How to Calculate length required for a length of metal that is being bent

[000lynx]

Good morning everyone,

I am a first time poster - so I hope that I have followed the rules correctly because I am not sure what type of maths question this is, but here goes.

I work in a manufacturing facility that processes metal and creates an end product for use on vehicles.

Here is background:

1. We have a Bar that must span X Length.
2. That bar arrives as a completely straight (180 degree) form.
3. The bar comes in lengths of 2900mm , and is cut down by our operator to suit each model of vehicle. Most sizes range from 1300-1400mm.
4. Once the bar has been cut to size, the bar goes through a bending machine which creates an "arc" shape out of the bar.
5. The operator then places the bar into a jig and pushes the centre of the bar down until the "arc" measures a distance of 88cm from the base of the table to the bottom of the arc.

The bar is now bent and ready to use.

Constants we know
1) We know the X Distance it must span, once bent.
2) We know the height the arc should be, measured in a flat position in the jig.

My Question:
1) How do we workout what size to cut the bar in the first instance (at step 3), so that it factoring in the bending process we end up with the correct X Span length?


Here is a drawing:



NOTE: Currently we have just used trial and error to find the size. E.g we would cut different lengths in step 3, and bend them and see if they fit until we got it right.
When you bend it the length gets shorter.


A calculation to solve this problem would be fantastic!

Thanks in advance,
Jesse

 

[tkhunny]

We're not really a consulting firm. You'll have to show YOUR work and we can comment on that.

One thing, the bending process is not well-defined. Is the whole bar bent into a curve or is the bending limited to just a piece of the bar>

Two thing, we don't have to have the ends of the bar ant any particular orientation?

 

[mmm4444bot]

After step 4, the shape of the arch is not clear, to me.

Does the bending machine produce a circular part? Parabolic? Some other shape?

In mathematics, these shapes are described by different equations.

If the bending machine yields a curve that is circular, then we would call the curved part an "arc", and there is a radius associated with it. Here's a diagram; the red section is a circular arc, and the blue sections are straight.

It's also unclear to me where the metal is bending in step 5. If the shape above were placed in a jig (to hold it upright) and downward force were applied at the center of the arc, it seems possible that the metal might bend where red meets blue or somewhere else along the straight parts. In other words, the final shape might be tend toward a somewhat flattened bell curve. The following diagram is exaggerated, to show what I'm thinking.

You're certainly welcome to wait, for a member who has both time and interest to reply with useful information for you. Please be patient; it may be awhile.

If I knew that the force in step 5 maintained a circular arc, albeit with increasing radius, and the remaining parts stayed straight, then I could come up with a formula. Yet, I'm not sure whether such a model would reflect real life.

I'm no engineer, but it seems like a materials engineer might inquire about other factors, like metal composition, initial dimensions, temperature, directional forces applied by the jig, etc.

Has anybody been keeping a record of the lengths required for various spans, so far? That is, do you have any real-life data from successful work already completed?

Cheers :cool:

 

[000lynx]

Hi guys,

Firstly, I cant see any attachement in either post.

1. The whole bar is being bent
2. it doesnt need to sit at a particular orientation.


I probably havent explained it well enough - its difficult to explain.

The shape is an arc, I believe. If I knew how many cm the bending process would reduce the overal length by, that would work because I would just get the total length needed and add the bending process and then cut the metal to that length.

That is a good idea aobut previous results. We do know the numbers for one other setup so I suppose I could derive some sort of pattern/formula just using those numbers? It might not be 100% accurate, and may involve some trial and error but its a good head start.

I just thought for someone good at Math it might be an easy thing - but its hard when the process is a bit complicated and explaining it online - so my apologies for that.

Short of anyone else answers, I guess I will revert to trial and error.

Thanks for the replies so far though!
Cheers,
Jesse