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.

Table of Contents

**Foreword**

**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**

**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 radius r of the bending workpiece on the bending force parameter table.

Generally r = (0.16 ～ 0.17) V.

Here take the radius-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 M_{1} = M_{2}, 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 radius-to-width ratio=0.16, otherwise it will cause great errors.

**New methods and steps for calculating bending forces**

**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 radius-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 radius-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 radius-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.

**Tensile Strength Table**

Material |
Tensile strength |
||
---|---|---|---|

American |
European |
China |
N/mm² |

6061 Aluminum | Alu50 | LD30 | 290 |

5052 Aluminum | Alu35 | LF2 | 303 |

1010 Mild steel | DC01 | 10/10F | 366 |

A 536 -80 G 60-40-18 | GGG-40 | QT400-18 | 400 |

A 351 G CF 8 | G-X 6CrNi 18 9 | Q235 | 450 |

A 572 G50 | S 355 MC | Q345 | 550 |

304 Stainless | Inox V2A | 0Cr18Ni9 | 586 |

316 Stainless | Inox V4A | 0Cr17Ni12Mo2 | 600 |

4140 Low alloy | 42 CrMo 4 | 42CrMo | 1000 |

**Conclusion**

**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.

**Further reading:**

HobieHello,

Not matter how I calculate the new formula. I can’t come to the same conclusion. Can you explain again with the values you used?

Thanks

MachineMfgCould you advise more details about your metal materials and sizes, and how did you calculate the bending force?

HobieK=(0,32+50/16,66)wurzel^2

No matter how I do the math.

I can’t get the 0,537

MachineMfgHi Hobie, we need to know what’s your metal material, bending length and thickness in order to help you do the calculation.

Homer SilvaK=(r+s/2) x 1.414

K=(16+6/2) x 1.414

K = 26.86

V = 50

K/V= 26.86/50 = 0.537

K = 0.537V

HobieI’ve been trying to recalculate their structure.

Material 450 mpa

Thickness 6 mm

Die 50 mm

Bending radius 16 mm

Length 4 m

MachineMfgTry to use our online calculator to make it easy: https://www.machinemfg.com/press-brake-bending-force-calculator/

HobieI do not want to have it calculated via an online calculator.

I want to understand the formula and the calculator.

Where did the 16,66 come from?

What do I put as V in the formula? 50?

Root 2 is also 1.41?

No matter what I put, I can’t get that 0,537V.

MachineMfgI believe this article is difficult for you, you can read this one to learn how to calculate: https://www.machinemfg.com/calculate-press-brake-tonnage/

SATOĞLUHello dear administrator,

I have 2 question,

you know there is different bending types (mostly use U, V, Z). you have shared Z calculator. But how we will calculate press force for other types?

Second one is about different bending methots Air bending, bottoming and coining. Can we call coining your these new mothot ?

SATOĞLUAnother one is check it equation (1) .P is not true if you equal M1=M2

MachineMfgYou can find answers here: https://www.machinemfg.com/metal-stamping-and-die-design-bending/#3_2_Calculation_of_bending_process_force

S LavanyaHi,

I feel that the bending force calculation formula that is derived here is applicable only for 90 degree bend angle. Can we use this formula for calculating the required bending force other than 90 degree.

MachineMfgIf not 90 degrees, then the inner radius will also be changed, the formula and calculator mentioned in our post are still applicable.

S LAVANYAOk. Thank you, and that means only the equation 1 is applicable in the case of bending to various angles.

MachineMfgThe easiest way is to use our calculator online.

Adam OswaldOn the ratios, your text says DIAMETER-to-width ratio, but the values for RADIUS-to-width are actually used in the example . Should the diameter or radius be used in the ratio?

Adam OswaldAlso, on the calculator, the final result had the units of “TON”, however the example problem has the final result in the units of “kN”. It appears that the unit label on the calculator should be changed to “kN”.

ShaneThanks Adam, the unit is been updated.

ShaneHi Adam, it should be radius, not diameter. We have made corresponding changes, thank you so much.