough time at stall, the inlet air will leak pas the vane at P2.) Figure .9 for the fudge factor.

So, for stall torque you can use P x fully extended vane area x moment arm (to the center of that area) x .9.

For running torque and power you can figure on a speed half of the free air running speed value. At this speed, torque will be half of the stall torque. The free air speed is based on the displacement of the motor, which you can calculate or by turning the shaft if you have the motor.

This catalogue from Parker pneumatic shows the characteristic air motor power curve on page 6.

For industrial purposes, figure 7 hp into a compressor for 1 hp out of an air motor.