Bending Force for Air Bending
Calculate the required bending force for air bending in a V-die using the established approximation F = k·Rm·s²·b/V. Enter material, sheet thickness, bend length and die width – the calculator returns the press force in kN plus guideline values for die width, minimum bend radius and minimum flange length, live on every input.
Bending Force Calculator (Air Bending)
Empirical approximation for air bending in a sharp V-die: F = k·Rm·s²·b/V. Coining, differing material properties, rolling direction and friction lead to different forces. The guideline values for die width, minimum bend radius and minimum flange length are practical values, not code requirements. Add a safety margin when selecting the press.
Results
Calculating …
Formulas and fundamentals
In air bending the punch presses the sheet into a sharp V-die without fully coining it. The required bending force follows from the empirical approximation F = k·Rm·s²·b/V, where Rm is the tensile strength of the sheet material, s the sheet thickness, b the bend length (length of the bend line) and V the die width (opening of the V-die). The dimensionless factor k lies between roughly 1.33 and 1.42 depending on the source and lumps together the lever ratios at the die shoulders and friction.
The quadratic dependence on sheet thickness is decisive: doubling the thickness quadruples the force. The force rises linearly with tensile strength and bend length and falls with a larger die width. The die width is usually chosen as V ≈ 6 to 12·s, with V ≈ 8·s as the standard. A die that is too narrow drives up the force and promotes cracking on the outer bend fibre, while a die that is too wide costs angular accuracy.
Further guideline values are a minimum bend radius of r_i ≈ 0.8·s (for ductile sheets; hard or work-hardened materials need more) and a minimum flange length of about 0.5·V so the sheet rests safely on both die shoulders during bending. These are practical design guidelines, not code requirements.
Worked example
A steel sheet with tensile strength Rm = 400 N/mm² and thickness s = 3 mm is to be bent over a bend length b = 1000 mm. The standard die width V = 8·s = 24 mm is chosen, with factor k = 1.42.
This gives the bending force F = 1.42 · 400 · 3² · 1000 / 24 = 213,000 N, about 213 kN. A safety margin is customary for a press brake, so a machine with roughly 250 kN rated force would be selected.
The guideline values for this example: recommended die width V ≈ 24 mm (band 18 to 36 mm), minimum bend radius r_i ≈ 2.4 mm and minimum flange length ≈ 12 mm. Halving the die width to 12 mm doubles the force to 426 kN – showing how strongly the die choice determines the press force.
Frequently asked questions
Which bending process does the formula apply to?
Air bending in a V-die, by far the most common process on modern press brakes. In coining, where the sheet is fully pressed between punch and die, the forces are many times higher (factor 5 to 10) and the approximation does not apply.
How do I choose the die width V?
As a rule of thumb V ≈ 8·s, with 6 to 12·s being sensible. A smaller die raises the force and the risk of cracking on the outer fibre but allows smaller bend radii. A larger die lowers the force but makes the bend less accurate and increases the resulting bend radius. The calculator warns when V is outside 6 to 12·s.
Which factor k should I use?
Typical values are between 1.33 and 1.42. The higher value (1.42) is conservative and often used as the standard. The exact value depends on material, friction and die geometry. When in doubt use the higher value so the press is not sized too tightly.
Why does thickness enter quadratically?
Because both the required bending moment and the section's resistance grow with thickness: the plastic moment of the bend zone scales with s². Thickness is therefore by far the most important factor – doubling it quadruples the bending force.
Is the calculated force the rated press force?
No. The formula gives the theoretically required bending force. A safety margin should be added when selecting the press brake, and the force is often listed per metre of bend length in press catalogues. Friction, rolling direction and varying material properties can further increase the real force.
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