The Math of Press Brake Air Bending: V-Die Width Selection and Minimum Flange Lengths

When mechanical engineers design sheet metal enclosures in SolidWorks or Autodesk Inventor, they frequently specify flange lengths that are physically impossible to form on standard CNC press brakes.

The sheet slips into the V-die cavity before completing the bend, producing distorted edges and scrapped parts.

Here is the mathematical relationship between material thickness, V-die opening width, and minimum allowable flange dimensions.

---

1. The 8x Rule for V-Die Opening Width

In precision air bending, the opening width ($V$) of the bottom die dictates the natural inside bend radius ($R_i$). For mild steel (tensile strength ~400–450 MPa):

$$V = 8 \times T$$

(where $T$ is sheet thickness).

For high-tensile stainless steel (304 / 316), increase to $V = 10 \times T$ to reduce required press tonnage. For soft aluminum (5052-H32), $V = 6 \times T$ can be utilized to achieve tighter corners without cracking.

---

2. Calculating the Minimum Flange Length ($b_{\text{min}}$)

To prevent the blank from dropping into the V-die opening during the downstroke, each flange must span at least 70% of the V-die width:

$$b_{\text{min}} = \frac{V}{\sqrt{2}} \approx 0.707 \times V$$

For a 2.0 mm mild steel sheet bent over a standard 16 mm V-die ($V = 8 \times 2.0$):

$$b_{\text{min}} = 0.707 \times 16 \text{ mm} = 11.3 \text{ mm}$$

Designing a flange shorter than 11.3 mm forces the shop floor to switch to expensive custom urethane tooling or special wiping dies.

---

3. Integrating Neutral Axis K-Factors

Once physical tooling limits are validated, flat blank unfolding requires solving the neutral axis shift:

• Bend Allowance: $BA = \frac{\pi \cdot A}{180} \cdot (R_i + K \cdot T)$
• Bend Deduction: $BD = 2 \cdot (R_i + T) \cdot \tan\left(\frac{A}{2}\right) - BA$

Solve these formulas interactively with the Sheet Metal K-Factor Calculator.

Inspect file compatibility with the AutoCAD DWG Version Checker and benchmark CAD software at CADGuide.tools.