# Bending Reaction Force

I am trying to determine the reaction force my bend tooling will see in a simple sheet metal box and pan break. From the book "Sheet Metal Forming Processes and Die Design by Vukota Boljanovic" I was able to get an equation for the torque required to bend my work piece but since the reaction force is (I believe) statically indeterminate I am having trouble working it out. If the reaction force was on a single point you can just use $$T = l * F_R$$ but my bend tooling is touching the part from $$l=0$$ to basically $$l=\infty$$ (relative to the material thickness). Choosing $$l=1.5 mm$$ vs $$l=3mm$$ gives vastly different results!

I have considered using a beam with a fixed end and a uniformly distributed load but since the bend tooling keeps the material on a single plane and not a parabola that did not seem to be an accurate representation.

Here are my real numbers, if that helps anyone think about the problem:

• Material - cold rolled steel
• Ultimate Tensile Strength = 440 MPa
• Young's Modulus = 200 GPa
• Material Thickness = 1.5 mm
• Expected torque = 500 Nm
• Bend length (into the page) = 1.2 m
• Flange length = 100 mm

The inner bend radius is 1.5 mm so I am expecting a full plastic deformation bend.

I feel I need to account for the material stiffness and how much force each infinitely short section of the material can transfer to its next neighbor but I cannot find any examples that seem similar.

The bend tooling pivots about a point, not shown, such that it does not slide along the work piece while traveling through the bend.

To cause permanent deformation, you need to induce a plastic moment on the cross-section, $$M_p = f_y * Z$$, in which

• $$f_y$$ = yield stress of the material

• $$Z$$ = plastic modulus of the cross-section = $$b*t^2/4$$

Finally, set the toque $$T = M_p$$ to get the minimum required force to bend the material ($$F_R = M_p/e$$).

• From the sheet metal book I mentioned, I believe your Z should be (b*t^2)/4, where b is the bend length. Commented Feb 2 at 20:47
• The question I still have is, what is e? I know M_p, I do not know F_r or e. Another way to ask is: If I am applying my torque to the bend tooling with a motor from the end, axially in line with the point of fixity, what is the radial load my bearing will have to take? Commented Feb 2 at 20:52
• I imagine you would need to attach two pieces of rigid bending plates and clamp the plates to the material (let's call it the bending leg), then simply assume the clamping force is uniform over the length of the bending leg and the force is approximately on the center. The bearing needs to resist the bending force throughout the rotation/bending.
– r13
Commented Feb 2 at 21:29
• To actually resolve the torque into Fr and e needs a stiffness based model of the plate , tool, rig, and motor. or support the bend tool in a bearing at each end and don't wreck your motor. Commented Feb 2 at 21:47
• @BeardedOne85 "b" is the width of the material to be bent. The cross-sectional area A = b*t.
– r13
Commented Feb 2 at 22:44