I had an opportunity to test my bearing-ball check valve idea, at least in terms of how it works in a pneumatic sense. I discovered that my idea was flawed by the need to incorporate two incompatible requirements. The first: the ball has to fit easily into the end of the tube to seal. The second: the force pulling the ball into the tube has to be small so the check valve works with a very small pressure differential.
The practical result of these requirements was that the hole in the piston where the ball goes has to be very nearly the same diameter as the ball. But this means that the air has to flow through a pretty small constriction around the ball. The end result was that there wasn't much of a difference in the flow rates. I thought of some ways to get around this problem but they all had their own complications -- including noticeably more machining work.
So instead of that approach I went with a much simpler flap valve arrangement, made with a square piece of acrylic film. The film is placed over a hole drilled in the base, which serves as the air inlet. To promote free flow of the air, I also milled a shallow slot from the end of the base up to the hole. I cut a square piece of the plastic film and then made three cuts in the form of a U, to free that portion of the plastic, enabling it to move up (away) from the hole, or down toward it to form a seal when the piston is being pushed into the cylinder. That worked OK, but it worked even better when I made more cuts to widen the gaps between the flap and the rest of the plastic sheet. I think the narrow slits didn't allow the flap to completely seal.
Putting a little lubricating oil in between the plastic and base would probably work even better -- for awhile, but the oil could attract dust and then the seal would likely fail. In this case a little less (of a seal) is more, in terms of longevity of the damper. That said, I also made the damper so it can be taken apart and cleaned if that becomes necessary.
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