This section is from the book "Machine Shop Work", by Frederick W. Turner, Oscar E. Perrigo, Howard P. Fairfield. Also available from Amazon: Machine shop work.
Lapping is a term applied to a particular method employed in the grinding out of holes. The lap consists of a cylinder of soft metal run rapidly inside the hole to be lapped, and covered with emery and oil at the same time. The surface of the lap should invariably be of soft metal. It may be made of copper, or it may be an iron bar with a covering of lead or tin. It should be turned slightly tapering at each end, so that it will enter the hole. At the middle, it should be a snug fit.
The end of the bar is run through the hole and set on the lathe centers with a dog to drive it like an ordinary mandrel. It is covered with oil and sprinkled with emery. The lathe is then run at a high speed, and the work moved to and fro over the lap. Light pieces may be held in the hand. When this is done, care should be taken to turn the piece so that the grinding may be even over the whole circumference. The tendency, when holding work in the hand, is to allow it to rest upon the top of the lap; this causes the grinding to be done on one side of the hole unless the piece is frequently turned. Laps may be used for grinding holes true and parallel. For this purpose the work should be accurately centered with the lap, and firmly bolted to the lathe carriage. The lap is then run at a high speed, and the work moved to and fro over it.
Laps are sometimes used for grinding flat surfaces. In such cases they are in the form of discs. They are put on the lathe spindle in the place of the faceplate. The work is then pressed against the disc. As the outer edge of the disc has a higher speed in feet traveled per minute than those portions nearer the center, the grinding is more rapid at the edges. The work must, therefore, be constantly turned if it is held in the hand. The best way is to clamp it firmly on the lathe carriage, and press it against the lap by means of the hand feed.
 
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