# Question about minimum wall thickness of an internally threaded tube.



## magpens (Feb 4, 2021)

In this thread, I am appealing to your love of engineering detail, and to your experience with engineering calculation.

I do the following calculations in metric but have also included inch dimensions in square brackets [ 1 mm = 0.03937" is used for converting units ]

I have made an internally threaded tube, two inches long, from a solid metal rod (aluminum or brass) .
The outside is a smooth cylinder with diameter of 11.25 mm [ = 0.443" ]

The starting rod is first drilled axially before tapping.  The internal threads are made with a M9 x 0.75 tap (Tapco).
According to usual practice, I chose a drill size for tapping of 9 - 0.75 = 8.25 mm [ = 0.325" ; actually drilled with 0.328" or 21/64" drill ]

Measuring the cylinder ID after threading now gives 8.32 mm [ = 0.328" ]. . The measuring calipers, of course, contact the valleys of the threads.
The OD of the cylindrical tube is the same after threading as before threading, so there has been no stretching of the cylinder OD.
This measured ID seems to be a reasonable result for the internal diameter after the specified threading operation.

The resulting internally threaded tube is weakest where the thread profile comes  closest to the external surface of the cylinder.

I now need to calculate the expected minimum material thickness in the wall of the cylinder after threading. . This cannot be measured.
What follows is all pure calculation and is based on the reasonable results described above for the threading operation.

I would expect the threaded wall to have a minimum thickness of ( 11.25 - 9 )/2 = 1.125 mm [ = 0.044" ] .... your opinion is needed on validity of this number.

This  "minimum thickness"  would occur at every peak of the threading.

Does this calculation/result seem to be reasonable and likely to be correct to a good approximation ? . Thank you for any input you can offer.

Final question ... how much do you think I could reduce the external tube diameter ( current value is 11.25 mm ) and still retain integrity during tapping ?
The material is either aluminum or brass. . Thank you for your input.


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## McKenzie Penworks (Feb 4, 2021)

Question back... What's "retain integrity" mean to you? The stresses on a pen are vastly different than say the stresses on a threaded lug nut...


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## Carl Fisher (Feb 4, 2021)

My perspective has been if the walls are thick enough to allow me to thread without cracking, that's good enough for a pen. If they crack while threading, that's too thin 

Anything else and you're overthinking pen making.


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## magpens (Feb 4, 2021)

McKenzie Penworks said:


> Question back... What's "retain integrity" mean to you? The stresses on a pen are vastly different than say the stresses on a threaded lug nut...



"Retaining integrity" means, as I tried to make clear, to "remain intact during the tapping operation" which creates the threads.

I am not so concerned about post-tapping stresses when the item is "functioning in normal operation", whatever that might mean.
The stress during tapping is, by far, the greatest stress this part will ever experience.

I realize that there is some subjectivity to the considerations I am posing.
It might even be possible to do the outer diameter reduction (from, say, 0.5" stock or 0.625" stock) after the tapping has been done.

Of relevance is the height of the thread. . For a M9 x 0.75 thread, assuming a 60-degree thread profile, each thread from valley to peak has a height of 0.75 mm [ = 0.030" ]. . That height far exceeds the wall thickness (typically about 0.010") of the brass tubes typically supplied with a pen kit.
Of course, brass is very malleable. . So a typical pen kit brass tube can be internally threaded to a profile height that exceeds the wall thickness if you can tolerate the stretching of the tube. . That would not be acceptable in my application. . I need to accommodate the full height of the thread profile without significantly stretching the material being threaded. . I need this in order to allow free motion longitudinally during frequent threading and unthreading of the finished threaded parts.


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## More4dan (Feb 4, 2021)

Your calculation is correct, the OD minus the Thread diameter of the tap divided by 2 to get wall thickness. I try to leave 0.020 inches as a minimum wall thickness for metals. I do tap first and turn down after if it is going to be close. Try it on some scrap and do some testing to see how it holds up to abuse. Of coarse any external threading of the pen body further reduces the wall thickness by the thread pitch. I will thread the ID of a pen body first and then the cap OD last if the wall is getting thin. One could always add a threaded ring to the OD for back up when tapping, or a threaded plug when threading the OD to be safe. 

Danny


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## magpens (Feb 4, 2021)

@More4dan

Thank you for your reply, for basically confirming my calcs., and for the suggestions. . In my application, no external threading will be required.

What is central to my considerations is the knowledge of the height of the thread (valley to peak) for typical tapping operations. . I think you have corroborated my thinking to a large extent. . Thanks for that.


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## More4dan (Feb 4, 2021)

Metric makes it a bit easier. The pitch is the maximum difference in OD and ID of the thread. The OD of the hole can be a bit larger based on the tap drill you use and the OD of the male thread can be a bit smaller depending on the tendon you turn. But a 9mm tap will usually cut a 9mm ID thread and a 9mm die will cut to 9mm minus the pitch. 

Here is a great reference that calculates all the critical dimensions and tolerances for threads:






						Metric screw thread: M Profile calculator
					






					theoreticalmachinist.com
				




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## magpens (Feb 4, 2021)

@More4dan 

Thanks again, Danny. . That is a very useful reference for when we get into the intricate details of threading.


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## Paul in OKC (Feb 6, 2021)

I would say you're very close with your calculations. Only thing is your internal thread major diameter may be slightly larger than 9mm just for the sake of thread clearances. 9mm would be the minimum major diameter on the internal part. I think most taps are slightly larger than nominal, but very slight. All that said, shouldn't be a problem.  I would think in metal you would be safe at that wall thickness for pens.


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## magpens (Feb 6, 2021)

@Paul in OKC

Thanks for your comments, Paul. . It is good to get another confirmation of the analysis.
As you say, the major diameter of the internal threading could be very slightly larger than 9 mm.
The amount of the "overage" would depend on the material and the lubrication during threading, among other factors.


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