The press brake tonnage formula
For air bending, The Fabricator and Bystronic give the same formula. Every length is in inches, and the result is in tons. Like Cincinnati's chart, the calculator counts a ton as 2,000 lb.
Tons = 575 x T² / V / 12 x L x material factor
T is the material thickness, V the vee die opening and L the length of the bend. The first part, 575 x T² / V, gives tons per foot of bend. Dividing by 12 gives tons per inch, and multiplying by the bend length in inches gives the total.
The baseline material is AISI 1035 cold-rolled steel with a tensile strength of 60,000 psi. For another metal, the material factor is its tensile strength divided by 60,000 psi. The Fabricator's example is 304 stainless at 84,000 psi, which gives a factor of 1.4.
In metric units, the calculator converts the same formula. NIST gives 1 ton-force of 2,000 lbf as 8.896 kN, and a foot is 0.3048 m. For mild steel, the formula works out to about 661 x T² / V kN per metre, with T and V in millimetres.
Worked example
Bending 10 gauge (0.135 in) mild steel over a 1.125 in vee die takes 575 x 0.135² / 1.125 = 9.32 tons per foot. Over a bend 8 ft long, that is 74.5 tons, or 663 kN.
In metric, a 3 mm mild steel part over a 24 mm vee die needs 661 x 3² / 24 = 248 kN per metre. Over a 2 m bend, that is 496 kN, or about 50.5 metric tonnes of force.
How the formula compares with a maker's chart
Cincinnati Incorporated's Press Brake Capacities booklet prints a mild steel air bend chart in tons per foot. On five of its rows at about 8 times the thickness, the formula comes out 4 to 17 percent above the chart.
| Mild steel, vee die | Cincinnati chart | This calculator | Difference |
|---|---|---|---|
| 20 gauge (0.036 in), 0.312 in vee | 2.3 tons/ft | 2.39 tons/ft | 4% higher |
| 16 gauge (0.060 in), 0.500 in vee | 3.8 tons/ft | 4.14 tons/ft | 9% higher |
| 14 gauge (0.075 in), 0.625 in vee | 4.7 tons/ft | 5.18 tons/ft | 10% higher |
| 10 gauge (0.135 in), 1.125 in vee | 8.5 tons/ft | 9.32 tons/ft | 10% higher |
| 1/4 in (0.250 in), 2.000 in vee | 15.4 tons/ft | 17.97 tons/ft | 17% higher |
Use the formula for a first estimate, and your press brake maker's chart or calculator when you size a machine.
The vee die opening rule of thumb
Cincinnati recommends a vee die opening of eight times the thickness for mild steel up to 1/2 in thick. Thicker mild steel can need up to ten times the thickness to keep it from cracking. Cincinnati rounds the result up to the next 1/8 in. For 14 gauge (0.075 in), 8 times the thickness is 0.600 in, which becomes a 5/8 in vee.
The vee opening sets the inside radius of an air bend. Cincinnati gives about 5/32 of the opening for mild steel, whatever the gauge. In a 2 in vee, 1/8 in sheet and 1/4 in plate both form about a 5/16 in radius.
The force divides by V, so a narrower die raises the tonnage and a wider one lowers it. Cincinnati's own tonnage calculator covers vee openings from 5 to 19 times the thickness, and the calculator warns you outside that range.
Material factors
For steel, the calculator uses the tensile ratio from The Fabricator. Cincinnati's bending factors relate both the tensile and the yield strength of a steel to those of mild steel. They also allow for a larger inside radius where plate cracks. The two methods disagree for some metals.
| Material | Tensile strength | Tensile ratio used here | Cincinnati formability factor |
|---|---|---|---|
| Mild steel (the baseline) | 60 ksi | 1.00 | 1.0 |
| Stainless 302, 304, 304L, 316, 316L | 80 to 90 ksi | 1.40 at 84 ksi | 1.3 |
| Aluminum 3004-H34 | 35 ksi typical | 0.58 | 0.6 |
| Aluminum 5052-H32 | 33 ksi typical | 0.55 | 0.7 |
| Aluminum 6061-T6 | 42 ksi typical | 0.70 | 0.8 |
The Fabricator's own list gives 1.0 to 1.2 for T6 aluminum and 0.5 for H-series aluminum. Both aluminum alloys bend harder than their tensile ratio says, so their presets use the highest published figure: 1.2 for 6061-T6 and Cincinnati's 0.7 for 5052-H32. A tonnage estimate that errs high sizes the machine on the safe side.
Bottoming, coining and special tools
The formula covers air bending only. The Fabricator adds a method factor of 5 or more for bottom bending and 10 or more for coining. Offset and hat tools can take five times the force, a hemming tool four times, and an offset tool in thick material ten times.
For bottoming with springback, Cincinnati's booklet gives about 1 1/2 to 2 1/2 times the air bend tonnage. True bottoming takes three to five times. Coining takes at least five times, and can approach ten times when the inside radius is half the thickness or less.
Check the machine as well as the part
The total force has to fit within the press brake's rating, and the force per foot has to fit within its centerline load limit. The Fabricator explains where that limit comes from. Most press brakes reach their deflection limit with the full rated load spread over 60 percent of the distance between the side frames.
Its example is a 100-ton press brake with 120 in between the side frames. The limit is 100 / (120 x 0.60) = 1.39 tons per inch, or 16.7 tons per foot. A short, heavy bend in the middle of the bed can pass that limit while the total stays well under the rating. Ask your press brake maker for the limit of your model.
Tooling has its own limit. The Fabricator notes that precision-ground tools carry a rated tonnage on the tool or in the catalogue.
Questions
How do you calculate press brake tonnage?
What does 575 stand for in the formula?
What vee die opening should I use?
How much more tonnage does stainless steel need?
Does the bend angle change the tonnage?
What is the difference between tons per foot and total tonnage?
How do I convert press brake tonnage to kN?
Is anything I type sent anywhere?
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