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# How many times to bend a large arc and how to calculate the bending angle?

## 1st method # As shown in the above figure: the plate thickness is T = 2mm, and the center angle is 90 °

1. First calculate the arc length:

arc length L = 90 ° × 3.14÷180° × center layer R59 = 92.632.

2. Select the bending die:

the upper die uses a acute punch and the lower die uses 8V die (when bending an arc, the minimum limit of V amplitude is 4T, which is normally 5-6t)

3. Calculate the feed rate per fold:

feed rate per fold = half of the V amplitude of the selected lower die

4. Calculate the number of folds:

number of folds = arc length L92.63 ÷ half of V amplitude 4mm = 23 folds

5. Calculate the positioning size of each fold:

after the positioning size of the first fold is calculated, the other folds decrease by 4mm (row from the inside to the outside when bending and arranging punches)

6. Finally, calculate the bending angle of each bend:

according to some algebraic calculation formulas of the triangle.

7. After the above calculation is correct, start to test bend with waste sheet metal, and process the product after testing the angle.

## 2nd method #

Let’s look at the picture below first. The plate thickness is 2mm, the bending angle is 120 degrees, the external radius of bending is 30, the radius of the neutral layer is 29, and the arc length of the neutral layer is calculated for arc bending.

Therefore, the bending times and the bending angle of each bend are also calculated according to the arc length of the neutral layer

The distance between the neutral layer and the edge is half of the plate thickness.

In the figure above, how many bends are needed for arc bending, and what is the bending angle of each bend?

If we feed 2mm per bend.

• Bend times = arc length / 2mm = 30.37/2 = 15
• Bending angle
=180 – {(2 / arc length) x (180-bending angle)} = 180 – {(2 / 30.37) ×60} = 176

If we cannot measure the arc length during bending, we can also calculate it according to the following formula：
Bending angle = 180 – {(2 / 3.14×neutral layer radius) ×180} = 180 – {(2 / 3.14×29) ×180} = 176

If you want to bend 3mm everytime, replace 2 with 3 in the above formula.

Of course, the above formula is a theoretical calculation formula. In actual processing, it should be adjusted according to the results calculated by the above formula. 