Sheet-Metal Forming, Hydraulic Press-Brake Tooling & Tonnage Protection
Press-Brake Air-Bending Tonnage & V-Die Opening Formula
Calculate V-Die Shoulder Opening V (mm), Floated Air-Bent Natural Inside Radius I_r (mm), Forming Force F (kN), and Required Hydraulic Press-Brake Capacity (metric tons-force).
In air bending, the V-die width—NOT punch tip radius—dictates floated inside bend radius AND inverse forming tonnage!
Over 85% of modern CNC press-brake work uses three-point Air Bending where the sheet touches only the punch nose and two lower V-die shoulders without coining into the die bottom! Consequently, two critical shop-floor laws surprise novices: (1) Natural Floated Inside Radius I_r is ~16% of V-die opening V = m_v * T in mild steel (~20% in stainless, ~14% in soft aluminum) regardless of a sharper punch tip (until punch radius exceeds I_r), and (2) Required Bending Force scales with Thickness SQUARED divided by V-die span: F_kN = (C_f * UTS_MPa * L_m * (T_mm^2)) / V_mm (where die friction/leverage factor C_f = 1.42 for standard V = 8*T dies, converting to metric tons-force via F_kN / 9.80665)! Trying to bend 6 mm plate in a narrow 4*T die doubles tonnage and cracks tooling!
Verify on a 2.40 m x 6.0 mm S275 Mild-Steel Plate Bend—Thickness T = 6.00 mm (B2), Bend_Length L = 2.40 m (B3), Tensile_Strength UTS = 450.0 MPa (B4), V_Die_Multiplier m_v = 8.0 (B5 -> Rule-of-8 V-Die = 48.00 mm in E2), Die_Factor C_f = 1.42 (B6), and Float_Radius_Ratio = 0.16 (B7): Natural Floated Inside Radius lands at 48 * 0.16 = 7.68 mm (E3), Forming Force hits 1,150.20 kN (E4), and Required Press-Brake Tonnage equals 117.29 metric tons (E5, comfortably inside a 150-ton press brake)!
| Press-Brake Air-Bend KPI (T=6 mm, L=2.4 m, UTS=450 MPa, V=8*T, Cf=1.42) | Formula | Verified Output |
|---|---|---|
| V-Die Opening Width V (mm) | Sheet_Thickness_T * V_Multiplier | 48.00 mm (60.00 mm @ 10*T 304 SS) |
| Natural Air-Bent Radius Ir (mm) | V_Die_mm * Material_Float_Ratio | 7.68 mm (9.60 mm @ 10*T) |
| Air-Bending Force F (kN) | (Cf * UTS_MPa * L_m * T^2) / V_mm | 1,150.20 kN (1,267.78 kN @ 620 SS) |
| Press-Brake Tonnage (metric t) | Forming_Force_kN / 9.80665 | 117.29 t (129.28 t @ 620 MPa 10*T) |
Three-Point Air-Bending Force (kN) & Metric Press Tonnage Formula
Validate Thickness T > 0, Bend_Length > 0, UTS in [80, 1600] MPa, V_Multiplier in [5, 16], Die_Factor C_f in [1.20, 1.65], and Float_Ratio in [0.10, 0.28]!
=LET(th_m, B2, ln_m, B3, ut_s, B4, vm_l, B5, cf_d, B6, rf_l, B7, IF(OR(th_m <= 0, ln_m <= 0, ut_s < 80, ut_s > 1600, vm_l < 5, vm_l > 16, cf_d < 1.2, cf_d > 1.65, rf_l < 0.1, rf_l > 0.28), "Invalid Press-Brake Input", LET(vd_m, th_m * vm_l, fk_n, (cf_d * ut_s * ln_m * (th_m ^ 2)) / vd_m, ROUND(fk_n / 9.80665, 2))))304 Stainless Steel 620 MPa Wide 10*T V-Die Relief Check (Set UTS = 620 & Multiplier = 10)
Switch to 304 Stainless Steel (UTS B4 = 620.0 MPa, +37.8% stronger) while widening the V-die to 10*T (B5 = 10.0 -> V = 60.00 mm in E2): wider V-die leverage limits Tonnage E5 to only +10.2% higher (129.28 t, 1,267.78 kN in E4) instead of overloading a 150-ton brake!
=IF(ISTEXT(E5), E5, ROUND((B6 * B4 * B3 * (B2 ^ 2)) / (B2 * B5), 2))Try the example
Use the original values or change them to test your understanding.