A few things to ponder in order of difficulty to test:
1. Using a compressor intake restrictor
2. Big compressor wheels in modified compressor housing
3. Vaned diffuser
4. Simple roller gear train for impeller input shaft
tldr;
Reduce the diameter on the compressor intake to "mock" a smaller inducer and get more acceleration in the wheel. I think this will increase the PR at low flow rates. NB. will cause choking at higher flow rates. Mostly speculative, probably not worth it for small compressors. Some info is floating around for WRC cars, where a restrictor is a requirement.
Put the biggest wheel you can in your compressor housing. If you can find one, choose a wheel with less sweep on the exducer edge, since this will increase the tip exit velocity. The reason they're swept back is to reduce wake at moderate to high flow rates -- but we are no where near that.
Reduce the compressor volute by filling with epoxy and machining out new volute (be creative). Should boost pressure in low-flow applications, but will act as restriction at high flow rates (for that compressor).
Add a little bit of an internal tongue diffuser, see:
https://data.epo.org/publication-ser.../document.html
Add diffuser fins to the back plate. Should benefit flow in this application since we have tight control of the compressor speed (unlike an exhaust driven turbo). Getting the angle right might be tricky, but there's plenty of math around to allow you to calculate the angle for a given (target) flow rate.
The rotrex epicyclical super-charger transmission is a thing of beauty. But what about just trying a conventional single stage reduction gear train using bicycle hubs and steel roller gears under heavy load?
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Compressor intake restrictors:
The WRC dictated that intake restrictors be used on competing cars. Kinna sucks, since it limits the top output... but it also has interesting (read good) effects at lower flow rates:
http://www.rallyandracing.biz/air-in...-n.html?lang=1
I figure if you go for an oversized compressor in the 500HP+ category, then restricting its 4 inch intake to 3 or even 2.5 inches is going to be no big deal. I reckon it's worth a go for anyone who's building.
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Big compressor wheels in modified housings
Have a look at the compressor map for the Paxton N2500:
http://www.stangtv.com/tech-stories/...werhat-review/
It maps a PR of ~1.2 at around 20k rpm and 60 CFM. In other words it's in the ball park for a BLDC direct drive that can make sufficient torque. It uses a dinner-plate for the impeller (the inducer is 94mm!).
But back in the real world you'll see a trend towards useable boost at lower compressor speeds (36K rpm for the T76) with increasing impeller exducer diameter. There's a catch. The boost is at flow rates, which would equate to around 200 HP. In other words, you could use it if you're already making 200+ HP!
But all is not lost (I think). If you can make your compressors internal volume (volute) "smaller"... Given that we're operating at relatively low pressures, temperatures, and flow rates within the compressor. I reckon a cut and shut job of the housing might be a goer. Even something as simple as filling the volute with an epoxy and chipping out a new smaller volute might work. I reduced volute should boost pressure in low-flow applications, but will act as restriction at high flow rates (for that compressor).
The best I can think of is to buy a cheap chinese "T76" fake from flea-bay and modifying the compressor intake, diffuser, and internal volute so that it is optimised for low flow rates and pressures.
Optimising this a step further leads to...
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Backplate Vaned Diffuser :
Google up "centrifugal compressor diffuser" and go to the images tag. You should see some pictures of vaned diffuser plates. Their purpose is to prevent the wake from the exducer blade tips from screwing up the high-speed/low-pressure to low-speed/high-pressure conversion that happens across the diffuser plate and to guide the flow angle as it enters the volute. They're not present in modern automotive compressors since the vane angle needs to change depending on flow rate. However, we're different since the BLDC drive restricts us to a low PR and quite low flow rates (for the compressor). +10 to anyone who implements variable vane control ;-)
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A roller gear train for the impeller shaft.
This one is hard. Rotrex has some beautiful supercharger transmissions. If you hunt you can find pictures of the internals on the internet. We (enthusiasts) can't do anything like a Rotrex (240,000 rpm!), but maybe we can get to 60,000 rpm?? using conventional roller gears.
Rotrex uses steel (?) planet gears in it's transmissions together with some funky self adjusting tensioners and secret "traction oil" to counteract the loss of traction at high speed.
Now the steel roller gears sound like a good idea to me. Given enough load (think locomotive) smooth steel wheels can hall hundreds of tonnes without slipping and with the lowest possible rolling resistance. But there is a challenge here ==> the loading requirements.
To make a single reduction gear train you will need to apply a large (20 kg+ ?) to the wheel-on-wheel surface. This load would be way too much for the puny little motors and impeller spindles.
The proper approach would involve lots of machine-shop work and expensive bits. But what if we used everyday axles designed to take heavish loads? The only thing I could think of was bicycle hubs. They're cheap, plentiful, and able to take 50kg + each.
I'm sorry I don't have any diagrams.
Imagine the impeller axle being supported by the rear bike hub (the axle moves in the hub and the is clamped)
The BLDC shaft would be connected through a polyprop-damped coupler to the front axle (hub also clamped).
Steel roller gears are mounted at the opposite ends of each of the axles.
They are made to engage under heavy load so that the gear train does not slip. The hubs should be able to easily carry this load. The gear train would hopefully be able to operate at high speed but this is asking a lot of bike bearings!
Ok. that's all i've got.. actually one more thing.
The Rotrex "traction oil". I reckon it might have the Post-It note low tack glue dissolved into the oil. Pure speculation.