Tap Cutter Geometry

This is my 14th post on the topic of making wooden screws. Most of the main points have been covered and the posts may even give enough information to create your own tooling. If any of the information is confusing or if you have questions please ask; you may provide topics for future posts.

The cutter for the tap is made from a piece of High Speed Steel drill rod, a little shorter than the diameter of the tap and approximately the same diameter of the thread pitch. For example, 1/4″ diameter would be good for a 4TPI thread. I make two at a time from one drill blank and then cut them to length. I can’t show the steps in making the cutter at this time but it the drawings and photos should give a good idea of the finished shape.

(above) View from the bottom showing the three relief angles at the cutting edges; one along each angled side and one to blunt the point. These are shaped last.

(above) A view from the end. The dashed (hidden) line shows the angled face that the (cup point) set screw will press against to hold the cutting face at the correct pitch angle in the tap. The flat cutting face is ground to half of the diameter of the cutter.

(above) A top view. The cutting face is shaped to the thread angle along its sharp edges. As mentioned previously my threads are angled at 80 degrees. The rectangular area is the recessed flat for the set screw to press against. (Side view below.)

A good way to start is to grind both ends to the thread angle.

Calculating the Pitch Angle

For a particular screw configuration both the tap cutter and the die cutter need to be set at specific angles to cut well. The tap cutter should be angled to match the pitch angle at the minor diameter of the nut. (see below) The die cutter (discussed in a previous post) should be set between the two pitch angles of the minor and major screw diameters so the cutter is ‘aimed in the right direction’ to follow the path of the thread being cut.

Below is an example of the method that I use to find these angles. A separate drawing must be made for each screw configuration. To get better accuracy the drawing is scaled up. I scaled this drawing up 2-1/2 times (1 : 2.5) because anything larger would not have fit my scanner.

The pitch for this screw (3 TPI or .333″) is represented by the vertical distance between the two parallel horizontal lines. Using Pi (3.14) and the major and minor diameters the 4 circumferences are calculated and laid out in vertical lines (A,B,C,D). Angled lines are drawn where the pitch and circumference intersect. These angles are measured with a protractor. This drawing shows that the recessed, angled face on the top of the tap cutter should be ground at 6 degrees to align the cutting face at that angle when the set screw is tightened. This orients the face of the die cutter at 90 degrees to the path of the thread at the inside (minor diameter) of the nut.

The two piece die cutter (see the previous post) needs to be set between the minor and major screw pitch angles; in this case between 6-1/2 degrees and 4-3/4 degrees. I would shoot for about 5-3/4 degrees. The main consideration is to leave space behind the cutting edges that is roughly equal on both sides.

Incidentally, this drawing is a good illustration of the fact that a screw is essentially a wedge wrapped around a cylinder. One of the most basic tools.

Some Interesting Facts about Wooden Screws

These observations may seem arcane, but I find them interesting.

Metal screws and wooden screws have some interesting differences. The geometry of screws is mind boggling (to me at least). As a practical matter the following observations are not very important. I spent a very productive decade or so making good, functional screws before I noticed that things were not quite as they seemed…

Metal screws are cut with a scraping action. The face of the cutter is set at the center line of the rotating screw blank. I have tried to illustrate this on the right in the illustration above. The radiating lines represent stages of the cut (every 10 degrees) to help visualize the shape of the face of the thread that is created. On the left I show the slicing/shearing action that forms a wooden screw thread. Again the stages of the cut are indicated by the radiating (but slanted) lines. When examining the finished screws, in either case you would be able to lay a straight edge along one of these (imaginary) lines showing no gap. But because the wooden threads were made with an angled, slicing cut they will be slightly hollow when viewed from the side. The drawing below is much exaggerated to show this effect.

If that isn’t enough…

Another way that the shape of the thread is distorted involves the V-shaped die cutter and its angle in the die. The sharp edges are ground to a forward slant on both ‘wings’ to create the shearing cut needed for cleanly cut wooden threads. But when the cutter is properly set the effect is to change the angles of the left and right cutting edges in respect to the axis of the screw. I have tried to show this above. The longer shearing cut of the left wing will create a greater concavity than the shorter shearing cut on the right. The two faces of the threads will be slightly different; more and less hollow and with slightly different angles. For large diameter screws with smaller threads this will be nearly undetectable. For small diameter screws with very large threads the difference will be more pronounced. (It may be possible to adjust the raking angles on the two halves of the cutter to minimize this. Perhaps I’ll try this sometime.)

You might be able to see the (very slight) difference between the left and right faces of the threads in this photo. This screw has the steepest pitch angle of my screws, with a large 3 TPI thread on a 1-1/4″ diameter screw and thus has the most hollow on the thread faces. Not much though!

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