Understanding Sheet Metal Bend Calculations
When sheet metal is bent on a press brake, the material undergoes intense plastic deformation. The outer surface of the bend stretches under tension, while the inner surface compresses. Between these two opposing forces lies an imaginary boundary called the Neutral Axis — a layer where the material experiences zero stress and retains its original unbent length.
What is K-Factor?
The K-Factor represents the location of the neutral axis expressed as a ratio of neutral axis depth (t) to total material thickness (T):
Because metal compresses more readily than it stretches, the neutral axis shifts inward toward the inside bend radius. In practical shop operations, K-Factor typically ranges between 0.30 and 0.50 depending on material composition, bend angle, tooling, and forming method (Air Bending vs. Bottoming vs. Coining).
Bend Allowance vs. Bend Deduction
Fabricators use two distinct methods to convert 3D CAD dimensions into flat sheet metal cut patterns:
- Bend Allowance (BA): The actual arc length along the neutral axis around the bend. Calculated as:
$$BA = \left(\frac{\pi}{180}\right) \times \theta \times (R + K \times T)$$
- Bend Deduction (BD): The amount subtracted from the sum of the outside flange dimensions to arrive at the exact flat layout length:
$$BD = (2 \times OSSB) - BA$$
Step-by-Step Flat Pattern Formula Reference
| Parameter | Symbol | Mathematical Formula | Shop Application |
|---|---|---|---|
| Bend Allowance | BA | (π / 180) × θ × (R + K × T) |
Length of material needed to form the radius curvature |
| Outside Setback | OSSB | tan(θ / 2) × (T + R) |
Distance from apex of outer flange extensions to bend line |
| Bend Deduction | BD | (2 × OSSB) − BA |
Value subtracted from (Flange A + Flange B) for CNC shearing |
| Flat Pattern Length | Lflat | L₁ + L₂ − BD |
Total unbent length of raw metal stock required |
Forming Method Guidelines
Air Bending
The punch contacts the metal at three points without pressing it into the bottom of the V-die. Material springback is highest. Typical K-factor: 0.33 – 0.38.
Bottom Pressing (Bottoming)
The metal is pressed firmly against the V-die surfaces under higher tonnage. Springback is reduced. Typical K-factor: 0.42 – 0.45.
Coining
Extreme tonnage penetrates the neutral axis, eliminating springback entirely. Neutral axis shifts nearly to center. Typical K-factor: 0.48 – 0.50.