Bending force when the bent part is freely bent
The bending force during free bending of a part is the force required to produce plastic deformation in the material without additional corrective forces. It is an important factor in selecting press tonnage and designing mold structures. The magnitude of the free bending force depends on factors such as the mechanical properties of the material, part size, bend radius, and bend angle. The accuracy of its calculation directly affects the selection of production equipment and the service life of the mold. Compared with corrective bending, free bending has a lower force and the contact area between the mold and the workpiece is smaller during the bending process. This makes it suitable for the production of bent parts with lower precision requirements and smaller batch sizes.
The free bending force is typically calculated using a theoretical formula. For V-bends, the formula is: Fself = (0.6×B×t²×σb)/(r + t), where Fself is the free bending force (N), B is the width of the bend (mm), t is the material thickness (mm), σb is the material’s tensile strength (MPa), and r is the inner bend radius (mm). For example, for a mild steel (σb=450MPa) V-bend with a width of 60mm, a thickness of 3mm, and an inner bend radius of 5mm, Fself = (0.6×60×3²×450)/(5+3) = (0.6×60×9×450)/8 = (0.6×243000)/8 = 145800/8 = 18225N ≈ 18.2kN.
The calculation of the free bending force of a U-shaped member is similar to that of a V-shaped member, but the simultaneous effects of both bending angles must be considered. The formula is: Fself = (0.7 × B × t² × σb) / (r + t). The coefficient of 0.7 is chosen because the two bending angles of the U-shaped member share the total deformation force. For example, for a U-shaped member with the same parameters (B = 60mm, t = 3mm, σb = 450MPa, r = 5mm), Fself = (0.7 × 60 × 3² × 450) / (5 + 3) = (0.7 × 60 × 9 × 450) / 8 = (0.7 × 243000) / 8 = 170100 / 8 = 21262.5N ≈ 21.3kN.
Material thickness and bend radius are key factors influencing free bending force. As material thickness increases, bending force increases in a quadratic relationship. For example, increasing thickness from 2mm to 4mm will approximately quadruple the original bending force. As the bend radius decreases, the material’s resistance to deformation increases, leading to a corresponding increase in bending force. This increase in bending force is particularly significant when r/t < 1. For example, decreasing the bend radius from 10mm to 5mm (t = 2mm) will increase bending force by 30%-50%. Furthermore, the bend angle has little effect on free bending force. When the bend angle is greater than 90°, the bending force does not change significantly because, beyond 90°, the primary effect is correction, not bending deformation.
Mold structural parameters have a certain impact on free bending force. The corner radius of the punch and die must match the part being bent. A too small punch radius increases bending force and can cause surface scratches on the workpiece, while a too large radius can affect bending accuracy. The die opening width (for V-die) or die spacing (for U-die) also influences bending force. A wider opening reduces bending force but reduces bending accuracy. For example, increasing the die opening width of a V-die from 8t to 10t can reduce bending force by 15%-20%, but the bending angle error will increase.
The actual application of free bending force requires consideration of a safety factor. The nominal tonnage of the press must be 1.2-1.5 times greater than the calculated bending force to account for factors such as material property fluctuations and operational errors. For example, when the calculated free bending force is 20kN, a press with a nominal tonnage of 24-30kN should be selected. The bending force must also be verified through actual testing during production. If the press tonnage is insufficient or the mold deforms during the bending process, the process parameters must be recalculated and adjusted. For example, the theoretical free bending force of a stainless steel bend was calculated to be 30kN. However, during actual production, the press load was found to reach 40kN. Upon inspection, it was found that the material’s tensile strength was higher than the design value. The process parameters were recalculated and adjusted to ensure production safety.
