Not quite model engineering but worth a try...

Heat works. I found this out many years ago when trying to remove an oil filter bolt frm a motorbik engine: it had been well and truly rounded and *nothing* would shift it. I arc welded an extension onto it and to my surprise, it turned easily. I've been a convert ever since.
Arc- welding a large nut or temporary tommy bar (it doesn't need to complete a full turn, just enough to work the bolt loose) to the bolt head will provide leverage and the thermal shock may well loosen it, even though the heat is going to the bolt, not the axle beam.

Other people have said that heating should help but I?m not sure how. All the parts involved are almost certainly steel and hence will expand at the same rate. I can only think that lots of heat (oxy/ acetylene to a dull red heat) might change the rust to something weaker so that a few good hammer blows will shift it.
So, any and all suggestions welcome.
Cheers
Toby
-------------------------------------------------------------------------------------- Heat can be very helpful when all else fails, but beware there are no heat sensitive components such as rubber, hydraulic lines, wiring etc. in the vicinity. I used this technique years ago on car steering ball joints when the tapered section rusted into the socket, although I only had a butane torch so it was nowhere near red-hot.
Cliff Coggin.

Heating it may well help - if you heat just the bolt head it will heat up faster than the surrounding steelwork and therefore expand slightly faster. You only need a tiny differential to crack the rust seal.
Nobby

Turn a 7/8" hex down drift down to fit the bolt as close as reasonable. Preferably harden to mid 40's HRC and drive it with a demolition hammer. If left soft, allow for more clearance
Mark Rand RTFM

In article , Toby writes I have had very good success with LH drill bits in this sort of situation. As you get closer to the ID of the tread they usually grab and spin the remainder out.
As others have said, heat is also good and the arc-welding a stub on trick has worked for me too,

Toby
As others have said heat will help.
I've done this sort of thing numerous times and watched other people in other places such as car exhaust centres who also use heat to get rusted together bolts etc undone.
You need oxy/acetylene to get enough heat, a big jet because of the size of work you are doing, a slightly 'soft' flame so you don't burn the metal and be prepared to get the job really hot - almost white hot. Wear leather gloves. Have your drift and a big club hammer ready and, if you can, have someone else do the drifting while you play the flame on the job. Try not to play the flame on to the guy who is doing the drifting - they don't like it!
John H

y Why don't you hack saw the nut axially in chordal fashion. Two cuts should do it. hard work but will work. Alan

Thanks to you all for the words of encouragement regarding heat. It looks like the way ahead. Several people have suggested using an arc welder to put the heat in, even without actually trying to weld something specific onto the bolt. But I like the idea of welding a big tommy bar onto the bolt head - two birds with one stone comes to mind. I'll give it a try and report back in a week or two - off to the South West on Wednesday. Might even pass some of you without knowing it at the Bristol show at the weekend.
cheers
Toby

here's a bit of a tutorial
starts half way down the page
all the best.markj

Hi Mark
that's a really useful link and idea, thanks.
cheers
Toby

Seems like a lot of work! Why not cut the nut with an oxy acetylene, or oxy propane cutting torch? That's how I deal with that sort of thing. Replace the nut with a new one.
Steve R.

I seem to remember that one car website suggested that Coke (the drink) in original formula actually works on engine and manifold studs when rusted in. Soak the offending part in Coke overnight!
Ian Matthews recently undid a rusted nut for me by spraying it with a german product (Rust-off in German) which is a freezing spray, the change in temperature breaking up the rust (like heat only negative).
Robin

I think I've come across that one before - Rostoff Ice?
Halfords do a similar product called "Shock and Unlock" for about =A34 a can.
Colin

On or around Mon, 17 Aug 2009 01:26:24 -0700 (PDT), jackary enlightened us thusly:
I think some of you are barking up the wrong tree. The bolt is solid in the hole, the nut's off and the protruding bolt been cut, as I read it.
I assume the OP has already been down the route of plenty of GOOD penetrating oil (not WD40!) and leave it for a week.
I'd second the thing about heat, and the one about the kango hammer is worth a try.
The final option is probably to remove the axle and take it somewhere where there's a big enough press. You might get results by removing the axle, laying it on something very solid (with, obvsiously, a hole for the bolt head to move into) and, with a suitable drift, pounding it with a big sledgehammer. The key is support: when the axle's on the tractor, as I tend to assume it is, hammering doesn't work so well as it's not held rigid enough. You need good, solid support around the bolt head (a bit of VERY thick wall tube would be good). You might end up making it: take a lump bar about 4", bore for clearnace around the bolt-head, place the whole on some very good concrete or put on a wide, stiff plate. The support has to be close around the head or the axle will spring (or even possibly be damaged). You need the close support for using a press, too - but most people with presses have a stock of such things.
Don't understimate the force a good swing with a sledgehammer can generate: I was once trying to get a tubular steel gatepost (about 2½" dia) into some quite hard ground, got a chap with handy JCB to lean it on the end, and it didn't shift. The JCB is about 7 tons, and half of it was off the deck, so at least 3 tons on the post. But hammering with a 10-lb sledge eventually drove it in.