Good day. I just finished the initial welding on a damascus billet I'm working on. The welding went suprisingly well! The piece is currently 1" thick by 3/4" wide by 6-1/2" long. I want to draw it out to about 1/2" thick by 1 inch wide by ??? long before cutting, folding, and welding again. I'm wondering, is there any sort of mathematical formula that I can use to figure out roughly how long the piece will be given the current and desired dimensions? I realize this is very dependant on several variables, but I'm looking for more of an approximation than anything. I also realize that I could just do it, and what I have is what I'm left with, but this would be useful information for many situations.

I did search for this question, and the little I found was more about "I know what finished dimensions I want, how much metal do I need?" Rather than how much I will end up with given what I have.

Thanks in advance. 

I think you can just do a volume calculation and be pretty close.  

You currently have 1 x .75 x 6.5 = 4.875 cubic inches.  So your target is .5 x 1 x ? = 4.875, so your answer is 4.875 / .5 = 9.75 inches long.

Just doing this in your head you could see that the current cross section is .75 sq inches, and you're going for .5 sq inches, so based on the cross section being 2/3 as much, the length will be 3/2 or 1.5 as much. 

-- Dave

In my opinion, the best way to determine this is "conservation of volume" (as long as we dismiss the metal you lose to scaling).

Before drawing out, and after, you have the same amount of metal. The same volume.

You start with  1" x 3/4" x 6-1/2" = 4  7/8  cubic inches, which is the same volume you have at the end.

So: 4 7/8 cu.in. =  1/2" x 1'' x ??? => Dividing, you get ??? = 4 7/8 divided by (1/2 x 1), which in this case equals 9 3/4''

 

EDIT: Well, WMG jsut beat me to it by a few seconds.

3 minutes ago, Andres Bello said:

EDIT: Well, WMG jsut beat me to it by a few seconds.

Two great minds!  I'm glad we came up with the same answer!  -- Dave

Thanks for the quick replies guys. That's actually what I was hoping to get to, about 10 inches. I appreciate the help, and I will definitely be recording these formulas for future note. 

For more obscure things, a lump of clay sometimes is happy to do some really complicated stuff.

I've heard of that, C-1. Never tried it myself though. I think it would be hard to do precisely though, clay is a little too maleable, it would seem. Like I said though, never tried it. 

When you reduce the diameter of stock by half it grows at a 4 to 1 ratio in length. One inch of one inch square reduced to one half inch square will be four inches long. Take your dimensions and do the maths! Happy forging!

Good Morning,

C-1 is correct. You should have a container of Play-Doh, Plasticene, Modeling Clay or Cookie Doh in your Tool Bag. The answer to your question would be in your hands. K.I.S.S.

Neil

 

Surprisingly, Neil, I have none of that around. Looks like I may have to make a trip to the local craft store to pick up some clay (or head down to the river bank with a shovel and a bucket lol)

Go for the plasticine from the hobby store: it's reusable and doesn't dry out like river clay.

I'll keep that in mind, JHCC. Thanks. 

Any time.

If you use this spreadsheet formula for the frustum of a taper (flat topped pyramid or cone) you can calculate the volume of any type of cross section, straight line taper, in round, square, octagonal, hexagonal and everything in between.

Just calculate the area of the top and bottom faces and provide the length...row 5 gives you the length of base section bar before tapering. Row 6 you need to alter by adding the area of the parent bar to give you the cutting length...the base of the taper may not be the same as parent bar if you have a step down or are forging an octagon from a round or square bar for example. The bottom two rows add in the weight depending on whether you have used mm or cm for the volume and length.

Will work with inches or feet (one or the other not both at the same time!) but the weight formula will obviously need altering.

I keep this on my phone so it is handy.

This obviously the starting point. Losses through scale and inefficient forging/multiple heats for large sections and small hammers will need to be accounted for...but it will give you a guide.

Alan

p.s when I say straight line taper....I mean not convex or concave but a constant straight taper. A convex taper will obviously have more volume and concave one will have less.

 

Alan Evans FRUSTRUM.xls

Quite often these days I do a quick 3d Cad model of a part I am trying to calculate the volume of. I can often do a quick approximation of things I am going to forge quicker than doing the math.  The software gives me the volume. 

4 minutes ago, JNewman said:

Quite often these days I do a quick 3d Cad model of a part I am trying to calculate the volume of. I can often do a quick approximation of things I am going to forge quicker than doing the math.  The software gives me the volume. 

What software do you use?

I find the modelling can sometimes take me longer than the forging! 

I did find it really handy on a project which had two 5 metre high gate side panels, each weighing around a tonne, which we had to rotate in under an archway. As they were the full height we could not just suspend them from the crane. No head room for the jib.

I modelled the panel and was able to let the software (FormZ) calculate the centre of gravity. I then made up a sacrificial bolt on bracket that gave me a lifting point just above that COG which made the panel slightly bottom heavy, but only by a few Kilos, so we could rotate it easily by hand with the crane jib halfway up the Arch height.

Alan

I use Solidworks which I have to admit is overkill for something like this and too expensive to buy for this use but it is the one I use for the patternmaking we do here as well.  I suspect a lot of the cheap or free Cad software calculates volume as well.

 I recently had a customer who wanted a mosaic hammer made.  The dimensions he had sketched out and the weight he wanted did not gibe to me so I modeled the hammer in about 2 minutes and showed him what he wanted would weight about 8lb rather than the 2.2 he wanted.  So a couple of  quick changes and I had some sizes to make the hammer to.