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# Rotary Vane Air Motor - Torque, Force, Power

08/25/2012 8:37 AM

I haven't been able to find a design manual for a vane motor online. I'm trying to evaluate one a friend built as to its torque, force, and power. I have all the dimension, input pressure, and rpm, and I know how to do all this stuff for piston motors, expansive, partially expansive, and full pressure. I thought vane motors would be easy too but not so.

I know the force is vane area x pressure. I know torque is from vane to shaft center (lever arm) x force. I know work is pressure x volume. But all that is vague, it doesn't really give me the numbers because I still have questions.

Force: vane area x pressure. What is meant by vane area? It can't be adding up the area of all the vanes or else you could double the force by adding twice the vanes. So it has to be all the exposed vane area added together divided by the number of vanes? That's all I can think of, average vane area?

Also, I know that what causes the rotor to spin is differential area, the larger area at front of a chamber that's defined by two vanes will have more force than the smaller one at the back, so it will turn toward the larger area. So it seems that for accuracy, any calculation involving vane area would have to have the smaller area subtracted from the larger? Or no?

One reference seemed to imply that torque is constant throughout the cycle, but that was about hydraulic motors. Would air motors have that same characteristic?

I assume that with a no frills vane motor like my friend made, there would be no expansion to speak of, just dumping air through and exhausting at the same pressure. But when it comes to vane motors, if there was a way for the air to expand, I don't understand what it might be.

Torque is lever arm x vane area x pressure, which is the same thing as lever arm x force. But what part of the vane do you use? Average vane area? As if the rotor were centered instead of eccentric? Area of a fully extended vane / 2? I really don't have a clue on how to do the calculations for a vane air motor, and I've been looking online all day.

I think I have figured out by drawing it and measuring the lines that the maximum extended width of a vane is a complementary sum, in other words, if a vane is only partly extended, a vane exactly across from it would have an extension distance that would add to it to equal the same quantity as the maximum extension.

Thanks.

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#1

### Re: Rotary Vane Air Motor - Torque, Force, Power

08/25/2012 5:47 PM

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

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

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#2

### Re: Rotary Vane Air Motor - Torque, Force, Power

08/26/2012 2:44 AM

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.

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#3

### Re: Rotary Vane Air Motor - Torque, Force, Power

08/26/2012 10:08 AM

You don't need to worry about areas, forces, moment arms etc. If you know or can measure the air flow you can estimate the output power, then divide by speed to get torque.

Power = P2*Q2*ln(P1/P2)*efficiency. P2 = atmospheric pressure ~ 1 bara = 100 kPa (to get answer in kW) Q2 = flow at standard conditions m3/s, P1 = inlet absolute pressure, kPa. Efficiency ~ 75%. Divide by speed in rads/s to give torque in kN.m.

Let us know how you get on.

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#4

### Re: Rotary Vane Air Motor - Torque, Force, Power

08/26/2012 7:11 PM

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.

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#5

### Re: Rotary Vane Air Motor - Torque, Force, Power

08/27/2012 2:44 PM

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.

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