Calculating the tensile strength of an M3 brass thread

In article , NoSpam writes Dave,
I can't be sure, but I think it highly probable that the limiting factor will be the tensile strength (or, more to the point, the yield point, which for common brasses is about 340 MPa, but with much variation, see below) of the core of the male thread. Unless you only have a couple of threads engaged, or have used a very low thread engagement % (well below 50%) the shear strength of the threads will be considerably greater.
To get the best result, use a fine pitch thread (greater core diameter) and ensure that thread engagement (nut thickness) is at least 1 diameter. You should be able to estimate the strength by calculating the UTS of that diameter brass, and apply a safety factor of your choice.
"Brass" comes in a (very) wide variety of compositions and heat treatments, so take care in selection. If you need to, you could probably find some material of brass-like colour with a yield point of 2-3 times that of common brasses. It's a bit of a minefield, if the calculations show you are near the limit you may need expert help.
David

Thanks David. The male thread is likely to be steel (hence the other question about long, fully-threaded cap screws) and the brass "nut" will be 3-5 diameters long/thick - maybe lack of experience is making me worry needlessly.
Dave

I'd go with 3 diameters[1]. Then assuming the limiting part is the screw, I don't think you will have too much trouble with strength, though you might want to avoid the cheapest and weakest options.
The maximum available force produced by a metric series nut and screw will be about 60% of the yield stress, which is the yield strength times the tensile stress area.
The yield strength will vary from about 200 MPa for ordinary brass and cheap steel, 300 MPa for 304 or A2 stainless, 500 MPa for 316 or A4 stainless, 650 Mpa for 8:8 high tensile steel, up to 1,080 MPa for 12.9 steel. [2]
The tensile stress area for a standard M3 thread is 5.0308 mm^2, so for an ordinary brass or steel screw the maximum force it can produce is 60% of 200 times 5.0308 Newtons, or 605 N, or about 60 kg.
A 12.9 M3 thread, the strongest readily available, can produce about 300 kg.
Finer threads will be a little stronger, maybe 5% - 10% or so.
An M4 thread will be almost twice as strong as a M3 thread though, and will be easier to adjust - plus the cap will almost certainly last longer before the socket gets stripped.
* And if you use eg M4 A4 or stainless or better you are now in the * comfort zone, where you aren't ever approaching the areas where things * might bend and break, which is generally much more - comfortable :)
If there's room, consider M5, or at least look at some for size.
I don't know where to get fully-threaded 60mm M3 or M4 cap screws, but some suppliers should have them but you will probably have to ask around.
Otherwise you can get partly threaded ones from eBay for about £3 for 10, and perhaps thread them to the end with a die? Again easier with M4 than M3.
-- Peter Fairbrother
[1] could the nut be bronze? A little stronger than brass, and considerably better friction and wear properties.
[2] the 8.8 and 12.9 numbers work as follows: the first number is the ultimate tensile strength in 100s of MPa, and the second is the ratio of yield strength to UTS times ten - so for an 8.8 bolt the UTS is 800 MPa, and the yield strength is 8/10ths of that, or 640 MPa.
Similarly for a 12.9 the UTS is 1,200 MPa and the yield strength is 9/10ths of that, or 1.080 MPa. These figures are minimums, the actual figures for real bolts are typically very slightly higher.

Thanks Peter, that's all very useful and has even woken-up a few brain cells in the memory department. It appears that I might have known this stuff way back in the general engineering part of my electronic engineering course - it's a shame I didn't pay more attention ;-)
I think 3mm is the largest I can get away with but I can certainly make the "nut" out of bronze.
These links show the kind of thing I'm planning to make: Or a typical complete instrument: Dave

Looking at 17, the screws seem to be about 5 mm diameter and 7mm apart - which isn't possible with socket cap screws, the heads of M5 screws are 8mm across.
M4 screws might just do, the heads are 6.7mm or so - but perhaps making square-headed screws from allthread would be better, as in many toolholders etc.
In fact, looking at it would seem that that's what was done, at least sometimes. :) Though I did think of it before I saw the picture.
This allows you to forget about buying screws to fit, and you can make your own from allthread aka studding. Just file the ends square, using a jig of some kind preferably.
As to size, if the ~5mm (3/16th?) of the first example is perhaps a bit large - there is only 2mm between threads, and the nuts may clash - M4, which should fit quite easily, might do.
I can't see the thickness of the screws in the second example, only the ends, which are about 1/8" across, implying probably a 3/16 screw is used in the second example as well.
One very big thing though, I just found out that there is quite a large bending component to the force, and the figures I gave earlier were for straight-line only, so I rather doubt that any kind of M3 thread would do. Depends on string tension I suppose, and I doubt you will be using high tension steel strings, but ..
I'd go for M5 or 3/16 in anything half-decent if it can possibly be made to fit at all, or an M4 thread in at least A4/316 stainless or 8.8 high tensile.
-- Peter Fairbrother

Which begs the questions of what the original was made from. Seems unlikely that such exotic materials were available let alone used. From the pictures the whole things looks to be made of some sort of brass.
What a fascinating group this is!
Henry

I plan to reduce the bending component by turning-down the end of the male thread so that it runs in a hole/bush and designing the female part so that it slides on the inner face of the front plate. I ruled-out square ends because of wear and the need to find/make a suitable key - I think I can get enough depth to stagger the screws so head size isn't the issue it might be. The hardness of cap screws is another part of their appeal.
Dave

Hi Dave, Could it be that the screws are supported at the "bottoms" in stead of the "tops"? In other words, could they be made to work in compression instead of tension?

That's certainly how they were made originally, but I wanted to minimise the thickness of the housing at the bottom and was also concerned about buckling - that's why I wanted to have them in tension.
Dave

How about making the screw length such that it's supported at both ends? You then have compression for strength and tension to combat buckling.