What is the formula for bend allowance?
How to Calculate Bend Allowance for Your Press Brake
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Getting the correct flat pattern layout is essential for achieving a high-quality finished part from your press brake. However, many CAD and CNC programmers often struggle with calculating the necessary values. In the past, seasoned experts used cheat sheets pinned to the wall and taught apprentices to apply the results rather than understand the calculations. Now that those experts have retired, it’s crucial for the new generation to learn how to determine the flat pattern layout accurately.
Figuring out the flat pattern length from a 3D part is not as complicated as it seems. While you might come across several formulas claiming to calculate Bend Allowance (See Bending Definitions), they generally use the same formula, often simplified by incorporating the angle or a K-factor. Indeed, knowing the K-factor is mandatory for calculating Bend Allowance.
Let’s start with a simple L bracket example. Assume the legs of the bracket are 2" and 3", with a material thickness of 0.125", an inside radius of 0.250", and a bend angle of 90 degrees. The flat length is the sum of the flat parts of both flanges plus the length through the arc of the bend area. But should you calculate this on the inside or outside of the material? Neither. This is where the K-factor, which is the percentage of the material thickness where no stretching or compressing occurs, comes into play—for instance, the neutral axis. For this simple L bracket, we’ll use a K-factor of 0.42.
The formula (See Bending Formulas) is:
Bend Allowance = Angle * (π / 180) * (Radius + K-factor * Thickness).
Plugging in our numbers: Bend Allowance = 90 * (π / 180) * (0.250 + 0.42 * 0.125) = 0.475".
So the flat pattern length is 1.625" + 2.625" + 0.475", which equals 4.725". By summing up the flat length of all the flanges and adding one Bend Allowance for each bend area, you get the correct flat length of the part.
But take a look at the drawing. This is not how sheet metal parts are typically dimensioned. Dimensions are usually to the intersection of the flanges or the Mold Line. This necessitates subtracting two times the material thickness plus the bend radius (Setback) for each bend area. Under these dimensions, calculating the Bend Compensation value is simpler. The Bend Compensation allows you to add the length of each flange using the Mold Line dimensions and then add one Bend Compensation per bend area to the total. It is -0.275, a negative number, meaning you will subtract this amount from the total flange lengths of 5" to get 4.725".
Definitions:
Bend Allowance = Angle * (π / 180) * (Radius + K-factor * Thickness)
Bend Compensation = Bend Allowance – (2 * Set Back)
Inside Set Back = tan (Angle / 2) * Radius
Outside Set Back = tan (Angle / 2) * (Radius + Thickness)
Bend Allowance: The length of the arc through the bend area at the neutral axis.
Bend Angle: The included angle of the arc formed by the bending operation.
Bend Compensation: The amount by which the material is stretched or compressed by the bending operation, assumed to occur in the bend area.
Bend Lines: Straight lines on the inside and outside surfaces where the flange boundary meets the bend area.
Inside Bend Radius: Radius of the arc on the inside surface of the bend area.
K-factor: Location of the neutral axis, measured as the distance from the inside of the material to the neutral axis divided by the material thickness.
Mold Lines: For bends less than 180 degrees, mold lines are the straight lines where the flanges bounding the bend area intersect on both inside and outside surfaces.
Neutral Axis: In the cross section of the bend, the theoretical location where the material is neither compressed nor stretched.
Set Back: For bends of less than 180 degrees, set back is the distance from the bend lines to the mold line.
How to calculate the "K" factor:
There is no simple formula for calculating the K-factor. While some advanced mathematical equations exist, they are often too complex for general use. The K-factor represents the percentage of the material thickness where no stretching or compressing occurs in the bend area—the neutral axis. Harder materials experience less compression on the inside of the bend and more stretching on the outside, causing the neutral axis to move inward. Softer materials compress more on the inside, keeping the neutral axis closer to the center of the thickness.
Bend radius also influences this effect. Smaller bend radii require more compression, moving the neutral axis inward. Conversely, larger radii keep the neutral axis near the center of the material thickness.
Diagram and Calculation Formulas for Bend Allowance
To help you master the calculation formula for unfolded bending length more quickly, we have listed four common coefficient tables and illustrated sixteen calculation formulas for unfolded bending lengths. We have also provided examples for better understanding. We hope the following content is practical for you. If you have any questions, please feel free to contact us.
Diagram and calculation formula for one-bend
A, B: Bending length of the workpiece
P': Bending coefficient of edge bending (bending factor: one factor minus one bend)
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L = A + B - P', or L = 25 + 65 - 5.5 = 84.5
According to Table 1, the plate thickness is 3, the lower die is V25, and the bending coefficient is 5.5.
Note: According to Table 1, different bending coefficients of lower dies and different plate thicknesses are different.
Diagram and calculation formula of two-bend
A(A1), B: Bending length of the workpiece
P': Bending coefficient of edge bending (bending factor: one factor minus one bend)
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L = A + T + B - 2 * P', or L = 50 + 2 + 50 - 2 * 3.4 = 95.2
According to Table 1, the plate thickness is 2, the lower die is V12, and the bending coefficient is 3.4.
Note: According to Table 1, different bending coefficients of lower dies and different plate thicknesses are different.
Diagram and calculation formula of three-bend
A(A1), B (B1): Bending length of the workpiece
P': Bending coefficient of edge bending (bending factor: one factor minus one bend)
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L = A + T + B + T - 3 * P', or L = 50 + 2 + 90 + 2 - 3 * 3.4 = 133.8
According to Table 1, the plate thickness is 2, the lower die is V12, and the bending coefficient is 3.4.
Note: According to Table 1, different bending coefficients of lower dies and different plate thicknesses are different.
Diagram and calculation formula of four-bend
A, B (B1): Bending length of the workpiece
P': Bending coefficient of edge bending (bending factor: one factor minus one bend)
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L = A + A + B + T + T - 4 * P', or L = 25 + 25 + 100 + 1.5 + 1.5 - 4 * 2.8 = 141.8
According to Table 1, the plate thickness is 1.5, the lower die is V12, and the bending coefficient is 2.8.
Note: According to Table 1, different bending coefficients of lower dies and different plate thicknesses are different.
Diagram and calculation formula of six-bend
A(A1), B (B1): Bending length of the workpiece
P': Bending coefficient of edge bending (bending factor: one factor minus one bend)
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L = A + T + A + T + B + B1 + B1 - 6 * P', or L = 50 + 1.5 + 50 + 1.5 + 150 + 20 + 20 - 6 * 2.8 = 276.2
According to Table 1, the plate thickness is 1.5, the lower die is V12, and the bending coefficient is 2.8.
Note: According to Table 1, different bending coefficients of lower dies and different plate thicknesses are different.
Diagram and calculation formula of bending 180 degrees
A, B: Bending length of the workpiece
P': Flattening fillet bending coefficient
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L = A + B - P', or L = 25 + 65 - 1 = 89
According to Table 2, the plate thickness is 2, the lower die is V12, and the bending factor is half of the plate thickness.
Note: According to Table 2, the selection of different lower dies has different bending coefficients and different plate thicknesses.
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R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L1 = (A1 - T) + (B2 - T) - P1, or L1 = (35 - 2) + (34 - 2) - 3.7 = 61.3
L2 = (B1 - T) + (A2 - T) - P1, or L2 = (50 - 2) + (34 - 2) - 3.7 = 76.3
L3 = A + B1 + B2 - 2 * P2, or L3 = 70 + 35 + 50 - 2 * 4.6 = 145.8
L = L1 + L2 + L3 - 2 * P3, or L = 61.3 + 75.3 + 145.8 - 2 * 1 = 280.4
According to Table 2, the plate thickness is 2, the lower die is V12, the inner corner bending coefficient is 3.7, the outer corner bending coefficient is 4.6, and the 90-bending coefficient is 1.
Note: According to Table 2, different bending coefficients of lower dies and different plate thicknesses are different.
Diagram and calculation formula of double-layer bending with one edge
A, A1, A2, B1, B2, L, L1, L2, L3: Bending length of the workpiece
P1: Bending coefficient of inner corner
P2: Bending coefficient of external bending angle
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L1 = (A1 - T) + (B2 - T) - P1, or L1 = (35 - 2) + (34 - 2) - 3.7 = 61.3
L2 = (B1 - T) + (A2 - T) - P1, or L2 = (50 - 2) + (34 - 2) - 3.7 = 76.3
L3 = A + B1 + B2 - 2 * P2, or L3 = 70 + 35 + 50 - 2 * 4.6 = 145.8
L = L1 + L2 + L3 - 2 * P3, or L = 61.3 + 75.3 + 145.8 - 2 * 1 = 280.4
According to Table 2, the plate thickness is 2, the lower die is V12, the inner corner bending coefficient is 3.7, the outer corner bending coefficient is 4.6, and the 90-bending coefficient is 1.
Note: According to Table 2, different bending coefficients of lower dies and different plate thicknesses are different.
Diagram and calculation formula of double-layer bending with two edges
A, A1, A2, B1, B2, L, L1, L2, L3: Bending length of the workpiece
P1: Bending coefficient of inner corner
P2: Bending coefficient of external bending angle
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L1 = (A1 - T) + (B2 - T) - P1, or L1 = (35 - 2) + (34 - 2) - 3.7 = 61.3
L2 = (B1 - T) + (A2 - T) - P1, or L2 = (50 - 2) + (34 - 2) - 3.7 = 76.3
L3 = A + B1 + B2 - 2 * P2, or L3 = 70 + 35 + 50 - 2 * 4.6 = 145.8
L = L1 + L2 + L3 - 2 * P3, or L = 61.3 + 75.3 + 145.8 - 2 * 1 = 280.4
According to Table 2, the plate thickness is 2, the lower die is V12, the inner corner bending coefficient is 3.7, the outer corner bending coefficient is 4.6, and the 90-bending coefficient is 1.
Note: According to Table 2, different bending coefficients of lower dies and different plate thicknesses are different.
Diagram and calculation formula of step bending
A, B: Bending length of the workpiece
R: Bend and fillet (generally plate thickness)
T: Material thickness
Unfolded length L = A + 1
Note: When the step is equal to the thickness of two plates, add 0.5 for each step and 1 for each step.
Diagram and calculation formula of bending special angle 1
A(A1), B (B1): Bending length of the workpiece
P': Bending coefficient of edge bending (bending factor: one factor minus one bend)
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L = (A - T) + (B - T) - P', or L = (66 - 1) + (26 - 1) - 2 = 65 + 25 - 2 = 88
According to Table 3, the plate thickness is 2, the lower die is V12, and the 60-bending coefficient is 2.
Note: According to Table 3, the neutral layer is selected as the bending length and width.
Diagram and calculation formula of bending special angle 2
A (A1, A2, A3, A4), B: Bending length of the workpiece
P: Bending factor of 135-bending angles
R: Bend and fillet (generally plate thickness)
T: Material thickness
The Expanded length L = A1 + A2 + A3 + A2 + A4 - P - P.
Note: Same pressure step bending only needs to reduce two coefficients.
According to Table 3: The plate thickness is 2, the lower die is V12, and the bending coefficient at 135 is 1.1.
Diagram and calculation formula of bending special angle 3
A (A1, A2), B (B1, B2): Bending length of the workpiece
P1: 120° bending coefficient
P2: 145° bending coefficient
P3: 90° bending coefficient
R: Bend and fillet (generally plate thickness)
T: Material thickness
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