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To enlarge a hole for a project such as putting a new lock set on a door, the best way to get an accurate-size hole is to use two hole saws on one arbor. Use one smaller hole saw the size of the original hole and a larger hole saw the size of the new hole.
Install the two hole saws, the small inside the large one. The small one should protrude at least 1/2" beyond the larger one. Insert the smaller saw into the old hole, and carefully guide the saw through the hole. Keep the drill on a straight, steady course as the larger saw cuts the new hole around it.
A teeth and hole saw is made to cut through tough material such as a metal-clad door, but doing so can dull the teeth of the saw. Also, the heat that is generated can discolor the material.
The solution is to lubricate the saw as you go. It's easy. Use a sponge.
Sandwich a sponge between a couple of boards -- pegboard on the top works well. Use the saw to cut through the sponge.