The General Idea

I want a vacuum pump. Mainly so that I can aluminize my own mirrors. Yes I know you can send them off to a company and get it done for pretty cheap. But I want to do it myself, in my garage, and this being Hackaday I trust that you are ok with that too. Plus, it occurred to me that hackers (or at least hackerspaces) having access to the high vacuum environment could open up some interesting new possibilities. So, my little experiment might actually be useful to other, smarter people than me doing really cool stuff. Here's some things that require a decent high vacuum to do (from this site, a great intro to vacuum technology and challenges):

Electron tubes, vacuum tubes, electron microscopes, hard X-ray tubes, thin film evaporation, particle accelerators, radiometers, light bulbs, thermos bottles, certain lasers, other cool stuff...

Why This Is Hard

Briefly, air doesn't behave properly at really low vacuum, so normal "displacement" style pumps don't work, and you need other exotic pumps to continue moving air. It goes from normal to "Knudsen" flow, then "molecular" flow at moderately low vacuum. The two most common types of pumps for this flow regime are oil diffusion and turbomolecular, though there are others. Oil diffusion pumps are only semi-cheap, very messy, and have a habit of catching on fire if too much air is accidentally vented into them. Turbomolecular pumps are awesome on the other hand. They are very fast, clean, and expensive (several $thousands). They are similar in construction to mini jet-engines (i.e., not something I can build in my garage). Also, they cannot exhaust to (or function in) atmospheric pressure, and thus require a small backing pump ($100 or so I think).

The Stretch Goals (this is where you can all laugh at me)

An inexpensive vacuum pump for the hobbyist / hacker community

Those familiar with vacuum technology will realize that these goals are ludicrous. I agree wholeheartedly. I also believe that good design strives to stretch the imagination and push the bounds of what is possible, so I think having something ludicrous to shoot for is actually a good thing. If I build this thing and it works, everyone wins. If I totally fail and it never works, I will still have learned something about fluid dynamics, mechanical engineering, and materials science, so I still win. If I document my failure well and you guys can read about what I've learned, then everyone wins! Point is, don't be writing in the comments saying this is impossible. I already know it is (most likely) impossible. I want to find out how close I can get.

Math-less Design Overview

My design concept is based on the "Bladeless Turbine" invented in 1909 by Nicola Tesla. Patent is here. For those unfamiliar, briefly, Tesla's design utilizes the boundary layer effect to move air, rather than blades, and so enjoys fairly simple construction. It consists of several closely spaced smooth discs with a hole in the center for the intake, spinning at high speed. Viscous fluids (liquid or gas) stick to the discs and are propelled towards the edge by centrifugal force, and from there are exhausted. To my knowledge (after much searching on the Google), it appears that no one except Tesla himself has attempted to use this style of pump for high vacuum applications. Intuitively (and experimentally) the pumps are more efficient and effective with high viscosity fluids. For air, viscosity and pressure are inversely related, thus the pump should become more effective as the pressure decreases.

My stretch goals could in theory be accomplished in a single stage. Picture the bottom of the vacuum chamber as a smooth plate of aluminum with about a 10cm hole in the middle. Centered on this hole is a large flat disc spinning at high speed with a very small (<.1mm) gap between it and the aluminum plate. Air would enter the gap from the hole in the chamber, get accelerated by the disc, and exhaust directly to the atmosphere. By my calculations, this disc would need to be nearly a meter in diameter spinning at 35,000 RPM, for an edge velocity of 2000 m/s. Frankly this scares the hell out of me, especially unshielded like this. For scale, 2000 m/s is about Mach 6. Pure carbon fiber tow is the only material that has a chance of holding up to this stress, burst speed would be 2200 m/s. In the event of fiber failure and subsequent disc rupture shards of carbon fiber would fly out at Mach 6. This already fails the stretch goal of "safe". So we'll have to do stages like everyone else. Shucks.

Instead we'll do a long-ish tube full of discs. The first disc has a big hole in the middle, and it's outer diameter is as close as we can get to the inner diameter of the tube. Below this disc (keyed to the same shaft) is a solid disc (no central hole) with a diameter just a bit less than the first disc. This is one "stage". Now cascade a bunch of these together on the same shaft and you get a vacuum pump! The number of stages needed decreases exponentially with a higher compression ratio, which in turn increases exponentially with the speed of the outer radius. At 2000 m/s you just need one stage, but that's scary. The best aluminum disc would explode at about 600 m/s. Carbon Fiber epoxy matrix gets to about 1000 m/s before exploding. But 400 m/s should be very safe for aluminum, and would require under 20 stages. Regular carbon fiber at 700 m/s gets us down to about 6 stages, and should be pretty safe (though this is about Mach 2).

The particular inner/outer diameters and spacing between the discs would be varied according to a beautiful geometric physics equation that I have yet to figure out :)

My ultimate goal would be to come up with the parametric equations that would allow anyone to tailor the pump design to their specific needs and resources. For example larger diameters would accommodate higher pumping speeds and lower RPM motors, but small diameter steel pipe for the shroud is easier to find at Lowe's. My Dremel does 35,000 RPM, but your's might do 70,000, so you could use smaller discs and still get the same compression ratio. If you already own a decent displacement vacuum pump (for air conditioning work) you could use that as a backing pump and reduce the number of stages required.

I have done a lot of math for this already, which I will post shortly in an update. I do NOT have a mechanical engineering background, so would love it if someone wants to check my math. I always welcome any comments/suggestions/criticisms.