This seems an interesting idea...

Woa!  This is a really interesting idea for storing energy.

Instead of compressed air, you could use cold gas - e.g. butane like in firelighters. It has a vapor pressure of 2 bar at room temperature and will last much longer than air.
The good thing is that it will stay in liquid state and won´t produce pressure greater than 2 bar but will have a proper density. Propane is also good (10 bar). There are several other liquid gases to consider, some are not flamable.
With compressed air you won´t be able to drive it more than a few seconds. Even with cold gas it will be difficult to get reasonable energy output.
What about a hot version which burns butane, like a jet.

Just wondering what is the smallest gas fired turbine to date...

Thanks! The ball valve is supposed to be manually opened when you expect the battery to operate and close when you are not using it. It is quite "raw" but for this first iteration may be good enough.

better to make it the form factor of 2 aa batteries. nothing much uses one ;).

Probably side by side, but you have the extra question: facing same ways, or opposite ways? Most of things use 2 batteries facing opposite ways, But not everything! My Logitech mouse uses 2 AA facing same way... 

Might be worth investigating PEEK filament as I hear it's tough af and might be easier to work with than metal. Also, conductive filament could then be printed on it (if you have printer capable of doing multiple filaments).

Regardless, good luck with your project and I shall follow it closely. You could potentially remove lithium and a whole bunch of other grim chemicals from batteries and at same time end up with a battery that's not just rechargeable but largely recyclable once it reaches EOL.

Thanks for following! I will investigate this material too, even if for the small scale tests I think more about metal 3d sinthering printed parts due to the small dimensions and tolerances..

Neat idea, but I would think one should try larger and scale down, if possible, rather than small and scale up.  Perhaps something like a car battery or one of those larger lantern batteries.  Using a car, one can use the alternator to power a small electric air compressor to repressurize the battery OR maybe use something other than an alternator powering an electric air compressor, such as directly driving a non-electric air compressor.
If car, perhaps a go-kart, golf cart, or equivalent first.

Hi, the goal here trying to get info about how miniaturization of a compressed air battery will works and what results we can achieve; plus I will make some parts metal 3d printed so small scale=lower cost for me to make prototype parts. Thanks for following!

Oh, okay.  For some reason I missed that. Good luck, regardless :)

Some questions:
What is the projected energy capacity of this device?
Is it better than conventional batteries?
How compressed is the air?
What are you doing about thermal expansion and contraction?
What kind of current output would you expect? 
How many compression cycles can the storage tank take?

Interesting idea!

Assuming it's similar to an aerosol can (as for more than prototyping, that's the easiest production style for the pressure vessel), 270 PSI is the burst rating, while 180 is the survivable point for using this in devices (buckling).  Assuming the entire battery volume is used for a pressure vessel, to simplify calculates, we get a whopping .007014 liters.  Now, compressed air energy storage is usually done at much higher pressures.  Taking an estimate from an MIT paper (which is more about a jumping robot, but mechanical work is mechanical work), we see a density of .1 MJ/L at 2900 PSI (197 Atmospheres).  That gives us a total energy of .19 Wh (if we use said 197 atmosphere air).  The closest AA battery? NiCd at 1.20.  Factor of six difference in energy, even without factoring the space for the turbine, wall thickness, or efficiency. 

NiCd is a rechargable chemistry too.  

It's a cool thought experiment.  But don't expect it to work.  

Hi. I do not expect this project in its current state to replace commercial AA batteries. Thank you for your calculations! Even reaching just 1/10 of a NiCd battery capacity would be a good result for me on this project as a starting point; I am trying to get info about how miniaturization of a compressed air battery will works and what results we can achieve, to make a fundation for future batteries that may also have commercial appliactions...

Hi, this project is still in the designing /testin phase.

I do not expect this to perform better than commercial AA batteries but instead to help me understand how miniaturization of a compressed air battery will works and what results we can achieve. And I will report all the technical results as the project will progress!