I tried it with a belt-driven lathe, couldn't get the metal red-hot without the help of a propane torch. The pieces stuck together but broke apart easily.
Unless the rod is well and closely supported it tends to bend and run eccentric once the surfaces start to gall together.
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You have no idea!
This is actually how the long shafts on many modern day jet aircraft engines are joined. I'm not sure exactly how many are, but I have seen the Pratt & Whitney promo video on this being done on the JT8-217 engine, and was told at the time it was also used on it's little brother, the JT8-D as well.
Theses engines were made famous on the McDonnell Douglass MD-80, and Boeing
727 aircraft.It's really a pretty amazing process.