I recently decided to build a compressed air dryer for use in my liquid nitrogen generator project. I will be using silica gel beads (the same stuff as found in those ubiquitous "do not eat" packets) to soak up moisture from the air. In order to do this, the silica gel must be contained in a vessel that will withstand the pressure of the compressed air. In this case, I designed the cylinders to have a working pressure of 150 psi. The system will normally operate around 100 psi. The vessel should also be fairly long and narrow to ensure the air flowing through it has enough time to make good contact with the silica gel.
I started with some basic engineering equations for a thin-walled cylindrical pressure vessel.
I already had some aluminum pipe that I felt would be suitable and checked it with these equations. The pipe is 3" in diameter and has a .0625" wall.
The tangential stress is = (150) * 3)/(2 * 0.0625) = 3600 psi
The axial stress is = (150 * 3)/(4 * 0.0625) = 1800 psi
The radial stress is = -(150) / 2 = -75 psi (negligible, the negative indicates compression)
In order to determine if this amount of stress is going to break my aluminum cylinder, I used the Von Mises stress calculation for multi-axial loading:
The Von Mises stress in the walls of my cylinder is:
= sqrt[ ( (3600-1800)^2 + (1800-3600)^2 + (3600 - -75)^2 ) / 2 ] = 3161 psi
In this case, the Von Mises stress is actually lower than the tangential stress component alone. This is because the walls of the cylinder are being pulled in two orthogonal directions, thus reducing the amount of shear that would be produced if the cylinder wall were being pulled in only one axis. In order to be as conservative as possible, I'll use 3600 psi as the load stress.
The cylinder is made from aluminum alloy 6061, which has a yield stress of at least 8000 psi. It's likely much higher with T4 or T6 heat treatments, but I will be welding this material, and I'm not sure what effect that will have on the yield stress, so I'll be very conservative and stick with 8000.
Clearly the 3600 psi load is much less than 8000, and this design has a safety factor of 2.2. Working backwards, the tank will hold 330 psi before suffering permanent damage. Again, these figures are likely to be very conservative.
I also calculating the plate deflection for cylinder's end caps, and it was insignificant.
I cleaned up the cylinder by turning it on the lathe and running some sandpaper over it.
The end caps are 1/8" thick and have a step turned on their edge to make placement and welding easy.
I made some bosses that will be threaded later. Luckily, the diameter of my horizontal belt sander drum matched the cylinders' diameters perfectly. The boss will sit flush up against the cylinder wall for easy welding.
I milled a flange for the pressure vessel to hold an O-ring the in groove and the holes will be tapped for 1/4-20 bolts. The flange will be bolted to a 1/2" solid aluminum plate. This was done so that the vessel could be removed from the plate, and the silica gel could be replaced easily.
I tested the vessel, and....... it leaked! I had a tiny pinhole leak in one of my welds. It was so tiny, I could barely see the imperfection. I repaired the leak, and pumped the tank up to about 220 psi. Nothing was leaking or breaking, so I considered it a success.