The tubs on later model washing machines are usually stainless steel, but typically as of companies now days getting all tight assed Charlie about it, the tubs are quite thin, they tend to bend quite easily, know a bloke that uses his old washing machine to puddle clays in, I had to make stainless steel washing paddles for him not a few days ago, the plastic ones lasting nothing but a few minutes, he's also having trouble with his water pump due to the small rocks blocking it up, so he's going for a small sludge pump from what he was saying, the other problem is its a real bi'arch to get all the material out, and then search through for pickers, he reckons he can sort it out, and when he does, "apparently" he's coming back to get the mods done...........
Seems like a lot of work to me, for something that can only be used at home.
As for the small quad bike motor, a few issues, 1, probarbly more horse power than you really need, and 2, most of those small motors are air cooled and need the speed of the bike to allow enough air flow past to cool the engine, for what it would cost to retrofit a small thermo fan and shrouding, you could pick up a 5-6hp motor of eBay
Hope this helps mate, best of luck.
