This post will attempt to explain a method of designing a thread of any size; a necessary step before starting to make the threading tools; tap and die.
(1) Choosing a Thread Angle
The first step is to decide on the THREAD ANGLE. Many threads in metal and in wood have 60 degree thread angles. I prefer a flatter thread of 80 degrees. This way the threads are less sharp and less vulnerable to chipping. They are also a little stronger since the forces created by the angled faces of the matching threads tend even more away from shear and towards compression as screws are tightened. All of the presses pictured in my website and posts use 80 degree threads. I will show how to design 80 degree threads using inch measurement. The same principles can be applied to other thread angles and to metric measurement.
(2) Establishing a ratio of Thread Height to Pitch
This triangle represents the geometry of a single thread in cross section. Measurements taken from this simple drawing can be used to calculate a wooden screw and matching nut of any size and pitch. There is likely a way to determine the height of an isosceles triangle with an 80 degree apex angle. Since I don’t know the math I use a protractor and rule to make an accurate drawing to measure from. Making the drawing large insures that the measurement will be more accurate. For this method all you need are a (somewhat arbitrary) thread PITCH (here represented by the 8.000″ base) and the THREAD ANGLE which is 80 degrees. Once I completed this drawing I took the measurement of 4.775″ from the drawing using a vernier caliper. This establishes a ratio which can be used to calculate the BASIC THREAD HEIGHT of ANY thread with an 80 degree angle.
(3) Using the ratio to calculate Thread Height.
Using 8″ as the pitch of this imaginary thread (which would make a truly huge screw) works very well for my collection of thread pitches. These include 4 TPI (1/4″ pitch), 3 TPI (1/3″ pitch), and 5 TPI (1/5″ pitch). All of these can be divided evenly into 8″ so determining the BASIC THREAD HEIGHT of any of these is simply a matter of dividing 4.775″ by the appropriate number:
8.000″/.250″ (1/4″ pitch) = 32. It follows that 4.775″/32 gives a basic thread height of .149″ for a 4 TPI thread.
8.000″/.333″ (1/3″ pitch) = 24. It follows that 4.775″/24 gives a basic thread height of .199″ for a 3 TPI thread.
8.000″/.200″ (1/5″ pitch) = 40. It follows that 4.775″/40 gives a basic thread height of .119″ for a 5 TPI thread. (I will use this thread as an example throughout this post.)
At some point I may attempt a 6 TPI extra small screw and a 2 TPI extra big screw. Both of these (or any pitch actually) can be calculated using the same 8 : 4.775 ratio.
(4) Truncated Thread Height
The next step is to calculate the TRUNCATED THREAD HEIGHT. It is best for the actual wooden threads to be truncated. Having sharp threads (internal or external) serves no useful purpose and makes the wooden screws vulnerable to damage. Subtracting 1/8 of the basic thread height from both the top and bottom of the basic thread height will give the truncated thread height. This leaves 3/4 so multiplying a basic thread height by .750 will yield the result that you need. As an example the truncated thread height for my 5 TPI thread would be .089″ (.119″ x .750 = .089″).
The drawing above shows how the original full-sized thread and the truncated thread fit within the context of a threaded hole.
(5) Establishing Major and Minor Nut Diameters
The best way to design a new thread is to start with a standard size TAP HOLE for which tooling will always be available. For wooden screws a Forstner bit used in a drill press is the best approach. Choosing the actual hole diameter and adding the truncated thread height (twice; once for each side) will yield the next two dimensions; the MINOR DIAMETER OF THE NUT and the MAJOR DIAMETER OF THE NUT. (“Nut” here refers to anything that includes a threaded hole even though it seems odd to refer to a press jaw as a “nut”). The minor nut diameter is fixed by the size of the hole which is bored to receive the threads. Using a tap to scrape away waste to create a thread to the depth of the truncated thread height yields the major nut diameter. Using the 5 TPI thread as an example the minor nut diameter is .875″ diameter (7/8″). Adding the truncated thread height (x2) to that yields a major nut diameter of 1.053″. (.875″ + .089″ +.089″ = 1.053″).
This drawing should be imagined as a screw passing through a threaded hole. The narrow spaces between the pairs of outlines represent the necessary clearance, ‘looseness’, or ‘play’ between the parts.
(6) Sizing the Screw for proper Clearance
The next step is to determine the dimensions of a screw to fit in the threaded hole. The screw needs to be sized to create the proper amount of CLEARANCE. Clearance is needed to insure that the screw and nut can work freely through all seasons of the year. As humidity increases in summer and decreases in winter dimensions change slightly. The pitch of the screw will remain constant (since wood doesn’t change dimension longitudinally) but the pitch of the nut will change (since wood changes significantly across the grain). If that isn’t enough the screw and the threaded hole will both become slightly oval during parts of the year. Creating enough clearance will prevent any of these fluctuations from becoming a problem.
To create clearance the nut diameters are reduced by same amount that was used to truncate the thread height earlier. To calculate the MAJOR DIAMETER OF THE SCREW subtract the same truncations (1/8 of the basic thread height) from the major nut diameter. Again I will use our example of the 5 TPI screw. First, divide the basic thread height of .119″ by 8 to get the result of .015″. This needs to be subtracted from both sides of the major nut diameter to create the MAJOR SCREW DIAMETER. In this case 1.053″ – .015″ – .015″ = 1.023″. This in fact is the size of the opening in my die which is used to make these 5 TPI screws.
Making the screw and nut to the above dimensions will still leave room for some adjustment. I prefer to tap holes deeply; leaving only a minimal truncation on the minor diameter. You can see this above. The internal threads are practically indestructible and only subject to wear, not breakage. Tapping the holes deeply leaves room to thread the screws with wider truncations on their major diameter to make them stronger and less liable to damage. You can see this below. I make the cutters (both tap and die) with sharper tips than those calculated above with the standard truncations; it is better to have the cutters more ‘pointy’ than less. How pointy is largely a matter of preference; I have seen screws cut to full depth with no flats left at the bottom between the threads. This would have no real effect on strength for either internal or external threads.
You may be wondering about the holes that need to be bored in the unthreaded side of a press. These need to be large enough for the wooden screw to pass through so than the two press halves can be pressed together. My solution is to choose the next bigger standard Forstner bit to drill these slip holes. A part of the shank is then turned oversize to fit these larger holes so that the fit isn’t too sloppy.
You can see the oversize diameters turned to fit the slip holes in the unthreaded half of a press. The thread can never be cut completely to the shoulder so a portion must remain at the smaller diameter as you can see on the left.