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Formula for Bead Cap


#1

Oh great and wise Orchidians, I’m the one writing the book. I’m
stuck with a problem. If I have a 6mm bead and I want to make a
bead cap for it, how large would I cut the sheet metal and to what
diameter would I take it to when I dap it. Let’s suppose I have
disk cutters and a block and dapping punches and a dapping block.
I’m thinking that there must be a formula for this, but I can’t find
one. I’m going to thank the Orchid list in my thank you page and
I’ll thank anyone who can give me the answer by putting their name
in the book and sending them a copy. I have an October 15 deadline
and yes, it’s really being published by a real publisher. Thanks in
advance for your help. Christine


#2

For determining the size disc needed for a bead cap, see
Silver-Smithing by Rupert Finegold and William Seitz, 1983 (still in
print). The authors present a method for determining the disc-blank
size needed for forming a bowl - which also is useful for
determining the disc size needed for any half-sphere size or less.
The authors present a graph that illustrates the method better than
words alone, but for your 6-mm bead:

-Draw a horizontal base line under a 6-mm circle,

-Draw a line perpendicular to the base line up through the diameter
of the circle,

-Draw a horizontal line through the diameter of the circle parallel
to the base line,

-Determine how far up the circle/bead you want the bead cap (your
choice), and draw a line from this point across the circle parallel
to the base line.

-Anchor the compass on the base line where it touches the circle
center line. Place the pencil end of the compass on the point where
the bead cap height is marked on the circle. Draw an arc from this
point down to the base line. Make another arc from the other side
(or make a big circle through both diameter points).

-Measure in-between the points made by the arc on the base line.
This is the disc size needed.

This method provides an estimated size because it does not account
for the thickness of the metal or the variable amount of stretching
during doming. However, most bead caps are made of thin metal and a
shallow dome does not stretch the metal very much. I included a
chapter in my book on determining the disc size needed for a
half-sphere. As well, I presented the disc size needed for 10
commonly used bead sizes. I suggest you include not only the
Feingold-Seitz method, but also (or at least) provide a table
listing the disc size needed for certain size bead caps. This is
easy enough to do and would be appreciated by your readers.

As a general rule, place your bead in a dapping block die that is
the same size; dome the bead cap only to the next largest die.
Again, this varies with the thickness of the metal and the
incremental die sizes available in your die block (it varies).

I hope this is helpful.
Nancy
www.psi-design.com


#3
   Oh great and wise Orchidians, I'm the one writing the book. 
I'm stuck with a problem.  If I have a 6mm bead and I want to make
a bead cap for it, how large would I cut the sheet metal and to
what diameter would I take it to when I dap it. 

Christine, there are two answers to this, the easy one and the righ
one. Lets look at the easy one first…

Thinking just in two dimensions (easy, OK?), the bead is a circle
of 6mm diameter. We want a strip which can be bent into a curve of
3mm radius, so that it fits snugly against the circle. Suppose we
want the strip to cover half of the circle. Now, the circumference
of a circle is Pi times diameter, or inthis case 3.14 times 6, say
approximately 18mm. Wanting to cover half the circle we take half
that length (9mm) and form it to a 3mm radius curve. If we wanted a
smaller cup, say covering just one third of the circle, we would
take a length equal to one third of the circumference. Fine, in
theory.

Going up one stage in realism and complication, but still in two
dimensions, lets say the strip is to be made from material that is
1mm thick. We require the internal radius to be 3mm, so we would
use a punch with a 3mm radius end. On the dapping block we would
use the hole of 4mm radius, to accommodate the material thickness.
Note that this is purely a geometric argument, and assumes that
there is no distortion of the strip other than pure bending i.e. the
dapping does not cause thinning and elongation. OK so far?

Now, in real life we we work in three dimensions, and there is
distortion. We can still take the geometric method as a starting
point. So now we cut or punch a circle of 9mm diameter, use the same
punch of 3mm radius and the same 4mm radius hole in the dapping
block. In all probability you will not end up with a perfect
hemisphere though. More likely a hemispherical lower portion with a
sort of collar around the top, possibly wrinkled, that would have to
be cut or ground away.

Point is though that at least you had a starting point. Now, if
this was for a one-off that would probably be the end of the story.
But if you were wanting to make a lot you would have to look
critically at how much excess material there was, and make your next
disk accordingly smaller. Then try to form it in the dapping block
using exactly the same amount of force on the hammer and the same
number of blows. But since there will always be some variation in
the forming process you would need to always use a disk that you
knew would give a slightly oversize result, so that you could cut it
back. If there is only a small amount of material to remove the
easy way is to rub the whole circumference in a circular and figure
of eight pattern on a pice of rathe coarse wet and dry paper, used
wet, supported on a flat surface.

Hope that helps, and Good Luck.
Kevin (NW England, UK)


#4

I can see some problems with the doming technique presented by Kevin
and suggestion that the discs should start out oversized. A bead
cap, sometimes purely decorative, generally is thin metal and, with
a small hole, is used to center a bead with a larger bead hole onto
a thinner strand with smaller beads. If the disc is too large (and
hit with a dapping punch that is too small), then the dome rim will
be warped as described by Kevin. But, a bead cap rarely is a plain
dome that can be sanded down past a warped or excessive size. Often
pierced, it is much easier to pierce a design on a flat disc than
after doming. And, for matching pairs, two or more discs can be
stacked and pierced as a unit. If a disc is slightly domed, the
pierce design can be over the entire surface without much worry
about distortion - as the arc of the dome is increased, the
stretching (and often destruction of the design) increases from the
disc center outward.

Also, many bead caps are scalloped into four or five lobes, as in
the petals of a flower, so that the caps will fit a range of bead
sizes. The lobed wire bead caps (decorative only) I recently made
were gently pressed, not hammered into the dapping die. These caps
extend beyond the bead diameter to overlap and were soldered in
place (that was tedious) but they could have been used on a wide
range of bead sizes. (It’s a necklace on my website.) Anyway, if
you start with the correct disc size and don’t get carried away with
forceful doming, you can make uniform and decorative bead caps
without much final finishing at the cap rim. I do agree with Kevin
about the estimated disc size being only a starting point. Whatever
method you use to determine the correct size, you need to try it out
and adjust accordingly. Hope this just adds a few more points.

Nancy
www.psi-design.com