Spring-Back Simulator — Elastic Recovery in Sheet Metal Bending

Automotive body panel pressing: Modern car bodies use 590-1180 MPa advanced high-strength steels and 6000-series aluminium for weight reduction, all of which spring back 2-5 times more than mild steel. Increasing sigma_y to 590 MPa in the tool gives K = 0.79 and a return angle of 18.5 deg, which is hard to compensate by angle correction alone. Centre pillars on cars like the Audi A8 or Tesla Model 3 use bottoming combined with multi-stage bending to hold the final angle within +/- 0.5 deg.

Press brake V-bending: The everyday workhorse of sheet metal shops produces V- and L-bends where the difference between the target angle and the formed angle drives most quality complaints. A 1.0 mm mild-steel sheet (sigma_y = 250 MPa) bent on a small R_i = 1.0 mm punch yields X = 0.00119 and K = 0.996 — essentially no recovery. Switching to t = 3.0 mm and R_i = 8 mm typical of air bending raises K to about 0.99 and the return angle to about 0.85 deg; with sigma_y = 780 MPa it grows to 2.4 deg, which a modern CNC press brake stores in its angle-correction table.

Roll forming profiles: In continuous bending of steel strip for solar panel frames or building cold-formed sections, the cumulative angle from each stand drives the final cross-section accuracy. The K from each stand sets the over-bend angle 1/K. For sigma_y = 350 MPa structural strip, t = 2.3 mm and R_i = 5 mm the tool gives K = 0.978 and a 2 deg recovery per stand, so each roll is set to 92 deg to land 90 deg after release.

Precision bending of aircraft skins: Aluminium alloys (2024-T3, 7075-T6) used for ribs and stringers have E = 70 GPa and sigma_y from 300 to 500 MPa, so X is large. With sigma_y = 400 MPa, E = 70 GPa, R_i = 10 mm and t = 1.6 mm the tool returns X = 0.0357 and K = 0.893 — essentially the same as the mild-steel default. Stretch forming, where tension is applied during bending, brings K above 0.95; that case is outside the scope of this tool but the pure-bending numbers serve as a useful upper bound on the recovery.

The most frequent misconception is that "K is a material constant". The formula shows that K depends on the dimensionless group X = sigma_y R_i / (E t), so the same material returns very different K values for different geometries. For example SPHC steel (sigma_y = 300 MPa, E = 210 GPa) with R_i = 10 mm and t = 4 mm gives X = 0.00357 and K = 0.989 — almost no recovery — but R_i = 100 mm and t = 1 mm gives X = 0.143 and K = 0.583, a dramatic spring-back. Use the sliders to see how the same material behaves completely differently as geometry changes.

The second misconception is that over-bend alone is enough. In practice the tooling design must combine (a) angle compensation, where the punch angle is set to theta_target / K, (b) radius compensation, with R_punch = R_target * K, and (c) optionally bottoming. Angle compensation by itself usually leaves the unloaded inside radius too large. Use the R_f reading from the tool to size the punch radius too. Once you move into bottoming territory the simple closed-form is no longer valid and explicit FE codes such as PAM-STAMP, AutoForm or LS-DYNA take over.

The third pitfall is extending the plane-strain plate formula to three-dimensional forming. This tool assumes pure bending of an infinitely wide sheet with no in-plane strain transverse to the bend. That is a reasonable model for press-brake V-bending or roll-formed flanges where the bend length is much greater than the part width, but it fails for deep drawing, flanging and hemming, where in-plane tension and compression couple to bending. Use the tool for first-pass estimates only and rely on physical try-outs and full 3D CAE for complex geometries.