I'm planning to make a "watch-key" tuner for a replica 1770s "guitarr".
The principle is simply that the strings are attached to a hook which is
part of a brass nut on a captive screw; the strings are tuned by turning
the screw.
How can I estimate the tensile strength of an M3 fine or coarse thread
in a brass nut to make sure that it's up to the task?
(ref earlier question in "watch key tuner" thread)
Dave
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:
http://www.art-robb.co.uk/EG4pix/17.jpg
http://www.art-robb.co.uk/EG4pix/18.jpg
Or a typical complete instrument:
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
http://www.art-robb.co.uk/EG3pix/fhead.jpg
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?
--
Regards, Gary Wooding
(To reply by email, change gug to goog in my address)
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
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