How much force does a bend take? Press brake tonnage by hand

What you need

The thickness t and the die opening V in millimetres, the tensile strength Rm of the sheet in N/mm², and the length of the bend. This is for a 90° air bend, where the punch pushes the sheet into a V-die without bottoming it. Bottoming and coining take far more force, and are not covered here: WILA says bottoming takes three to five times as much.

1. Work out the force per metre

F = Rm × t² ÷ V × (1 + 4 × t ÷ V). The answer is in N per mm of bend, which is the same number as kN per metre. Bystronic prints this as reference data for air bending, but in the copy we could read both fractions have nothing under the line. V is our reading: it brings the formula within 5 % of 68 of the 77 figures Bystronic’s chart gives for Rm 420 N/mm².

For 3 mm mild steel at Rm 420 on a 24 mm die: 420 × 3 × 3 ÷ 24 = 157.5. Then 1 + (4 × 3 ÷ 24) = 1.5. And 157.5 × 1.5 = 236.25 kN per metre.

2. Multiply by the length of the bend

Force per metre × length in metres. A bend 2.5 m long in that sheet takes 590.6 kN, which is 60.2 metric tons (1 t = 9.80665 kN; Bystronic rounds to 10 kN) or 66.4 US tons.

3. See what the die does

The die opening is the lever you control. The same 3 mm sheet takes 236.3 kN per metre on a 24 mm die, 162.4 on 32 mm and 122.9 on 40 mm. But a wider die also leaves a larger inside radius (about 16 % of V in mild steel, Bystronic) and needs a longer flange (about 0.7 × V, see the minimum flange guide).

The force does not rise smoothly down this table, because the die steps up with the thickness: 8 mm on 80 and 10 mm on 120 take about the same as 6 mm on 48.

4. Adjust for the material

Bystronic takes stainless at Rm 650–700 N/mm² as 1.6 × the mild steel figure (3 mm on 24 mm: 378 kN per metre), and aluminium at Rm 300 N/mm² as 0.65 ×. WILA takes stainless as 1.5 ×, soft aluminium as 0.5 × and heat-treated aluminium as 1.0 ×, so for a heat-treated alloy use at least the mild steel figure. If you have the tensile strength from a mill certificate, put it in the formula as Rm. High-strength and wear-resistant plate has its own limits on radius, die and force: use the plate maker’s bending data.

5. Compare it with what the tools can carry

Two limits apply, and the second is the one that gets missed. The machine has a total. The tools have a limit per length: Bystronic marks its tools with a maximum bending force in kN per metre. Take 10 mm on an 80 mm die, a bend only 100 mm long: 78.8 kN in all, about 8 metric tons. But that is 788 kN per metre on that short length of tool, and that is the figure to compare with the marking on the tool. (The example marking on Bystronic’s p. 3 reads 600 kN per metre, on one particular punch: read your own tools, as ratings differ.) A short bend in thick plate can be well inside the machine’s total and still over the tool’s limit. Your machine’s chart and manual, and the tool maker’s limits, decide.

How far to trust the answer

It has been compared with two makers’ charts, not with measured bends. Against Bystronic’s chart the formula runs a little low: below it in 64 of 77 figures, by up to 13 %. Against WILA’s chart it runs high, by a median 7 %: for 3 mm on 24 mm, Bystronic prints 240 kN per metre and WILA 22 t per metre, about 216 kN taking its tons as metric. Mill scale can add a factor of 1.05 to 1.1 (Bystronic), and real plate can be stronger or thicker than you assumed. In the worst case the real force can be 20 % or more above the figure, so stay well inside your limits.

Common mistakes

• Scaling an air-bending figure up for bottoming. The range is too wide to rely on: use the figures for your own tools.
• Checking the machine’s total and not the force per metre on the tool.
• Using a die much narrower than 6 × the thickness. The charts stop there or nearby, and the formula alone adds about 30 % from 6 × to 5 ×.
• Using 0.65 × for a heat-treated aluminium alloy, which WILA takes at the full mild steel figure.
• Treating the answer as exact. The formula sits a median 7 % above one maker’s chart and mostly below the other’s.

How this matches the tool

The press brake tonnage calculator does this arithmetic in mm or inches, with the warnings above. The numbers on this page were produced by its code when the page was built.

Sources

1. Bystronic, Tools RF-A catalogue, “Calculation basics for air bending”, pp. 4–6: capacity chart at Rm 420 N/mm² over 1 m, the formula as reference data, die openings, aluminium × 0.65, stainless × 1.6, mill scale 1.05–1.1; p. 3: tools marked with a maximum bending force in kN/m
2. WILA catalogue GB, p. 110, air bending tonnage chart: tons per metre for mild steel at 90°; soft aluminium × 50 %, heat-treated aluminium × 100 %, stainless × 150 %; bottoming three to five times air bending. P. 111: Rm 42 kN/cm² on the flattening chart
3. Mate Precision Tooling, TWS catalog LIT01120 Rev D (2017), p. 4 “Bending Basics”: V-die by thickness (6, 8, 10, 12 × t)