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The process for cutting a pet door into a metal door is essentially exactly the same as that of a wooden door, except for the tools you'll need. It'll take a lot more power to cut through a steel security door, or some other kind of metal door. Because you'll need to get the right angle on it and be safe, it's better to remove the door and lay it out in a flat position. Remove the pins from each of the hinges in the door by removing the cap and gently tapping the pin out. Pull the door free and lay it out on two sawhorses placed a foot or two from the top and bottom of the door. Just as you would on a wooden door, use your level to place the template straight on the door wherever you want it to be placed. Tape it on and trace it using your marker, then remove the template and discard it. To get your cuts started, use a heavy-duty drill to start the holes at each corner of the template as before. With a metal door, it's a better idea to start with a small drill bit, about a quarter-inch or so, and make a pilot hole to open up a space for the larger half-inch hole. After you've gone around and drilled a pilot hole at each corner, put a larger drill bit in the drill and go back around to open up a half-inch diameter space. You'll need a heavy-duty saw to cut through the metal, as well as extreme caution. Make sure you've got a heavy blade in the saw and that you go slowly, so you don't snap the blade while you're making your outline cuts. Go just as you would through a wooden door, starting in the bottom left corner and working your way around from corner-hole to corner-hole. You'll probably need to hammer out the cut after you've run the saw around it. A few taps should do it, and the loose metal should fall out easily. After cutting through the metal, it's likely that the edges will be somewhat rough with burrs and little shards of metal. It's a good idea to use a file and clean up those edges to make sure the pet door fits in securely and safely, and to make sure you or the pet won't catch on any sharp metal pieces while you're working. File off especially large burrs to create a smooth edge. You don't need to be militant, just gently work off any large burrs you notice from your cuts with the saw. Don't go around so much that you make the hole bigger. After the hole has been made, installing the pet door will be exactly the same. Fix both sides into the hole, sandwiching them together and fixing them into place with screws. Hand-tighten them each, one at a time, then work your way back around the screws tightening them until the door is secure and doesn't jiggle in the space.
Remove the door from the hinges and lay it out. Trace the template onto the door in the desired location. Cut holes with a heavy-duty drill motor. Use a commercial-grade cutting jigsaw. Clean up the edges with a file. Install the door as directed.