Since this thread is so long with lots of different suggestions/ thoughts, I figured I would add some of my own. It may or may not add to the OP original problem, but may help think about future projects.
The info about the smartest engineer who said 3 threads are needed for greatest strength, may be right, but only for a given size of thread.
I was alway told that generally, you only need the length of the thread equal to the diameter of the thread. But, when you start doing the actual calculations, you need to know a lot more variables. What is the materials type of threads. Aluminum, vs steel is going to make a big difference.
Fine thread, or course thread? Fine thread usually has a higher clamping force, and shear force, and thus a higher torque number too. But when you think about it closely, this is because the root of the threaded bolt is bigger in diameter, because the threads are not as deep as coarse ones.
What type of class fit. And are the threads in tolerance? The class of fit is basically how much metal to metal interlap contact is there theoretically. If I am single pointing threads, I can make over size the pilot hole size in the female thread but still get a tight fitting thread even though the root diameter is much bigger than tolerances call for. You would not realize it is not as strong a thread as normal.
A couple weeks ago, I was making a change on a part I was fabricating. I was reducing the length of thread engagement, and I needed to verify that I still had the needed strength. I needed to know the material, pitch of thread, diameter of thread, and the class of thread to make the calculation. Still then, I am still slightly over whelmed with the actual math needed to make the calculations. I am not a degreed engineer, I just play one at work.
But I work in hydraulics. If one of my threads fail, someone can get hurt. So we needed some math backup to quantify our changes were sufficient for job at hand.
Threads can be a huge rabbit hole to run down, realizing how many different variables it can have.
Oh, I have also been finding a lot of problems with store bought nuts lately. It seems quality control is a big problem in factories today. The threaded holes can be off .030” perpendicular to the nut end. I sometimes have to take a trueing cut on the nut, so it will tighten down properly. In order to do this correctly, I tighten it down on my threaded part so I know I am machining the face consistent to the thread. I can’t trust the threaded hole to be in alignment with the hex body. This is fun because I usually use Nylock inserted nuts, and I need to use the face I am facing off, for the locking to the threads. ( usually these nuts are 1-1/2” or 2” x 12tpi. A lot bigger than most of you deal with in home shops, but my problems can be the same, just on a bigger scale)
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