Spring Rate Equation for Regulator Spring?

[grumpyoldman]

Hey Guys! Does anyone know an equation to determine the spring rate for a regulator spring? It would be for an inline regulator along the lines of Ragnarok's design, pictured at end of post. From reading old posts on SpudFiles, I have a general idea of how to do it (I think).

Would the equation be something like this?:

Spring Rate = PSI output wanted * piston face area / compression distance

Compression Distance = spring free length - spring solid length

another way to do it?:

PSI Output = Spring Rate * Compression Distance / Piston Area

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Say you want a PSI output of 350 PSI and have a .5 inch piston.

Pi * r * r = Area
3.14159 * .25 * .25 = 0.196349375 in2 (piston face area)

350 PSI * 0.19635 in2 = 68.7225 PSI

68.7225 PSI / .09 in. (Compression Distance) = 763.5833 PSI Spring Rate


So you would need a spring with a spring rate of 764 PSI with a compression distance of .09 inches?

Ragnarok's design

[Ragnarok]

I should point out that design is slightly over simplified - it should really have a piece to retain the sliding piston!

As far as calculating spring rate, you need to work out the appropriate force on the piston - so, roughly as you started...

3.14159 * .25 * .25 = 0.196 in^2 (piston face area)
350 PSI * 0.196 in^2 = 68.7 lbf (not psi - you've multiplied psi by square inches, so you get pounds-force)

You then need to achieve 68.7 lbf on the piston... the spring rate will be this force divided by the desired pre-compression (in inches) on the spring at the "sealing point" of the regulator.
If you want to compress the spring by one inch, then it'll need a spring rate of 68.7 lbf/in. Compress it by two inches, and it'll only need a 34.4 lbf/in spring rate.

The spring does not necessarily need to be at full compression when the piston has sealed. It can in theory travel a little beyond this (provided the piston is long enough to keep the input supply sealed)... and, in theory, could have a vent to atmosphere, also acting as an over-pressure (however, that's not suitable for all applications)

Two ideas I'd had for that regulator design in order to allow the output pressure to be adjusted would be:
1) to have a screw mechanism to push on the other end of the spring - tighten it and compress the spring to increase the pressure output, and vice versa to reduce output.
2) using a "gas spring" - basically, seal the area behind the piston and then pressurise it. This easily saves force calculations, as the equal areas on each side of the piston mean that the output pressure will equal the pressure in the pilot area.

[grumpyoldman]

Thanks Ragnarok. I was thinking of a design kinda like this:

Reg.jpg (12.34 KiB) Viewed 2522 times

[Ragnarok]

That may have a problem.

I'm assuming you're expecting the regulator to able to vent overpressure to atmosphere (hence the port on the right), but the increased area in on the spring side of the pilot will give it a "pop-off" effect - with pressure exposed to the increased area, the force on the piston will increase, and it won't seal until the pressure has fallen significantly.

At which point, the pressure will have fallen, the regulator will start to refill the chamber and then the regulator will close... and if it's got too little margin between the "closed" and "pop-off" points, the inertia of the piston may carry it too far and result in rapid farting as it empties your entire air source.

Aside from that, you will need to be careful about the dimensions there, as I think the exact o-ring positions as you have them there may let the input vent to atmosphere.

Moving the bottom o-ring up would effectively resolve both problems, as it would increase the margin between the "closed" and "venting" positions, as well as avoiding the input ever being connected directly to atmosphere.

[grumpyoldman]

Got it. I see what needs to be done now. Thanks again! And a big thanks to PCGuy for this great forum!