In the field of sheet metal design, terms such as bend allowance, bend allowance, and K-factor are often heard. But what exactly do these terms mean? And how can we calculate them?
In this post, we will provide detailed answers to these questions.
1 . Introduction to Sheet Metal Calculation Method
Engineers and salespeople involved in the design and production of sheet metal parts use various algorithms to calculate the actual length of the material in its unfolded state to ensure the desired dimensions of the part after bending and final forming.
The most commonly used method is the simple “finger pinch rule”, an algorithm based on personal experience, which takes into account factors such as the type and thickness of the material, the bend radius and angle, the type of machine and the speed. of flexion.
With the emergence of computer technology, computer-aided design (CAD) is increasingly used to take advantage of the computer's superior analytical and computational capabilities.
However, even when a computer program simulates the bending or unfolding of sheet metal, it still needs a method for accurate calculation.
Most commercial CAD and 3D solid modeling systems provide a general and powerful solution for this and are usually compatible with the original pinch rule method and offer customization options to insert specific content into your calculation process.
SolidWorks is the leader in providing this capability for sheet metal design.
In conclusion, two popular sheet metal bending algorithms are widely adopted today: one based on bend tolerance and another based on bend deduction.
To improve readers' understanding of the basic concepts in sheet metal design calculation, the following points will be summarized and explained:
- The definitions of the two bending algorithms: bend tolerance and bend deduction, and their connection to the actual geometry of the sheet metal.
- The relationship between fold deduction and fold margin and how users using the fold deduction algorithm can easily convert their data to the fold margin algorithm.
- The definition of the K factor, its practical use, and the range of K factor values applicable for different types of materials.
2. Bending tolerance method
For a clearer understanding of bend tolerance, see Figure 1, which illustrates a single bend in a sheet metal component. Figure 2 shows the part in its unfolded state.
figure 1
Figure 2
The bending allowance algorithm describes the unfolded length (LT) of a sheet metal part as the sum of the lengths of each segment after the part is flattened, plus the length of the flattened bend area.
The bend tolerance (BA) represents the length of the flattened bend area. Thus, the total length of the part can be expressed as equation (1):
LT = D1 + D2 + BA (1)
The bending area (illustrated in light yellow in the illustration) is the area that theoretically undergoes deformation during the bending process.
To determine the geometry of the unfolded part, follow these steps:
- Cut the folded area from the folded part.
- Lay the remaining two sections flat on a flat surface.
- Calculate the length of the flattened bend area.
- Join the flattened fold area between the two flat sections and the result will be the desired unfolded piece.
The task of determining the length of the flattened bending area, represented by BA in the figure, is a little more challenging.
The BA value varies based on factors such as material type, material thickness, bend radius and angle, as well as bending process, machine type and machine speed.
The BA value can be obtained from several sources, including sheet metal material suppliers, experimental data, experience, and engineering manuals.
In SolidWorks, you can enter BA values directly or use the K factor (which will be discussed later) to calculate the values.
The bending table method is the most accurate way to specify different bending tolerances for different situations with different thicknesses, radii and angles.
Creating the initial bending table may take some time, but once formed, parts of it can be reused in the future.
The same or different information can be entered for each fold of the part.
1) Standards for common flexion
2) Patterns for Z-flexion
3) Patterns for V-Bending
4) Patterns for U-Bending
Related Reading: V and U Shaped Bending Strength Calculator
3 . Flexion deduction method
Bend deduction is a term used to describe the amount of indentation in the sheet metal bending process. This is another simple algorithm to describe the process.
Figures 1 and 2 also apply to this concept. According to the flexure deduction method, the flat length (LT) of the part is equal to the sum of the lengths of the two flat sections extending to the “tip point” (the hypothetical intersection of the two flat sections), minus the flexion deduction (BD).
Thus, the total length of the part can be expressed as shown in equation (2):
LT = L1 + L2 – BD (2)
The BD value can be determined or obtained from various sources, such as sheet metal material suppliers, experimental data, experience, engineering manuals with equations or tables, etc.
Figure 3
4 . Relationship between flexion allowance and flexion deduction
It is important for users familiar with the Bend Deduction method to understand the relationship to the Bend Allowance method, which is commonly adopted in SolidWorks.
The relationship between the two values can be easily deduced using the two bending and unfolding geometries of the parts.
Comparing equations (1) and (2), we have:
LT = D1 + D2 + BA (1) LT = L1 + L2 – BD (2)
And therefore,
D1 + D2 + BA = L1 + L2 – BD (3)
In Figure 3, angle A represents the bending angle, which describes the angle swept by the part during bending, and also the angle of the arc formed by the bending area, which is shown in two halves.
Using the dimensions and principles of right triangles, we can derive the following equations:
D1 = L1 – (R + T)TAN(A/2) (4) D2 = L2 – (R + T)TAN(A/2) (5)
Substituting equations (4) and (5) into equation (3), we can obtain the relationship between BA and BD:
BA = 2(R + T)TAN(A/2) – BD (6)
And when the bend angle is 90 degrees, this equation simplifies to:
BA = 2(R + T) –BD (7)
These equations (6) and (7) provide a convenient method for converting from one algorithm to another, using only material thickness, angle/radius of curvature, etc.
For SolidWorks users, these equations provide a straightforward method for converting bend allowance to bend allowance.
The bend tolerance value can be used for the entire part or for each individual bend, or it can be included in a bend data table.
5. K-factor method
The K factor is an independent value that explains the bending and unfolding of sheet metal in various geometric scenarios.
It is also a stand-alone value used to calculate bending tolerance (BA) under various conditions such as different material thicknesses, bending angles and radii.
Figures 4 and 5 are provided to help clarify the in-depth definition of the K factor.
Figure 4
Figure 5
We can confirm that there is a neutral axis in the thickness of the sheet metal part. The sheet metal material in this neutral axis in the bending region is neither stretched nor compressed, meaning it is the only area that does not deform during bending.
Figures 4 and 5 show the boundary between the pink and blue regions.
During bending, the pink region compresses and the blue region stretches. If the neutral layer of sheet metal remains undeformed, its arc length in the bend region remains the same whether the part is bent or flattened.
As a result, the bending tolerance (BA) must be equal to the arc length of the neutral layer in the bending region of the sheet metal part, which is shown in green in Figure 4.
The position of the neutral layer of sheet metal depends on the properties of a specific material, such as ductility.
The distance between the neutral layer of the sheet metal and the surface is assumed to be “t”, or the depth from the surface of the sheet metal part to the material in the thickness direction.
As a result, the arc radius of the neutral layer can be expressed as (R + t). Using this expression and the bending angle, the arc length of the neutral layer (BA) can be calculated.
BA = Pi(R+T)A/180
To simplify the definition of the neutral layer of sheet metal and make it applicable to all materials, the concept of the K factor was introduced.
The definition of K factor is: it is the ratio between the thickness of the neutral layer of the sheet metal and the total material thickness of the sheet metal part. In other words, the K factor is defined as:
K = t/T
Therefore, the value of K will always be within the range of 0 to 1. If a K factor is 0.25, it indicates that the neutral layer is situated at 25% of the total thickness of the sheet metal material.
Likewise, if it is 0.5 it means that the neutral layer is located at 50% of the entire thickness and so on.
Combining the equations mentioned above, the following equation (8) can be obtained:
BA = Pi(R+K*T)A/180 (8)
Therefore, the value of K will always be between 0 and 1.
If the K factor is 0.25, it means that the neutral layer is located at 25% of the sheet metal material thickness of the part.
Likewise, if it is 0.5 it means that the neutral layer is located at 50% of the entire thickness and so on.
The origin of the K factor can be traced back to traditional sources such as sheet metal material suppliers, test data, experience, manuals, etc.
However, in some cases, the given value may not be expressed as a clear K-factor, but it is still possible to find the relationship between them.
For example, if a manual or literature describes the neutral axis as “positioned at 0.445x the thickness of the sheet metal surface material,” this could be interpreted as a K factor of 0.445, meaning k = 0.445.
When this 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)
By comparing the two equations, it is easy to determine that 0.01745 * k = 0.00778 and therefore k can be calculated as 0.445.
It was discovered that the SolidWorks system also provides a bend tolerance algorithm for specific materials when the bend angle is 90 degrees. The calculation formula for each material is as follows:
- Soft brass or soft copper: BA = (0.55 * T) + (1.57 * R)
- Semi-hard copper or materials such as brass, carbon 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, by simplifying equation (7) and setting the bending angle to 90 degrees, the constant can be calculated and the equation can be transformed as follows:
BA = (1.57 * K * T) + (1.57 *R)
Therefore, comparing the above calculation formula, the value of K for soft brass or soft copper materials can be obtained as 1.57xk = 0.55 or K = 0.35.
Using the same method, it is easy to calculate K-factor values for the different types of materials listed 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 previously, there are several sources from which the K-factor value can be obtained, such as material suppliers, test data, experience, and manuals.
To establish an accurate sheet metal model using the K-factor method, it is crucial to find the appropriate K-factor source that meets your engineering requirements. This will ensure that the physical results are as accurate as desired.
In some situations, it may not be possible to obtain accurate results using only a single K-factor value, especially when it is necessary to accommodate a wide range of bending scenarios.
In these cases, it is advisable to use the bend allowance (BA) value directly for a single bend of the entire part, or to use a bend table to describe the different BA, bend allowance (BD) or K-factor values corresponding to different values of A, R and T throughout the range.
Additionally, equations can be used to generate data such as the bend table example provided by SolidWorks. If necessary, the fold table cells can also be modified based on experimental or empirical data.
The SolidWorks installation directory includes bend tolerance tables, bend deduction tables, and K-factor tables, which can be edited and customized as needed.
- Sheet Metal Bending Calculator
6 . Summary
This post provides a comprehensive overview of common calculation methods and their underlying principles used in the design and manufacture of sheet metal parts.
Covers the calculation of flexion allowances, flexion deductions, and K-factors, and explains the differences between these methods and their interrelationships.
It serves as a useful reference for engineers and technical professionals in the industry.
Observation:
- Tan refers to the simplified representation of the tangent trigonometric function.
- PI represents the constant pi (3.14159265…).
