Somewhat dreading this but here we go.
The Stirling cycle is well described all over the net so lets not go there. I believe our device is best described as working on a free piston Stirling cycle. In our engine, the piston is replaced by a diaphragm. In addition to a free piston, the engine also has a free displacer. The diaphragm & the displacer will work out of phase (by 90 degrees).
OUTER CAN / HOT CAP
Heat from any source is applied to the bottom end of the "hot cap" or outer can (green in diagram). The bottom of this is the hot end of the device. The top is the cold end. The outer can serves to heat & cool the gas & keep the gas in place.
We have choice with gas. The choices are as follows.
A. Normal air as normal or high pressure.
B. Helium at normal or high pressure.
C. Hydrogen at normal or high pressure.
We are likely to start with air at normal pressure then migrate to helium at normal pressure & then helium at high pressure. The choice of gas & the pressure of gas will only effect efficiency, it will not interfere with the basic workings of the device.
INNER CAN / DISPLACER (shown in Blue)
Inside the outer can is an inner can. The inner can is the DISPLACER This hollow can is the same as the outer can, just 1 mm smaller. Enough to allow for free movement of the inner can. It should be a snug fit but have the ability to move freely. The bottoms of both cans should be slightly rounded as flat surfaces are prone to deformation. The displacer moves back & forth moving the gas from the hot end to the cold end.
The inner surface of the outer can and the outer surface of the displacer also act as a regenerator. This is important for efficiency but less important for understanding.
All the gas would stay at the same temperature if the displacer was static. (Well, if it were an ideal gas with zero viscosity & ours is not). The temperature variance happens because the displacer is moving.
PLANAR SPRING (Shown is Yellow)
The displacer is mounted underneath the planar spring. The spring keeps the displacer in the correct position & allows the displacer to move to its own rhythm
DIAPHRAGM. (Shown in red)
Made from Beryllium copper, the diaphragm moves back & forth (out of phase with the displacer) depending on the pressure in the outer can.
Flanges. (2 fairly fat yellow bits, one at the top of the drawing, other around the hot cap)
These are bolted tightly together holding everything in place. The entire assembly is put on springs to allow the device & displacer to both move increasing overall efficiency & allowing for a natural rhythm.
There are many more parts but they are not in the 3D representation. Key part are the upper & lower caps enclosing the diaphragm & planar spring, the bulkhead displacer, casing springs, various Gaskets, clamping rings & then entire magnet array that goes on top of the device. These parts will be added later.
The total pressure/volume gas is changing as its average temperature is changing (pV=nRT for ideal gas, where p is pressure, V is volume, n is the number of moles of the gas, R is a constant, and T is absolute temperature in kelvins). V is almost constant, it changes a bit because of the membrane deflection; the p is what pushes on it. n is the amount of gas in the can, that's constant. R is also a constant, so we can count nR as a constant specific for the given assembly. T is the average temperature of the gas in the can (the active volume, displacer does not count). As the displacer is itself serving as a re-generator, it stores the heat of the gas along its length. So a material with low thermal conduction is used . In other words, gas flowing from hot to cold end is heating the displacer's left end (assuming hot end is left) and on its way back cools the right end.)
PROJECT LOG CONCLUSION.
If the above does not make sense, do not worry, it is me, not you. The diagram is incomplete & the explanation is poor. The next log will show representations of the missing bits & hopefully an overall explanation. I suspect the only way to demonstrate this effectively is with pics of actual parts & a video of the device being assembled. Both will follow someday....& this log will probably be heavily edited once the thought process is more clear....