Calculation of the development of a metal sheet

The calculation of the development of a metal sheet is a typical question often asked by many of our customers. Fortunately their experience is a degree and if not, today there are many drawing programs that do this calculation, in the same way that many CNC bending machines have this possibility.

Obviously here we are going to explain things theoretically, but as many know in the process of bending a metal sheet, many factors intervene; type of punch and / or die, thickness of the sheet, type of material of the sheet, direction of the fibers of the sheet, etc., for this reason, before making a large series of pieces, it is always advisable to carry out a small test to check that all the parameters are correct once the sheet is bended.

But for those who still have doubts, we will give two options to calculate said development;

FIRST

It is the simplest calculation, since we do NOT perform the calculation of the neutral fiber of the material, but unfortunately it is only valid for thicknesses of up to 2 m/m maximum and consists of eliminating twice the thickness for each bend of 90º and thus obtaining the total development of the sheet.

We go better with a practical example; with a thickness of 1,5 m/m and to calculate the development of the following sheet (see sketch) we will do the next calculation:

70 – (2 x 1,5) + 25 – (2 x 1,5) + 15 = 104 m/m is the length of the piece (before being bended).

SECOND

It is the most reliable method, but above all before making such a calculation we must calculate the neutral fiber of the material to be bended.

What is the neutral fiber of the material?

Once the material has been folded we have a deformation of it, technically we call it BENDING FIBERS. Therefore there is an external area where the material has been lengthened resulting in TRACTION FIBERS and an internal part where the material has been shortened, COMPRESSION FIBERS. But just between these two areas there is one where the material has not suffered compression or traction, this area or more precisely this line is the so-called neutral line or NEUTRAL FIBER.

Neutral line situation

There are many methods to calculate the position of the neutral fiber, but we believe that the following table is very practical, since it perfectly defines that its position basically depends on the internal radius of the bend and its relation to the thickness.

Inner

0,2 ——————————— 0,347 x thickness

0,5 ——————————— 0,387 x thickness

1 ———————————– 0,421 x thickness

2 ———————————– 0,451 x thickness

3 ———————————– 0,465 x thickness

4 ———————————– 0,470 x thickness

5 ———————————– 0,478 x thickness

10 ———————————– 0,487 x thickness

To give an example; if the inner radius is 3 m/m in a bend made of metal sheet with a thickness of 2 m/m, the following calculations will be done.

0,465 x 2 = 0,93 will be the position of the neutral fiber, see attached sketch

One thing is clear; the position of the neutral fiber is always between 0,3 and 0,5 of the thickness of the sheet

How to calculate the development of a bended metal sheet knowing the position of the neutral fiber?

We are going to give two very simple formulas to calculate the neutral fiber in an “L” shape and another one for a “U” shape and we will see it with an example for each case.

L shape

Formula:

Development = Flat face A + Flat face B + ¶ / 2 x (inner radius + neutral fiber)

Let’s put an example with real measurements to do the calculation;

25 + 30 + 3,1415/2 x (3 + 0,93) = 61,17 m/m will be the development of the sheet

U shape

Formula:

Development = Flat face A + Base + Flat face B + ¶ / 2 x (2 x inner radius + neutral fiber)

Let’s put an example with real measurements to do the calculation;

40 + 30 + 20 + 3,1415/2 x (2 x 5 + 1,912) = 111,71 will be the development of the sheet

Reverse engineering

As the sheet is a “live” material and the bending action depends on many factors (thickness of the material, quality and type of material, width of the die and a large etc), it is recommended that before making a large series , a small sample of metal sheet is bended, verifying the measurement before bending and rechecking measurements once bended, so we can adjust the development according to our own measurements and with the maximum controlled factors.