Stamping processes, press selection, and mold design heavily rely on the bending force. Various factors such as blank size, material properties, die supports distance, bending radius, and clearance determine the magnitude of bending force. However, due to the complexity of bending methods, it is common to use empirical formulas from Table 1 for initial force estimation.
I. Theoretical calculation basis and methods for bending force
Theoretical bending force calculations are based on static equilibrium where external forces and internal resistances balance out. Different bending methods and die structures lead to varying stress distribution and pressures. Methods like free bending or contact upsetting bending are utilized for bending V-shaped and U-shaped parts, as illustrated in Figure 1.
- a) V-shaped parts
- b) U-shaped parts
- 1 – Bending punch
- 2 – Bending part
- 3 – U-shaped die
- 4 – Top tool
- L – Width of U-shaped die opening
- t – Thickness of part
- h – Depth of V-shaped die cavity
While V-shaped parts utilize concentrated loads for bending, different bending methods like free bending or impact correction bending exert different pressures, resulting in varying required forces based on the bending process.
It is important to consider material properties, such as yield strength and elastic modulus, when calculating bending forces, as they directly impact the amount of force required to achieve the desired bend. Additionally, factors like die material and surface finish can also influence bending force calculations.
II. Calculation of bending force by various bending methods
Table 1 provides formulas for calculating bending force using various methods. Parameters such as material width (b), tensile strength (R), and length (L) are crucial in determining the necessary force. Specific coefficients and correction pressures are also significant in accurate force estimation.
Key Formulas for Bending Force
P-Total bending force (N)
B-Width of the bent part (mm)
t-Material thickness (mm)
σb-Tensile strength (MPa)
r-Inner bending radius (mm)
A-Correction part projection area (mm2)
It is important to carefully consider these key formulas when calculating bending force using different methods. The material thickness, tensile strength, and other parameters play a significant role in accurately determining the force required for bending. Correctly applying specific coefficients and correction factors will ensure precise results in the bending process.
III. Calculation of bending work
Bending work for V-shaped parts involves a specific formula that incorporates correction coefficients and bending forces. The depth of the die cavity also plays a role in influencing bending work.
- Wv – Bending work of V-shaped parts (J)
- m – Correction coefficient
- Fv – Bending force of V-shaped parts (kN)
- h – Depth of die cavity (mm)
h=0.5L~0.4(t+r)
- L – Distance between supports
- t – Thickness
- r – Bending radius
IV. Simplified graphical method for bending force and bending work
Figure 2 provides a graphical representation for the calculation of bending forces and work, which is suitable for on-site use. The chart enables quick calculations, ensuring practical and accurate results.
- F – Bending force of parts (kN)
- W – Bending work of parts (J)
- H – Bending stroke (mm)
- L, Lmin – Opening width of V-shaped die, minimum width (mm)
- r – Inner bending radius (mm)
- t – Thickness
Example calculations in Figure 2 demonstrate the derivation of bending forces and work for V-shaped parts based on specific parameters and materials.
Mastering the calculation of bending force is crucial when working with press brake machines. This article serves as a guide through the process, explaining the key factors influencing force calculation to optimize bending operations.
Additional tips for calculating bending force:
- Consider the material type and thickness when determining bending force.
- Make sure to account for the bending radius and stroke length in your calculations.
- Consult the machine’s manual for specific instructions on calculating bending force.
- Regularly check and maintain your press brake machine to ensure accurate bending force calculations.
Introduction
Press brake machines are extensively used in various industries, and understanding bending force calculation is paramount. Exploring the original bending force formula aids in comprehending the concept, assisting in machine settings and material selection for projects.
F: bending force, N
Rm: tensile strength, N/mm 2
T: sheet thickness, mm
V: lower die opening, mm
L: sheet length, mm
Tensile strength of common materials
The tensile strength of a material determines its deformation capabilities and is critical for maintaining material integrity. Understanding the role of tensile strength in plastic deformation and resistance is essential for evaluating material behavior under stress.
Regular material tensile strength
Knowing the key tensile strength values for different materials aids in material selection for bending operations. Ensuring the appropriate strength of the metal is vital for achieving successful bending results.
Lower Die Vee Opening Selection Rule
The width of the lower die opening in press brake machines varies according to material thickness to ensure precise bending results. Adhering to the opening guidelines based on material thickness enhances accurate bending results.
Allowed minimum bending edge length
During bending, the material undergoes compression inside the fillet and stretching outside, while maintaining its original length and forming an arc line at the neutral line of sheet mechanics. The arc length should not exceed half of the plate thickness.
Case study
Material: 20 mm thick
Bend length: 7500 mm
For the given case study with a material thickness of 20 mm and a bend length of 7500 mm, the allowed minimum bending edge length would be 10 mm, which is half of the material thickness. This ensures that the arc length formed during bending does not exceed half of the plate thickness, maintaining the integrity of the material during the bending process.
Common simplified formula
Most materials used in bending production are low carbon steel (420 Mpa) with a thickness of 3-8mm. The formula is simplified as:
After simplification, with t in mm, l in m, the result is in tons.
For example, when bending a 2.8mm low carbon steel plate with a length of 2.5m, tonnage calculation is required.
Note: The formula is for estimation purposes only.
Bending force table
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Table data is calculated based on 90-degree bending, material strength Rm=420 MPa, and a bend length of 1m.
Bending Calculator
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About Jimmy Chen
Author & editor at HARSLE specializing in delivering content for the metalworking industry. His technical writing experience focuses on providing articles and tutorials for manufacturers, engineers, and professionals in sheet metal processing, including CNC press brakes, hydraulic presses, and shearing machines.
Metal brake bending machines are widely used in industries, yet there is a lack of systematic discussion on bending force calculation. Press brake bending machine manuals recommend two types of formulas:
P – bending force, KN;
S – sheet thickness, mm;
l – sheet bend length, m;
V – lower die opening width, mm;
σb – Material tensile strength, MPa.
Manufacturer-recommended bending force parameter tables are also calculated according to the above formula.
The derivation process and application scope of bending force calculation formula
Figure 1 illustrates a schematic diagram of sheet bending, showing the derivation process of the bending force calculation formula with additional parameter conditions. The lower die opening width V in free bending should be 8 to 10 times the sheet thickness S. Aspect ratio .
Stress diagrams are shown in Figure 2.
The bending moment on the cross-section is:
Bending moment due to bending force in the deformation zone (Figure 1):
When using general molds for free bending, the sheet metal typically bends 90°. The correction factor K is:
Substitute K into equation (1) to get:
With ordinary materials and σb=450N/mm2, substitute formula (2) into:
The derivation process indicates that additional conditions such as aspect ratio = 9 and diameter-to-width ratio = 0.16 must be met when using equation (2) or equation (3) to calculate bending force to avoid errors.
Figure 3 Free bending
New methods and steps for calculating bending force
When design or process requirements make it challenging to meet additional criteria, do not use the recommended formula but follow these steps:
(1) Calculate the aspect ratio and diameter-to-width ratio based on plate thickness S, bending radius r, and lower die opening V.
(2) Calculate the deformation zone projection width according to sheet deformation.
(3) Apply formula (1) to calculate bending force.
A new calculation method example is shown in Figure 4.
Given values: S=6mm, l=4m, r=16mm, V=50mm, σb=450N/mm2. Find the bending force for free bending.
First, find the aspect ratio and diameter-to-width ratio:
Next, calculate the deformation zone projection width:
Finally, use equation (1) to find the bending force:
If the recommended formula is used:
The 1.5 times difference indicates that a large bending radius in the example requires more force. The diameter-to-width ratio exceeding 0.32 showcases the advantages of the new method over parameter conditions.
Conclusion
The steps and formulas for bending force calculation also apply to arc bending. A specially shaped mold is required for arc bending. When designing an arc-shaped mold, use the method described in the article to calculate the bending force for satisfactory results.
An online calculator can accurately determine sheet metal bending parameters within seconds. Simply input project data to obtain tonnage, inner radius, and minimum edge.
Die opening
The die opening is selected based on the sheet metal thickness:
Thickness < 6 mm
die opening = thickness x 8
Thickness > 6 mm
die opening = thickness x 10
The die opening can be adjusted based on the desired flange length and internal radius.
A die-to-thickness ratio less than 8 reduces springback but increases bending force and stress, potentially leading to cracks and material damage.
Minimum flange
The minimum flange length achievable is determined by the die opening and bend angle, ensuring the material does not fall in. The outer face is considered for easier measurement.
Bending radius
The inner radius depends on the die opening and material strength, with the ultimate tensile strength of the sheet metal used for calculations.
Learn the sheet bending force calculation method or directly utilize the calculation formula on our website.
Expansion calculation principle
During bending, the outer layer of the sheet material experiences tensile stress, while the inner layer experiences compressive stress.
Neutral Layer
Understanding the Neutral Layer in Bending
When a part is bent, there is a layer called the neutral layer that remains unchanged in length between tension and compression. This neutral layer plays a key role in calculating the expanded length of the bent part, with its position dependent on the degree of deformation.
For bends with larger radii and smaller angles, the neutral layer is located closer to the center of the sheet thickness. However, as the bending radius decreases and the angle increases, the neutral layer moves inward, with the distance denoted by λ.
Utilizing the Calculation Method
When calculating bending forces, the basic formula to use is: Unfolded length = in-material + in-material + compensation amount. For Z-fold calculations, the same principles apply, such as dividing the bend into two 90˚ angles when C≧5. The bending force on metal sheets will vary based on the design.
Determining Bending Force
To calculate the necessary tonnage force for bending, utilize the formula P=650*S*L/V, taking into account the equipment tonnage, V groove selection, and material type (e.g., stainless steel).
Exploring Bending Methods
Two popular methods for bending sheet metal are die bending, suitable for complex structures, and using a bending machine, ideal for larger structures. Bending tools and press brake machines are commonly employed for bending workpieces.
Key Principles for Bending Workpieces
When engaging in bending processes, it is important to follow certain principles: begin bending from the inside out, progress from small to large bends, tackle special shapes first, and prevent interference between different processes.