Dissecting the principles behind volume compression

Lately as part of my silly ongoing hobby of hacking trash I've been mulling over building a stirling engine. The stumbling block is the power piston -- you generally don't just happen to find a cylinder and piston with the right fit no matter how many hard drives you take apart, and since I am doing this for fun and trying to find minimum-effort solutions, I took a little time to consider the problem of the airtight compression of a gas volume.

In doing a bit of research I think I have managed to distill the basic problem somewhat, and I think this "back to the basics" thought experiment might be useful to anyone studying machinery. Or maybe not. But here goes anyway.

There are, as far as I can tell, exactly two commonly used devices for compressing a gas volume: the bellow and the piston. A third kind is also used: acoustics, but the concept is a bit less tangible and as such doesn't attract as much attention from joe bandsaw. Let's take each in turn.


Many of us think of the bellows as being constructed from an accordian-fold between two solid surfaces. So we assume the principal here is that a flexible polyhedron is being used to constrict volume. The idea is attractive because folds in material are airtight, and though there is some wear and tear when a material is repetitively folded, some common materials can withstand this abuse pretty easily.

However, though it is possible to build a flexible polyhedron, that is not what an accordian is. Accordians rely on material that can stretch slightly. If they were made out of entirely rigid material, you would not be able to squeeze them. We don't notice this because the area of stretching is small and unobtrisive (the leather on the corners.)

A mathematical proof of the theory that no flexible polyhedra (in our normal 3-dimensional space) can change its volume has been found. The theory itself is called the "bellows conjecture." You can read more about all this here.

So, if you take out all the fancy folds and seams, what a bellows boils down to in its most basic form is a plastic ball. It is only the pliability of the plastic that allows the volume to be changed. And we know that pliable plastic, over time, can age and crack, especially if exposed to heat changes and oxygen. Though there are materials where this is not a much of a problem, they are not as conveniently available as other types of scrap.

I'm including diaphrams and also solids that expand due to heat/electricity/magnetism as a type of bellows.


The second major type of device for volume compression is the piston. Pistons work by allowing surfaces to slide past each other, getting around the bellows conjecture by allowing the length of a side to be changed. The piston's most basic form is indeed the one we use the most -- a cylinder sealed on one side and open on the other, with a plug that slides in and out of the open side.

Other forms of pistons are usually a combination of the bellows and the piston concept. They look simple on paper, because unlike polyhedrons, flexible polygons can and do change their area when flexed. What might not register when seeing such a device is the fact that the surface above and below the changing polygon consititutes a piston.

Airtight pistons require a liquid seal made from lubricant that blocks airflow between the cracks. If you accept a bit of leakage, then unlubricated pistons are possible but usually require precision machining and careful selection of just the right materials to make them durable and low-maintenence.

Even a very well lubricated piston will have some level of friction between the sliding surfaces. The more sliding contact area, the more friction. This is why classical pistons are usually round -- a circle is the most efficient shape with the lowest amount of edge in proportion to its area.


Acoustic compression actually doesn't change the volume of the container, but rather it causes part of the gas inside to compress while another part of the gas expands. This is usually done with a sound wave. When combined with a temperature gradient in a finely tuned system with a dominant harmonic, this can be as effective as any piston or bellows system in turning heat into mechanical motion.

Acoustics are limited a bit because the only mechanical motion they produce is vibration in the gas. In order to get this vibration into a more usable form of energy, a piston or bellows system is required. However, since they can work at much higher frequency, one can take advantage of the very small amount of flexibility in durable, solid materials that will not wear out over time. (Acoustic engines are often said to have "no moving parts" and are "solid state." For all practical intents and purposes that is true, because they do not suffer from the disadvantages of large amounts of motion, but it's not entirely accurate. They vibrate, and that's technically a moving part.)

Very small thermo-acoustic electrical generators are being researched and offer an exciting possibility, along with the additional MEMS technologies of capillary ion capture and thermopiles, for very cheap "solid state" heat-to-electricity devices to be mass produced. But who has gas diffusion and wafer etching equipment in their garage? Not me.

So those are the options

...And unless someone cares to point out any I have missed (bri@abrij.org), that's what we are stuck with in the pathetic three-dimensional Euclidian world of common experience.

Rolling steel sheets

As a followup, my current thoughts are revolving around a peice of steel strap drive I have sitting on my desk. This calls to mind a flexible steel sheet, and one could fasten one end to the large side of a rectangular cylinder, and the other to the opposite side, and then roll the steel inward with a rod. Then the only air leakage would be on the short edge of the rectangle, which are easy enough to adjust inward with thumbscrews.

I'm mulling over whether those edges could be sealed enough to make this an easy to build piston for those that lack precision tools, and whether the heat generated by flexing the steel would be a good trade-off versus the friction of a sliding piston.

Coil in a bottle

Another train of thought revolves around the more miniature -- would it be possible to use a solid-core inductor under magnetic stress (which expands the core) to compress a very tiny amount of air, and then recover the power along with the power from the gas cycle? Doubtful, due to losses in the electronics -- and I'm not even sure if the magnetostrictive effect is reversible -- but it might me another interesting not-so-microscopic quasi-solid-state option like acoustics are. Also note that a tightly fit inductor inside a tube would create a long, thin helical air channel that might have interesting physical properties, while a loosly fit/wrapped one could act as a parametric oscillator/amp based on the inter-related spring action of the coil and the variation in fringing/linkage.