Idler pulley Bolt broke, can the Bolt be replaced?

Welcome to our world. This happens too often. First check if the broken bolt is in a bracket that can be removed so it can be worked on, on a workbench. Most often this happens when the bolt is run into a piece of aluminum. Drilling the bolt out is the least preferred method. It's almost impossible to keep the drill bit centered. We don't want to drill through the threads. This is even more critical if the bolt goes into a "wet" hole, meaning coolant or oil is on the other end it. Liquids will sneak out past the threads if we drill into them.

I've had unexpectedly good luck with welding a nut to the remaining part of the bolt. If there's enough left sticking out that you can grab it with a vise-grip pliers, heat the bolt first with an acetylene torch, then quench it with cold water. That will shrink and shock the bolt and crack the bond between the threads. Wind the bolt out with the pliers.

When that doesn't work or when the bolt is snapped off flush, my procedure is to use a pair of pliers to hold a new nut centered over the bolt. First heat the bolt orange-hot with the torch. You may never get it that hot as the heat will be sucked away too quickly, but any heat is better than none at all. Have a helper standing by with a wire-feed welder. One of you takes the torch away then the other places the nut centered over the bolt, holding it with a pair of pliers. Use the welder to fill the hole in the nut. The goal is to hit the bolt with the weld, not the nut. The metal the bolt is screwed into is going to act as a heat sink and quickly try to cool the bolt. The goal of heating it first with the torch is so the weld can develop good penetration and melt solidly into it. As the weld builds up, it will fill the hole in the nut. That nut should be kept as cool as possible to reduce the chance of melting it. Stop welding if you see the nut start to melt away. Let it cool for a minute, then hit is lightly with cold water to shock it. Use a box wrench or a socket to unscrew the bolt.

Don't panic when the nut breaks off the stud. A student broke one of the bolts for the thermostat housing on my '88 Grand Caravan. It turned into a dandy teaching opportunity, but it took five tries before the stud came out. Use a new nut each time. If access is limited, heat the bolt first, then immediately weld a small ball of metal to it without the nut in the way. Here again, the goal is to get good penetration so that blob won't twist off. Once the weld is solid, put the new nut over it, then continue welding right away while the heat is still there. Stay away from the nut as long as possible so as much heat as possible goes into the bolt first, then finish up by welding the hole closed in the nut. Don't use water on it right away. Wait about a minute, then sprinkle on a little water. This is a very poor way to expect to make a quality weld. If it's cooled too quickly, the shock is likely to crack the nut off. If left to cool a little first, the bolt will have time to shrink, and the weld is very likely to be good enough to let you run the bolt out.