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Your typical screw-extractor system involves drilling an ordinary hole into the end of the broken bolt, and then jamming a special tapered tool into the hole. The tool grips the bolt and lets you turn it, to remove it.
It is not always effective, though. Some bolts are made of tougher stuff than
others, and the special tool fails to grip properly, so it turns, while the bolt doesn't.
So, here is a better way (see link).
It is possible to drill a hole that is mostly square, instead of round (the corners will be rounded slightly, instead of being perfectly angled). The trick has two parts, of which one is a somewhat special drill bit.
The most important part of the trick, though, is the chuck that holds the bit. This chuck not only rotates, it also revolves (the way the Earth both rotates while revolving around the Sun). That motion, coupled with the shape of the drill bit, causes a mostly square hole to be drilled.
After you have a mostly square hole, all you do is insert a matching mostly square tool that resembles an "Allen wrench" (which has a hexagonal instead of a square cross-section). Now you can easily turn the broken bolt until it comes out.
Drilling a square hole
As mentioned in the main text. [Vernon, Aug 18 2012]
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||Nice idea. Question, though - it's not clear to me
how the square-hole-drilling arrangement is braced.
I get the impression that you can't just apply the
square-hole-driller to a bolt in the same way that
you can apply a round bit to a bolt.
||I thought this was going to be a method of getting Usain
Bolt off the track after some disastrous injury.
||It should be possible to drill a narrow pilot
hole, then use that as a guide for the
metaeccentric follower drill.
||It might be better to drill a regular polygon
rather than a" square" hole.
||I have a sneaking suspicion that any bolt hard enough to
give a traditional extractor problems is also going to give
this style of square bit problems. You're looking at a lot of
side load on a (relative to hole size) very narrow bit.
||The object is to remove the damaged bolt.
One way of assisting in that process would be
to have a left-hand twist on the polygon bit,
run at low or moderate speeds, and provide a
||The work would be deeply heated by the action
of the drill, and the applied torque would tend
to loosen or indeed unscrew the stub.
||Best case, you might not actually need a
polygonal wrench at all.
||Use a very narrow end mill to cut X pattern slots in the bolt and and use a Phillips screw driver?
||Great of you've got the part on the bench.
Maybe not quite so great if you're lying on the
tarmac reaching up into a confined space to
try and extract a sheared manifold stud
without having to pull the entire powerplant
out of the vehicle.