# How to Calculate Bending Allowance, Bending Deduction and K-Factor?

In sheet metal design, we often hear about bend allowance, bend deduction and K factor, so what is bend allowance?

What is bending deduction?

And what is the K factor?

In addition, how to calculate the bending allowance, bending deduction and K factor?

In today’s post, we will answer you in details.

## 1. Introduction to the calculation method of sheet metal

Engineers of sheet metal parts and sellers of sheet metal materials use various algorithms to calculate the actual length of the prepared material in the unfolded state in order to guarantee the desired dimensions of the part after the final bending and forming.

The most commonly used method is the simple “finger pinching rule”, that is, the algorithm based on their own experience.

Generally, these rules take into account the type and thickness of materials, the radius and angle of bending, the type of machine and bending speed, etc.

On the other hand, with the emergence and popularity of computer technology, computer-aided design is increasingly used to make better use of the computer’s superb analytical and computational capabilities.

However, when the computer program simulates the bending or unfolding of sheet metal, it also needs a calculation method to accurately simulate the process.

Although each software can customize a specific program implementation according to its original finger-pinching rules only to complete a certain calculation, most commercial CAD and 3D solid modeling systems have provided more general and powerful solutions.

In most cases, these applications can also be compatible with the original experience-based and pinch rule methods, and provide a way to customize the specific input content into their calculation process.

SolidWorks has become a leader in providing this sheet metal design capability.

To sum up, there are two popular sheet metal bending algorithms widely adopted today, one is based on bending allowance, the other is based on bending deduction.

In order to make readers better understand some basic concepts in the calculation process of sheet metal design in a general sense, I will summarize and elaborate on the following aspects:

• The definitions of two algorithms of bending allowance and bending deduction, and their corresponding relationship with the actual sheet metal geometry
• How does the bending deduction correspond to the bending allowance? How can users who adopt the bending deduction algorithm easily convert their data to the bending allowance algorithm
• Definition of K factor, how to use K factor in practice, including the applicable range of K factor value for different material types

## 2. Bending allowance method

For a better understanding of bend allowance, refer to figure 1, which shows a single bend in a sheet metal part. Figure 2 shows the unfolded state of the part.

Figure 1

Figure 2

The bending allowance algorithm describes the unfolded length (LT) of the part as the sum of each length after the part is flattened, plus the length of the flattened bending area.

The length of the flattened bend area is expressed as the bend allowance value (BA). Therefore, the length of the whole part is expressed as equation (1):

LT = D1 + D2 + BA    (1)

The bending area (shown as light yellow in the figure) is the area that is theoretically deformed during bending.

In short, to determine the geometry of the unfolded part, let’s think in the following steps:

• Cut the bending area from the bending part
• Lay the remaining two flat sections on a table
• Calculate the length of the bending area after its flattening
• Bond the flattened bending area between the two flat parts, and the result is the unfolded parts we need

The slightly more difficult part is how to determine the length of the flattened bending area, that is, the value represented by BA in the figure.

Obviously, the value of BA will vary with different situations, such as material type, material thickness, bending radius and angle, etc.

Other factors that may affect BA value include bending process, machine type, machine speed, etc.

Where does BA value come from?

In fact, there are usually the following sources: sheet metal material suppliers, experimental data, experience and some engineering manuals.

In SolidWorks, we can directly input BA values and provide one or more tables with BA values, or use other methods such as the K factor (which will be discussed in detail later) to calculate BA values.

For all these methods, we can enter the same information for all bends in the part or enter different information for each bend separately.

For various situations with different thicknesses, bending radii and bending angles, the bending table method is the most accurate way to allow us to specify different bending allowance values.

In general, there is a table for each material or combination of materials/processes.

The formation of the initial table may take some time, but once it is formed, we can continuously reuse some part of it in the future.

1) Standards for Common Bending

2) Standards for Z Bending

3) Standards for V Bending

4) Standards for U Bending

## 3. Bending deduction method

Bending deduction usually refers to the amount of fallback. It is also a different simple algorithm to describe the process of sheet metal bending.

Referring also to Fig. 1 and Fig. 2, the bending deduction method means that the flattening length lt of the part is equal to the sum of the theoretically two flat parts extending to the “tip point” (the virtual intersection of the two flat parts) minus the bending deduction (BD).

Therefore, the total length of the part can be expressed as equation (2):

LT = L1 + L2 – BD    (2)

The bending deduction is also determined or provided through the following ways: sheet metal material suppliers, test data, experience, manuals for different materials with equations or tables, etc.

Figure 3

## 4. Relationship between bending allowance and bending deduction

Because SolidWorks usually adopts the bending allowance method, it is very important for users familiar with the bending deduction method to understand the relationship between the two algorithms.

In fact, it is easy to deduce the relationship equation between the two values by using the two geometries of bending and unfolding of parts.

In retrospect, we have two equations:

LT = D1 + D2 + BA (1)

LT = L1 + L2 – BD (2)

The above two equations are equal on the right and can be changed into equation (3):

D1 + D2 + BA = L1 + L2 – BD (3)

Make several auxiliary lines in the geometric part of Figure 1 to form two right triangles, as shown in Figure 3.

Angle A represents the bending angle, or the angle swept by the part during bending.

This angle also describes the angle representing the arc formed by the bending area, which is shown in Figure 3 as two halves.

If the inner bending radius is represented by R, the thickness of the sheet metal part is represented by T.

A right triangle is used to help clearly express various geometric relationships, such as the green right triangle in Figure 3.

According to the dimensions and trigonometric function principle of the right triangle shown in the figure, we can easily get the following equation:

TAN(A/2) =(L1-D1)/(R+T)

After transformation, the expression of D1 is:

D1 = L1 – (R+T)TAN(A/2) (4)

Using the same method and the relationship of the other half right triangle, the expression of D2 can be obtained as follows:

D2 = L2 – (R+T)TAN(A/2) (5)

Substituting equations (4) and (5) into equation (3) can obtain the following equation:

L1+L2-2(R+T)TAN(A/2)+BA = L1+L2-BD

After simplification, the relationship between BA and BD can be obtained:

BA = 2(R+T)TAN(A/2)-BD (6)

When the bending angle is 90 degrees, this equation can be further simplified because Tan (90 / 2) = 1:

BA = 2(R+T)-BD (7)

Equation (6) and equation (7) provide users who are only familiar with one algorithm with very convenient calculation formulas for converting from one algorithm to another, and the required parameters are only material thickness, bending angle / bending radius, etc.

Especially for SolidWorks users, equations (6) and (7) simultaneously provide a direct calculation method for converting bend deduction to bend allowance.

The value of bending allowance can be used for the whole part / independent bending or form a bending data table.

## 5. K-factor method

K-factor is an independent value that describes how sheet metal bending bends/unfolds under a wide range of geometric parameters.

It is also an independent value used to calculate bending allowance (BA) under a wide range of conditions such as various material thickness, bending radius/bending angle.

Figures 4 and 5 will be used to help us understand the detailed definition of the K-factor.

Figure 4

Figure 5

We can be sure that there is a neutral layer or axis in the material thickness of the sheet metal part.

The sheet metal material in the neutral layer in the bending area is neither stretched nor compressed, that is, the only place that does not deform in the bending area.

Figs. 4 and 5 show the junction of the pink region and the blue region.

During bending, the pink area is compressed and the blue area extends.

If the neutral sheet metal layer is not deformed, the length of the neutral layer arc in the bending area is the same in its bending and flattening states.

Therefore, BA (bending allowance) should be equal to the length of the arc of the neutral layer in the bending area of the sheet metal part.

The arc is shown in green in Fig. 4.

The position of the neutral layer of sheet metal depends on the properties of a specific material, such as ductility.

It is assumed that the distance between the neutral sheet metal layer and the surface is “t”, that is, the depth from the sheet metal part surface to the thickness direction into the sheet metal material is t.

Therefore, the radius of the arc of the neutral sheet metal layer can be expressed as (R + t).

Using this expression and bending angle, the length (BA) of the neutral layer arc can be expressed as:

BA = Pi(R+T)A/180

In order to simplify the definition of sheet metal neutral layer and consider the thickness applicable to all materials, the concept of K-factor is introduced.

The specific definition is: K-factor is the ratio of the thickness of the neutral layer of the sheet metal to the overall thickness of the sheet metal part material, that is:

K = t/T

Therefore, the value of K will always be between 0 and 1.

If a K-factor is 0.25, it means that the neutral layer is located at 25% of the thickness of the part sheet metal material.

Similarly, if it is 0.5, it means that the neutral layer is located at 50% of the whole thickness, and so on.

Combining the above two equations, we can get the following equation (8):

BA = Pi(R+K*T)A/180 (8)

This equation is the calculation formula that can be found in SolidWorks manual and online help.

Several of these values, such as A, R and T, are determined by the actual geometry.

So back to the original question, where does the K-factor come from?

Similarly, the answer is from the old sources, i.e. sheet metal material suppliers, test data, experience, manuals, etc.

However, in some cases, the given value may not be obvious K or may not be fully expressed in the form of equation (8), but in any case, even if the expression is not exactly the same, we can always find the relationship between them.

For example, if the neutral axis (layer) is described in some manuals or literature as “positioned at 0.445x material thickness from the sheet metal surface”, it is obvious that this can be understood that the K factor is 0.445, that is, k = 0.445.

In this way, if the value of K is substituted into equation (8), the following formula can be obtained:

BA = A (0.01745R + 0.00778T)

If equation (8) is modified by another method, the constant in equation (8) is calculated, and all variables are retained, the following can be obtained:

BA = A (0.01745 R + 0.01745 K*T)

Comparing the above two equations, we can easily get: 0.01745xk = 0.00778. In fact, it is also easy to calculate k = 0.445.

After careful study, it is known that the SolidWorks system also provides the bending allowance algorithm for the following specific materials when the bending angle is 90 degrees.

The specific calculation formula is as follows:

• Soft brass or soft copper material: BA = (0.55 * T) + (1.57 * R)
• Semi-hard copper or materials such as brass, mild steel and aluminum: BA = (0.64 * T) + (1.57 * R)
• Bronze, hard copper, cold-rolled steel and spring steel: BA = (0.71 * T) + (1.57 * R)

In fact, if we simplify equation (7), set the bending angle to 90 degrees and calculate the constant, the equation can be transformed into:

BA = (1.57 * K * T) + (1.57 *R)

Therefore, for soft brass or soft copper materials, 1.57xk = 0.55 can be obtained by comparing the above calculation formula, K=0.55/1.57=0.35。

Using the same method, it is easy to calculate the K-factor values of several types of materials listed in the above:

• Soft brass or soft copper material: K = 0.35
• Semi-hard copper or materials such as brass, mild steel and aluminum: K = 0.41
• Bronze, hard copper, cold-rolled steel and spring steel: K = 0.45

As discussed earlier, there are many sources to obtain K-factor, such as sheet metal material suppliers, test data, experience and manuals.

If we want to use the K-factor method to establish our sheet metal model, we must find the correct source of K-factor value to meet the engineering needs, so as to obtain the physical part results that fully meet the desired accuracy.

In some cases, because it is necessary to adapt to a wide range of bending situations, it may not be possible to obtain sufficiently accurate results only by inputting a single number, that is, using a single K-factor method.

In this case, in order to obtain more accurate results, the BA value should be directly used for a single bend of the whole part, or the bend table should be used to describe the different BA, BD or K-factor values corresponding to different A, R and T in the whole range.

We can even use equations to generate data like the bend table listed in the sample table provided by SolidWorks.

If necessary, we can also modify the contents of cells in the bending table based on experimental data or empirical data.

The installation directory of SolidWorks provides a bending allowance table, bending deduction table and K-factor table, which can be edited and modified manually.

## 6. Summary

This post introduces in detail several calculation methods and their basic theories commonly used in the design and forming of sheet metal parts so that you can know how to calculate bending allowance, bending deduction and K-factor.

At the same time, it details the differences between the bending allowance method, bending deduction method and K-factor method and the relationship between them.

It provides an effective reference for the majority of engineering and technical personnel in the industry.

Note:

• Tan – Simplified representation of the tangent trigonometric function
• PI – Pi constant (3.14159265…)

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