# Calculation of Sheet Metal Bending Force in Air Bending (Universal Formula)

At present, the commonly used bending force calculation formulas are transplanted from foreign brochures, and there is no information on its origin and scope of application.

This article systematically discusses the derivation process of the bending force calculation formula and the parameter conditions that must be met.

In order to expand the scope of application, a new method for calculating bending force is introduced.

## Foreword

In recent years, the press brake machine has been widely used in various industries, and the processing range of the bending machine is also expanding.

However, there is no systematic discussion on the calculation of the bending force.

At present, there are roughly two types of bending force calculation formulas recommended in the product manuals of various press brake manufacturers. In the formula:

• P- bending force, kN;
• S- sheet thickness, mm;
• l -sheet bending length, m;
• V- lower die opening width, mm;
• σb- material tensile strength, MPa.

The bending force parameter table recommended by the manufacturer is also calculated according to the above formula.

These two formulas are also transplanted from different product brochures, and there is no data to prove their accuracy.

## The derivation process and applicable scope of the bending force calculation formula

Figure 1 is a schematic working diagram when the sheet is bent. • P-bending force
• S-sheet thickness
• V-lower die opening width
• r-Inner radius when the sheet is bent
• K-the width of the horizontal projection of the bending deformation zone

The derivation of the bending force calculation formula and the two additional parameter conditions are described below.

First, there are such recommendations in the product instruction manual.

In free bending, the opening width V of the lower die selected is 8 to 10 times the sheet thickness S. Here take the width to thickness ratio V/S = 9.

Second, the press brake manufacturers list the corresponding values of the die width V and the inner diameter r of the bending workpiece on the bending force parameter table.

Generally r = (0.16 ～ 0.17) V.

Here take the diameter-to-width ratio = 0.16.

During the bending process of the sheet, the material in the deformation zone is in a highly plastic deformation state, and it is turned at an angle around the centerline.

In some cases, tiny cracks can also appear on the outer surface of the curved area.

Except for the vicinity of the central layer, the stresses at other points on the cross-section of the deformation zone are close to the tensile strength of the material.

The upper part of the neutral layer is compressed and the lower part is tensioned.

Fig. 2 is a section and corresponding stress diagram in the deformation zone. • S-sheet thickness
• l- sheet bending length

The bending moment on the section of the deformation zone is: The bending moment generated by the bending force in the deformation zone is (see Figure 1): From M1 = M2, we get: When bending with a universal mold on a bending machine, most of the sheets are bent by 90°, as shown in Figure 3, K is: Substituting K into equation (1) we get: The tensile strength of ordinary materials σb = 450N / mm2, which can be substituted into formula (2) to obtain: The bending force calculation formula obtained here is very consistent with the data on foreign brochures. • S-sheet thickness
• r-Inner radius when the sheet is bent
• K- the width of the horizontal projection of the bending deformation zone

It can be seen from the derivation process that when using formula (2) or formula (3) to calculate the bending force, the two additional parameter conditions proposed above must be met.

That is, the width-to-thickness ratio V/S = 9 and the diameter-to-width ratio=0.16, otherwise it will cause great errors.

## New methods and steps for calculating bending forces

Due to design or process requirements, it is sometimes difficult to satisfy both of the above additional requirements.

In this case, it is not appropriate to use the recommended formula for the calculation of the bending force. Instead, follow the steps below.

(1) Calculate the width-to-thickness ratio and diameter-to-width ratio according to the plate thickness S, the bending radius r, and the lower die opening V, respectively.

(2) Calculate the projection width of the deformation area according to the deformation of the sheet.

(3) Apply the formula (1) to calculate the bending force.

In the calculation process, the difference in bending radius and the corresponding deformation zone have been taken into account.

The bending force calculated from the above steps is more accurate and reliable than the result calculated by the usually recommended formula.

Here is an example to explain it, as shown in Figure 4. Known: sheet thickness S = 6mm, sheet length l = 4m, bending radius r = 16mm, lower die opening width V = 50mm, material tensile strength σb = 450N / mm².

Question: how to calculate the bending force required for air bending?

Here are the steps:

First, calculate the width-to-thickness ratio and diameter-to-width ratio: Then calculate the projected width of the deformation area: Finally, use formula (1) to calculate the bending force: If the usually recommended formula is used to calculate the bending force: From P1/P2 = 1.5, it can be seen that the difference between the two is 1.5 times.

The reason for this error is that the bending radius is relatively large in this example, and the corresponding deformation area is increased, so a larger bending force is required when bending.

The diameter-to-width ratio in this example = 0.32, which has exceeded the additional conditions of the parameters introduced earlier. It is obviously inappropriate to calculate the bending force using the usually recommended formula.

You can see the advantages of using the new calculation method in this example.

You can also use the following online calculator to calculate the bending force by new methods.

## Conclusion

The steps and formulas for calculating the bending force introduced here are applicable not only to the angular bending of the sheet, but also to the arc-shaped bending (strictly speaking, it should be called an angle bending with a very large bending radius).

It should be noted that the bending of the sheet into an arc shape has a special mold shape. When calculating the projection of the deformation area, it must be calculated according to the process parameters set in the process, which cannot be expressed by a simple formula.

For a certain iron tower factory, we successfully bent a cylinder with a wall thickness of 12mm, the pipe diameter of 800mm and the length of 16m on a 28000kN press brake machine with a circular mold. When designing an arc-shaped mold, the method described in this article is used to calculate the bending force and obtain satisfactory results.  