Hi Jim,

Two points:

(1) Yes, tapered threads are supposed to be tightened until they “jam” together forming a tight seal. In fact, the two surfaces are supposed to slightly deform each other (very slightly), from what I understand. However, in *theory*, there should be *no voids* for a perfect thread, screwed into a perfect nut or coupling. (Okay, some minor technicalities at the rest and roots of the thread, but the flat parts of the thread profile should, in theory, generate no voids if geometry were perfect.)

(2) I’m almost sure, that the deviation from the normal frame will not be consistent for a tapered thread. I’ll try to make a demo for this. In fact, I thought exactly as you do, and was then *confused* about why my surfaces didn’t join together.

Some initial intuition for now:

(A) A 2d Archimedes spiral, or arithmetic spiral is actually *pretty weird*. Every time it crosses the x-axis, it crosses at a *different angle*! This is extremely different from a geometric spiral, which always crosses the x-axis at the *same angle*.

(B) Our tapered thread is based on an Archimedes spiral, just one that moves upwards in the Z-axis.

If you like, a 2d Archimedes spiral in the XY-plane is just an extreme version of a tapered helix. It’s so tapered, it’s flat! (Taper isn’t just a few degrees, it’s 90 degrees.) So if your intuition is correct for all tapered threads, then it should be true for threads that are (almost) tapered at 90 degrees. Say, extreme cases where the taper is 89 degrees (almost flat!).

I’ll make a demo of this, and post it shortly.

btw, I’ve been interested in posting about all this, because I was very surprised by it, myself. And I had the same intuition as you did, until I tried making actual geometry in Rhino.

Sincerely,

–Anthony K. Yan