Morse tapers are used throughout in machine tool design in spindles and other areas that accept tooling. The tapered arbor or center is inserted in a matching tapered hole that effectively locks the tool against rotation or pulling out. Morse tapers are rated by numbers from 0 to 6 with #1 through #3 being the more common sizes used in most small to medium size machines more likely found in home shops. The angle or the degree of taper does not change but instead, the cross section of the morse taper becomes wider as the number increases. Other types of taper configurations exist but we will not likely need to get involved with them.

There are some rather difficult formulas to figure out the exact angles to set the lathe compound to cut a taper of the same degree of slope. I think that some people like to make things as difficult as possible to sort of show the world how bright they think they are. The easiest most painless way to duplicate a morse taper is to chuck an existing dead center or better yet, a morse to straight shank adapter by the straight portion and then snug up the lathe live or dead center against the center hole that will be found at the tapered end of the morse adapter to make sure that it is being held as true as possible. With a right to left cutting tool on the tool post, adjust the angle of the compound slide so that when the slide is advanced from the far right ( tail end ) toward the head stock, the tip of the tool is just touching the tapered side of the adapter. If it touches only on one side and then moves away from the tapered surface, you will need to reduce the angle slightly and vice versa. Play around with the compound adjustments until the tool is constantly touching the taper along the whole length of the sample morse taper. The length of the tapered shank is a constant as are the diameters at both the widest and narrowest portions of the taper. measure these points on your sample morse taper adapter and save them for future reference Starting from the right, begin to take light passes toward the left by advancing the compound slide and advancing the cross slide .010" after each turning pass to deepen each cut. As you begin to reach a point where you are tapering the total length of the taper, you will need to begin to measure the two diameters at each end to determine how much further you need to continue cutting. The last two thousand should be cut at high speed with a good cutting oil to help produce a smooth clean surface. You can directly check for fit by removing the tail stock center and after loosening the tail stock, slide it over and insert the newly machined center into it should lock after only slight pressure.