And some more recipes from a thread at AR that I can't link to...
Put your cases in a small bucket and pour boiling water over them. Put in half a handfull of Cascade and agitate for a few minutes, rinse well. Add one cup white vinegar, agitate and rinse well. Let dry on old towel.
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Home built brass tumbler...
http://www.speedsoft.com/theashes/tumbler/tumbler.html.........
For heavily tarnished and dirty brass you can use a mixture of 1 quart white vinegar to which you add a tablespoon of salt. Soak and occasionally agitate the brass. It will be clean, if not quite polished, in about 30 minutes. Can't get any cheaper than that.
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You can buy a Krazy Kloth, an impregnated cloth, in the kitchen utensils section of your supermarket. Wipe the brass with that, let it set a few seconds, then wipe with a paper towel. Really polishes it up. Some folks use that to clean the brass immediately after firing but if you're as cheap as you say, that would mean the cloth would gather lots of carbon over a couple of hundred round of shooting and you'd have to spend another $3.95.
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I use a bit of white vinegar, a little truck wash and hot water. In say, a 2 gallon bucket, about a cup of vinegar,2 capfulls of truck wash and half fill with hot water.Stir occasionally.After an hour or so, tip out ,pick up shells and rinse with hot water.I then usually leave them on the hot water system for a day or so to dry out.
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I made my case tumbler from a $5.00 thrift store Ice cream maker. The kind with the bucket on the outside for ice and a canister inside for the ice cream.
All I did is remove the agitator from inside, I put some thin foam rubber stuff with a sticky back on the inside of the canister just because I thought it might work better. Then I took a small 2X4, about 6" long I guess, and attached it to the top outside of the bucket. Throw in some tumbling media, brass, tip it on its side (thats what the 2X4 is for) and plug it in.. Walk away and an hour later Voila! youve got clean brass.. The media costed more than the tumbler..