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I took this out of a serpentine belt tensioner the other day. A former student brought it in and asked if I had any left handed drill bits to see if he could drill the broken bolt out. Instead of drilling it out, I welded a piece of rod to it and it backed right out. Most of the time they come out pretty easy. The tough ones are when someone has over-tightened a bolt that is too long into a blind hole or one that has rusted badly. Here's the procedure:
Grind a taper on a piece of round stock that's about the same diameter as the broken bolt. Make the rod long enough to serve as a handle.
Put the tapered end right next to the bolt and MIG weld the rod to the bolt. I usually start up on the rod and run down onto the bolt. An auto-darkening helmet helps to keep the rod from moving while tacking but I always keep my helmet adjusted so all I have to do is just nod my head and the helmet swings down into position easily. Either way, you have to use two hands. One for holding and one for welding. Most welding machines have a capacitor that keeps a little juice in the wire so I usually pull the trigger and feed out a little wire then snip it off. This helps get a nice start without the wire popping when you tack. Because I start the weld on the rod. I usually hook my ground clamp directly to the rod.
Spray some penetrating oil on the weld while it's still hot. This shrinks the metal and allows the oil to penetrate better. It also makes a lot of smoke so keep your head back.
Give the top of the weld a couple of cracks with a hammer. This also allows the oil to work it's way down in.
Twist the rod to back it out. Usually you have to wiggle it both counter-clockwise and clockwise. If you move it back and forth a few times, that too gets the oil down in the threads. Once it starts to move, it will usually come right out. If it feels a little rough, give it some more oil and a few more wiggles. Patience is the key.
In the worst case scenario, the rod will break off and you have to repeat the process a couple of times. The one I took out the other day was in an aluminum housing. They usually come out fairly easily because the aluminum will expand with the heat and the weld won't stick to it. Really rusty bolts like in an exhaust manifold may require some heat around the outside of the bolt to get the expansion necessary to break the rust bond. You can usually get anything from 1/4" diameter and up out this way. 3/8" and larger you can often weld a nut on top of the bolt rather than a rod as long as it's broken off flush or slightly above. Use plain steel nuts rather than galvanized, if possible. For the real tuffies, weld the rod on it, spray it, whack it and then wait for the oil to soak in. Repeat the spray and whack steps, even letting it sit over night if time allows. Patience is the key, don't forget. It took me about five minutes to get the one in the photo out. That includes dragging all the tools out and rummaging around under the bench for a piece of scrap rod.
When they come out easy like this one did you look like a genius and you don't have to worry about a hole drilled off center or breaking a tap off getting the rest of the metal out. Or worse yet, getting the easy-out out of the hole after you manage to break that off in a hole that's been drilled off center.
There you go. A shop tip from Shop Teacher Bob.