A sheet-metal flat pattern must account for the length of material within each bend. During bending, material on the outside of the bend is in tension and material on the inside is in compression. The neutral layer has no longitudinal extension in the idealized bend model; its position is represented by the K-factor.
This guide uses a bend angle β measured as rotation from the flat state: a flat sheet is 0° and a right-angle bend is 90°. The opening angle between the flanges is 180° − β. The setback, deduction and worked examples below cover simple bends with 0° < β ≤ 90°, a single inside radius and consistent outside-flange dimensioning. Hems, bends beyond 90° and other dimensioning conventions require the appropriate CAD bend rule or validated bend table. Use one length unit throughout.
Sheet Metal Bending Calculation: Bend Allowance (BA)
Bend allowance (BA) is the arc length of the neutral layer through the bend. Add BA to the straight lengths measured up to the bend tangent points to estimate the flat length. It is not the gap between a punch, die and sheet.
Bend Allowance Formula
For this angle convention, calculate bend allowance as follows:
BA = (π × β / 180) × (R + K × t)
Where:
- BA: bend allowance, in mm or inches.
- β: bend angle from flat, in degrees.
- R: inside bend radius, in the same unit as t.
- t: sheet thickness.
- K: distance from the inside surface to the neutral layer, divided by t; dimensionless.
If the angle is in radians, use BA = βrad × (R + Kt) without π/180. This relation is also described in Autodesk Inventor’s unfold equations.
Bend Deduction (BD) In Sheet Metal Bending Calculation
Bend allowance versus bend deduction. Left: A and B are straight lengths ending at the bend tangent points. Right: A and B are outside flange lengths extending to the virtual sharp. They are lengths, not the bend angle β used in this article.
Bend deduction (BD) is the amount subtracted from the sum of the two outside flange lengths to obtain the flat length. Both outside lengths must be measured to the virtual sharp: the intersection of the extended outside flange surfaces. For the simple bends and dimensioning convention defined above:
The formula for Bend Deduction is:
BD = 2 × OSSB − BA
Where:
- BD: bend deduction, in the selected length unit.
- OSSB: outside setback, measured along a flange from its bend tangent point to the virtual sharp.
- BA: bend allowance calculated for the same bend.
Worked bend-allowance examples: R = 2.000 mm, t = 1.000 mm and an assumed K = 0.400 in every row. K = 0.400 is an arithmetic assumption only, not a recommended value for any material or Prolean process. Values are rounded to three decimal places after calculation.
| β from flat (°) | R (mm) | t (mm) | K | BA (mm) |
|---|---|---|---|---|
| 30 | 2.000 | 1.000 | 0.400 | 1.257 |
| 45 | 2.000 | 1.000 | 0.400 | 1.885 |
| 60 | 2.000 | 1.000 | 0.400 | 2.513 |
| 90 | 2.000 | 1.000 | 0.400 | 3.770 |
Bending Outside Setback (OSSB)
Outside setback (OSSB) is the distance along an outside flange from the bend tangent point to the virtual sharp. It is a geometric distance, not an allowance for springback or the distance to a machine bend axis.
Use the same inside radius, thickness and angle convention for BA, OSSB and BD. Mixing an opening angle with an angle measured from flat produces the wrong setback.
Formula for Outside Setback
To calculate outside setback, use the formula below:
OSSB = (R + t) × tan(β / 2)
Where:
- R: inside bend radius.
- t: sheet thickness, in the same unit as R.
- β: bend angle from flat, in degrees; use degree mode for tan(β/2), or convert β/2 to radians.
- For β = 90°, tan(45°) = 1, so OSSB = R + t.
Setback and deduction for the same examples: R = 2.000 mm, t = 1.000 mm, assumed K = 0.400. Calculate from unrounded values, then round the results.
| β from flat (°) | OSSB (mm) | BA (mm) | BD (mm) |
|---|---|---|---|
| 30 | 0.804 | 1.257 | 0.351 |
| 45 | 1.243 | 1.885 | 0.600 |
| 60 | 1.732 | 2.513 | 0.951 |
| 90 | 3.000 | 3.770 | 2.230 |
Development of Flat Blank Layouts
There are two equivalent ways to develop a flat blank for one bend. Choose the formula that matches the dimension origins on the drawing; do not mix tangent lengths with outside flange lengths.
- Using straight tangent lengths: Lflat = s1 + s2 + BA, where s1 and s2 end at the bend tangent points.
- Using outside flange lengths to the virtual sharp: Lflat = L1 + L2 − BD. Each straight tangent length is s = L − OSSB.
90° worked example: with R = 2 mm, t = 1 mm, assumed K = 0.400 and outside flange lengths L1 = 40 mm and L2 = 30 mm, BA = 3.769911 mm, OSSB = 3 mm and BD = 2.230089 mm. Therefore Lflat = 40 + 30 − 2.230089 = 67.770 mm after rounding. The tangent-length check gives (40 − 3) + (30 − 3) + 3.769911 = the same result. Validate the bend rule with test pieces before releasing a production blank. Tube bending needs its own process assessment; see bending stainless steel tubing.
K-Factor Calculation Sheet Metal Bending
In sheet metal bending, the K-factor describes the neutral layer’s position through the thickness. It is a process-dependent modeling input, not a universal material constant.
K-Factor Formula
In mathematical form, the K-factor is expressed as:
K = y / t, where y is the distance from the inside surface of the bend to the neutral layer and t is the sheet thickness.
Where,
- Neutral layer: the layer with no longitudinal extension in the idealized bend model.
- y: the neutral layer’s offset from the inside surface, not from the outside surface.
- t: the sheet thickness used by the bend model.
K = 0.5 places the modeled neutral layer at mid-thickness. A smaller K places it closer to the inside surface and reduces calculated BA when R, t and β are held constant. This does not by itself predict total thinning, springback or cracking.
How to establish a usable K-factor
| Check | Record or validate |
|---|---|
| Material | Grade, temper/condition, thickness and grain direction. |
| Bend process | Air bending, bottoming or other method; punch, die opening and actual inside radius. |
| Test result | Known flat length, measured flange dimensions and final unloaded angle. |
| CAD rule | Calibrated K-factor or a measured bend allowance/deduction table for those conditions. |
Use measured test bends or a validated bend table for the actual material, thickness and tooling. A K-factor selected solely from a material name can produce an incorrect blank. Autodesk’s bend-table guidance explains using measured samples for unfold rules.
Facts About K-Factors
- K is dimensionless; it locates the neutral layer relative to the inside surface.
- Do not assume K automatically decreases when thickness increases; radius-to-thickness ratio and forming conditions also matter.
- For a measured BA and nonzero bend angle β in degrees, K = [BA / (πβ/180) − R] / t. Use consistent measured dimensions and validate the result.
- Material-specific forming considerations still matter for bending aluminum and bending stainless steel.
- Recheck the unfold rule when material condition, tooling or process changes.
Springback In Sheet Metal Bending Calculation
Springback In bending
Springback is elastic recovery after the forming load is removed. The bend usually opens slightly and the inside radius increases. During bending, the outer fibers are in tension and the inner fibers are in compression; a shift in the neutral layer is not itself the cause of springback.
Compensate with a validated bend program, suitable tooling and controlled overbending where appropriate. The required compensation depends on material strength and condition, thickness, radius and forming method; simply increasing force is not a universal correction. Measure the final unloaded angle and dimensions on test pieces. See SSAB’s explanation of springback.
Sheet Metal Bending Design Tips
Below are some simple but critical pointers you should consider when employing sheet metal bending techniques. These tips cover bending practices to avoid problems. Moreover, covers solutions for those issues.
Minimum Flange Length
Flange length In bending
Minimum flange length depends on the die opening, tooling geometry, thickness and forming method. Check the toolmaker’s guidance and the fabricator’s setup; a bend-allowance chart does not establish the minimum flange length.
Chamfered Edges
When designing the chamfered flanges, be sure to leave enough material near the chamfer to keep the bending angles intact. Do not extend chamfers up to the bend line to prevent deformation. Furthermore, minimum flange length results in accurate bends.
Hole Position Relative to Bend
Hole position In bending
Holes close to the bend may distort. Choose hole-to-bend clearance using the hole geometry, material, thickness, bend radius and tooling; do not substitute a minimum flange dimension or a press-brake force chart for a feature-clearance check.
Symmetry in Design
It is less of a challenge to design symmetrical parts. When possible try to design the symmetrical layout to minimize operator error and incorrect bends. However, Asymmetry can cause the operator to misjudge the bend direction. In cases where full symmetry cannot be achieved, be very keen to provide clear signals to direct the bending process to achieve the expected results.
Rivet Nut Positioning
Keep rivet-nut holes and hardware clear of bend deformation zones and tool contact. Choose installation before or after bending based on access, tooling clearance and hardware specifications; installing before bending is not a universal way to prevent hole distortion.
Small Flanges on Large Parts
Small flanges on large components are difficult to produce. These setups should be avoided because handling is usually difficult and may involve lifting by hand and incur higher costs. Try to find alternate ways to reduce the complexity of the manufacturing process each time you can.
Consecutive Bends
When bends are sequential they need to be planned carefully. Always verify if your part will fit on the die afterward and at each progressive step during its creation. For forming U-bends, the middle part of the U-bend is made longer than the side flanges to facilitate correct die positioning, not marred by difficulties.
Align Bends Along One Line
The introduction of bends at a single line is cost-effective due to a reduction in the steps involved in production. Maintaining bends in line reduces the number of times that parts must be repositioned, which decreases the amount of time and money required. If the bends are isolated, each one must be corrected individually. This process can be time-consuming and costly.
Flattening Line Along an Edge
Make bending lines parallel to one side so that the parts can fit into position with ease. An adjacent side helps in the proper position of the machine. If there is no such alignment, then holding precision becomes a challenge, and can cause some disparities.
Bend Relief
Bend relief
Bend reliefs should also be used for bending and to provide structural support where necessary. A slit or cutout in the edge of the flange prevents tears and stress fractures. It is advisable to design these cutouts slightly larger than the thickness of the material and give a small fillet to minimize stress on the material.
Bending a Box
Leave small gaps between box flanges to prevent interference. Without these gaps, final bends can interfere with previous bends hence causing structural failures. Small allowances enable the control of bends and maintain the form of the box.
Check the Flat Pattern
Use a flat pattern view in CAD frequently. Regular checks help prevent design flaws not seen in flat forms. Position it in a way to fit the piece tightly to avoid using excessive material and perhaps print several pieces of a model on a single sheet.
Minimum Bend Radius
Bending radius guide
Select the minimum inside bend radius using the material grade and temper, thickness, grain direction, tooling and forming method. A radius equal to the thickness is not a universal safe limit. Confirm material-supplier guidance and validate critical bends with samples.
Orientation of Fiber Flow concerning Bending
Bends that lie in the plane of the rolled section are designated as alignment bends. They lie perpendicular to the grain of rolled materials. Aluminium and certain types of steel for example are known to crack if they are bent along the grain direction. By bending the material against the grain the resulting surfaces are stronger and more uniform.
Hemming Techniques
A hem is useful in strengthening edges but avoid creating an inside radius which should be small. To completely flatten the radius you need more pressure and can cause cracking. This risk is minimized when a precise, sheet metal bend radius calculator is used to ensure material consistency.
Material Selection
Assess material grade, thickness, temper, grain direction and required bend radius against the available tooling and press-brake capacity. There is no universal 3 mm limit that establishes whether a steel sheet can be bent.
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