I've used several methods over the years, and often achieved bad outcomes in cases where the head of the bolt or screw was missing and the thread was locked in place over a considerable length. Here is what I consider a sensible list of approaches for cases where the situation is not too bad:
http://www.motorcycle.com/how-to/how-to-extract-stuck-screws-3440.htmlIn fairly extreme cases, where the screw is either heavily bottomed in the thread or is frozen along its length, and the entire head and shank of the screw or bolt are broken off below surface level, there are a couple of correspondingly extreme remedies that may be worth a try. Strange as it may seem, I've succeeded fairly often with a simple solution. I find or make a hard, sharp punch that I can apply as near as possible to the outside of the broken off end of the screw, and tap it anticlockwise with a small hammer. It usually can be made to unscrew, unless the screw or bolt has broken off a long way below surface-level. Remember, the tip of the punch has to cut into the surface of the screw or bolt, but not touch the internal thread in the mating component. I always try this method first, because the alternatives are more difficult and more likely to make the situation worse.
If that won't work, there are two other things I choose between, depending on circumstances. If the internal and external threads are not all that heavily bonded to each other (i.e. the bolt was broken off or bottomed and twisted off, rather than rusted-in), I usually drill down the center of the screw or bolt and use a stud extractor. I only use an easy-out if the screw is actually loose in the housing, because they always expand the shell of the screw and make it a lot harder to remove. Instead, I use a proper stud extractor: a very strong parallel device with a few very shallow splines down its length. These do not expand the shell of the screw much, and can deal with rather high applied torque levels.
If the internal and external threads are heavily bonded to each other by loctite or corrosion, I try the use of heat. Use a small tip on an oxy torch, and apply the tip of a neutral or reducing flame to the center of the screw (Preferably don't heat the external component: you may ruin it). Briefly heat the screw red hot and let it cool. Repeat a few times. Then proceed to try the punch solution above. If that fails, drill the screw and try the stud extractor. If that fails too, I am stuck with either drilling the whole screw out and tapping the hole oversize, or taking the component to a commercial place that removes the screw by electrical discharge erosion. This will destroy the external thread, of course, so I tend to drill it out myself and retap it, to save the cost of the spark erosion process.
