Modified Square Threads

Since no one has replied yet, I'll just ask this : Where does it say that a ten degree thread is more difficult to machine than an Acme ? (I'm just curious - I expect it is, somewhat). What I can tell you is why a square thread is more difficult than an Acme or ten degree, although I expect you know that. If you are basically making a worm, why not make it, say, 20 degree (you'll get stronger teeth), and design the thread form just as you would for a worm. I think you are going to have to make custom tooling anyway, so you might as well design it from scratch using gear theory. I doubt if you could get an off-the-shelf die for a ten degree thread form. Even Acmes are sometimes difficult to find.

By now, I would have expected you to respond and say that I've completely misunderstood what you are doing and my answer is mostly irrelevant. I daresay the screw does not drive the rack directly by meshing with it - you probably have a nut fixed to the rack. Right?

I have read that a 10 degree modified square thread is more producible than a square thread. The standard ACME thread has a 29 degree included angle. So I am only assuming that an ACME thread is more producible than a 10 degree modified square thread, based on the larger included angle.

I have inherited an existing design, and am not able to make significant changes (i.e. changing the thread form) at this point. During initial grooming of this equipment, this design has had considerable problems with the meshing of the threads (once per revolution clunks, etc.). I'm not sure if this thread was dimensioned properly, but reference material on this thread is extremely limited. I have found the information provided in Machinery's Handbook duplicated in other references, but nothing beyond that.

The screw directly drives the rack. The rack is basically a segment of a nut. Since the nut does not fully encircle the screw, the height of the rack relative to the screw must be established at assembly. At each revolution of the screw, the start and end of the thread are engaging/disengaging the discontinous thread on the rack. This is where the once per revolution clunk originates. Which brings up another question... what should the start of the thread (Higby cut?) look like?

So I did interpret it correctly (sort of).
There is a big difference between cutting a square thread and cutting a thread with angled flanks, especially if you are doing it on a lathe with a single point tool. When you cut a conventional thread, you normally arrange to remove nearly all the material on just one side of the thread - you get a much better finish that way. You do this by setting the tool up so that it can be progressively fed in at an angle (29.5 degrees if you are cutting a standard thread, 9.5 if cutting a 10 degree). But with a square thread, you can't do this. You have to finish each side of the thread separately, and use a narrower tool. But the difference between a 10 degree and an acme would not be so great.
As I said, can't help much with the dimensions. You need to reverse engineer them by the sound of it. You may need to try and figure out the intended profile using an optical projector - you can use castable metrology resin to investigate the nut threads. I've never heard of a "Higby" cut (along with many other things !). But I don't see why you should get a major "clunk" if everything is made and set up correctly. However, if you are remaking the external thread component, (which appears to be shorter than the rack), you could easily arrange for a progressive lead-in and lead-out at the ends of the thread simply by chamfering the blank before cutting the threads, (or chamfering the threads themselves if you prefer).

For pure power transmission with no requirement for backlash control a square thread is the best, for accurate backlash control the thread angle must increase...friction goes up as well. The Acme is a good compromise.

Higbee cuts should have a 45 degree lead-in although I have seen cuts beginning with a milled half radius on some equipment. To prevent your clunking problem use 2 half nuts that fully release at the end of your stroke/cycle much like a lathe lead screw. The single half nut idea your working with is pure nonsense, why reinvent the wheel?

icepack : There is nothing wrong in principle with your concept - it has been successfully used for many years for large machine tool table dives and I'm not aware of any "clunking" problems. We had one on a machine at the last company I worked at - worked fine. One version (the Johnson Drive) uses a hydrostatic worm - I think the worm thread is about 12 degrees on those, but I could be wrong. But I still don't know what a Higbee (Higby?) cut is - apparently everybody knows but me !

By the way - the reason they don't use a square thread on a Johnson drive is partly because of assembly and disassembly considerations.

Another place this principle is used in on chucks. I have a four jaw lathe chuck in my home shop, and have been examining it. In this case they appear to have used an Acme thread. But there is no special lead-in at the ends of the "worm thread" - just a 45 degree chamfer. There is no once per rev "clunk", even when the chuck jaw "rack" has passed beyond the end of the "worm" thread. In my view, something has been made or designed incorrectly in your case - but the only way to find out is to measure everything.