Bend Allowance vs Bend Deduction vs K-Factor: How to Calculate Sheet Metal Flat Patterns (With Examples)

Quick Answer

Quick Conclusion

The most commonly used process: By determining parameters such as bending angle (A), plate thickness (T), inside radius (R), K factor (K), etc., first calculate BA, then calculate OSSB or BD, and finally obtain the flat pattern length.

For consistent results: don’t rely on a single memorized K-factor. It is recommended to calibrate with test pieces and establish your own bending table or material database.

Reduce rework and scrap: To ensure stability, choose the right tooling, ensure machine accuracy/compensation is in place, and store test-bend results in a bend table (material database).

30 second comparison table

Why is “flat pattern length” the easiest to step on?

In the field of sheet metal bending, once the flat pattern length is calculated incorrectly, it may result in the final bent dimensions won’t match the design, causing rework or scrap. For some parts with holes, symmetrical parts, and assembly parts, it is even more troublesome.

In reality, many engineers may have the same confusion: they understand the formulas, but results are still inconsistent on the shop floor. In fact, the reason usually lies not in the formula itself, but in the K factor, inside radius, bending method, and consistency between the tooling and equipment.

This article will explain the concepts and relationships of BA(Bend Allowance), BD (Bend Deduction), and K factor, provide calculation examples, and teach you how to reduce trial and error and rework rates through CNC numerical control systems, specimen calibration, and bending tables.

Core premise: What is the neutral axis?

What happens to the material during bending?

When the sheet metal is pressed into the lower die, the material on the outer side of the sheet metal will be stretched, while the material on the inner side will be compressed. The ratio of stretching and compression will vary with the thickness of the material, the radius of the inner corner, and the bending process.

Definition and significance of neutral axis

Between the stretching zone and the compression zone, there is an imaginary line/plane that does not produce significant stretching or compression, has the smallest deformation, and has the most stable length. This is called the neutral axis.

The essence of our calculations is to establish a mathematical model around the neutral axis and determine the required material length for the bending area.

What is K-Factor

K-Factor Definition Formula

Why is the K factor important?

Because the K factor determines the position of the neutral axis, which in turn affects the arc length of the neutral axis, i.e. BA, ultimately affecting the flat pattern length and the size of the bent workpiece. Once the K factor is selected incorrectly, it is likely to lead to incorrect calculation of the flat pattern length, resulting in rework or scrap.

Why is K not a constant

K cannot be used as a fixed empirical value because its value is influenced by the following factors:

Starting Range of Experience

When starting the calculation, we usually use a common range of K values as the starting point, typically between about 0.30-0.50.

But this is only a starting point for preliminary estimation, and the final K value should be based on the calibration of the test piece.

BA vs BD: Definition, Formulas, and Core Differences

BA (Bend Allowance)

Definition: Refers to the arc length along the neutral axis within the bending arc area, which is the actual length of material consumed during the bending process.

BA calculation formula:

A=bending angle, R=inside radius, T=sheet thickness, K=K factor.

BD（Bend Deduction）

Definition: Due to the stretching and compression of the material during bending, in order to ensure the correct external dimensions after bending, we usually add the lengths of the two external flanges of the bent part and subtract another number to obtain the correct flat pattern length. The deducted amount is BD.

Before calculating BD, we need to first understand the concept of OSSB (Outside Setback) , which is the setback distance (related to R, T, and angle) from the theoretical outside corner to the tangent point, used as an intermediate value to calculate BD.

OSSB calculation formula:

BD calculation formula:

Table Conclusion

How to do a single 90 °bend

Gradually expand the size calculation process

Step 1: Confirm the material thickness T, bending angle A, and target/actual inside radius (R)

Step 2: First, select a starting K value within a common range, and then calibrate it through trial bending

Step 3: Calculate BA value

Step 4: Calculate OSSB and BD values

Step 5: Calculate the flat pattern length

Five common pitfalls for multi pass bending/perforated parts

Calculation Example

Example 1:

Here is a complete calculation procedure:

Condition: Low carbon steel, T=2mm, A=90 °, R=2mm, L1=50mm, L2=50mm, K=0.44 (initial value)

① Calculate BA

② Calculate OSSB

③ Calculate BD

④ Calculate the flat length

Example 2:

If only one variable is changed, what will happen to the flat length?

Only change K: 0.44 → 0.33

① Calculate BA

② Calculate OSSB

③ Calculate BD

④ Calculate the flat length

We can see that after changing the K value from 0.44 to 0.33, there is a difference of 0.346mm in the final flat pattern length.

Only change R：2mm → 3mm

① Calculate BA

② Calculate OSSB

③ Calculate BD

④ Calculate the flat length

We can see that after changing the R value from 2mm to 3mm, there is a difference of 0.429mm in the final flat length.

So, paper calculations must be deeply bound to the consistency of actual R, tools, bending methods, and equipment. A small systematic error will lead to a deviation in the final flat length, resulting in rework or scrap.

Why is your unfolding always inaccurate?

Inconsistencies between actual fillet R and drawing R

In the most common air bending process, the actual formed inside radius (R) is generally determined by the lower die V-die opening, the material, and the process. The R here is different from the R in the drawing. If you fill in the R value in the calculation formula as shown in the drawing, but the actual R after bending may be larger or smaller, it will cause calculation errors in BA, OSSB, and BD, resulting in deviations in the flat length.

Different bending methods result in different springback and neutral axis positions

Equipment and Process Consistency

Even if the formula is correct, the final accuracy cannot be achieved without the stability of the equipment and process. Mainly reflected in:

How do tools and equipment affect the calculation results?

How V-die opening affects the actual inside radius (R)

The V-die opening size directly determines the actual size of the inside radius (R), thereby affecting the BA, BD, and K values. If the selection of V-die opening is incorrect, it may lead to deviation in the calculation results.

So, it is recommended to bind and manage the unfolding rules with “material, thickness, V-die opening size, bending method”.

Machine tool accuracy and consistency

How to reduce trial and error and rework of Raymax CNC press brake

In short, the accuracy of flat length is not only achieved by calculation, but also by the system capability of “correct calculation+specimen calibration+stable execution”.

Free tool download

Resource 1: Sheet Metal Unfolding Automatic Calculation Table

Function: Simply input parameters such as T, R, A, K, and the table will automatically output BA, OSSB, BD, and flat length.

Resource 2: Bend Test Sheet Calibration Record

Function: Record material, thickness, V-die opening size, bending method, target angle, measured angle, and reverse calculate actual K/BD value.

Value: Help factories establish their own bending tables and reduce trial bending.

Resource 3: Inquiry/Process Parameter Checklist

Including: material, thickness, bending length, angle, tolerance, target inside radius (R), V-die opening size, batch size, surface requirements, etc.

Value: The more complete the parameters, the faster and more accurate the engineering evaluation and quotation will be.

The above tables can help you quickly complete basic calculations; If you wish to convert the calibration results of the test piece into a bending table and improve batch consistency, please feel free to submit your relevant parameters to us. We can provide you with suitable bending schemes and equipment configuration suggestions.

CAD/CAM software setting guide for avoiding pitfalls

BA/BD/K are interchangeable in software, but the rules must be consistent with the workshop

Many CAD/CAM software allow you to define bending rules using K, BA, or BD, which can often be converted to each other in the software. But the key is that the rules used by the design department in the software should be consistent with the actual bending results in the workshop.

It is strongly recommended to establish a unified bending table in the background to ensure that the rules used in the software and the actual bending in the workshop use the same program, avoiding the situation of “designing one set, workshop one set”.

Common Error List

Conclusion

The core process of unfolding calculation is to determine the neutral axis position, determine the K factor, calculate BA/BD, and obtain the final flat length.

However, the formula is only a starting point. To maintain high consistency and stability in mass production, it is necessary to rely on correct calculations, strict specimen calibration, and the stability of equipment and processes. Unifying CAD rules with workshop rules is the most effective way to significantly reduce our rework and delivery risks.

Please submit your materials, thickness, bending length, angle, target inside radius (R) and V-die opening. Raymax engineers will assist you in creating a bending table and provide you with bending solutions and equipment configuration suggestions.

If you need to evaluate the tonnage, length, number of axles, and tooling scheme that are suitable for your working conditions, you can also provide us with your parameters, and we will provide professional technical consultation and quotation suggestions.

Frequently Asked Questions (FAQs)