Sheet Metal Bend Allowance Equation
Determines the flat sheet length required to form a bend with a specific inside radius, thickness, and K-factor.
Primary Mathematical Expression
Design Schematic
Nomenclature & Variables
| Symbol | Variable Name | Metric Unit | Imperial Unit | Description |
|---|---|---|---|---|
| BA | Bend allowance | mm | in | The length of sheet metal neutral axis in the bend region. |
| \theta | Bend angle | deg | deg | The angle of the bend in degrees. |
| R | Inside bend radius | mm | in | The internal radius of curvature of the bend. |
| K | K-factor | dimensionless | dimensionless | The ratio of neutral axis depth to total sheet thickness (typically 0.3 to 0.5). |
| t | Sheet thickness | mm | in | The nominal thickness of the sheet metal. |
Step-by-Step Derivation
- 1
When sheet metal is bent, the outer fibers stretch while the inner fibers compress.
- 2
The transition boundary between compression and tension is the neutral axis, where no length change occurs.
- 3
The distance from the inner surface to the neutral axis is defined by K * t, where K is the K-factor.
- 4
The radius of curvature of the neutral axis is therefore R_n = R + K * t.
- 5
The length of the neutral axis around the bend angle \theta (in radians) represents the flat length allowance: BA = \theta_{rad} * R_n = (\theta * \pi / 180) * (R + K * t).
Worked Example Calculation
A piece of sheet metal (t = 2.0 mm) is bent to 90 degrees with an inside radius of 3.0 mm and K-factor of 0.40. Calculate the bend allowance.
- •Identify input parameters: \theta = 90 deg, R = 3.0 mm, K = 0.40, t = 2.0 mm.
- •Apply the Bend Allowance Formula: BA = (\theta * \pi / 180) * (R + K * t).
- •Convert angle to radians: 90 * \pi / 180 \approx 1.5708 rad.
- •Calculate neutral axis radius: R_n = 3.0 + (0.40 * 2.0) = 3.8 mm.
- •Compute BA: BA = 1.5708 * 3.8 = 5.97 mm.
Engineering Assumptions
- •Deformations are confined strictly to the bend region.
- •K-factor stays constant during the plastic forming process.
Design Limitations
- •Deflection springback and tool tolerances are not compensated for by this direct formula.
Academic References & Standards
Standard Handbook of Machine Design, 3rd Edition
Standard handbook reference for sheet metal design and flat patterns.