Amount of tanks

[Gary Dillard]

Give someone a fish, and they can eat for a day. Teach them to fish and they will eat for a lifetime. I’m going to answer the question I’m sure you meant to ask, which is “How do I determine how many tanks to use based on my selected actuators (pistons) and their usage?”

First some background you need to understand:

1. The volume of each tank is pi x (diameter/2)^2 x length. The volume of air used in each stroke of the actuator is pi x (diameter/2)^2 x stroke. It uses that volume each stroke, both extending and retracting.
2. Since all the volumes are linear functions of pi, you can take it out of the equation to simplify the calculations. (make your volume unit in^3/pi)
3. The pressure on the gage is the gage pressure (duh), which means the absolute pressure minus ambient pressure (about 14.7 psi for a standard atmosphere). This is the pressure used for force calculations (and the regulator settings).
4. From ideal gas laws, pressure x volume is a constant for some amount (mass) of air. In this case the pressure is the absolute pressure. So 100 in^3 of air at 60 psi absolute is the same amount of air as 200 in^3 of air at 30 psi.
5. You can fill the tanks to 120 psi. The maximum pressure allowed to actuate the actuators is 60 psi (the setting of the fixed regulator), which you will probably use for pushing or forcing a mechanism. To position something (like shifting gears in a gearbox or opening/closing against a stop that will take the load) 20-30 psi will probably be OK. You’ll need to use the extra regulator to set that pressure.
6. Each stroke of an actuator uses some amount of air from the tanks, which causes the remaining air in the tanks to expand and fill up the volume. This reduces the pressure in the tanks. You can continue to do this until the tank pressure drops to the operating pressure you need to operate your actuator.
7. The air in the plastic tubing is additional volume used for each stroke but it is very small compared to the actuator so we’ll ignore it.

So here (finally) is how you do the calculations:

For each tank, d=2.0, L=6.0, volume = 6 in^3/pi (at 120 psi). Suppose you want to run your actuators at 60 psi; the amount of air in each tank is equivalent to 6 x (120+14.7)/(60+14.7), or 10.82 in^3/pi at 60 psi. You will leave 6 in the tank – after that the pressure will drop below 60 – so you have 10.82-6=4.82 in^3/pi usable air at 60 psi.

Suppose you are using ¾ inch bore actuators. That’s 9/64 or .14 in^3/pi per inch of stroke. So each tank gives you 4.82/.14=34.27 stroke inches. For a 4 inch stroke actuator, that’s 8 strokes, or 4 cycles (extend and retract = 1 cycle)

Now suppose you are using 1-1/2 inch bore actuators. That’s 9/16 or .56 in^3/pi per inch of stroke. So each tank gives you 4.82/.56=8.56 stroke inches. For a 4 inch stroke actuator you will get 2 strokes (1 cycle). For the 2 inch bore actuator, it is 1 in^3/pi per inch of stroke. So each tank gives you 4.82 stroke inches, and you can only get 1 stroke out of a 4 inch stroke actuator.
Now try running the actuators at 30 psi. Using the calculations above at 30 psi, usable air in the tank is 12.08 in^3/pi at 30 psi. Scaling by 12.08/4.82, you get about 2.5 times as many cycles per tank.

You should be able to use the information for different combinations of pressures and actuators. I usually put it in an Excel spreadsheet so I can see the sensitivity to different changes. Good Luck.