At one time I also thought a lot about thread dimensions and tolerances. After looking at the drawings in Machinery's Handbook and the tables showing the dimensions and the allowable tolerances for the various classes of fit I found myself very confused.

It was only after I thought about how screws, bolts, and nuts are MASS PRODUCED that the above drawings and tables started to make sense. We, poor machinists have very little say in how these drawings and tables were drawn up. It is the manufacturers that make the threads by the hundreds of millions, by the billions who have the real input here. You need to think about how an exterior thread is ROLLED between two dies with the thread form on them. About how those dies will WEAR. About where they start when new, before that wear occurs. About how they are adjusted as they wear. You need to think about things like that. And how many threads can be produced before the dies must be adjusted. How many can be produced before the dies must be replaced.

Those are the considerations that are the primary reasons for the thread drawings and the tables and the tolerances.

When you see a dimension as a fraction of the pitch that is NOT a typical number. It is a maximum or a minimum number that represents the point where one of those dies is worn past the point of producing a thread that is in tolerance. Thus, your drawing shows a crest on the exterior thread as P/8 and the size of the valley in the interior thread as the same P/8 dimension. BUT those numbers almost never occur in the life cycle of a pair of dies or of a tap for making the nut. Those numbers are where the two threads, external and internal, will MEET lacking any clearance. Then clearance is added to one or both to allow them to not interfere. And that is still the end of life of the dies and taps. So even more is added or subtracted when making the dies and taps so that there is some room for them to wear while still guaranteeing that there will be the amount of clearance required by the class of fit being made.

And I only mentioned one pair of numbers. But the same applies to all of the numbers involved in making the threads. The wear on the dies and taps may be greatest at the tops of their teeth, but they will wear at other parts as well and different amounts of allowances must be made to ensure that all parts of the thread form will be in tolerance through out the life of the dies and taps.

A good example of how this actually works is if you notice the P/4 dimensions for the valleys between threads. If you examine any number of commercially available screws and nuts, you will find that you almost NEVER see any that approach that number. In fact, they ones that I have examined under magnification almost always have this dimension a lot closer to P/8. And I must conclude that P/8 is the real nominal number that these manufacturers always shoot for. And they retire their dies and taps long before they are producing anything remotely close to the P/4 number. YET, P/4 is the number that you always see. It is the absolute limit of permissible wear, not a nominal or average dimension.

When I reached this conclusion, this revaluation I finally understood the real purpose of the published drawings and tables. This is when I knew that it was completely useless to try to model threads in any CAD system with any exactitude.

If you need a 3D CAD model of a thread for 3D printing I will suggest two things. First, most 3D modeling programs will have threads built in. JUST USE THEM and make a test print. Adjust as needed. If you absolutely must do the modeling yourself, then do this:

1. Make the OD of an external thread a bit smaller than the nominal screw diameter. This is what the published tables show anyway.

2. Make the pitch diameter a bit small on external threads and a bit large on internal ones. Again, the published tables can help here.

3. Make the flat at the top and the fill in the valley P/8. Either can be either flat or a radius, but keep the final form INSIDE of that P/8 straight line.

Threads that are 3D printed with those rules will probably fit each other and also purchased fasteners. If you must have a percentage number for the smaller and larger numbers, use 2% or a minimum of 0.001" / 0.025mm.