1. Arborless Bender Analytical Model

2. Arborless Bender Geometry Diagram - top viewCorresponding geometry

3. Arborless Bender Geometry Diagram - top viewCorresponding geometry

4. Constraint: Keep the arc length of the coil constant throughout the bend R f = Final Inside Bend Radius  f = Final Bend Angle R 1 = Intermed. Bend Radius  = Intermed. Bend Angle u = Neutral Axis Offset Neutral Axis Length Initial: L 0 = R f  f Intermediate: L 0 = (R 1 +u)  Bend Radius Neutral Axis:(R 1 + u) = (R f  f )/  Inside:R 1 = (R f  f )/  – u Bend Geometry

5. Clamp Adjustment Bend Geometry e = (R 1 +u) tan(  /2) a = R 1 tan(  /2) a = [(R f  f )/  – u] tan(  /2) Clamp Adjustment Initial: a 0 = e 0 = (R f  f )/2  a = a – a 0  a = [(R f  f )/  – u] tan(  /2) – (R f  f )/2

6. Clamp Adjustment Spreadsheet

7. Offset Bend Radius Bend Angle Calculated Clamp Adjustment vs Bend Specifications (1/2 Coil Thickness) (Inside)

8. Moment-Curvature Relationship

9. Estimating Springback

10. Springback Calculation Spreadsheet Input Output